Tools for the formation of optimised
X-80 steel blast tolerant transverse
bulkheads
by Ian K. Raymond
Masters of Engineering (Research)
2001
The University of New South Wales
Abstract
Surname: Raymond First name: Ian Other name: Kenneth Abbreviation for degree as given in the University calendar: ME School: Mechanical and Manufacturing Engineering Faculty: Engineering Title: Tools for the formation of optimised X-80 steel blast tolerant transverse bulkheads
The Australian Maritime Engineering Cooperative Research Centre, and its partner organisation initiated this research effort. In particular, BHP and the Defence Science and Technology Organisation held the principal interest, as this research effort was a part of the investigation into the utilisation of X-80 steel in naval platforms. After some initial considerations, this research effort focussed on the development of X-80 steel blast tolerant transverse bulkheads. Unfortunately, due to the Australian Maritime Engineering Cooperative Research Centre not being re-funded after June 2000 and other project factors, the planned blast tests were not conducted, hence this research effort focussed on the tools needed for the formation of optimised blast tolerant transverse bulkheads rather than on the development of a single structural arrangement.
Design criteria were formed from the worst case operational requirements for a transverse bulkhead, which would experience a 150 kg equivalent blast load at 8 m from the source. Since the development of any optimised blast tolerant structure had to be carried out using finite element analysis, material constants for X-80 steel under high strain rates were obtained. These material constants were implemented in the finite element analysis and the appropriate solid element size was evolved. The behaviour and effects of stress waves and high strain rates were considered and the literature reviewed, in particular consideration was given to joint structures and weld areas effects on the entire structural response to a blast load. Furthermore, to support the design criteria, rupture prediction and determination methodologies have been investigated and recommendations developed about their relevance. Since the response of transverse bulkheads is significantly affected by their joint and stiffener arrangements, separate investigations of these structures were undertaken. The outcomes of these investigations led to improvements in the blast tolerance behaviour of joints and stiffeners, which also improved the overall response of the transverse bulkhead to air blast loads. Finally, an optimisation procedure was developed that met all the design criteria and its relevant requirements. This optimisation procedure was implemented with the available data, to show the potential to develop optimised X-80 steel blast tolerant transverse bulkheads. Due to the constraints mentioned above the optimisation procedure was restricted, but did show progression towards more effective blast tolerant transverse bulkhead designs. Factors, such as double skin bulkheads, maximising plate separation, and the use of higher yield steel all showed to be beneficial in the development of optimal X-80 steel blast tolerant transverse bulkheads, when compared to the ANZAC- class D-36 steel transverse bulkheads.
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Dedication
This thesis is dedication to my parents, brother, and my fiancée.
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Declaration
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Table of contents
Tools for the formation of optimised X-80 steel blast tolerant transverse bulkheads i
Dedication ii
Declaration iii
Table of contents iv
Chapter 1: Introduction 1 1.1. Introduction 2 1.2. Warship survivability 2 1.3. Explosives and their blast loads 15 1.4. Structural response to blast loads 27 · Material elasticity 50 · Influence of finite displacement 50 · Material strain rate sensitivity 50 · Combined influence of finite displacement and strain rate sensitivity 51 · Transverse shear and rotatory inertia 51 · Material strain hardening 52 · Bound method 52 · Mode approximation methods 53 · Dynamic plastic buckling 53 iv · Dynamic progressive buckling 54 · Scaling 55 · Ductile-brittle fracture transition related to size 58 1.5. Stress waves and strain rate 61 1.6. The J-integral and material failure 62 1.7. What is X-80 steel 64 1.8. What is being attempted in this research 67 1.9. Conclusion 68
Chapter 2: Design criteria for X-80 steel blast tolerant transverse bulkheads 70 2.1. Introduction 71 2.1.1. Transverse bulkhead attributes to naval platform survivability 71 2.1.2. Current transverse bulkhead formation 72 2.2. Operational requirements 73 2.2.1. Pre air blast loads 75 2.2.2. Air blast load 75 2.2.3. Post air blast load 76 2.3. Design criteria 76 2.3.1. Pre air blast loads 76 2.3.2. Air blast load 78 2.3.3. Post air blast load 80 2.3.4. Other relevant factors 81 2.4. Conclusion 82
Chapter 3: High strain rate data and analysis 84 3.1. Introduction 85 3.2. Experimental set-up 85 3.3. Constitutive Models 86 3.3.1. Cowper-Symonds model 86 3.3.2. Johnson-Cook model 87 3.4. Results from the compression Hopkinson bar tests 88 3.5. Results from the microscope investigation 94 3.6. Conclusion 98 v
Chapter 4: Development and evaluation of a finite element modelling technique 99 4.1. Introduction 100 4.2. Modelling parameters 100 4.3. Initial finite element models 101 4.3.1. MSC/NASTRAN models 101 4.3.2. Simple LS/DYNA finite element models 103 4.4. LS/DYNA modelling of the D-36 steel transverse bulkheads 109 4.4.1. Shot 1, 4, 9, and 10 initial observations 111 4.5. Comparison of the finite element data set to the photometric data set 118 4.6. Conclusion 120
Chapter 5: Factors related to the design constraints 122 5.1. Introduction 123 5.2. Stress waves and strain rate in steel due to a blast load 123 5.3. Prediction of rupture 128 · MSC/PATRAN, MSC/NASTRAN, and LS/DYNA 137 · Check_set.for 139 · Solve_num.for 139 · Nastran_position.pm 140 · Nastran_stress.pm 140 · Dyna_position.pm 140 · Dyna_stress.pm 140 · Solve_stress.for 141 · Stress_dyn.for 141 · Check_element.for 141 · Face_Numbering.for 142 · J-integral.for 142 5.4. Conclusion 144
Chapter 6: Bulkhead component investigation 145 6.1. Introduction 146
vi 6.2. Joint structures 146 6.3. Stiffener structures 164 6.4. Conclusion 201
Chapter 7: Development of an optimised X-80 steel blast tolerant transverse bulkhead 202 7.1. Introduction 203 7.2. Optimisation procedure 203 · Step 1 203 · Step 2 204 · Step 3 205 · Step 4 206 · Step 5 206 · Step 6 206 · Step 7 206 · Step 8 206 7.3. Optimisation cycles 208 · Cycle 1 209 · Cycle 2 211 · Cycle 3 213 · Cycle 4 216 7.4. Additional outcomes 219 7.5. Conclusion 222
Chapter 8: Conclusion 223 8.1. Summary 224
Acknowledgements 229
Bibliography 230
Appendix A: Sheppard Interpolation 259 A.1. Sheppard interpolation explanation 260
vii A.2. Fortran codes 261
Appendix B: Sea Australia 2000 paper 267 B.1. Raymond et al. (2000a) 268
Appendix C: Structures Under Shock and Impact paper 276 C.1. Raymond et al. (2000b) 277
Appendix D: Structural Failure and Plasticity paper 287 D.1. Raymond et al. (2000c) 288
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Chapter 1 Introduction
Abstract: In this ‘Introduction’ chapter a literature survey of the topics covered in this research project is given. Additionally, an explanation of the research project is given and its interconnection to the literature survey.
1 1.1. Introduction
In this chapter a survey of literature relevant to the research task has been covered. Due to the extreme broadness of the topics covered, the literature survey is quite diverse. The diversity of the literature topics ranges from ‘Warship survivability’ to ‘What is X-80 steel’, specifically focusing on blast loads, structural responses to blast loads, stress waves, strain rate effects and the J-integral.
To finalise this chapter a brief explanation of the research project is given as well as the interconnection between this project and the literature survey.
1.2. Warship survivability
Survivability of warships, i.e. resilience of warships, up to and through World War 2 had continually improved. These improvements were aimed at reducing the vessels vulnerability to kinetic weapons above the waterline and explosive weapons below the waterline on the side of the vessel, as mentioned in Begg et al. (1990),
“From September 1943 to October 1944 the German battleship Tirpitz sustained direct hits from 2 underwater mines and 22 aerial bombs, totalling 22 tons of explosive charge – and survived. In November 1944 she was hit by a further 6 high explosive bombs of 5 tons each before capsizing through flooding. The Tirpitz can be described as a resilient warship. This can be attributed towards her 22 watertight subdivisions and armour plating up to 12 inches thick around her sides and deck, giving a displacement of 50,000 tons.”
Post World War 2 the perception was that nuclear weapons would be used frequently in any future conflict, therefore designing warships to be resilient was not considered as highly as throughout the war. Additionally, since World War 2, torpedos and mines have been designed to explode under the keel of a vessel, making it almost impossible to deal with the blast pressure wave/bubble. Hence from 1950’s to late 1980’s warships were made lighter, and had more of their displacement directed to offensive
2 capabilities. Thus there was an improvement in their attacking capabilities and also a significant increase in battle damage, as supported in Dawson and Orton (1990), 16 out of the 23 warships sent by the Royal Navy to the Falklands War were damaged. Additionally, taking into consideration the incidents that have occurred in the Persian Gulf, modern warships are now being developed with greater consideration of survivability requirements.
Before discussing the factors and the undertakings to improve survivability, the following recent examples of warship battle damage are canvassed.
On the 17th of May 1987, two Exocet missiles from an Iraqi aircraft hit USS Stark. According to Fritz (1997), the first missile was a dud that did not explode but started fires, while the second missile did explode. Both of these missiles hit around the port side enlisted quarters. From this incident 37 sailors were killed. The following figures (Figures 1.2.1 to 1.2.4) show USS Stark post the missile hits; these photos are from the United States Navy (USN) collection of photos.
During the Falklands war, an Exocet missile hit HMS Sheffield, a Type 42 destroyer. The subsequent fire lead to 20 deaths and the ship was abandoned. Figure 1.2.5 shows the gutted HMS Sheffield before it was sunk. Additionally, Figure 1.2.6 shows HMS Arrows helping to fight the fires on HMS Sheffield, unsuccessfully.
Figure 1.2.1: USS Stark post the missiles attack, trying to drain off the excess water from the fire fighting effort. It was this excess water that nearly led to the USS Stark capsizing.
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Figure 1.2.2: USS Stark with a significant list due to excess water onboard
Figure 1.2.3: Close up picture of the damage done to USS Stark
Figure 1.2.4: Another view of the damage done to USS Stark from the Iraqi missile attack
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Figure 1.2.5: Gutted HMS Sheffield, from http://www.thenews.co.uk/news/falklands/shiny.html
Figure 1.2.6: HMS Arrows fighting the fires on HMS Sheffield, from http://www.ted.murphy.ukgateway.net/arrow_assisting_the_sheffield.html
Also during the Falklands war, bombs dropped from an Argentinian Skyhawk hit the frigate HMS Coventry. The result was 19 killed, 30 wounded and the vessel capsizing 20 minutes after the attack. The following sequences of photos (Figures 1.2.7 to 1.2.12), from the Royal Navy (RN) collection, are of the HMS Coventry just after the hit, the secondary explosion, listing and finally capsizing.
The above three examples demonstrate the responses of warships to threats from above the waterline, i.e. anti-ship missile and bombs. Slater (1998) discusses the response of USS Princeton to an acoustic mine in the Persian Gulf. Although in this instance two mines detonated, the major response and damage to USS Princeton came from the initial explosion below the hull. The effect of this was devastating to the ship’s structure – the aft of the vessel nearly separated, and the shock knocked out many systems 5 onboard. Slater (1998) covers in detail the response of USS Princeton to the entire event, and unquestionably shows the destructive capability of under-water weapons to modern naval platforms.
Figure 1.2.7: HMS Coventry just after being hit by a bomb from an Argentinian Skyhawk.
Figure 1.2.8: HMS Coventry covered in smoke from the fire onboard
Figure 1.2.9: Secondary explosion aboard HMS Coventry
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Figure 1.2.10: HMS Coventry beginning to list to port, due to flooding and battle damage
Figure 1.2.11: HMS Coventry listing further to port
Figure 1.2.12: HMS Coventry capsized
These examples demonstrate that warships based on older (Cold War era) design philosophies are significantly impaired in their ability to survive threats – above or below the waterline. This lack of survivability covers both active measures, such as anti-missile missiles; and passive measures, such as reduced radar cross-section and blast tolerant structures. It should also be noted that the spread of fire throughout a warship due to anti-ship missiles can often be the most critical and significant issues in the vulnerability of a warship to the anti-ship missile, especially in regards to small and
7 medium size anti-ship missiles. Therefore, it becomes extremely important to be able to restrict the spread of fire and in doing so restrict the blast pressure\load throughout the ship.
Deficiencies can still be seen in warships currently being built. One class that has attempted to overcome some of these deficiencies is the Arleigh Burke Destroyer Class for the USN. In the terrorist bombing of USS Cole, an Arleigh Burke Flight I destroyer, on the 12th of October 2000, which has been discussed in AP(2000) and Ingalls (2000), it is noted that the damage has been localised. This localisation of the damage is a clear example of the successful application of improved survivability requirements in the Arleigh Burke class design. Two factors that have been particular critical in this, are the blast tolerant structures used within the design and the fire retardant systems within the ship. It should be noted that this incident was one where a high blast pressure was applied to the side of the hull below the waterline. Further, the major threat to the ship from this incident was secondary fire spreading throughout the ship. As can be clearly noted this did not happen and therefore the implementation of the improved survivability requirements have been achieved successfully. Figures 1.2.13 to 1.2.16 show the external and internal damage to USS Cole from the terrorist attack, plus USS Cole returning to the US for repairs. All of these photos are from the USN website.
Figure 1.2.13: Damage to USS Cole from the terrorist attack
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Figure 1.2.14: Wider shot of the damage to USS Cole, please note that the damage is localised to one area
Figure 1.2.15: Damaged propeller shaft inside USS Cole
Figure 1.2.16: USS Cole returning to Ingalls ship yard for repair
So what is survivability? Reese et. al. (1998a) gives the following definitions, whereby
“Survivability is the mathematical complement of killability, which is, in turn, the product of the probability of being hit (susceptibility) and the probability of being killed if hit (vulnerability).”
9 Often a third item is included in this survivability analysis, that of recoverability. Said (1995) gives the following definition of the three elements;
“Susceptibility refers to the inability of a ship to avoid being damaged in the pursuit of its mission and to its probability of being hit”.
“Vulnerability refers to the inability of the ship to withstand damage mechanisms from one or more hits, to its vincibility, and to its liability to serious damage or loss when hit by threat weapons”.
“Recoverability refers to the ability of a ship and its crew to prevent loss and restore mission essential functions given a hit by one or more threat weapons”.
In the analysis of a ship’s survivability there are many characteristics considered. These are, but not exclusively, as follows:
· Susceptibility: Ø Operational conditions Ø Countermeasures Ø Stealthiness or detectable range Ø Self defences (offensive and defensive)
· Vulnerability: Ø Redundancies in all system, i.e. electronics, power supply, fuel, sensor, weapons. Ø Compartmentalisation or zoning of the internal structure and entire ships functions Ø Level of self-autonomy in individual compartments Ø Ship size Ø Structural detail Ø Shock hardening Ø Separation distance of the redundant mission critical functions
10 · Recoverability: Ø The level of damage control teams and their capabilities Ø Semi- and fully automated systems Ø Secondary/redundant systems and components Ø Shipboard allowances for damage
Another essential factor that must be considered in a survivability analysis is the type of threat that is being directed towards the warship. Figure 1.2.17, from Said (1995), shows all the major threats that can be directed against a warship. In the post-Cold War geo-political environment warships are intended to be deployed in more littoral warfare, i.e. close to the shoreline and in restricted coastal zones. Coupled with this is the proliferation of sophisticated weaponry, especially radar guided artillery and long-range anti-ship missiles, which have increased the threat risk to modern warships. In particular, the radar guided artillery is of considerable threat in littoral warfare, due to the warship being within range of their projectors, the ability to use hit and run tactics in artillery deployment and the relative cheap cost of an artillery platform when compared to a modern warship.
Other examples are available from Reese (1998b), USN (2000), and Edney (1988). As an aside, much of the work on reducing radar cross-section and other detectable emissions from military platforms have been done by the United States Air Force and associated aircraft supplies. Paterson (1999) discusses some of this work and more importantly the operational effects it has. These issues can be equally applied to future naval platforms and their operations.
As has been stated above, the survivability of naval platforms was lacking. In this investigation the principal focus is on the naval platforms response to an internal blast load. Generally in Western navies, warships susceptibility have received high consideration, while the crew’s professionalism was generally high in the recoverability of their vessel. The deficiency has been in the vulnerability of the ships structures to the blast load and the subsequent extra work needed in recoverability. Articles discussed above and Garriques (1995) are calling for increased survivability, or more specifically reduced vulnerability, in future naval platforms because of the new operational environments that these vessels will be operating in. Additionally, with the current 11 restriction on many defence budgets around the world there will be fewer ships with less crew. Improved survivability for these future naval platforms offers the benefit that fewer damage control personnel are needed for recovery and that these vessels will be able to operate with some level of damage. This offers a multiplier effect for the navy, as the warships are capable of meeting mission requirements even though they are damaged.
Figure 1.2.17: Anti-ship threats that can be directed against modern warships
The work described in Said (1995), Reese (1998a) and Reese (1998b) has led to a significant body of OPNAV (Naval Operations) Instruction documents. OPNAV Instruction guide future procurement programs and fleet readiness standards. Although not a complete list, the OPNAV Instructions relevant to this are (in no particular order): Edney (1998), Pilling (1998), Pilling (1996), Jay (1985), OP-3C (1995), Went and Edney (1989), Mullen (1996), Busey (1987), Taylor (1995), and Nyquist (1987). In response to some of these OPNAV Instructions, effort has been put into qualifying the level of ship protection that is needed, Hockberger (1999). Additional effort has been directed at determining ways that ship-borne activities can be modified to optimise the operational ability of future naval platforms, while improving the survivability of these vessels to the necessary operational environments, Giffin (1997), and Mulhern et al. (1999).
To support the developments in survivability requirements for naval platforms, new research efforts have been undertaken. Particular focus has been on reducing the vulnerability of the naval platform to blast loads. These research efforts in USA have covered such generalised topics as material aspects of damage control, Shan Khan et al.
12 (1994), and cracks and structural redundancy, Stenseng (1996). Additionally, more specific research has been done on improving the survivability of naval platforms; from Naval Sea System Command (NavSea) this work has been covered in Bogner and Wunderlick (2000), Wilson (2000), Everstine and Cheng (1996), Graham and Bosworth (1991), and Beach (1991). Specifically, Graham and Bosworth (1991) discuss a future fleet strategy to improve the entire fleet survivability with specific focus on reducing the detectability of USN task groups and fleets. Beach (1991) covers many developments in surface ship hull and structural developments, in particular the use of double hull structures to reduce the vulnerability of the ship, which is also covered in Everstine and Cheng (1996). Bogner and Wunderlick (2000) discuss current results and programs aimed at reducing the vulnerability of naval platforms to blast load and improving the recoverability of the platform post damage occurring. Finally, Wilson (2000) covers the research work being undertaken to prevent catastrophic ship loss due to an explosion within the missile magazine. Mair et al. (1998) and Mullin (2000) give descriptions of two facilities in the USA that are used for empirical investigations (with follow up finite element analysis) of blast loads onto structures.
Walsh et al. (1996) and Walsh and Burman (1998) cover the work that has been undertaken at the Defence Science and Technology Organisation (DSTO) within Australia on naval platforms structures subjected to a blast load. While Slater et al. (1990) covers a research effort undertaken by the Defence Research Establishment Suffield (DRES) in Canada on blast loads being applied to panel(s) on a ship structure. In Netherlands work on improving their navy’s platforms survivability has in part been undertaken by the SEAROADS (Simulation, Evaluation, Analysis and Research On Air Defence Systems) program covered in TNO-FEL (2000).
Additional research and development work has also been directed solely at investigating the structural requirements needed to reduce a naval platforms vulnerability to blast load, and in particular how this affects the overall design process. The use of compartmentalisation (or zoning) is a continuing theme that is supported by the previous success seen in World War 2 vessels that were resilient to attacks and current research conclusions. Some of the current research efforts and the utilisation of this research effort are covered in the following articles: Begg et al. (1990), Pattison (1990), Dawson and Orton (1990), Fuller (1990), Brown (1990), Tupper (1990), Prange (1997), 13 and Harms (1997). Interestingly, Harms (1997) discusses the vulnerability issues of a frigate size platform constructed out of high strength steel.
As discussed in Jordon (1997), the final level of research and development for improving the survivability on naval platforms is the conducting of total ship survivability trials at sea. These trials mainly focus on the recoverability elements of the ship and its crew’s performance but also investigate the shock hardening of the ship sub-systems and the ability to attenuate the shock loads.
Future naval platforms will be affected by the requirement for improved survivability. In Australia DSTO Cannon et al. (1999) discusses the many factors that will drive the next major surface combatant for the Royal Australian Navy (RAN). The USN currently has two major ship programs under development, the LPD-17 and DD-21, and have had significant survivability issues included in their development, as can be seen to some extent in Figures 1.2.18 and 1.2.19. Of note is the defensive weapon suite on the LPD- 17 and the blast hardened bulkheads on both platforms. This development is not only restricted to the USA, Sweden is currently constructing the Visby class corvette. Due to its size, blast hardened bulkheads are not practical, but its use of composite and carefully shaped hull and super structures has reduced detectability by sonar and radar.
Figure 1.2.18: LDP-17, the new USN Landing Dock Platform, from the USN web page
There is significant interest and work being applied in improving the survivability of future naval platforms. In particular, the improved survivability has been directed to reducing the vulnerability of these platforms from attack. In this research the focus has been on the structural response to an internal blast load, and in particular how blast tolerant transverse bulkheads can be optimally formed.
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Figure 1.2.19: Team Blue proposal for the DD-21, from the Defence Systems Daily
1.3. Explosives and their blast loads
Baker et. al. (1983) define an explosion as:
“In general, an explosion is said to have occurred in the atmosphere if energy is released over a sufficiently small time and in a sufficiently small volume so as to generate a pressure wave of finite amplitude traveling away from the source. This energy may have originally been stored in the system in a variety of forms; these include nuclear, chemical, electrical, or pressure energy, for example. However, the release is not considered to be explosive unless it is rapid enough and concentrated enough to produce a pressure wave that one can hear. Even though many explosions damage their surroundings, it is not necessary that external damage be produced by the explosion. All that is necessary is that the explosion is capable of being heard.”
Equivalently, a blast load, also known as a blast wave or shock wave is always formed in an explosion. These waves are the outer most edge of the blast field. Bulson (1997), describes the blast field as:
“The explosive action of high explosive and nuclear fission (and fusion) are similar in that the release of energy happens so quickly that the sudden expansion compresses the surrounding air into a dense layer gas. This dense layer expands so fast that it forms a shock wave, the face of which is
15 known as the shock front. It moves supersonically, in contrast to a sound wave that moves at ‘sonic velocity’ and does not ‘shock-up’, to use the jargon of the explosive scientist. The instantaneous rise of pressure at the shock front falls away and declines gradually to sub-atmospheric pressure.”
The following, from Bulson (1997), is a brief history of conventional explosive development and a comparison between several of the current explosive substances in use today.
Nitric acid and nitrates have formed the basis of most modern high explosives. One of the first such explosives was created by Sobrero. He developed nitroglycerine by treating glycerine with a mixture of concentrated nitric and sulphuric acids. The study of nitroglycerine introduced probably the most famous developer of explosives to the scene, Alfred Bernhard Noble. In 1867 he combined nitroglycerine with a diatomaceous earth to form dynamite. This made the commercial use of nitroglycerine possible.
By the end of the nineteenth century, it was found that methylbenzene (toluene) reacted with nitric acid in the presence of concentrated sulphuric acid to form trinitrotoluene (TNT). TNT is a much safer and more economical to produce than other explosives. Due to TNT’s universal use it has become customary to class all types of explosives (conventional or nuclear) using TNT as a standard.
Military research has developed the use of fuel-air explosives (FAE). A FAE obtains some of its oxygen from the surrounding atmosphere. This means that a given weight of FAE produces over seven times the energy of TNT, as the TNT mass is used up in storing oxygen for the explosions. The peak overpressure of a FAE is much lower and the duration of the impulse much greater than TNT-based explosions as the detonation of the FAE is over a wider area.
Table 1.3.1 gives a comparison of the mass specific energy, TNT equivalent, density, detonation velocity, and detonation pressure for an array of commonly used conventional high explosives.
16 Table 1.3.1: Conversion Factors (TNT Equivalence) for some of the common conventional high explosives, from Baker et. al. (1997)
Mass TNT Specific Equivalent, Detonation Detonation Energy, (E/M)x/(E/ Density Velocity Pressure Explosive E/M, kJ/kg M)TNT Mg/m^3 km/s Gpa
Amatol 80/20 (80 % ammonium nitrate, 20 % TNT) 2650 0.586 1.6 5.2 ----
Baronal (50 % barium nitrate, 35 % TNT, 15 % aluminum 4750 1.051 2.32 ------
Comp B (60 % RDV, 40 % TNT) 5190 1.148 1.69 7.99 29.5
RDX (Cyclonite) 5360 1.185 1.65 8.7 34
Explosive D (ammonium picrate) 3350 0.74 1.55 6.85 ----
HMX 5680 1.256 1.9 9.11 38.7
Lead Azide 1540 0.34 3.8 5.5 ----
Lead Stypinate 1910 0.423 2.9 5.2 ----
Mercury Fulminate 1790 0.395 4.43 ------
Nitroglycerin (liquid) 6700 1.481 1.59 ------
Nitroguanidine 3020 0.668 1.62 7.93 ----
Octol, 70/30 (70 % HMX, 30 % TNT) 4500 0.994 1.8 8.48 34.2
PETN 5800 1.282 1.77 8.26 34
17 Table 1.3.1: Continue Mass TNT Specific Equivalent, Detonation Detonation Energy, (E/M)x/(E/ Density Velocity Pressure Explosive E/M, kJ/kg M)TNT Mg/m^3 km/s Gpa
Pentolite 50/50 (50 % PETN, 50 % TNT) 5110 1.129 1.66 7.47 28
Picric Acid 4180 0.926 1.71 7.26 26.5
Silver Azide 1890 0.419 5.1 ------
Tetryl 4520 1 1.73 7.85 26
TNT 4520 1 1.6 6.73 21
Torpex (42% RDX, 40 % TNT, 18 % Al) 7540 1.667 1.76 ------
Tritonal (80 % TNT, 20 % Al) 7410 1.639 1.72 ------
C-4 (91 % RDX, 9 % plasticizer) 4870 1.078 1.58 ------
PBX 9404 (94 % HMX, 3 % nitrocellulose, 3 % plastic binder) 5770 1.277 1.844 8.8 37.5
Blasting Gelatin (91 % nitroglycerine, 7.9 % nitrocellulose, 0.9 % antacid, 0.2 % water) 4520 1 1.3 ------
60 Percent Straight Nitroglycerine Dynamite 2710 0.6 1.3 ------
18 Note: The value for mass specific energy and TNT equivalent in this table are based on reported experimental values for specific heats of detonation or explosion. Calculated values are usually somewhat greater than those in first column of this table.
Celmins (1981) is one of the most complete explanations of how to determine all the variables from an empirical blast test. In particular Celmins (1981) describes a method for reconstructing the blast field using only pressure observations. The requirement for such a capability is that, usually in a blast test the only recorded data is the magnitude and arrival time of the overpressure. Therefore to know the effect that such a blast will have on a structure, the entire blast field properties needs to be reconstructed so that the whole load case from the blast field can be determined.
The assumptions and theory within this problem involves numerically solving the governing equations for a flow field with boundary conditions derived from pressure history and shock observations. This problem is mathematically ill-posed because the boundary conditions over determine the solution in some parts of the flow field. At other times they may not be sufficient to compute the complete flow history for the full duration of a pressure history observation at some other station. There are two approaches that can be used to overcome this problem. The first is to delete the data that would over determine the problem. The second is to remove one of the governing equations. This later approach is preferred as it keeps the data and permits the removed governing equation to be used as a check of the final solution. Following the work of Makino, the continuity equation is usually removed, as the pressure time history, p(r,t) , is known.
To solve this flow field problem, the following assumptions need to be made:
a) the flowing medium is an ideal gas with zero viscosity and no heat conduction b) the event is spherically symmetric and the flow has only a radial velocity component u .
At the target area the pressure is in the order of one megapascal, which is in the regime where air acts like an ideal gas. This should not be mistaken with one mega-atmosphere,
19 which does not act like an ideal gas, and the situation is closer to the explosion source and so contains parts of the explosive. Therefore the first assumption holds. The second assumption holds as long as the distribution due to wind, and surface effects are negligible, i.e. the explosion happens in a free field.
The governing equations for a flow field are Dp + r Ñ u = ,0. (1.3.1.) Dt s Du r + Ñp = ,0 (1.3.2.) s Dt and
De pss Dr r s =- ,0 (1.3.3.) Dt rs Dt in which D ¶ = + ()uÑ (1.3.4.) Dt ¶t is the material derivative. The equation of state is
1 ps es = , (1.3.5.) g -1 r s where g is the ratio of specific heats, p is the pressure field from the blast load, rs is the density of the air behind the shock front, and t is the time.
By combining equations (1.3.3.) and (1.3.5.), the specific internal energy, es , is eliminated and gives dp 11 dp g =- .0 (1.3.6.) ps dt r s dt
Integrating equation (1.3.6.) along a particle path line leads to the known formula for a particle in an adiabatic flow
1 g rs æ ps ö = ç ÷ , (1.3.7.) r A è pA ø where the subscript A indicates reference values at a point A on the particle path.
20 By substituting equation (1.3.7.) into equation (1.3.2.) the following is obtained
1 g dus 1 æ p A ö ¶p -= ç ÷ . (1.3.8.) dt r A è ps ø ¶r Using the known function p(r,t) , equation (1.3.8.) can be integrated numerically together with the path line equation dr = u . (1.3.9.) dt s
The integration provides the path line starting at a point A and the particle velocity along it. The density along the same path line is given by equation (1.3.8.). All other flow variables such as, internal energy, dynamic pressure, and the speed of sound can be computed from ps , us , and r s .
As can be seen the continuity equation, (1.3.1.), has not been used, as this is the equation which has been removed from the numerical solving technique. Now the continuity equation can be used as a check for the procedure, and especially for confirming the accuracy of the assumption if the recorded data is precise. This check can never be perfect as the observed data has systematic errors that will affect the final result of equation (1.3.8.).
The control calculation, checking procedure, is done by first combining equation (1.3.6.) to equation (1.3.1.), to obtain
1 dps Ñ.us =+ ,0 (1.3.10.) gps dt or
2 ¶ 2 2 1 ¶ps r ¶ps ()()r us + r us + = .0 (1.3.11.) ¶r ps ¶r gg ps ¶t Integrating along the line t = const. yields
2 1 æ r ö æ p ö g 1 u C . C + ´ u(r, t) = C ç ÷ ç ÷ 1 è r ø è p(r, t) ø r 2gp(r,t) g
rC 1 ¶p(x,t) ò 2 p()xx ,. t g dx. (1.3.12.) r ¶t
21
The subscript C indicates the value at the point C with coordinates (rC ,t). From this equation the velocity field u(r,t) can be calculated as long as the pressure field p(r,t) and the initial velocity are known.
The numerical integration and accuracy estimates of these values are obtained by model fitting of shock and pressure observations. The results of the shock model fitting are two functions of the radial distance r and of a model parameter z describing the shock arrival time ta (r;z ) and the shock overpressure ps (r;z ), respectively. From these shock functions, the shock density, r s , and particle velocity, us , can be solved. The model fitting of the observed pressure histories produced an overpressure field function
pO (r,t;z ) .
The differential equation for the path line is dr ü = u dt s ï ï ý, (1.3.13.) du ï s = F()r,t;z ï dt þ where
1 g 1 æ ps ()rA ;z + pi ö ¶pO ()r,t;z F()r,t;q -= ç ÷ , (1.3.14.) ps ()rA ;z è pO ()r,t;z + pi ø ¶r and pi is the ambient (~1 atmosphere) pressure.
The control calculation, Equation (1.3.12.), is solved after the substitution of pi and pO into it.
The accuracies of the integration algorithms and the data will determine the final result. Reducing the size of the integrating steps can reduce the errors in the integration algorithms. The linearised law of variance propagation is used to estimate the errors from the observed data.
22 The least square data fitting programs provide an estimate of the variance-covariance matrix, Vz , of the parameter vector, z , in terms of the estimated standard error of the observations. An estimate for the error of pO (r,t;z ) is
1 T 2 é¶pO ¶pO ù eO = ê Vz ú . (1.3.15.) ë ¶ ¶zz û
The standard error of ps (r;z ) can be calculated by a corresponding function, and the standard error of r s can be calculated by using the relation (1.3.7.) between density and pressure.
For the particle velocity the standard error is found in a similar way as above except that equation (1.3.13.) now becomes
d æ ¶r ö ¶us ü ç ÷ = ï dt è ¶ ø ¶zz ï ï ý. (1.3.16.) ï æ ¶u ö d s ¶ ¶FF ¶r ï ç ÷ = + dt è ¶ ø ¶ ¶r ¶zzz þï
The end point of each path line has an uncertainty in the t-direction, which again can be computed by the variance propagation function using the derivatives
¶tB ¶ts (rA ;z ) 1 é ¶r ù = + ê ú .. (1.3.17.) ¶z ¶z uB ¶z ë û =rr B
r u 2 For the computation of the standard error of the dynamic pressure, ss , one needs 2 to know the variance as well as the covariance of r s and us . The full variance- covariance matrix of the flow field at an end point of a path line is calculated with the formula
T ¶H æ ¶H ö VH = Vz ç ÷ , (1.3.18.) ¶ è ¶zz ø where
T H = (t up r BBBB ) ,,,, (1.3.19.) 23
is a vector that characterises the flow field. VH contains the covariance between velocity and density that is needed for the dynamic pressure error estimate.
The overpressure model fitting initially considers the shock overpressure, and is modelled by the following three-parameter function c c c p ()r; ,, ccc 1 2 ++= 3 , (1.3.20.) s 321 r r 2 r 3 and the shock arrival time is modelled by
r dx t r; ,,, cccc += , (1.3.21.) a () 44321 ò r g + 1 æc c c ö 1 u 1 + 1 2 ++ 3 a ç x 2 3 ÷ 2gpi è x x ø where ua is the ambient speed of sound and r1 is an arbitrary reference distance.
Similarly the overpressure field function is modelled by
nC Q nC pO (r, t; BBAA ,,,, C12121 ; ps , ta ) [ps C1r ]e +-= C1r , (1.3.22.) where
nA 2 nB Q [ tt a ]( AA 21 )rr [ tt a ] ( +-++-= BB 21 )rr . (1.3.23.)
n A , nB , and nC are determined by analysis of the trends of the observed pressure histories.
The model fitting is done in two steps. The first is determining the shock functions ps and ta , followed by solving the overpressure field function pO . This procedure was tested against theoretical models and real life situations and showed good agreement.
Although the above explanation and equations can be used in the development of blast tolerant structures, in this research effort only the pressure history supplied by Mr. Terry Turner, Turner (1999), of DSTO is used. Therefore, the above is given for completeness on the subject of blast loads and the environment in which they occur. This is because, although the equations and solutions for blast loads in a free field are known and readily solved, this is not the case for blast loads in a restricted space, as shown below.
24 The use of scale blast loads to predict the blast properties of large explosions from small-scale blast tests/devices can offer significant cost savings. A common form of blast scaling is the Hopkinson-Cranz or “cube root” scaling, i.e. self-similar blast waves are produced at identical scaled distances when two explosive charges of similar geometry and of the same explosive material, but of different sizes, are detonated in the R same atmosphere. Generally a scaled distances, z = 1 , where R is the distance 3 Es from the centre of the explosion and E is the total energy of the explosion. More information about the Hopkinson-Cranz scaling method can be found in Baker (1973) and Chapter 2 where it has been used.
Bulson (1997) mentions that the availability of ground bursts, or explosive tests that are interfered with by a solid surface layer, is greater than free field explosions. From this work throughout World War 2, it was observed that the ground surface led to a greater scattering of the pressure and impulse. In particular, the detonation of a high explosive on or near a flat surface will produce a localised impulsive load on the surface, as well as the propagation of the blast wave through the air. This impulse, which is influenced by the size and shape of the charge, produces a shattering effect, or a ‘brissance’.
Additionally, in such an event there are three different wave fronts; these are the incident shock front, reflected shock front and Mach stem. The reflected shock front is formed when the incident shock front comes in contact with the surface. The reflected shock front travels faster than the incident shock front, due to the reflected overpressure being greater than the overpressure of the incident shock front. When the reflected shock front meets up with the incident shock front, this is termed the triple point, the fronts merge to form a Mach stem, which is named after Mach due to his analysis of it in 1877 with Sommer. The Mach stem is assumed to be straight, between the surface and the triple point.
This work on ground bursts can be extrapolated to internal and restricted environments where explosions have or could occur. In these situations the detonation occurs close to the structure, thus the loading onto the structure will not be uniform. In such cases the load history either needs to be calculated or measured over the entire structure. A deficiency in our current abilities to deal with such situations is our inability to 25 accurately predict the amount of energy absorbed by the structure and reflected back as a reflected shock front out of the initial shock front. Nevertheless, the development of blast traps, especially in long tunnels, has been successfully developed.
Bulson (1997) states that from the detonation of a high explosive in a confined space, which has infinitely strong inflexible and airtight boundaries, there can be no escape of the gaseous products. The blast wave will continuously reflect off the faces, until the energy of the explosion is expended in heat and perhaps by some form of absorption into the walls. If the main method of expending the energy from the explosion is through the raising of the temperature, then the final pressure will be greater than the original pressure.
As no chamber is unyielding or completely enclosed from the outside, therefore, venting and the structural changes, such as elastic deformation, have to be considered when investigating explosions that occur inside chambers.
The internal pressure loading consists of two phases. The first is due to the direct reflection waves from the internal walls plus reflection pulses that arrive at the walls. The waves would be attenuated in amplitude and be very complex in waveform. The initial maximum pressure can be found from data for normal blast wave reflection from flat or curved surfaces, but oblique reflections can generate Mach stems (waves) and lead to concentration of high pressures in corners of the chamber. The second phase occurs when the blast waves that have been reflected inwards strengthen as they implode towards the centre of the chamber and reflect again to load the structure impulsively for a second time.
It can be approximated that the second shock is half the amplitude of the first and the third is half again. Further reflections are assumed to be irrelevant. The time delay between shocks can be assumed to be twice the time of arrival, ta , of the initial shock.
From empirical and other forms of investigation, it is clear that the judicious use of vents can significantly reduce the pressure from an internal explosion. It is important to note the use of the word judicious, as in this case it is meaning the total vent opening of
26 a chamber in relation to the explosive charge size. For example the vent formed from the penetration of a missile into the chamber is unlikely to vent the effects of a weapon explosion, while a chamber with large vents and a smallest explosion will be less damaged than expected due to venting.
Finally, Youngdahl (1970) states, “the effect of the pulse shape is virtually eliminated if the pulses have the same total impulse and “effective load”. The “effective load” is defined as the impulse divided by twice the mean time of the pulse, where the mean time is the interval between the onset of plastic deformation and the centroid of the pulse”. This has been challenged by the work of Owen and Watson (2000), which states “Air blast acting on structures in the real world rarely takes the idealised form of instantaneous pressure rise followed by smooth exponential decay. Reducing a composite load history to a simple equivalent pulse in calculations to determine damage risk overlooking additional damage that may result as a coincidence of repetitive blast pulses with the dynamic behaviour of the structure”. It is for these reasons that within this research a blast pressure history supplied by Mr. Turner, Turner (1999), of DSTO has been used. Furthermore, no attempt has been made to develop a theoretical blast pressure history, as this would not have been as appropriate as the supplied data. In regards to shock front structural interaction, no attempt has been made to investigate this, and the focus has solely been on the structural response to a known blast pressure history.
1.4. Structural response to blast loads
The investigation of structural responses to blast loads is an extremely difficult and challenging exercise. Although, our present ability to predict the structural response of a system to a pressure history is sufficient, it is limited by the requirement for specialised material data and high computer processing requirements. As stated above our abilities to predict the amount of energy absorbed by a structure and the amount reflected when a shock wave interdicts the structural system is still lacking. This is currently being investigated by the mixing of computational fluid dynamics (CFD) codes and dynamic non-linear finite element modelling packages.
27 To start this review of previous work related to structural responses to blast loads, let’s first look at a simple specimen response to blast loads. Four papers that are some of the earliest published work on the subject from the viewpoint of naval platform research and development are Snelling (1946), Muller et al. (1949), Mikhalapov (1951) and Mikhalapov and Snelling (1954). All four of these come from the Ship Structures Committee and relate to work for blast and projector tolerant structures and steels for large naval combatants.
Principally in these papers the discussion is directed towards the use of direct explosion tests on steel specimens of prime (parent) and welded plates. One of the issues faced in this body of work, as these four papers are directly connected to each other, is to make sure the explosive output was constant or standardised.
This is important, because a brisant explosion is where there is a rapid rate of detonation. This type of explosion is characterised by a spall or a hole when the test plate is subjected to it. While a gas volume type of explosion, or in other words a slow explosion, low brisance, tends to move or deform the material in its vicinity more than is seen in a brisant explosive event.
It can be noted from Snelling (1946) that stress-relieved plates can handle greater explosive loads than un-stress-relieved plates. In particular, it was shown that furnace stress-relieved plates gave better blast tolerant performance compared to torch stress- relieve plates. It should be noted that failure was evaluated against rupture only.
In Part I of Muller et al. (1949), the continuing evaluation of the direct explosion test is discussed. From this evaluation the following was found: · A plate of 18 in x 18 in x t in is the minimum size for the direct explosive test to obtain the same behaviour as large plates. · It made no difference to the Mn-Mo steel test plate if it was supported along all four edges by loose bars arranged in pinwheel configuration or by a rigid welded box-like frame. · A concrete base is preferred over just placing the lower steel plate of the test rig on the ground. This is because there is no effect from the ground, such as the earth drying out over the test period and thereby coming harder. 28 · The shock limit, or the amount of explosive required for failure of the test plate, decreases with increasing detonation velocity. · As the detonation velocity increases, the dish, or deformation of the plate before failure decreases. · The failure of the test plates was similar to a spall. · Further investigations are required on unusual differences in the same batches of explosives.
In Part II (Muller et al. (1949)) a significant theoretical discussion is undertaken on the effect of the shock waves travelling through the steel plates. The principal outcome was the following relation:
s æ L ö T ç 1 ÷ 2 lnç ÷ u C -= uupu ,2 (1.4.1) r p èz 1 ø where s T is the tensile stress developed in the thickness direction of the plate, r p is the density of the plate, L1 is the original thickness of the plate, z 1 is the thickness of the spalled part, uu is the uncorrected velocity of the impact, and C p is the speed of the plastic wave.
Mikhalapov (1951), continued the work on direct explosive tests and how simple welded structures handle blast loads. The outcomes from this series of tests was the following: · Low hydrogen, low alloy electrodes, AWS E-10016, noticeably improved performances of joints of ship plates, as compared to the performance when the joints were welded with E-6010 electrodes. · This improvement was far greater in the case of fully killed steel than in the case of semi-killed steel. · Joints fabricated from the multi-pass submerged arc process are greatly superior to those fabricated out of E-6010 electrodes.
Mikhalapov and Snelling (1954), investigated the performance of the direct explosion test and compared it to the Stand-off (Explosion Bulge) test. Unfortunately the prime plate had inconsistencies in its properties and so the accuracy of the results is not as high as was hoped for. Still the following results can be assumed with confidence: 29 · Fully killed steel had a higher performance when welded with low hydrogen electrodes compared to cellulose type electrodes. · The performance differences were much less noticeable for semi-killed steel. · The Direct Explosion Test is more discriminatory than the Stand-off (Explosion Bulge) Test insofar as the performance of the two electrodes is concerned.
From this test series the following points of interest can be made: · The maximum dish observed in the Direct Explosion Test does not exceed 20% surface strain on the backside of the plate. · In the case of overmatching electrodes, the surface strain of the heat-affected zone is nearly double that of the weld. · The Explosion Bulge Test produces a reasonably uniform biaxial strain over nearly the entire specimen, while the strain in the Direct Explosion Test is localised to a comparatively small circular area 2 in. (~50 mm) in radius directly under the charge. · The maximum reduction in thickness in the high concentration areas is 18 % for the Direct Explosion Test and only 10 % for the Explosive Bulge Test; however the area of thickness is approximately the same for both tests. · The stress gradient in the direction of the thickness is much greater for the Direct Explosion Tests compared to the Explosive Bulge Tests. · This greater stress through the thickness produces a condition of triaxial tension not unlike that present in the root of a notch. This is most likely why the Direct Explosion Test is more discriminating than the Explosive Bulge Test.
As an overview of the development and research efforts that have been undertaken on non-actual structures subjected to blast loads, the following papers are available on the topics: · for simple plate structures: Baker (1975), Westine and Baker (1975), Nurick et al. (1987), Nurick and Martin (1989a), Nurick and Martin (1989b), Celmins (1990), Nurick and Teeling-Smith (1992), Nurick et al. (1996), and Wiehahn et al. (2000).
30 · for cylindrical tubes: Ewing and Hwang (1995), and Li and Norman (1995). · for structural components: Huang and Liu (1985), Houlston and DesRochers (1987), Slater et al. (1988), Chong et al. (1989), Schubak et al. (1989), Slater et al. (1990), Schubak et al. (1992), Nurick et al. (1995), Clayton et al. (2000), and Rudrapatna et al. (2000). · for blast resistant investigation: Cichocki (1999), Krauthammer (1999), Karagiozova and Jones (2000), Guruprasad and Mukherjee (2000a), and Guruprasad and Mukherjee (2000b). · for miscellaneous events: Galiev (1996), Hiroe et al. (1999), Tao et al. (2000), and Owen and Watson (2000).
In regards to the simple plate structures, these papers looked at the response for plates to blast loads. Baker (1975), and Westine and Baker (1975) discussed prediction methods for deformation due to the blast load with consideration to approximate methods and energy solutions. Nurick et al. (1987), Celmins (1990), Nurick and Teeling-Smith (1992), Nurick et al. (1996), and Wiehahn et al. (2000) discuss the deformation and tearing behaviour of a plate to a blast load, with empirical evidences directly associated with it. Investigations towards tearing have also included the initiation of necking. Mentioned in many of these papers is the work of Menkes and Opat. Menkes and Opat defined three failure modes for beams subjected to impulsive loads. These are: · Mode I – large inelastic deformation · Mode II – tensile tearing at the edges · Mode III – shear failure at the edges
From experimental results of the above papers, the following results cases were noted for the clamped boundary of the test specimens:
i. no necking
31 ii. necking around part of the boundary iii. necking around the entire boundary iv. tearing around part of the boundary v. tearing around the entire boundary
Mode I failure encapsulates i, ii, iii; while iv is termed Mode II* and Mode II is v. Due to this Mode I can be redefined as:
· Mode I – large inelastic deformation with no necking at the boundary · Mode Ia – large inelastic deformation with necking around part of the boundary · Mode Ib – large inelastic deformation with necking around the entire boundary
These results at the clamping boundary, i-v, or the Modes of failure I-II, occur in consecutive order with a progressively increasing impulsive load onto the plate. It should be noted that Modes Ia and II* are experimental phenomena due to a variety of inherent physical parameters such as speed of detonation of the explosive and inconsistent material properties, which could result in an asymmetrical response.
The two most significant papers out of the collection for simple plate structures are Nurick and Martin (1989a) and Nurick and Martin (1989b). These papers give a further review of the Theoretical and Experimental knowledge of plates subjected to blast in 1989. Table 1.4.1, from Nurick and Martin (1989a), gives theoretical relations for the predicted maximum mid-point deformation of simple plates to blast loads in the second column. These functions are given for impulse, plate dimensions and material properties. The third column lists the predicted deflection-thickness ratio as a function of a dimensionless number. Nurick and Martin (1989b) discuss this dimensionless number in more detail.
Table 1.4.2, from Nurick and Martin (1989b), gives the results of experimental techniques of impulsively loaded plates.
Johnson defined a dimensionless damage number, so that a comparison could be made using results from different experiments. This dimensionless damage number is
32 2 r pus ad = , (1.4.2.) s d where r p is the density of the metal, us is the impact velocity and s d is the damage stress. Table 1.4.3 shows the damage regime as a function of the damage number. From this table it can be seen that the damage number predicts an order of magnitude deformation. In this prediction the method of impact, the interpretation of s d , the target geometry and boundary conditions or the target dimensions are not considered.
Table 1.4.1: Approximate Methods for Predicting Deformation of Thin Plates Subjected to Uniform Impulsive Loading
Deflection-thickness ratio Mid-point deflected predicting (see note 4) Comments (refer to prediction dimensionless form footnote)
A. Circular plates 4a
Hudson, 1951 1a: 2a: 3a 318.0 i t pf 1 2 t R r ppp s y )(
Wang and
Hopkins, 1954 028.0 i 2 277.0 f 2 1b: 2a: 3a 22 t R r ppp s y
Wang, 1955 051.0 i 2 505.0 f 2 1c: 2a: 3a 23 t R r ppp s y
Noble and
1 Oxley, 1955 R 2 2 1a: 2a: 3b - Conical p éæf 2 ö ù 1 l ç + ÷ -11 2 2 êç 2 ÷ ú é 2 ù l æ 101.0 i ö ëêè ø ûú êç + ÷ -11 ú êç t R 22 r s ÷ ú ëè ppp y ø û Profile
33 Table 1.4.1: Continue Deflection-thickness ratio Mid-point deflected predicting (see note 4) Comments (refer to prediction dimensionless form footnote)
080.0 i 252.0 f 1a: 2a: 3b - Circular
t R ()r ppp s y Profile
Duffey, 1967 1 1 1a: 2a: 3b - Various i(1242.0 +- uu 2 ) 2 761.0 f(1 +- uu 2 ) 2 1 2 t R ()r ppp s y Profile
Johnson, 1967 1 R(l em -1) 2
2 æ P ö 2 æ P ö 1a: 2a: 3a e ç2 + e ÷ = e ç2 + e ÷ = m ç m ÷ m ç m ÷ 3 s y 3 s y è ø è ø 2 2 101.0 i æ f ö 42 ç ÷ t R r ppp s y è l ø
Wierzbicki and
Florence, 1970 027.0 i 2 267.0 f 2 1a: 2a: 3a: small 23 t R r ppp s y Deflections (bending)
055.0 i 173.0 fl2 1a: 2a: 3a: large 1 23 2 ()t R r ppp s y Deflections (bending and membrane)
Batra and Dubey, 1972 382.0 i 201.1 f 1a: 2a -not in this form: 1 2 t R ()r ppp s y 3a
34 Table 1.4.1: Continue Deflection-thickness ratio Mid-point deflected predicting (see note 4) Comments (refer to prediction dimensionless form footnote)
Westine and
1 1 Baker, 1974 2 1a: 2b: 3b æ 082.0 i 2 ö 2 ( f + 101.0811.0 ) 2 ç + 101.0 t 2 ÷ ç 22 p ÷ - 0.637 è t R r ppp s y ø
- 637.0 t p
Lipman, 1974 132.0 i 415.0 f 1a: 2a: 3b - sinusoidal 1 2 t R ()r ppp s y
Ghosh and Weber, 1976 392.0 i 233.1 f 1a: 2a - not in this form: 1 2 t R ()r ppp s y 3b
Symonds and Wierzbicki, 1979 212.0 i ---- 1a: 2c: 3b - fixed mode 1 2 t R ()r ppp s y
Guedes Soares,
1 1 1981 2 1a: 2a: 3b æ 068.0 i 2 ö 2 ( f ) 2 -+ 11673.0 ç + 2 ÷ - ti ç 22 ÷ p è t R r ppp s y ø
Calladine, 1984 225.0 i 708.0 f 1a: 2a: 3b - circular 1 2 t R ()r ppp s y
Perrone and Bhadra, 1984 117.0 i 368.0 f 1a: 2c: 3a 1 2 t R ()r ppp s y
35 Table 1.4.1: Continue Deflection-thickness ratio Mid-point deflected predicting (see note 4) Comments (refer to prediction dimensionless form footnote)
Jones, 1988 260.0 i 817.0 f 1a: 2a: 3a 1 2 R t ()r ppp s y
Experimental evidence 135.0 i 425.0 f 1a: -: -: (see part 2) 1 2 R t ()r ppp s y
B. Quadrangular plates 4b
Jones et. al.,
1970 1 1 1a: 2a: 3a: 33.0 i 2 éæ B 2 ö 2 f 2 éæ l1 ö 2 êç3 + ÷ - êç332.1 + ÷ - 23 ç 2 ÷ ç 2 ÷ t L r pp s y êè L ø êè bb ø ë ë 2 2 B ù 1 ù ú ú L û b û
Jones, 1971 t 1 1a: 2a: 3a: 4b - b =1 p éæ 4f 2 ö 2 ù 1 êç1 + ÷ -1ú é 2 ù ç ÷ æ i 2 ö êè 6b ø ú êç1 + ÷ -1ú ë û êç 6r s t L24 ÷ ú ëè p y p ø û
776.0 t p 0.776 1a: 2a: 3a: 4b - b =1.616 1 1 é 2 2 ù é 2 2 ù æ ö æ 98.1 i ö ê 92.7 f ú êç1 + ÷ -1ú ç1 + ÷ -1 êç 6r s t L24 ÷ ú êè 6b ø ú ëè p y p ø û ë û
Jones, 1988 t 1 1a: 2a: 3a: 4b - b =1 p éæ 4f 2 ö 2 ù 1 êç1 + ÷ -1ú é 2 ù ç ÷ æ i 2 ö êè 6b ø ú êç1 + ÷ -1ú ë û êç 6r s t L24 ÷ ú ëè p y p ø û
36 Table 1.4.1: Continue Deflection-thickness ratio Mid-point deflected predicting (see note 4) Comments (refer to prediction dimensionless form footnote)
857.0 t p 0.857 1a: 2a: 3a: 4b- b =1 1 1 é 2 2 ù é 2 2 ù æ ö æ 56.1 i ö ê 24.6 f ú êç1 + ÷ -1ú ç1 + ÷ -1 êç 6r s t L22 ÷ ú êè 6b ø ú ëè p y p ø û ë û
Baker, 1975 1 1 1a: 2c: 3a: 4b - b =1 é 2 ù 2 é 308.0 f 2 ù 2 077.0 i 2 + 177.0 - ê + 177.0 t p ú ê ú 2 2 ë b û ëêt L r pp s y ûú 0.421 - 421.0 t p
1 1 1a: 2b: 3a: 4b - b =1.616 é 2 ù 2 é 484.0 f 2 ù 2 121.0 i 2 + 189.0 - ê + 189.0 t p ú ê ú 2 2 ë b û ëêt L r pp s y ûú 0.435 - 435.0 t p
Experimental evidence 235.0 i 470.0 f 1a: -: -: (see part 2) 1 2 t ()Lrb pp s y
Notes: 1. Boundary condition: (a) clamped; (b) built-in; (c) simply supported.
1 é n ù 2. Strain rate considered: (a) no; (b) yes; (c) ss 1+= æ e ö . i ê ç e ÷ ú ëê è i ø ûú 3. Assumed deformed shape: (a) no; (b) yes. R 4. Dimensionless form: (a) circular 0.318i ; p ; (b) quadrangular f = 1 l = 2 2 t R t ()r ppp s y p
i b L f = ; l = ; b = . 2 1 2 t B 2t p ()BLr ps y p
Where B is the breadth of quadrangular plate, i is the total impulse, L is the length of the quadrangular plate, Rp is the circular plate radius, t p is the plate thickness, r p is the plate density, s y is the static yield stress, and n is the Poisson ratio.
37
Table 1.4.2: Resumé and Results of Experimental Techniques of Impulsively Loaded Plates
Plate Deflection to Dimension Specimen thickness thickness Response (mm) type (mm) ratio time ( m s)
CIRCULAR PLATES
Diameter
Underwater blast
Travis and Stainless steel 0.9 35-54 Johnson, 1962 150 Mild steel 0.9 20-45 1.2 16-36 1.6 17-24 Brass 0.9 31-48 2 15-23 Titanium 0.9 22-37 Aluminium 0.9 22-35 2 11.0-20.0 Copper 0.9 27-48 2 16-24
Finnie, 1962 140 Steel 1.2 47 1.6 36-38 2.7 18 3.3 17 6.4 8 Titanium and alloys 1.3 38-48 3.2 9.0-18.0 6.2 4.0-9.0
Boyd, 1966 200 Aluminium 1.3 53
Bednarski, 1969 200 Mild Steel 0.83 60 1700
38 Table 1.4.2: Continue Plate Deflection to Dimension Specimen thickness thickness Response (mm) type (mm) ratio time ( m s)
Air Blast
Witmer, Balmer, 610 Aluminium 3.2 16 Leach, Piaan, 6.4 1963 9.6 9
Inertial forming machine
Ghosh et. al., 120 Lead 0.61 44 1976; 1979; 1984 Aluminium 0.31 42
Sheet explosive blast
Florence and 100 Aluminium 6.3 1.6-7 Werzbicki, 1966; Mild Steel 6.3 0.4-4 1970 Duffey and Key, 150 Aluminium 1.6 4.0-9.0 200-250 1967; 1968 3.2 1.5-1.7 200-250 Mild Steel 1.6 3.0-4.0 200-250
Bodner and 64 Titanium 2.3 0.9-6 60-75 Symonds, 1979 Mild Steel 1.9 0.5-7 100-200
Nurick, 1986 100 Mild Steel 1.6 4.0-12.0 140-190
NON-CIRCULAR PLATES
Underwater blast
Taylor, 1942 1830x1220 Steel 3.1 51 4.4 6.0-25.0 5.9-6.4 12.0-35.0 9.3 2.0-21.0
Sheet explosive blast
39 Table 1.4.2: Continue Plate Deflection to Dimension Specimen thickness thickness Response (mm) type (mm) ratio time ( m s)
Jones, Uran and 129x76 Mild Steel 1.6 3.5-7.0 Tekin, 1970 2.5 1-4.5 4.4 0.3-1.7 Aluminium 3.1 1.8-3.5 4.8 0.8-2.4 6.2 0.2-1.4
Jones and Baeder, 128x32 Mild Steel 2.7 0.3-1.2 1972 Aluminium 2.7 0.5-1.2 128X64 Mild Steel 2.7 0.8-4 Aluminium 2.7 1.2-3 128x96 Mild Steel 2.7 0.7-7.5 Aluminium 2.7 2.0-4.5 128x128 Mild Steel 2.7 1.6-9.5 Aluminium 2.7 3.0-6.0
Nurick, 1986 113x70 Mild Steel 1.6 3.0-12.0 120-200 89x89 Mild Steel 1.6 6.0-12.0 90-180
Table 1.4.3: Regime of Damage and Some Related Examples
Plate Example Damage Number, 1 Regime i (Ns) 2 t p (mm) Rp d f ad ad ad t p t p
-6 ´101 -5 0.0032 Quasi-static 2.95 0.2 25 0.1 6.6x10 elastic 1.17 0.1 64 0.5 1x10-5 1.17 0.15 64 0.7 2.4x10-5
´101 -3 0.0316 Plastic 0.61 0.28 98 11.5 0.004 0.001 behaviour starts 6.22 35 16 0.6 0.013
40 Table 1.4.3: Continue Plate Example Damage Number, 1 Regime i (Ns) 2 t p (mm) Rp d f ad ad ad t p t p
´101 -1 0.316 Moderate 0.61 1.36 98 46 0.09 0.1 plastic 1.6 5.7 31 3.8 0.1 behaviour (slow 1.9 3.1 32 2.6 0.16 bullet speeds) 6.2 138 16 4.6 0.2 1.6 14 31 11.1 0.6 1.9 7 32 6.4 0.77
´101 1 3.162 Extensive 10 plastic deformation (ordinary bullet speeds)
´101 3 31.622 Hypervelocity impact
Where t p is the thickness of the plate, i is the total impulse, Rp is the circular plate radius, andd f is the final deflection of the plate.
There are many other dimensionless parameters that are used in comparing different plate experiments to one another. These other parameters are summarised in Table 1.4.4 from Nurick and Martin (1989b).
Where Ap is the area of the plate, L is the length of the quadrangular plate, B is the breadth of the quadrangular plate, and RL is the radius of the loaded area on a circular plate. The modified damage number isf , while fc is the modified damage number for a circular plate, and f p is the modified damage number for the quadrangular plate.
41 This is an overview of the results from these papers. For a greater understanding the original material is recommended.
Table 1.4.4: Dimensionless Parameters
Johnson's damage number 2 2 ad r pus i or 22 s d A t r s dppp
Circular geometry Quadrangular geometry
Geometry number b ---- L
B
2 2 m = a d b i i 22 23 A t r s dppp B Lt r s dpp
Geometrical damage 1 y = ()m 2 i i 1 1 2 2 A t ()r s dppp Bt ()BLr s dpp number
Aspect number l Rp B
2t t p p
Loading parameter z ---- æ Rp ö 1 + lnç ÷ è RL ø
f =ylz i i ì 1 1 ï 2 2 2 2 í R t ()rp s dppp 2t ()BLr s dpp ï îf1 =ylz æ æ R öö ç p ÷ iç1 + lnç ÷÷ è è RL øø 1 2 2 R t ()rp s dppp
Dimensionless numbers reported by others
42 Table 1.4.4: Continue Circular geometry Quadrangular geometry
Guedes Soares [37] 22 4i Rp 2 42 = 4l ad r s 0 A t ppp 2 = 4fc
Jones [22, 23] 22 i L 22 42 = 4 bl a d r ps y A t pp 2 = 4bfq
For the cylindrical structural components that are subjected to blast loads, Ewing and Hwang (1995), and Li and Norman (1995), discuss finite element modelling and failure modes associated with such situations.
The effect of a blast load onto a plate that is being compressively loaded is investigated in Chong et al. (1989). It can be noted that the in-plane load has limited effect but the boundary conditions have a greater effect. The accuracy of finite element codes to predict the scale structural response of a steel vessel containing an explosion is covered in Clayton et al. (2000). In particular the predictability of LS-DYNA (3D), AUTODYN-2D and EDEN with FLUENT are compared. The results showed very limited differences for 2D and 3D models, but it should be noted that permanent set deformation was not achieved.
In Huang and Liu (1985), Schubak et al. (1989), and Schubak et al. (1992) simple methods, using the rigid-plastic approximations have been developed and discussed for calculating the deformation history for stiffened panels to blast loads. Houlston and DesRochers (1987), Slater et al. (1988), Slater et al. (1990) similarly discuss the developmental work undertaken by DRES for the Canadian Navy. This work was focussed on the development of improved blast tolerant ship panels, with a final evaluation of the work on ship panels at the US Defence Nuclear Agency’s large-scale blast events MINOR SCALE and MISTY PICTURE. It was noticed from this work that when correlating the results from the conventional-scale blast there were two situations. Firstly, where the blast load has a low overpressure; this caused a response, which was 43 essentially elastic with negligible permanent deformation. In this situation the damage is defined in terms of the peak dynamic levels of response. Secondly, where the pressure and impulse have a high magnitude, causing significant plastic deformation. Thus the damage was measured in terms of the maximum permanent levels of deformation.
A correlation was made between the response of the panel or plate to the duration of the positive phase of the blast load compared to the vibrational period and response time of the target. These tests were in the impulsive realm, and therefore essentially independent of the overpressure. From this a nondimensional impulse parameter was introduced. This nondimensional impulse parameter was plotted with the nondimensional response data, which was obtained by using the thickness of the target structure.
For impulsive loads onto the plates and stiffened panels the following categories of responses were noticed: · elastic response of plating · elastic response of plate-beam stiffener · rigid-plastic response of plating and stiffened panel of equivalent thickness
From these experiments it was observed that elastic deflection up to 6 times the plate thickness occurred before significant plastic deformation was observed. Similarly accelerations of up to 850g occurred before significant plastic deformation was noticed.
An iso-response curve can be plotted that covers different levels of blast loads and ~ ~ structural response, by using normalised pressure, P , and impulse, I , parameters per unit of deflection. Table 1.4.5 gives the values for the normalised pressure and impulse. Noticeably the test at DRES were in the impulsive realm while the nuclear-scale test (MINOR SCALE and MISTY PICTURE) are in the quasi-static realm.
~ ~ There is an asymptotic limit of I = 1, for impulsive loads and P = 3, for quasi-static loads. The effective condition for causing damage is at the apex of the curve where the normalised peak pressure and specific impulse are at a minimum. This section of the curve relates to the dynamic response realm where the duration of the blast load is close
44 to the response time of the structure. This is the load condition that should most predominantly be considered in design criteria for blast tolerant structures, as the damage is a maximum for any explosive energy. It should be noted that the response time of a structure would reduce under large deflection, as the stiffness of the structure increases due to the nonlinear membrane stress effects. Areas of confinement such as re- entrant corners are more likely to suffer significant damage due to multiple shock fronts and it is possible that the situation will become dynamic.
Table 1.4.5: Load-permanent deflection data and pressure-impulse parameter for square plates (series 2) and stiffened panels (series 3 and series 4 (MINOR SCALE and MISTY PICTURE))
Peak Specific Pressure Impulse Deflection ~ ~ Trial P(kPa) I(kPa-ms) w(mm) P I
242 3610 1090 27* 3.25 1.06 242+ 3610 1090 30.5 2.88 0.94 253 3200 910 63* 2.55 0.82 264 5500 980 34* 3.93 0.76 226 6960 1410 35* 4.83 1.06 207 6930 1320 74* 4.71 1.02
315 6500 6300 98 20.43 3.72 315+ 6500 6300 365 5.48 1 327 7800 2110 90* 26.7 1.36 338 5160 3140 290 6.73 0.77
441 345 (240) ‡ 15700 25 (2.96)‡ 36.3 441+ 345 (240) ‡ 15700 28 (2.64)‡ 32.4 441++ 345 15900 50 2.12 18.4 442 1100‡ 30200 164* 2.08 10.71 442+++ 1100‡ 30200 250 1.36 6.98
* - Deflection corrected for boundary slippage + - Numerical prediction using measured loading function ++ - Numerical prediction using pre-shot loading prediction +++ - Numerical prediction using averaged pressure loading ‡ - Effective peak pressure load level 45 ~ æ t ' ö p ~ ~ p ~ ( - 23 b )b2 p where or P = C , where s P = ç ÷P, P = , 2 C2 = è w ø Pc w 12s yt p '
1 1 2 2 2 ~ æ t p ' ö é 4 - b ù 12s yt p ' ~ ~ i I = ç ÷ I, where I = i ()s and P = or I = C , where ç ÷ ê ()32 - P h' wrb ú c 2 1 è w ø ë s c p û b ()- 23 b s w
1 ~ é( )(-- 234 bb )ù 2 æ b ö C = s s ç ÷. 1 ê ú ç ÷ ëê ()324 - b s s y r p ûú è t p ' ø
Nurick et al. (1995) and Rudrapatna et al. (2000), discuss a series of simple one-way stiffened plates, with built-in boundary conditions that are blast loaded. Due to the blast loads elastic deformation, plastic deformation, limited rupture and failure of the simple one-way stiffened plate was observed. These empirical results and test series were subsequently repeated within finite element modelling with failure criteria. The failure criteria are based around relationship between direct strain and transverse shear stress. Although the comparison between empirical and numerical results seem to be in agreement, the element size and approximations used within the numerical results limit the potential of this method.
Cichocki (1999), Krauthammer (1999), Karagiozova and Jones (2000), Guruprasad and Mukherjee (2000a), and Guruprasad and Mukherjee (2000b), discuss blast resistant or tolerant structures and sub-structures. In particular Guruprasad and Mukherjee (2000a), and Guruprasad and Mukherjee (2000b), discuss the analytical and experimental work on a sub-structure that could be used to absorb a blast load. These sub-structures would be situated between two plates and when one plate has a blast load applied, the sub- structures fold to absorb energy. With the sub-structures absorbing energy from the blast load, the other plate (non-loaded plate) will deform less than if the sub-structures were replaced by normal stiffeners. A similar structural arrangement is covered in Karagiozova and Jones (2000). So as not to overlap this work, the present researcher has not considered these sub-structures, but used other sub-structures with a variety of mechanisms to introduce energy absorption within the stiffeners between double skin transverse bulkheads.
Hiroe et al. (1999) and Tao et al. (2000) discuss some of the material factors of interest in a blast load situation, with particular reference to fracture and rupture mechanics. As stated earlier, Owen and Watson (2000) looked at the effect of a blast pulse train on 46 simple structures. Galiev (1996) discusses the unusual structural response called counterintuitive deformation, where the plate’s final deformation is directed towards the direction where the blast load comes from.
Following on from the work on blast loading parent plate and simple structures, work has been undertaken on more complex (fuller) structures. Schleyer and Campbell (1996), Preece et al. (1998), and Schneider and Alkhaddour (2000), discuss the response of large stiffened steel panels/structures to blast loads and how to improve their survivability. Weinstein (2000) proposed a prototype blast resistance aircraft luggage container. This paper covers the development of these blast resistant luggage containers from the designs goals to proof of concept. Ettouney et al. (2000), Weidlinger Associates (2000), and Rittenhouse (2000) discuss the work done by Weidlinger Associates in developing blast tolerant civilian structures, in particular embassies for the United States of America. Similar to these papers is Eytan (1992), which discusses a comprehensive database of observed damage to structures from conventional weapons and terrorist explosive instances in Israel. This database totals 20,340 individual events from 1968-1991 and covers blast loads from car bombs, terrorist explosive charges, artillery shells, air bombs and long-range ground-to-ground missiles. The structures generally were office buildings and residential structures. Five conclusions where reached about blast induced structural damage · the actual damage to structures is substantially different than the estimated damage from theoretical means · in most cases the conventional weapons and terrorist explosive devices induced mainly localised blast loadings and structures less sensitive to local failure exhibited lower damage · structural damage due to the explosive decreased rapidly with increasing distance between the explosion and structure, especially in short range events · injuries to people was seen to be dependent on “secondary effects”, such as spalling, flying objects, shock-induced displacement and especially glass fragments
47 · the need for the development of a reliable analytical tool to analyse the blast effects on structures, and especially to estimate the number of injured people.
Returning to steel structures, Bulson (1997), and in particular stiffened panels undergoing a weapon effect have several types of damage configurations, depending on the lateral damage. Different types of damage configuration are the lateral damage being confined to the plate between stiffeners, and spreading across a stiffener with the stiffener remaining intact, or spreading across a stiffener with the stiffener failing. This last case is the critical case in vulnerability assessment of the stiffened plate. Stiffeners provide a crack-arresting capability, which can significantly improve the residual strength of a battle-damaged structure. The residual strength in a structure that has undergone a blast load, which is a function of time, will continue to extend the damage due to fatigue and cyclic loads. Therefore the ability to reduce lateral damage in a structure can be seen to be directly proportional to the structures ability to survive operational damage.
As mentioned throughout this section, a weakness in the numerical methodology to predict structural responses to blast loads, is the fluid structural interaction. In Cabridene and Garnero (1992), one of the proposed methods to overcome this weakness is to use two different numerical packages. In this system the blast wave is modelled in an Euler computational fluid dynamic package, while the structure is modelled in a Lagrangian finite element package. In this paper the two-dimensional code FLU2D is used to model the propagation of the blast waves. This code uses an explicit upwind scheme with second-order accuracy in space and time for a perfect gas. EFHYD is a three-dimensional hydrodynamic computation code that computes target deformation on the basis of pulses supplied by the FLU2D code.
From a comparison between real tests and use of the combined codes it is noted that acceptable accuracy can be obtained. A similar combination of computer codes has been obtained by DSTO with Combustion Dynamics (3D version) Blast Workstation for the blast wave and LS/DYNA for the structural response.
48 An important case where this interaction between the blast wave (and its reflections) and the structural response is internal blast situations, such as within a ship. Smith and Rose (1998), discuss experiments that relate to blast loads within a ship structure. Walsh et al. (1996), and Walsh and Burman (1998) discuss the work undertaken by DSTO in investigating the blast tolerance of RAN vessels to blast loads. These reports are focused on transverse bulkheads and water-tight doors. From this work it was noted that previous (Cold War era) design standards were not capable of dealing with current anti- ship missile blast loads and therefore improvements to the blast tolerance of the transverse bulkheads and water-tight doors was necessary. This has led to a continuous development program within DSTO to overcome this shortfall and additional research program.
To conclude this section on blast loaded complex/entire structures it can be noted that for stiffened panels there is an increasing amount of data and theory available. Most of this information only deals with Mode I and II failure due to the blast load situations under investigation. This is a shortcoming as blast loads on internal structures is usually in the region of Mode II and III for structural failure. The work in Mode III is primarily from experimental work with limited numerical and theoretical work. The availability of information in this area of research is very limited (due to the nature of the research), especially for ships, with most publications involving entire ships and blast loads related to only underwater events and the resulting whipping response in the ship structure.
Often the structural responses observed due to blast loads, are similar and interconnected to the responses observed from impulsive and ballistic events. In Jones (1989), a thorough review of the subject of dynamic plastic behaviour of structures is given.
As the temporal and spatial characteristics of the dynamic impact loads are often poorly defined, together with the lack of material data under the dynamic conditions, the estimations from simple rigid-plastic methods of analysis are adequate for many purposes, in particular design development and analysis. The following is covered in Jones (1989):
49 · Material elasticity
If materials are being subjected to large dynamic loads that cause extensive material plasticity then the materials elastic behaviour is not going to play an important role. Consequently, the elastic material effects can be neglected if the dynamic load is at least three times that of the maximum elastic strain energy capacity and the pulse duration is smaller than the fundamental period of the structure.
A large energy ratio in the pulse, to which the material is subjected, is a necessary, but not a sufficient condition, for a rigid-plastic method to give a good estimate of an elastic-plastic solution.
More recent studies have shown that the elastic wave involved in these situations after reflection delay the progress of the dynamic wave and final effects of the dynamic load.
· Influence of finite displacement
In many theoretical analyses of dynamic loads onto a material, infinite displacement is incorporated. This leads to a conflict if material elasticity is neglected and large energy ratios are required. It has been found that finite displacements, or geometry changes, are important to predict the final outcome.
· Material strain rate sensitivity
For strain rate sensitive material, the effect of material strain rate is significant and needs to be considered. A simple relationship that can predict the material behaviour under high strain rates is the Cowper-Symonds relationship. The Cowper-Symonds relationship only requires two constants from experimental test and is relatively accurate.
Another method is the Perrone’s simplification. The Perrone’s simplification has allowed the influence of material strain rate sensitivity to be incorporated into rigid, perfectly plastic analyses with little additional effort, and without sacrificing accuracy.
50 This method is acceptable as long as the infinitesimal displacement does not introduce changes in the geometry.
· Combined influence of finite displacement and strain rate sensitivity
In many practical problems, including plate structures, both nonlinearities of finite displacements or geometry changes, and material strain rate sensitivity occur. This makes the analytical solution of these problems very complex. In many of the analysis techniques it is practical to include one but often impractical to include both of these nonlinear effect(s). An example of this difficulty is in trying to include material strain rate sensitivity after the introduction of finite displacement to rigid, perfectly plastic structures. The difficulty is associated with the fact that the initial condition cannot be used to estimate the strain rates. This is due to the dynamic flow stress for the entire response, because the relative importance of bending moments and membrane forces varies throughout the motion. In particular, the bending moments dominates the small deflection behaviour, while the member forces develop with increased deflection and therefore, dominate the response for large deflections.
The maximum strain rate in the structure occurs when one-half of the initial kinetic u energy has been absorbed, or when the transverse velocity of the mass is s , where 2
us is the impact velocity. Additionally, the maximum strain rate has been observed to occur when the transverse displacement is about two-thirds of the final or permanent æ2d ö values ç f ÷ . This suggests that the dynamic flow may be estimated from the strain è 3 ø u æ2d ö rate when the transverse velocity is s and the transverse displacement is ç f ÷ . 2 è 3 ø
· Transverse shear and rotatory inertia
Rotatory inertia is not of practical importance in these types of investigations. Transverse shear force has greater influence over the final deformation in dynamic cases than in static load cases. The transverse shear force is initially infinite at the supports of a beam, which is loaded impulsively, and when the plastic yield of the beam is 51 controlled by the magnitude of the bending moment alone. Transverse shear forces would also be important for strong anisotropic beams and plates that undergo dynamic loads.
Thus for dynamic loads it is necessary to consider the influence of transverse shear forces and bending moments when predicting of the final outcome.
· Material strain hardening
Currently this effect is not seen to be significant, and as such has not been studied in as much detail as other issues. Some theoretical and numerical procedures that have been developed use Cauchy strains, which do not include the larger strains and so overlook where these effects could become significant.
It has been shown that if the maximum transverse deflection is up to twice the corresponding plate thickness of the material with moderate strain hardening characteristics, such as mild steel, then material strain hardening effect is insignificant. On the other hand a maximum transverse deflection of seven times the material thickness could produce a final strain of 0.03 in mild steel. Thus, the flow stress at the cessation of motion is roughly 10 % larger than the static yield stress.
Experimental evidence thus far on structures suggests that material strain hardening is not very important in determining the final outcome. This could be due to the level of dynamic loading, which has been investigated, suggesting that it could become more relevant for larger dynamic loads. It is usually assumed that material strain hardening would reduce the final displacement of the structure. This may not be the case, as the increased strength could cause a transfer of energy from one mode of deformation to another mode of deformation, which is less efficient in absorbing the energy of the dynamic load.
· Bound methods
Many researchers in this field have developed bounding methods, as they are simple to use, and provide strict bounds on the maximum permanent transverse displacement and 52 response time. These methods render considerable assistance during preliminary design and for constructing experimental test programs. Bounding methods conflict with the simplification of the infinitesimal displacement, which is usually compared with the requirements for large energy ratios, and the neglection of elastic effects. Some of these methods overcome this conflict but lose their simplicity in the progress.
· Mode approximation methods
Mode approximation methods were developed for structures that undergo infinitesimal displacements. The mode approximation method for the transverse velocity has been applied successfully to examine the finite-deflection behaviour of structures subjected to dynamic loads. Mode approximation methods have been extended to include the influence of material elasticity and strain rate effects. Additionally, these methods have been extended to handle pulses with arbitrary pressure-time histories. Results have been reported for mild steel and aluminium alloy for portal frames and expressed as an ‘exact’ solution from ABAQUS finite-element computer code. The simplified elastic- plastic method (SEP) has the advantage that complex numerical procedures are replaced by simple schemes, using available wholly elastic solutions, and capitalise on the important simplifications of rigid-plastic methods of analysis.
· Dynamic plastic buckling
The previous parts of Jones (1989) have focused on large dynamic loads, which produce stable inelastic responses. Some structures will undergo an unstable response, such as dynamic plastic buckling. In this type of buckling the inertia forces play an important role, as well as material strain rate sensitivity for the relevant materials. The impact is such that the thermal and other effects are not important and the material does not act like a fluid. Inertial resistance during dynamic plastic buckling leads to more highly wrinkled profiles with higher mode numbers than in the corresponding static buckling problem.
Design guidelines and insight into dynamic plastic buckling has been opted over the use of perturbation methods. The shortcomings of these methods are that they are restricted to simple structures and only small departures from the dominant solution. 53
Following the perturbation method approach to investigating dynamic plastic buckling, many other simple numerical schemes have been developed. These schemes have problems, such as an initially imperfect elastic-plastic column, which is governed by two distinct types of response, known as direct and indirect buckling. The direct buckling of column parameters controls the response of the column. Direct buckling develops rapidly and is sensitive to time steps used in the calculation. Indirect bucking occurs after considerable lapses of time and depends on the maximum allowable displacement. Therefore the computation of this problem is difficult, as the associated ranges of the controlling parameters would not be known before starting the analysis. Therefore, structures declared stable are shown to reveal unstable behaviour with more extensive computing.
Counterintuitive behaviour in an elastic, perfectly plastic beam has been noticed, as mentioned above. In this a beam is pinned at both ends and subjected to a pressure with a rectangular shaped pressure-time history distributed uniformly over the whole span. The unexpected response is related to snap-buckling.
· Dynamic progressive buckling
Dynamic buckling is where the inertia forces are negligible are termed dynamic progressive buckling. The dynamic plastic response is closely related to static behaviour, and is a quasi-static situation as the inertial forces can be neglected. This buckling is known as dynamic progressive buckling because wrinkles, or buckles, form progressively from one end of the tube as the deformation proceeds with dynamic progressive buckling the material rate sensitivity is important.
The separation between dynamic plastic buckling and dynamic progressive buckling is not fully understood. Dynamic progressive buckling has been suggested to occur when the axial force on a tube, is smaller than the plastic squash load, which is evaluated using the enhanced plastic flow stress due to the material strain rate sensitivity.
Theoretical studies in this area have led to the development of various progressive crushing modes for square tubes loaded axially. This theory predicts four deformation 54 modes which govern the behaviour for different ranges of the parameter L where L tt and tt are the side length and thickness, respectively. This leads to asymmetric deformation modes, which cause an inclination of a column and could produce a collapse in the sense of Euler for even relatively short columns.
Stiffened members on a plate have been shown to improve the energy-absorbing characteristics of thin-walled structures.
· Scaling
The use of small-scale models to predict the response of impact loads to large structures is often required as it is impractical to directly test the large structure. The advantages of testing small-scale models are practical and affordable, when compared to full-scale tests.
Table 1.4.6 shows a method of classifying structural impacts. The five categories are elastic structures, local plastic structures, global collapse structures (stable), global collapse structures (unstable) and brittle structures. From investigations of scaled and full size tests of structural impacts in all of these categories, it has been shown that material strain rate effects, gravitational accelerations and fracture do not scale.
Table 1.4.6: Different Categories of Structures (from Jones (1989)).
Category Description Typical Examples
Category 1 elastic structures billiard balls
Category 2 "local" plastic structures impact limiters
Category 3 global collapse structures (stable) steel building frames
Category 4 global collapse structures (unstable) ships; automotive structures
Category 5 brittle structures large castings
55 Category 1 structures are expected to obey the geometrically similar scaling laws, provided that strict scaling is used on structural geometries, material data, and dynamic loadings.
Category 2 structures appear to also satisfy the geometrically similar scaling laws. From experiments conducted with mild steel in category 2 situations, it seems that material strain rate sensitivity is not an important factor.
Category 3 structures also from empirical evidence satisfy the geometrically similar scaling laws.
Category 4 structures do not satisfy the geometrically similar scaling laws. In one case researchers found that the post-impact deformation might be as much as 2.5 times greater in a full-scale mild steel prototype than would be expected from extrapolated results obtained on a one-quarter scale model. This can be lessened if the effects of specimen thicknesses depart from the nominal values; the yield stresses are different at the various scales and material strain rate sensitivity. This scaling process is significantly different from the geometrically similar scaling law and is much more complex. Fractures have also been observed to be greater in the full-size specimens compared to scale specimens. For all these reasons, there are serious reservations about the use of scaled models to predict the final outcomes of full scale category 4 structures.
Calladine (from Jones (1989)) investigated category 4 structures that undergo a nonlinear load-displacement with an initially high load and subsequent load-carrying capacity which decreases with increasing displacement. In this theoretical investigation the laws of fracture mechanics were ignored, a relationship was assumed for the strain- rate-sensitive behaviour of mild steel, and the expressions for the strain rate and energy associated with a nonlinear load-displacement relation was simplified. Even though this work is a simplification of the actual problem, it gave much insight into the scaling and mechanism behind these types of situations. Furthermore, it was shown that the well known size effect associated with material strain rate sensitivity, which arises from the elementary scaling requirement of constant impact velocity (us ) at different scales, is
56 exacerbated in the presence of nonlinear load-displacement characteristics. This can be overcome by
us µ lGS , (1.4.3.) where lGS is the geometrical scale factor (lGS £ 1) .
u This the dimensionless parameter s , where C = E r is the elastic speed of a wave C through the material, is invariant with the initial moment and kinetic energy being scaled in a structural problem. In order to achieve a constant initial kinetic energy per unit volume, it is also necessary to scale the structural mass with respect to lGS . Thus,
2 3 the initial linear moment varies as lGS instead of lGS . This leads to further difficulties when scaling results from smaller models to full size structures. If us were proportional to lGS , then the critical mode number of the buckled profiles in a model and a prototype could be different and lead to difficulties in interpreting the results.
Category 5 structures are dominated by fracture mechanics. These types of structural situations can be scaled when recognising that the scaling factor has to be inversely square rooted when considering the stress to propagate a crack through a linear elastic material. Even though this scaling is possible; guidance on how it could be done is still lacking.
Atkins (from Jones (1989)) has investigated scaled and full-size structures that were subjected to quasi-static and dynamic loads, which produced large plastic strains. This type of situation was not fully covered in the categories mentioned in Table 1.4.6.. From this Atkins (from Jones (1989)) developed a theoretical method that equated the total external work to the plastic work consumed in a volume of material and the fracture work required to create new surface areas. In regards to the plastic flow, new material
x and fracture are important and the total energy would be scaled by lGS , where £ x £ 32 . When x equals 2 it gives an area factor representing fracture and when x equals 3 for volume factor representing a new material. Much more work is required to be able to scale this type of situation properly.
57 · Ductile-brittle fracture transition relate to size
The transition between ductile and brittle material behaviour can occur due to changes in temperature or increased strain rate, hence its importance in dynamic load situations. Work by Kendall (from Jones (1989)) in this area has shown that ductile-brittle fracture transition occurs for compression split specimens having a critical size, which is characterised by the dimension Dc .
32EEUF Dc = 2 , (1.4.4.) 3s y where E is the Young’s Modulus, EUF is the fracture energy required to break a unit area of the material, and s y is the yield stress of the material.
As noted in Bulson (1997), the analysis of dynamic impact is an important feature in the study of explosive effects on structures. This is partly due to military or terrorist activities frequently involving the transportation of explosive charges by high-speed projectiles, and partly because the explosion of the charge is often accompanied by the high-speed distribution of fragments of disintegrating casing and structures in the local area.
When the warhead eventually explodes, fragments, small pieces of virtually undeformed metal from the warhead case, are projected outwards at high velocities. The striking of these fragments against the relatively light structures or cellular walls of naval craft causes the fragments to stay in good shape but the sheet metal is penetrated and deformed. Associated with this is the stress due to the impact of the fragment on the sheet metal. In Metz’s work (discussed in Bulson (1997)), he showed that an instantaneously applied load produces double the stress compared with same load applied gradually. These penetrations, holes, can lead to faster growth of cracks in poor quality and/or brittle metals.
For soft materials, e.g. metals, penetrated by non-deforming projectiles the material is pushed to one side following plastic deformation. This produces a clean hole with ‘petals’ around the circumference. With increased hardness of the metal, which the
58 projectile is penetrating, a plug is usually formed. The plug, ejected out of the rear of the metal, has a diameter between one-third and the full diameter of the projectile.
Marchand and Cox (1989):
“Recent work at Southwest Research Institute (SwRI) has shown that the damage caused by the combined impact and blast loading of steel flying metal plate is significantly more damaging to concrete barrier panels than the loading generated by approximately three times the weight of uncased explosive”.
Due to this, the combined loading is considered to be synergistic in the sense that the combined damage is greater than the sum of the fragment and blast loading. Much of this difference is due to the onset of material failure and degradation locally in the material where the fragments impact. This material failure and degradation is not considered in the response calculation, if only the simple momentum addition is done for the introduction of fragments to a blast load situation. The significant feature of the wall loaded with the case explosive is the extent of spall zone on the rear face of the panel, and along the free edges of the panel.
Another feature from the investigation of explosives inside a case is that the blast load, when it arrives at the target wall, has a lower pressure and has taken longer compared to an uncased equivalent explosion. At least 30 % of this decrease can be put down to the expansion of the case, which encases the explosives. The rest, up to 70%, can be modelled by assuming that the amplitude of the pressure wave is reduced.
The modes of response of the structures to the combined loading of fragments and blasts are flexural and local shear or breaching. For structural elements to have adequate flexural response, they require: · continuous reinforcement for increased ductility, · matrix toughness for structural integrity at large flexural deformations.
While for structural members to have adequate local shear or breaching response, they require: 59 · low stiffness in the system for load transfer to surrounding members responding in flexure, · high fracture strength of matrix material, not necessarily ductile.
Similarly Malherbe and Deletombe (2000), discuss from a numerical analysis point of view the structural response of an armoured vehicle to ballistic impacts. In particular, how design engineers could reduce the subsequent shock load throughout the vehicle. Ben-Dor et al. (1998), looks at and developed numerical equations for ballistic resistance mutli-layers structural targets with air gaps.
Following on from the considerations of ballistic impact, structural responses and resistance, are the dynamic responses of simple structures to impact loads. This is important in this research work, as the structures (stiffeners) between the two outer plates of the double-skin transverse bulkheads, need to absorb energy from the blast event. The absorption of this energy in the stiffeners can be related to dynamic impact loads on structures. Norman et al. (1970), Wierzbicki and Abramowicz (1983), Rollins and Xia (1989), Kröger and Popp (1998), Wu (1998), Yamazaki and Han (1998), Harrigan et al. (1999), DiPaolo et al. (2000), Jones and Jones (2000), Kim et al. (2000), Yamazaki and Han (2000), ERG (2000), Bignell et al. (2000), and El-Sobky et al. (2001) are a collection of works that covers the structural response (empirically, theoretically and numerically) of simple structures to dynamic impact events.
Investigations into more complex and entire structural responses to dynamic impact loads have been done. These can support the current research work, as the dynamic loads and size of structures are more akin to the current structures under investigation in this body of work. This has not been a significant part of the literature review and only the following material has been considered: Jones (1991), Jones (1993), Abramowicz (1998), Thacker et al. (1998), Simonsen and Ocakli (1999), Lyle et al. (2000), and Bouchet et al. (2000). In addition to the empirical, theoretical and numerical work that has been undertaken in the field of dynamic impact loads and their associated structural responses, work has also been undertaken on the formation of design tools, as mentioned in Dallard and Miles (1984).
60 As mentioned above, one of the intentions in this research effort is to use the stiffeners between the plates of the double-skin transverse bulkheads as an energy absorber. This is so that the plate which is not loaded with the blast pressure wave deforms less than under the current structural arrangements. Furthermore simple, complex and entire structural responses to impact loads are discussed, where generally the load is idealised. Over the last 30+ years investigations into reducing the accelerations and inertial forces applied to human occupants in a light or rotary aircraft during a crash landing have been undertaken. This includes the concept such as the stoker seat legs that break open to increase the time period of the impulse due to the crash landing and in so doing reduce the acceleration and inertial forces experienced. The material used in this topic are: Underhill and McCullough (1995), Ditter (1997), Hajela and Lee (1997), Donaldson (1998/1999), Jaggi et al. (2000), and NASA (2000).
As this section on structural responses to blast loads demonstrates, the current research project is very broad, as it covers topics from material/structural failures from the application of a blast pressure history onto the subject specimen to structures acting as mechanisms in an effort to absorb energy and momentum. In the following chapters, the implementation of this knowledge is shown and the recommendations for this work are given, but in particular it has been shown that double-skin transverse bulkheads with an energy absorbing structure offers the best potential for the formation of blast tolerant transverse bulkheads.
1.5. Stress waves and strain rate
Although the issues of stress waves and strain rate in steel due to a blast load is covered in Chapter 5, it is prudent for some general comments to be made at this stage. As with all areas of study, the initial investigation has been centred on simple plates being experimentally tested to obtain observations. This initial empirical investigation continues to date whilst trying to prove and improve the theoretical knowledge and numerical modelling accuracies. One of the first articles to cover the development of theory from the empirical results was Muller et al. (1949), with particular focus on stress wave propagation throughout a shock loaded plate. On the issue of empirical investigations, with subsequent theoretical development, of stress waves and strain rate
61 on simple plates, the following articles give a broad spread of the material currently available. Bitans and Whitton (1972), Billington (1972), Wulf (1978), Lindholm et al. (1980), Johnson and Cook (1983), Cimpaeru (1993), Epstein et al. (1995), Sogabe et al. (1995), Murr et al. (1997), Tong (1997), Zhou and Clifton (1997), and Zhao and Gary (1997). As is generally the case, following the empirical investigation is the development of the numerical and computational methods. Chen (1975), Youngdahl (1989), Wang and Lok (1997), and Sandler (1998) cover some of the outcomes in the development of numerical and computational methods relevant for stress waves propagating throughout a material and/or materials which are loaded in such a way to cause a high strain rate situation.
Thus far only simple (plate) structures subjected to stress wave propagation or high strain rates have been considered. Tvergaard (1999), Kuroda and Tvergaard (2000), and Szuladzinski (2000) discuss the effect of non-uniform structures, i.e. void formation to structural joint location, on the materials responses to stress wave propagation and high strain rate.
1.6. The J-integral and material failure
Similar to ‘Stress waves and strain rate’, material more relevant to the J-integral and material failure issues related to this current research effort are more thoroughly discussed in chapter 5.
The initial work and development of the J-integral comes from Rice (1968), followed by many other researchers in the field, notably Shih and Hutchinson (1976). In this research project the material developed by the Electric Power Research Institute (EPRI) is used in the calculation of the J-integral, specifically EPRI (1981) with the additional utilisation of Tada et al. (1973) and Miannay (1988). The development and investigation of the J-integral, even with a static load situation from the perspective of empirical and theoretical work continues even today, as discussed in Ritchie (1983), Dowling (1987), Anderson (1990a), Anderson (1990b), Li (1997), Machida (1997), McClung et al. (1997), and Pascaud et al. (1997).
62 Following the normal progression in the development of empirical and theoretical knowledge, work on J-integral for welded and non-uniform structures in static load cases has occurred, as canvassed in Graham et al. (1992), Read and Petrovski (1992), and Szanto and Read (1992). This has led to damage criteria and therefore modelling (numerical methodologies) to be formed for static load situations, as mentioned in Beremin (1983), Anderson (1989), Yoon et al. (1992), Wang (1994), Homma et al. (1995), and Weng and Sun (2000). Anderson (1999) mentions that, the J-integral is not the only parameter that can be used in determining the crack growth or potential of a material. Also in Anderson (1999), the J-integral is compared and related to the Crack Tip Opening Displacement (CTOD), while in Shih (1981) the J-integral is related to Crack Opening Displacement (COD) and Crack Opening Angle (COA).
In this research work, due to the blast load, the interest in the J-integral and other parameters that can be used to calculate crack growth is directed towards dynamic load situations. There is a limited amount of literature available on the dynamic J-integral and the other parameters, with much of it directed at theoretical and approximation work. The following gives a cross-section of the material available: Nakamura et al. (1986), Zehnder et al. (1990), Gifford (1995), Kawano et al. (1995), Lee et al. (1995), Nishioka et al. (1995a), Nishioka et al. (1995b), Bassim (1995), Richter et al. (1996), Guduru et al. (1998), Lee and Prakash (1998), Byun et al. (1999), and Richter et al. (1999).
A significant issue in this research project is the ability to predict rupture of the transverse bulkhead due to the blast load, or in other words the through thickness crack growth or fracture. The J-integral and other related parameters mentioned above, are interrelated to the issue of through thickness crack growth. Although it is expected that the use of the dynamic J-integral offers the best possibilities in determining rupture failure in blast loaded transverse bulkheads, other fracture mechanical methods are also important to consider. With this in mind, Holmes et al. (1990), Fatt and Fux (1995), Trinh et al. (1995), Nakagaki et al. (1995), and Wierbicki (1999), gives a taste for the work related to dynamic fracture of metal structures. Wierbicki (1999) looks at fracture related to dynamic and impact loads from the view point of an explosive situation. This work by Wierbicki is relatable to Marchand and Cox (1989) work on blast and fragment loaded concrete structures. The Marchand and Cox (1989) showed the synergism in 63 these types of events. Following this synergism between blast and fragment load situations, is the material on fracture due to the impact load only situation, such as covered in Shanmugam et al. (1995), Libersky et al. (1997), Mullin et al. (1997), Rajendran (1998). To conclude the considerations of fracture mechanics, issues related to damage or failure criteria for dynamic fracture situations have been canvassed in Fyfe (1984), Melin (1986), Bammann et al. (1990), Nilsson and Ståhle (1995), Espinosa et al. (1998), and Macdougall and Harding (1999).
1.7. What is X-80 steel
X-80 steel is a Thermo-Mechanically Controlled Processes (TMCP) steel that obtains its high strength characteristics from the rolling and cooling process instead of the addition of alloy elements. In particular, in this research work the focus is on the BHP developed X-80 steel (many other organisations and steel makers around the world are investigating the X-series of steels). The development of the X-series of steel at BHP is covered in BHP (2000), Williams (1998), and Williams (1995). From these publications, plus Hughes (1988a), Hughes (1988b), Hrovat (1988-2001), and Hrovat and Hoffman (1988), Table 1.7.1 and Table 1.7.2 have been developed. Table 1.7.1 covers the chemical break down of X-80 steel and other steels, while Table 1.7.2 gives the mechanical properties.
Additionally, BHP results by Barbaro (1998-1999) state that the fracture toughness, determined by the CTOD test, was greater than 0.329mm in the weldzone for a 9 mm thick 273 mm diameter ERW seam welded pipe. For an experimentally determined 1/2 blunting line (m=1.4) this converts to a plane stress KC of 245 MPa.m (plane strain 1/2 KIC = 269 MPa.m ).
In Williams (1995) the driving demands by industry (notably the linepipe industry) for these steels are to provide higher strength grades that permit pre-heat free welding with high hydrogen electrodes, high steel cleanliness and controlling centre-line segregation (banding effect) to ensure higher toughness and weld performance. Therefore, the higher strength grades have evolved whilst limiting the amount of alloying additions
64 used to strengthen the steel. As noted above the main initial client for these steels was the linepipe industry for use in gas pipelines.
Table 1.7.1: On the chemical break down of X-80, D-36, HSLA-80, HY-80
Steel C % Mn % Si % Ni % Cr % Cu % Mo % Nb % Ti % Other % Total CE CE pcm alloy % X-80 0.065 1.56 0.28 0.025 0.02 0.01 0.28 0.076 0.02 0.0271 2.397 0.435 0.175 D-36 0.14 1.37 0.34 0.03 0.01 0.01 0.91 0 0 0.031 2.881 0.612 0.282 HSLA-80 0.05 1.4 0.25 0.9 0.7 1.15 0.25 0.04 0 0.005 4.765 0.652 0.253 HY-80 0.17 0.3 0.2 3.1 1.65 0 0.56 0 0 0 5.97 0.9 0.363
Table 1.7.2: Mechanical properties of X-80. D-36, HSLA-80, HY-80
Steel Yield Ultimate Stress Tensile Stress X-80 579 688 D-36 350 450 HSLA-80 585 685 HY-80 550 700
In the construction of naval platforms the use of high strength/yield steels (i.e. HY- series steels) is currently limited due to the cost of fabricating with these materials. Therefore, it has been proposed that the use of X-80 steel, with its more durable welding ability, could permit greater use of high strength/yield steel within naval platforms without the cost associated with the HY-series steels. This proposal is covered in Butler (1996) for the Royal Navy (RN), Ritter (1997) for the Royal Australian Navy (RAN) and Cannon et al. (1999) where the proposal has been extended.
As an example of the advantages of X-80 steel over conventional ship steel, D-36, Raymond et al. (1999) showed through a simplistic optimisation of ship panels that the following results would be possible: · 3% reduction is structural weight could be achieved · 4% reduction in welding would be possible; assuming same width is available for both steel parent plates · 40% increase in panel strength 65 · 45% increase in panel strength to weight ratio
Thus the vessel could be fabricated cheaper, while also having increased strength. It should be noted that the thinner scantling and slightly increased surface area will increase the risk of fatigue and corrosion and therefore a more intensive maintenance may be required.
The idea of using a highly weldable high strength/yield steel in naval platform construction did not begin with X-80, but with HSLA-80. High Strength Low Alloy (HSLA) steels were investigated by the United States Navy (USN) in the late 1980’s and throughout the 1990’s as a direct replacement for High Yield (HY) steels in many applications and expansion into more general hull material uses. This was due to the increasing fabrication costs associated with the HY steels and the possibility of reducing naval platform structural and hull weight while not losing any performance abilities and if possible increasing them. Smith (1984), Kvidahl (1985), Montemarano et al. (1986), Anderson et al. (1987), Czyryca et al. (1990), Wilkins (1990), DeGiorgi and Matic (1991), Malakhoff (1991), Biswas (1992), and Christein and Warren (1995) are papers that show the development of the proposed uses of HSLA steels in the USN to the implementation of these steels into the USN. Similarly, within the RAN, the Defence Science Technology Organisation (DSTO) investigated the possibility of HSLA-80 before X-80 was developed, Phillips and Ritter (DSTO IR) and Phillips (1993).
Of course the interest in using high strength/yield steels in civilian structures has had a parallel development to that of the military industries developments. The maritime/shipping industry interest in using high strength/yield steels has focussed on the possibility of reducing the structural weight and the associated cost savings. Löseth (1994) covers many of the economical considerations related to such a proposal and in particular the maintenance concerns that can rise due to the thinner scantlings, while Sumpter (1997) deals with some of the fracture safety issues changing from mild steel to high strength steels.
Consideration has also been given to using X-80 and HSLA-80 steel(s) in automotive wheel rims, Gregoire (1987), and jack-up drilling platforms, West (1987).
66 An extensive part of the investigation into X-80 (and HSLA-80) steel(s) suitability for constructions has focussed on welding. This is particularly important for X-series steels, as casting is impractical due to the formation process of rolling and controlled cooling. A variety of welding processes and responses by the steels are covered in the following papers: Thaulow et al. (1987), Gill and Crooker (1990), Dittrich (1992), Dixon and Taylor (1993), Price et al. (1993), Price (1995), Irving (1995), and Sampath et al. (1995). Although some of these papers deal with HSLA-series steels, including BIS 812 EMA, welding issues, these issues are very similar to those faced by the X-series steels.
As mentioned in Okumoto (1998), TMCP steels suffer from additional residual stress being introduced into the steel due to the formation processes using rollers and rapid controlled cooling. This is specifically a concern since thinner scantlings are intended with the utilisation of these steels (X-80). It must be recognised that this paper only gives general viewpoints and that the residual stress within the BHP X-80 steel for ship construction currently has not been quantified.
1.8. What is being attempted in this research
X-80 steel is a Thermo-Mechanically Controlled Processed (TMCP) steel. Due to this fabrication process, X-80 steel is a high strength steel with low alloying additions and carbon equivalence. The low alloying additions and carbon equivalence of X-80 steel leans itself to having a high weldability. Thus X-80 steel was developed for the linepipe industry where cellulosic electrodes are used regularly.
In Australia, DSTO and others such as Dynamic Structures saw the potential advantage of using X-80 steel in future naval platform and maritime structures. This is because X- 80 steel has similar material properties to HY-80, a quenched and tempered steel, while being cheaper to buy and having massively better weldability.
At present ships, are not built of HY-80 steel but this steel is used in high stress areas and as crack arresters. Naval platforms are generally constructed out of mild steel, such as D-36, compared to which X-80 steel is approximately 1.5 times the cost (or less) but
67 1.6 times in yield strength. The weldability of X-80 to D-36 steel is approximately identical.
Therefore, it is possible to fabricate a vessel out of X-80 steel and obtain one or more of the following benefits: · A lighter vessel, therefore increasing the operational range or reduction in the operational cost · Cheaper per unit cost to produce by having fewer welds and stiffeners · More efficient to run as the corrosion and fatigue margins are increased · Improved survivability due to greater redundancy in the material and structural strength
To explore the implementations of X-80 in future maritime structures this research will focus on the structural arrangements of the main transverse bulkhead. This choice comes from the unique role transverse bulkheads play in the structure of modern naval platforms. In naval platforms the main transverse bulkheads, in addition to withstanding the common static and quasi-static loads, are also required to tolerate a dynamic load related to an air-blast from an internal explosion. Therefore, in this research program the main transverse bulkhead will be investigated in regards to the formation of optimised X-80 steel blast tolerant transverse bulkheads. Specifically, the: · finite element modelling requirements for dynamic non-linear transient situations · material tearing and rupture failure criteria · maximum deformation requirements of a transverse bulkhead · post blast load requirements that a transverse bulkhead must meet.
1.9. Conclusion
From the above it can be observed the literature review is quite broad, and that the topics covered in this research project are in many ways independent, but with areas of inter-dependencies, e.g. in fragmentation of blast loaded structures and dynamic J- integral or fracture. This has been necessary so that design criteria for blast tolerant
68 transverse bulkheads could be developed and others factors related to its implementation could be considered.
Throughout this thesis much of the knowledge and direction has being derived from the above literature material. It is for this reason that a specific effort has been made to refer to all the literature material used, even if not associated with an extensive discussion on the article(s).
69
Chapter 2 Design criteria for X-80 steel blast tolerant transverse bulkheads
Abstract: With increasing importance being placed on survivability of naval platforms, this chapter looks at a structured approach to the development of design criteria to fulfil the operational requirements of naval transverse bulkheads with the use of finite element modelling and rupture analysis. By their very nature, plus to improve survivability of the naval platform, naval transverse bulkheads must have some level of air-blast load tolerance. After a brief discussion on current design practices for transverse bulkheads, the operational requirements are established, followed by an explanation of the design criteria with respect to the transverse bulkheads formed out of X-80 steel. The X-80 steel of interest is manufactured by BHP and has been covered in the previous chapter, but with consideration of future manufacturing abilities. The design criteria are to be used as the constraints in an optimisation procedure, which will be able to develop more capable naval blast tolerant transverse bulkheads.
70 2.1. Introduction
Survivability is becoming an increasingly important issue, and as stated in Chalmers (1993), “currently little information on the design of bulkheads to withstand internal blast effects” exists. A structured approach related to operational requirements is therefore needed to generate design criteria and the subsequent optimisation procedure.
These operational requirements have been developed into design criteria by considering appropriate safety factors to account for inaccuracies in the finite element modelling and uncertainties in measuring and determining the loads. The design criteria are used to clearly identify what attributes or constraints are being considered in the development of a design or the optimisation procedure. In this regard this work is similar to Makovièka (2000). This is particularly important in the development of such items as a naval platform where the procurement cost is so high that mistakes are unacceptable.
These design criteria will attempt to meet the requirements for transverse bulkheads put forward or implied in Begg et al. (1990), Brown (1990), Said (1995), Reese et al. (1998a), and Reese et al. (1998b), and in addition the recommendations that have come from work undertaken at DSTO. Therefore from this the survivability of future naval platforms will increase.
2.1.1.Transverse bulkhead attributes to naval platform survivability
In recent years western navies have given greater emphasis to the survivability of their naval platforms. This has been due to the changing operational environment, recent incidents where the survivability of naval platforms have been tested (as discussed in Chapter 1), reduction in defence budgets and shrinking of crew sizes aboard ships.
To improve the survivability of a naval platform many different aspects need to be addressed, with special focus on redundancies of all critical components. Most of the components are non-structural, but the transverse bulkheads aid survivability by restricting the spread of the blast load and related effects, along the length of the vessel. Transverse bulkheads are required to be at least a watertight boundary, if not an airtight
71 boundary, against flooding or fire in a post-explosion environment. Therefore, no rupture of the transverse bulkheads can be permitted and the post-explosion redundant strength must be such that the transverse bulkhead can withstand the flooding load. Naval transverse bulkheads are expected to accomplish these requirements so that personnel and equipment in other compartments, or sections, of the naval platform are protected from the blast load, flooding and fire.
With these operational requirements it is intended that if an explosion occurs inside a naval platform the blast load and related effects of flooding and fire would be contained within the compartment in which the explosion occurred. This would mean that only minimum damage control would need to be undertaken since that compartment would be assumed lost. The adjacent compartments would be protected by transverse bulkheads and automatic or semi-automatic facilities such as fire-suppression sprinklers. The principal effect that would require damage control personnel is the repair of the transverse bulkheads that have been penetrated by fragments and projectiles due to the explosion. Optimising the transverse bulkhead against the penetration of fragments is not considered in these design criteria, as the weight penalty was not seen as justifiable. Armour protection is used sparingly in naval platforms, to surround particular components of the platform and is not used on transverse bulkheads.
2.1.2.Current transverse bulkhead formation
Chalmers (1993), Hughes (1988) give a broad description of the development of ship structures. Although Hughes (1988) focuses on commercial vessels, its work on first principles is very complete, but does not consider blast load situations specifically. Chalmers (1993) is directed towards the formation of naval platform structures and covers the issues related to blast loads, but this is limited due to the nature of this information. Using these sources of information the ability to develop blast tolerant transverse bulkheads would be impossible as they give an incomplete picture. An equivalent commercial document to these publications is BV 104-1 (1982) which is used for designing warships, mainly focussing on hull structural loads.
Development in the field of structural load determination for static, quasi-static and random dynamic loads, plus the material and structural response and in some cases 72 active and passive protection to these loads is covered in Ghose and Nappi (1994), Dow et al. (1994), ISSC’94 (1994), and Amdahl et al. (1997).
Specific work directed towards blast tolerant structural formation is limited. Hyde (1991) and Weidlinger (2000b) are some of the few sources that give some direction to the design of blast tolerant structures. The short fall of this literature is that the papers are directed towards buildings and underground structures that have effects and situations not seen within maritime or naval structures.
Shupe et al. (1984) discusses an interactive model for the development of damage tolerant structures. It is this type of methodology that is being used in this research and will have to be used in the formation of any blast tolerant structures, especially if it is to be optimised and meet post-blast load case requirements.
Müller (1992) makes limited mention of consideration given in the development of naval platforms of shock load cases, which includes air-blast load cases. While Cannon et al. (1999), mentions that survivability and blast tolerance are being given greater consideration in future naval platform designs. This improvement is being achieved through empirical work on individual structural components of naval platform structures which have a history of failure during an air-blast load situation.
2.2. Operational requirements
As discussed by Williams (1990), the determination of the customer’s requirements for the product under consideration must be completed in the initial step. These will be termed the operational requirements. Furthermore, the design requirements permit a clear understanding between the customer and the developer of what they believe the capabilities of the product should be.
In short, this is a structured approach for developing the operational requirements that the product must meet, turning these requirements into design criteria and then implementing a development program to form this product. Although this sounds simple, this technique is often overlooked, leading to unsatisfactory outcomes.
73
In this research project a naval platform broken up into compartments is considered, due to the significance for improved survivability and reduced vulnerability by the spreading out of mission critical functions between the compartments. The number and size of compartments would not be set arbitrarily, but would be determined with consideration to the weapon threat, size of the naval platform and the operational profile of the vessel. This would be applicable to naval platforms of length greater than 100m, as smaller vessels generally lack the size and structural strength to withstand an internal air-blast load. From this greater determinability of the naval platforms abilities and performances would be obtained, than is currently the case.
The operational requirements will be based around the capabilities that a transverse bulkhead on deck 3 at 19.2 m from the bow on a vessel 118 m long moving at 30 knots, (see Figure 2.2.1) should be able to fulfil. This is potentially the worst position for a transverse bulkhead due to the following reasons:
a) the depth of the bulkhead would mean the pressure head due to a tank or flooding load would be greater than at the mid-ship, b) this distance forward means that the dynamic factor from the ship motion, including slamming, would be present c) the vessel would be wide enough to have all the capabilities and requirements that are under consideration in this design criteria for a transverse bulkhead. Principally, at this distance from the bow, this vessel is wide enough to house heavy equipment and the bow is unlikely to separate due to the air-blast load.
This transverse bulkhead will be considered as a generic worst-case naval transverse bulkhead for the operational requirements and subsequently used in the design criteria and the proposed optimisation procedure. The final optimised naval transverse bulkhead structural arrangement that fulfils all the operational requirements of a naval transverse bulkhead in this position would therefore be assumed to be used with confidence anywhere else in a naval platform.
74
Figure 2.2.1: The position of the worst-case generic transverse bulkhead.
2.2.1.Pre air blast loads
There are two loads that must be considered in this situation. These are:
a) A hydrostatic load, pH , due to a tank on one-side of the transverse bulkhead, needs to be applied laterally onto the transverse bulkhead. This load includes the effect of sloshing due to the vessel’s motion.
b) Structural loads, pS , need to be applied in the plane of the transverse bulkhead on its sides and top. The structural load will cover the loads due to equipment above, and bending loads on the hull, from such occurrences as dry-docking.
The response of the transverse bulkhead to all of these loads must be in the elastic regime and no rupture is permitted.
2.2.2. Air blast load
The air blast load against the naval transverse bulkhead will be assumed to be 150 kg of TNT equivalent explosive at 8 m. This load is comparable with the critical blast load considered by some western navies in the design of new vessels, Reese et. al. (1998a) and Edney (1988). This work only considers that one such instance occurs, but there
75 have been suggestions that multiple instances need to be considered. This is more of an issue for post air blast load requirements, but due to this the maximum deformation and maximum crack length, which relates to the rupture analysis, have been significantly restricted.
The response of the transverse bulkhead to this blast load will be critical in two situations. Firstly, as with the pre-air-blast loads, no rupture is permitted within the transverse bulkhead structure. Secondly, a maximum permanent deformation of the transverse bulkhead will be set. This is due to pipes penetrating through the bulkhead, equipment and walkways close to the bulkhead, and that a post air blast load has to be supported by the bulkhead.
2.2.3. Post air blast load
The post-air-blast load is the flooding of the compartment after an explosion has occurred. The deformed transverse bulkhead is required to be able to support this load without extensive deflection and no rupture in the bulkhead structure.
2.3. Design criteria
The design criteria describe the values that must be met in a finite element analysis and subsequent optimisation procedure.
2.3.1.Pre air blast loads
As stated in the operational requirements there are two separate load cases for this situation. Firstly, the hydrostatic load due to a tank. This hydrostatic load is solved by the method given in BV 104-1 (1982). In this method a value, bzq , is used to approximate the effect that sloshing has on the hydrostatic load. The hydrostatic load is obtained from the following equations from BV 104-1 (1982)
r [ ( ++= 3.01 bhhgp )], kN (2.3.1.) H 20 zq ( m2 )
76 where r is the density of water, g is acceleration due to gravity, h0 and h2 are given in Figure 2.3.1, and bzq is
é ù ê x ú bzq Fn ()++= Fn ,251 (2.3.2.) ê L1 ú ë 2 û
where Fn is the Froude number, x is the distance that separates the centre of the vessel from the bulkhead ( x = 39.8 m) and L1 is the half length of the vessel ( L1 = 59 m). In 2 2 this case the value of the hydrostatic pressure due to a tank is pH = 90 kPa.
h0
h2 Deck 3, liquid tank on this deck
Figure 2.3.1: Height of the tank and release value.
This method has built in safety factors relevant to differences between the idealised bulkhead and a fabricated bulkhead, so no further safety factors are implemented.
The structural loads are obtained from Chalmers (1993), where for the sides of the bulkhead the load is determined to be 93.15 MPa and for the top of the bulkhead the load is 22.5 MPa. The side load is obtained by following the method given in Chapter 3 of Chalmers (1993), where the pressure head comes out to be approximately 103.5 kPa. The pressure head value is then multiplied by the length of three frames separation and divided by the plate thickness, to obtain the above pressure. This method is also applied for the top load but the original pressure head is 25 kPa. This is a conservative approximation and no advantage would be gained through the implementation of an additional safety factor.
77 Figure 2.3.2 shows the applied loads against the sample transverse bulkhead. The optimised transverse bulkhead is being based around the DSTO Bulkhead Test Rig (BTR) dimensions of 2400 mm by 2400 mm. In the figure below the hydrostatic pressure is applied as a pressure over the bulkhead plate area and the structural loads are applied as a pressure field along the side and top edges of the bulkhead. The pressure field is used so that the pressure value can change with changing thickness of the transverse bulkhead plate.
In the analysis of these combined loads it is required that the solution stay within the elastic regime. This is more in consideration of the strength and stiffness requirements for the air-blast load situation than for the pre air blast load requirements.
No rupture of the bulkhead or associated joints and connections are permitted. Rupture analysis techniques are covered in Chapter 5 In particular, the use of a J-integral method to determine crack growth and maximum crack length.
pS
pS
pS
pH
Figure 2.3.2: The positions of the applied pre-air-blast loads.
2.3.2.Air blast load
The air blast load of a 150 kg TNT equivalent explosive at 8 m inside a vessel is approximately equivalent to, by the Hopkinson scale method, 7 kg of Comp-B at 3 m in the DSTO BTR. Turner (1999) has supplied the blast pressure data for this situation.
78 The data that Turner supplied consists of two separate position pressure profiles from the blast. The approximate positions of the pressure gauges relative to the centre of the bulkhead are 550 mm and 1150 mm in a radially outward direction. The blast pressure profiles both start at zero pressure and end at zero pressure and last 5 msec, which can be assumed to be less than the period of the 1st natural harmonic of a transverse bulkhead. A simiplified version of the blast pressure profiles is given in Figure 2.3.3.
5.000 4.500 4.000 3.500 3.000 2.500 2.000 1.500 Pressure (MPa) 1.000 0.500 0.000 0.000 0.140 0.360 0.520 0.620 1.140 1.480 1.860 2.200 2.640 3.400 3.900 5.000 -0.500
Time (msec)
550 mm Blast Pressure Profile 1150 mm Blast Pressure Profile
Figure 2.3.3: Blast pressure history of 7 kg of Comp-B at 3 m in the BTR.
Figure 2.3.4 shows how the two blast pressure profiles are applied to the transverse bulkhead in a finite element model. This finite element modelling needs to be carried out with solid elements in a non-linear dynamic modeller to capture all the relevant responses of the structure to the air blast load. The pressure profiles are applied to the surface of the bulkhead plate and need to be in a non-linear transient form.
The maximum permanent deformation that can be accepted by a naval transverse bulkhead is 100 mm. This maximum deformation was established due to pipes penetrating though the bulkhead as well as equipment and narrow walkways that may be situated near the bulkhead. A safety factor needs to be introduced, as the accuracy of
79 modelling the response of an air blast load against a transverse bulkhead is within 10% to 20%, Turner (1999). Therefore, taking the worst case, in finite element modelling the maximum permanent deformation that can be permitted is 80 mm.
1150 mm blast pressure profile
550 mm blast pressure profile
600 mm in length
Figure 2.3.4: Application regions of the blast pressure profiles for the transverse bulkhead.
Due to the high strain rate experienced in an air-blast situation, material data is required. This material data was obtained through undertaking Hopkinson bar tests, with the use of constitutive equations such as Johnson-Cook and Cowper-Symonds (Wang and Lok (1997)) to give general constants that can be used in finite element modelling. This work is described in the next chapter.
As stated in the pre air blast load situation and the operational requirements, no rupture of the transverse bulkhead or associated joints are permitted. This could be tested for by the methods mentioned in Chapter 5.
2.3.3. Post air blast load
The post-air-blast load that is being considered is flooding. BV 104-1 (1982) gives the following equation for the flooding load
F r ( += bghp zq ),3.01 (2.3.3.)
where hh 2 += 1, bzq is given in Equation (2.3.2.) and the other parameters are as mentioned previously.
80
Using this method, the flooding load equates to 52 kPa, i.e. pF = 52 kPa. This is applied in the same way as the hydrostatic tank load, shown in Figure 2.3.2. As with the hydrostatic load the effect of sloshing has been covered in determining this value. Safety factors are built into this method. Therefore, there is no need for additional safety factors.
The deformed transverse bulkhead, due to the air-blast load, is permitted to deflect a further 5 mm due to the flooding load. No rupture is permitted in the transverse bulkhead or its associated joints. In relation to the structural load, it is assumed that structural redundancy within the vessel will absorb these loads.
2.3.4.Other relevant factors
The other factor that must be recognised is that the transverse bulkheads are to be fabricated out of BHP X-80 steel. In regards to the fabrication a minimum plate thickness of 4 mm is set by industry. X-80 steel plate is available with thickness from 4 mm up to 9 mm in intervals of 0.1mm, although current manufacturing capabilities at BHP sets this maximum thickness of X-80 steel, other steel manufacturers are able to produce X-grade steel much thicker.
In the fabrication of the transverse bulkhead it is assumed that distortion is less than the thickness of the plate. This is to fit in with the recommendation of Ghose and Nappi (1994), where it is recognized that modelling results are comparable to empirical results of actual structures as long as distortion is not greater than the thickness of the plate. The distortion is assumed to be reduced by the use of constraints, pre-fabrication cambering and post-fabrication straightening. It is also recognised that modern reduced heat input welding techniques reduces the distortion and residual stress in the final fabricated structure.
The use of constraints in the welding process will reduce distortion as stated, but will increase the residual stress as mentioned by Okumoto (1998). Therefore the residual stress has to be considered in the analysis. It is not practical to model this quantitatively as mentioned by Okumoto (1998), since steels such as X-80 have relatively high 81 residual stress due to the rolling and cooling processes during manufacturing and there is little data on the residual stresses that form during the fabrication of actual structures. Hence, residual stress is considered in the following manner:
a) The effect of residual stress on the final deformation of the transverse bulkhead due to the air-blast load is one of the reasons why the accuracy of the modelling is between 10% to 20%, Turner (1999). Therefore, the effect of residual stress is taken into consideration when reducing the maximum permanent deformation to 80 mm. b) The safety factors built into the static loads cover effects such as residual stress.
Therefore, no further constraints or safety factors will be introduced to deal with the effect of residual stress in the transverse bulkhead.
2.4. Conclusion
In this chapter a design criteria for X-80 steel blast tolerant transverse bulkheads has been proposed. Outside of defining the maximum deformation that is permitted for each load case and why they have been set to these values, it has also been noted that no rupture of the transverse bulkhead or its joints can be permitted. The testing of the rupture requirements is covered in Chapter 5. In the following chapters other factors such as finite element modelling blast load situations and the propagation of stress waves are investigated, culminating in a proposed optimisation procedure for this design criteria and recommendations for the formation of blast tolerant transverse bulkheads.
The above design criteria drove and gave the guidance for much of the following work within this research project and thesis. Chapters 3, 4, and 5 deal with much of the initial knowledge needed in such an endeavour for example the high strain rate material constants, finite element modelling techniques, material response to stress waves and high strain rate, and material crack length and/or rupture prediction. Following on from these Chapters, Chapter 6 deals with individual structural members (joints and stiffeners) that can enhance the performances of transverse bulkheads being blast
82 loaded. From the work on joints and stiffeners, in particular stiffeners used in double skin transverse bulkheads, recommendations have been developed and implemented into the optimised blast tolerant transverse bulkhead. Chapter 7 gives an optimisation methodology that has been developed from the design criteria and the results from a limited run through. There has been on-going developmental work while these optimisation cycles were being undertaken. Much structural change was seen and introduced to the transverse bulkhead. Nevertheless, recommendations are given for a technique to develop optimised blast tolerant transverse bulkheads and what would be the likely structural arrangement for such a transverse bulkhead. Chapter 8 concludes the thesis with comments on future possible research and development work in this field.
83
Chapter 3 High strain rate data and analysis
Abstract: This chapter covers the 30 compression Hopkinson bar tests that were performed at the Defence Science and Technology Organisation facilities in Melbourne, in 1999. From these 30 tests, 29 were successful. The stress strain curves for these 29 test results were obtained by using the program HOP1_3.exe.
With the stress strain data available, material constants have been obtained for the constitutive models of Cowper-Symonds and Johnson- Cook. It has been decided to use only the material constants from the Cowper-Symonds models, as the values from the Johnson-Cook seem dubious. Additionally, an investigation of the deformation of the banding lines has shown that only the higher strain rate situations show any effect.
The results from this work have been used in the finite element modelling of a transverse bulkhead fabricated out of X-80 steel undergoing an air- blast load and structural components that were also investigated.
84 3.1. Introduction
Material constants for high strain rate situations are needed in the finite element modelling of structures undergoing air-blast loads. These constants relate to variables from the Cowper-Symonds and Johnson-Cook constitutive models (Wang and Lok (1997), and Johnson and Cook (1983)). To solve these constitutive models empirical data are required. Compression Hopkinson bar tests were conducted to obtain the data. The experimental procedure and analysis are discussed in this chapter.
3.2. Experimental set-up
The experimental work is composed of 30 compression Hopkinson bar tests. Figure 3.2.1 shows the compression Hopkinson bar rig and gives an explanation of all the components. Mr. Pattie of the DSTO supplied the following explanation of the operation of the compression Hopkinson bar:
“A suitable ramset charge is selected and the impact bar is placed inside the housing at a nominal distance in from the end of the ramset breach plug. The ramset charge is activated by pulling the trigger cord which fires the charge, propelling the impact bar towards the target secured on the Hopkinson bar itself. On passing the photonic sensor, the impact bar flutes are recorded on a Nicolet storage unit to record the velocity of the impact bar. As the impact bar impacts the specimen, a shock front travels down the Hopkinson bar which is observed by the strain gauge on the bar itself and this is also recorded on the Nicolet storage unit”.
In this series of compression Hopkinson bar experiments 30 samples were tested. The test specimens were cylindrical in shape and had approximate dimensions of 4.76 mm in diameter and 4.76 mm in height. Half of these samples were cut parallel to the rolling direction and the other half were cut perpendicular to the rolling direction. Ramset charges of Brown, Green, Yellow and Red were used. These ramset chargers relate to strain rates between 3,000 s-1 to 1,000 s-1.
85 The data obtained for each of these tests was saved onto a 5.25 in floppy disc on the Nicolet storage unit. This data was then processed in two stages. Stage one used the program VUPOINT. In VUPOINT the range, which was processed in the HOP program to evaluate the data, was selected. During the second stage HOP1_3.exe was executed, after renaming the output file from VUPOINT to HOPIN.dat. The output from this included outputted stress, strain, strain rate, velocity, volts, force, height to diameter ratio, and time data.
Figure 3.2.1: At the bottom left, just in the photo, is the photonic sensor control box. The Photonic Sensor snakes out and is attached to the end of the impact bar housing. Below the impact bar housing on the bench is the impact bar. The bar in the Hopkinson bar rig is the Hopkinson bar, which have the associated strain gauges connected and the sample is placed at the end, which comes in contact with the impact bar. Between the photonic Sensor control box and the Hopkinson bar there is the firing trigger mechanism, the ramset gun, and the impact bar housing.
3.3. Constitutive Models
The following explanation of the Cowper-Symonds and Johnson-Cook constitutive models were obtained from Wang and Lok (1997), Johnson and Cook (1983), Jones (1989) and Lindholm et. al. (1980).
3.3.1.Cowper-Symonds Model
The Cowper-Symonds constitutive model is
1 s ¢ & q o 1+= (e ) , (3.3.1.) s o D 86 æ YS +ss UTS ö where s o is the static flow stress ç = ÷ (MPa) è 2 ø
s o¢ is the dynamic flow stress (MPa) e& is the strain rate (per second) D is a material constant q is a material constant
s YS is the yield strength (550 MPa)
s UTS is the ultimate tensile strength (720 MPa)
The material constants are solved by converting equation (3.3.1.) into the following format,
& æs ¢ ö e = qlnln ç o -1÷ + ln D , (3.3.2.) è s o ø and using the material data obtained from the compression Hopkinson bar tests.
Then q and D can be simply solved by considering q as the slope of a linear equation and D as the y-intercept.
3.3.2.Johnson-Cook Model
The Johnson-Cook constitutive model is
ss Be n 1+-= C ln e & - T m ,1 (3.3.3.) ( YS )( ( e ))( h ) where s is the stress from the results (MPa) e is the strain from the results
Th is the homologous temperature (Kelvin) m = 0 (as temperature effects are not considered) B is a material constant n is a material constant C is a material constant
87
Using three stress and strain values from the high strain rate stress-strain curve, the material constants can be solved from these three simultaneous equations. Since one of the material constants is a power, Maple (in Scientific Workplace), was used of obtain the values to these material constants.
3.4. Results from the compression Hopkinson bar tests
Table 3.4.1 shows a brief summary of the test data collected during the conduction of the test, while Figure 3.4.1 gives a collection of the stress strain curves from this compression Hopkinson bar test series. In this figure, Shots 1 and 2 are for the low range of the strain rate tested, and as can be noted the stress strain curve does not go all the away across when compared to the other curves given. Shots 18 and 19 are for medium-strain rate, while Shots 24 and 25 are for the high-strain rate tests. Additionally, Shots 1, 19 and 25 are for parallel specimens, while Shots 2, 18 and 24 are perpendicular specimens.
The non-successful compression Hopkinson bar test, was shot number 15 as the photonic sensor did not register the impact bar’s passing, therefore no results for shot number 15 were recorded.
Table 3.4.2 gives the material constant values for the Cowper-Symonds model for the shots for which data was recorded. Similarly, table 3.4.3 gives the Johnson-Cook model material constants. These material constants are averaged over 9 different cases: a) 3,000 – 5,000 s-1 strain rate parallel test samples b) 3,000 – 5,000 s-1 strain rate perpendicular test samples c) 5,000 – 7,000 s-1 strain rate parallel test samples d) 5,000 – 7,000 s-1 strain rate perpendicular test samples e) 7,000+ s-1 strain rate parallel test samples f) 7,000+ s-1 strain rate perpendicular test samples g) Parallel test samples h) Perpendicular test samples i) All test samples
88
Table 3.4.1: Data record of Hopkinson bar test.
Date Shot Charge Direction of Bar Velocity Hopbar No. Sample Details (mm) Colour the Material (ms) (m/s) Impact Bar to the Roll
4/20/99 1 Brown parallel 518 19.1 No.1,A Di = 4.72, Hi = 4.64, Df = 5.38, Hf = 3.71
4/20/99 2 Brown perpendicular 446 22.2 No.1,A Di = 4.72, Hi = 4.72, Df = 5.67, Hf = 3.36
4/20/99 3 Brown parallel 408 24.2 No.1,A Di = 4.66, Hi = 4.71, Df = 5.83, Hf = 3.21
4/20/99 4 Brown perpendicular 421 23.5 No.1,A Di = 4.74, Hi = 4.72, Df = 5.8, Hf = 3.22
4/20/99 5 Brown parallel 388 25.5 No.1,A Di = 4.7, Hi = 4.71, Df = 5.94, Hf = 3.11
4/20/99 6 Brown perpendicular 382 25.9 No.1,A Di = 4.68, Hi = 4.68, Df = 6, Hf = 3.03
4/23/99 7 Brown parallel 400 24.7 No.1,A Di = 4.75, Hi = 4.72, Df = 5.53, Hf = 3.58
4/23/99 8 Brown perpendicular 414 23.9 No.1,A Di = 4.74, Hi = 4.71, Df = 5.82, Hf = 3.22
4/23/99 9 Green parallel 400 25 No.1,A Di = 4.74, Hi = 4.71, Df = 5.92, Hf = 3.11
4/23/99 10 Green perpendicular 392 25.2 No.1,A Di = 4.74, Hi = 4.71, Df = 5.69, Hf = 3.3
4/23/99 11 Yellow parallel 306 32.2 No.1,A Di = 4.77, Hi = 4.7, Df = 6.8, Hf = 2.41
4/23/99 12 Yellow perpendicular 279 35.4 No.1,A Di = 4.73, Hi = 4.72, Df = 6.75, Hf = 2.5
4/23/99 13 Yellow parallel 173 28.6 No.1,A Di = 4.71, Hi = 4.68, Df = 6.33, Hf = 2.76
4/23/99 14 Yellow perpendicular 179 27.7 No.1,A Di = 4.75, Hi = 4.71, Df = 6.75, Hf = 2.41
4/23/99 16 Yellow perpendicular 305 32.4 No.1,A Di = 4.75, Hi = 4.73, Df = 6.9, Hf = 2.35
4/23/99 17 Yellow parallel 314 31.5 No.1,A Di = 4.67, Hi = 4.64, Df = 6.72, Hf = 2.44
4/23/99 18 Yellow perpendicular 324 30.5 No.1,A Di = 4.74, Hi = 4.72, Df = 6.52, Hf = 2.55
4/23/99 19 Yellow parallel 349 28.3 No.1,A Di = 4.75, Hi = 4.7, Df = 6.32, Hf =2.77
4/23/99 20 Yellow perpendicular 358 27.6 No.1,A Di = 4.75, Hi = 4.7, Df = 6.25, Hf = 2.82
4/23/99 21 Yellow parallel 342 28.9 No.1,A Di = 4.7, Hi = 4.65, Df = 6.39, Hf = 2.8
4/23/99 22 Brown perpendicular 428 23.1 No.1,A Di = 4.7, Hi = 4.65, Df = 5.8, Hf = 3.22
4/23/99 23 Brown parallel 430 23 No.1,A Di = 4.71, Hi = 4.65, Df = 5.8, Hf = 3.35
4/23/99 24 Red perpendicular 304 32.5 No.1,A Di = 4.73, Hi = 4.7, Df = 6.85, Hf = 2.38
4/23/99 25 Red parallel 294 33.6 No.1,A Di = 4.71, Hi = 4.67, Df = 7.1, Hf = 2.26
4/23/99 26 Red perpendicular 281 35.2 No.1,A Di = 4.74, Hi = 4.7, Df = 7.34, Hf = 2.09
4/23/99 27 Red parallel 294 33.6 No.1,A Di = 4.69, Hi = 4.65, Df = 7.09, Hf = 2.21
4/23/99 28 Red perpendicular 283 35 No.1,A Di = 4.75, Hi = 4.71, Df = 7.22, Hf = 2.19
4/23/99 29 Red parallel 302 32.7 No.1,A Di = 4.77, Hi = 4.71, Df = 6.89, Hf = 2.33
4/23/99 30 Red perpendicular 308 32.1 No.1,A Di = 4.74, Hi = 4.71, Df = 6.87, Hf = 2.38
In this averaging of data, shots 7 to 14 have been omitted, due to the fact that the photonic sensor did not detect the impact bar in the correct position. This lead to unreliable results for the bar velocity and therefore gave distorted values for the strain rate and other factors that were obtained through executing HOP1_3.exe. Additionally, Shot 6 is not considered since to solve the Cowper-Symonds material constants the
æ s 'o ö absolute had to be taken of ç -1÷ , which for this case would have been a negative è s 0 ø number and hence is incorrect in regard to the theory. 89
Hopkinson stress strain curve for X-80 steel
1.00E+09 9.00E+08 8.00E+08 Shot 1 7.00E+08 Shot 2 6.00E+08 Shot 18 5.00E+08 4.00E+08 Shot 19 Stress (Pa) 3.00E+08 Shot 24 2.00E+08 Shot 25 1.00E+08 0.00E+00
3.645E-028.912E-021.439E-011.948E-012.460E-012.995E-013.547E-014.122E-014.719E-015.333E-015.973E-016.646E-01 Strain
Figure 3.4.1: Stress strain curves for parallel and perpendicular specimens for low-, medium-, and high- strain rate values from the compression Hopkinson bar test series
Taking the exemptions into consideration, the 9 remaining cases relate to the following shot numbers a) 3,000 – 5,000 s-1 strain rate parallel test samples –shot numbers 1, 23 b) 3,000 – 5,000 s-1 strain rate perpendicular test samples – shot numbers 2, 22 c) 5,000 – 7,000 s-1 strain rate parallel test samples – shot numbers 3, 5, 19, 21 d) 5,000 – 7,000 s-1 strain rate perpendicular test samples – shot numbers 4, 18, 20 e) 7,000+ s-1 strain rate parallel test samples – shot numbers 17, 25, 27, 29 f) 7,000+ s-1 strain rate perpendicular test samples – shot numbers 16, 24, 26, 28, 30 g) Parallel test samples – shot numbers 1, 3, 5, 17, 19, 21, 23, 25, 27, 29 h) Perpendicular test samples – shot numbers 2, 4, 16, 18, 20, 22, 24, 26, 28, 30 i) All test samples – shot numbers 1, 2, 3, 4, 5, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
90 Table 3.4.4 gives the average values for the Cowper-Symonds material constants, while table 3.4.5 similarly gives the Johnson-Cook material constants.
Table 3.4.2: Material constants for the Cowper-Symonds Model.
Shot q D number
1 -4.75 3885 2 -4.43 4741 3 -1.84 6364 4 -2.32 5467 5 -4.41 5855 6 -4.53 7527 7 -7.48 8140 8 -2.35 5375 9 -2.75 6471 10 -3.56 6532 11 -8.43 10208 12 -3.15 9174 13 -6.49 6247 14 -5.87 5977 16 -5.20 7673 17 -5.06 7469 18 -3.92 6880 19 -5.64 6172 20 -1.73 6466 21 -4.13 6730 22 -2.68 5038 23 -3.32 5061 24 -3.00 7846 25 -4.66 8308 26 -3.93 8786 27 -3.44 8970 28 -3.91 8690 29 -6.19 7403 30 -4.22 7730
The ranges in the values of q within the parallel and perpendicular series and between these series are acceptable. These ranges can be explained due to the data used in their development not being at the same strain rates between the series and general experimental scatter. The range in the situation of 5,000 to 7,000 s-1 strain rates is the greatest, but for this situation the range in D value is very small, therefore this q range is explained by the different strain rate data used in its formation. For the D values, the 91 ranges in the parallel and perpendicular series and between these series are equivalent or comparably smaller than for the q material constants. Therefore the values for ‘All Samples’ shall be used with confidence in the finite element modelling.
Table 3.4.3: Material constants for the Johnson-Cook Model.
Shot B C n number
1 3.136E+03 1.179E-01 -4.301E-03 2 -1.384E+01 4.471E-02 -1.745E+00 3 1.211E+02 -1.945E-03 5.353E-01 4 -8.731E+01 5.326E-02 -1.511E+00 5 5.864E+02 -8.204E-02 5.471E-01 6 -5.830E+01 1.450E-02 -9.930E-01 7 8.010E+01 -6.880E-02 -1.130E+00 8 -4.100E+01 5.500E-01 -1.800E+00 9 4.790E+02 -8.190E-03 2.300E+00 10 1.580E+02 -2.220E-02 3.280E-01 11 -1.230E+02 -1.470E-02 3.190E+00 12 -3.300E+01 2.780E-02 -3.530E-01 13 5.300E+02 -2.200E+00 -9.300E-03 14 -1.100E+01 5.000E-02 -1.700E+00 16 -9.056E+00 3.504E-02 -1.099E+00 17 -7.051E+01 5.071E-02 -7.127E-01 18 4.066E+02 -1.025E-01 1.136E-01 19 3.977E+02 2.002E-02 9.622E-01 20 -2.259E+01 3.629E-02 -1.572E+00 21 1.013E+03 1.844E-01 1.537E-04 22 -2.074E+02 6.988E-02 -1.053E+00 23 -2.291E+01 4.471E-02 -1.513E+00 24 -3.968E+01 3.480E-02 -1.085E+00 25 -3.219E+02 6.401E-02 -4.168E-01 26 -4.989E+02 7.032E-02 -5.027E-01 27 1.179E+02 1.663E-02 1.078E+00 28 1.452E+02 1.747E-02 8.679E-01 29 -7.201E+01 6.338E-02 -1.015E+00 30 3.587E+02 6.499E-04 6.853E-01
92 Table 3.4.4: Average values of the Cowper-Symonds material constant values.
Situation q D
3,000 - 5,000 s-1 Parallel -4.04 4473 3,000 - 5,000 s-1 Perpendicular -3.56 4890 5,000 - 7,000 s-1 Parallel -4 6281 5,000 - 7,000 s-1 Perpendicular -2.66 6268 7,000+ s-1 Parallel -4.84 8038 7,000+ s-1 Perpendicular -4.05 8145 All Parallel -4.34 6622 All Perpendicular -3.53 6932 All Samples -3.94 6777
Table 3.4.5: Average values of the Johnson-Cook material constant values.
Situation B C n
3,000 - 5,000 s-1 Parallel 1.557E+03 8.130E-02 -7.590E-01 3,000 - 5,000 s-1 Perpendicular -1.110E+02 5.730E-02 -1.400E+00 5,000 - 7,000 s-1 Parallel 5.300E+02 3.010E-02 5.112E-01 5,000 - 7,000 s-1 Perpendicular 9.890E+01 -4.320E-03 -9.900E-01 7,000+ s-1 Parallel -8.660E+01 4.870E-02 -2.670E+01 7,000+ s-1 Perpendicular -8.750E+00 3.166E-02 -2.247E-01 All Parallel 4.890E+02 4.780E-02 -5.390E-02 All Perpendicular 3.172E+00 2.600E-02 -6.910E-01 All Samples 2.460E+02 4.080E-02 -3.724E-01
There seems to be a greater inconsistency in the Johnson-Cook material constant values within and between the parallel and perpendicular series of data compared to the Cowper-Symonds results. Of special concern are the differences in values between the parallel and perpendicular series for the following situations: a) B for the 3,000 – 5,000 s-1 93 b) C and n for the 5,000 – 7,000 s-1 c) n for the 7,000+ s-1 d) B for ‘All parallel’ and ‘All perpendicular’
These differences suggest that the behaviour and response of the X-80 steel to high strain rate is highly roll direction dependent. Although there is some roll direction dependences in X-80 steel, the results obtained from the Cowper-Symonds analysis and other relevant available evidence disagrees with the extent of the difference observed in the conclusions drawn from the Johnson-Cook analysis. Especially since similarity of results for all of the Johnson-Cook material constants does not even exist in either rolling direction. This suggests that the Johnson-Cook material constants are dubious. There are two possible reasons for this. The Cowper-Symonds model is a much more precise model in that it has a greater theoretical development compared to the Johnson- Cook model. Also, in the development of the Johnson-Cook material constants, it was assumed that the temperature did not change through the entire experimental series, therefore m could be set to zero. As this is unlikely to be the case, this may have introduced errors into the results. Therefore the Johnson-Cook material constants will not be used in the subsequent finite element modelling of the X-80 steel transverse bulkheads.
3.5. Results from the microscope investigation
For the sake of completeness Mr. Hrovat has investigated the bands on shots 1, 2, 19, 24, and 25 to see if there were any effects. From this investigation it is noted that band bending was very limited and only noticeable on the higher strain rate situation. Figure 3.5.1 shows a photo of the bands for shot number 1. It is observed that in this case there is hardly any deformation present.
Figure 3.5.2 shows the banding for shot number 2, where the banding region is evident but no deformation is seen. Shot 19 is given is Figures 3.5.3 and 3.5.4, where in Figure 3.5.3 slight bending can be seen and Figure 3.5.4 is a close up of this bending. No deformation is seen for shot number 24 in Figure 3.5.5, but the banding lines are observable. Bent band lines for shot number 25 are shown in Figures 3.5.6 and 3.5.7.
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Figure 3.5.1: Photo of the banding lines for Shot number 1
Figure 3.5.2: Photo of banding lines for shot number 2
95
Figure 3.5.3: Photo of banding lines for shot number 19
Figure 3.5.4: Close up of photo in Figure 3.5.3
96
Figure 3.5.5: Photo of banding lines for shot number 24
Figure 3.5.6: Photo of banding lines for shot number 25
97
Figure 3.5.7: Photo of banding lines for shot number 25
3.6. Conclusion
Analysis of high strain rate data obtained from a series of compression Hopkinson bar tests for the constitutive models of Cowper-Symonds and Johnson-Cook are presented. It has been decided that the Cowper-Symonds data will be implemented in the future finite element modelling for the formation of optimised X-80 steel blast tolerant transverse bulkheads.
Additionally, a short investigation of the deformation on banding has been undertaken to see if there has been any significant effects. From this investigation it has been shown that deformation of the bands are extremely limited.
98
Chapter 4 Development and evaluation of a finite element modelling technique
Abstract: The ability to accurately model the response of a bulkhead to a blast load in MSC/PATRAN and LS/DYNA is critical to this body of work. In this chapter a modelling methodology is developed, followed by its comparison to the actual deformation set for four previous blast loaded bulkheads carried out by DSTO. From these comparisons it is observed that the accuracy of this modelling method is within the requirements for this research work.
99 4.1. Introduction This chapter covers the finite element modelling method that was developed and implemented to model the blast response of four previous D-36 steel transverse bulkhead blast tests that were conducted in Defence Science and Technology Organisation (DSTO) Bulkhead Test Rig (BTR). The attached CD to this thesis contains all the figures and animation files developed from this work, while generalised figures are included within this chapter.
Initially the requirements sought from the outputs of this finite element modelling are discussed. Followed by the procedure of how the modelling method was developed. Finally, the results from the finite element modelling are discussed, including the accuracy obtained. This has been determined by the use of a Sheppard’s Interpolation.
4.2. Modelling parameters
From discussions with DSTO a minimal level of inaccuracy between the empirical displacement of the bulkhead and the finite element bulkhead model displacement was set to 10-20% for the blast load. In the finite element modelling for these four previous D-36 steel blast tested bulkheads and the sequential modelling related to the research task a maximum inaccuracy was set to 20%, with an intention of obtaining an average inaccuracy of about 10%.
Material properties and data for D-36 steel were obtained from Mr. Turner (1999) of DSTO for this finite element modelling series. This material data should not be confused with the material discussed in Chapter 3, which was for X-80 steel, as this material data is for D-36 steel.
Shots 1, 4, 9, and 10 were chosen due to the fact that no rupture had occurred to the transverse bulkhead or the joints between the bulkhead and the deck from the blast test. This is in agreement with the intention of the research task to develop transverse bulkheads that do not rupture due to a blast load being applied to them and shows a continuous deformation form.
100 4.3. Initial finite element models
To develop a modelling methodology for these situations some initial simple finite element models were undertaken to test the abilities of the finite element packages and see the type of responses that could be obtained from MSC/NASTRAN and LS/DYNA.
This started with simple model runs on MSC/NASTRAN to see how structures respond to having large surface loads applied and then being removed. Following this was some simple structural arrangements modelled for and run on LS/DYNA to see the propagation of stress waves and the structural responses.
4.3.1. MSC/NASTRAN models
For the MSC/NASTRAN models a simple structure of a plate with a small edge containment structure was investigated. The model was made from plate elements and the boundary conditions were applied to the ends of the containment structure. Eight different load cases were investigated. These load cases ranged from 0.4 MPa to 2.0 MPa applied to the face of the plate. In the first case, 0.4 MPa, the load was applied and not removed. In all the other cases the load was applied then removed, i.e. two loads cases were solved. The advantage of having an unloaded load case was that the results obtained were for the relaxed structures, i.e. it gave the permanent deformation set of the structure due to the active load case.
The results from these investigations can be found on the CD under the directory of ‘Initial MSC NASTRAN Models’. All the filenames have the following format: they start with ‘Bulk’, followed by the load which was applied in units of 0.1 MPa with a ‘U’ if it had been unloaded, and finishing with ‘stress’ or ‘disp’ if the fringe pattern is for the Von Mises Stress or the displacement respectively. Additionally, a ‘1’ or ‘2’ is added to the end if different views of the same situation have been included. As an example, ‘Bulk_20U_stress2.jpg’ is for the Von Mises Stress pattern for the load case of 2.0 MPa with an unloading load case from the second viewpoint. As an example of the results, in the Figures below the situation for 1.7 MPa loaded and then unloaded is
101 given. Figure 4.3.1 is the final von Mises Stress pattern, while Figure 4.3.2 is the final displacement pattern.
Figure 4.3.1: Final von Mises Stress pattern for the loaded (by 1.7 MPa) and then unloaded situation
Figure 4.3.2: Final displacement pattern for the loaded (by 1.7 MPa) and then unloaded situation
102 It can be noted from this work that the general deformation shapes seen in the blast loaded transverse bulkheads are also observed in these finite element model results. In particular, the hinge lines coming from the corners at approximately 45o can be observed, while the general shape was a bulging outward. With no stiffeners in this structure the bulging outwards is much more uniform than is seen in the bulkhead blast test that have three vertical stiffeners. It is additionally noted from this work that smaller element sizes assist in obtaining more accurate results. This element size is taken into the next section of work as a beginning size for the size determination of the solid elements to be used in the modelling.
4.3.2. Simple LS/DYNA finite element models
Following the work done with MSC/NASTRAN regarding permanent deformation response of a structure and the initial sizing of the elements (at least from the plate element viewpoint), an investigation of a dynamically loaded cantilever was undertaken. This cantilever was modelled out of solid elements, with a single time-dependent shock load applied to one edge of the free end of the cantilever in a direction perpendicular to the cantilever, while the other end was clamped. The number of solid elements through the thickness of the cantilever was increased from one to four.
The results from this investigation are shown on the CD in the directory titled ‘Cantilever’. The results are given in two formats, jpg (a picture format) and avi (an animation movie format). The picture results were obtained from MSC/PATRAN, while the avi files were obtained from the Finite Element Model Builder, which comes with LS/DYNA. The filenames for the jpg files start with ‘Cantilever’, then the number of solid elements through the thickness, i.e. ‘1’ through to ‘4’, and finally ‘stress’ or ‘disp’ for either the Von Mises Stress pattern or the displacement pattern respectively. For the filenames of the avi files, it starts with ‘Cantilever’ followed by the number of solid elements through the thickness. The avi images show the deformation with a fringe pattern of the Von Mises Stress pattern. Figure 4.3.3 is the final displacement for the Cantilever with only one solid element through the thickness, while for comparison Figure 4.3.4 gives the final displacement for the Cantilever with four solid elements through the thickness.
103
Figure 4.3.3: Final displacement of the cantilever with only one solid element though the thickness. Please note that the cantilever shrunk, and did not bend.
Figure 4.3.4: Final displacement of the cantilever with four solid element though the thickness. Please note that the cantilever bent as expected.
104 These results show that the cantilever with only one solid element through the thickness performs poorly. This leads to significant differences between the observed results given in the jpg file, or how MSC/PATRAN understands the results, and the avi file, or how the Finite Element Model Builder comprehends the results. Either way, the results given for the Cantilever with only one solid element through the thickness don’t agree with what would be expected in such a situation.
It can be noted that the stress patterns are not uniformly positioned across the width of the finite element model of the cantilever at any time period. This is not surprising as these stress waves are due to a time-dependent shock load situation and as such are not static or quasi-static load cases. The observed stress patterns are the result of release stress waves from the side of the cantilever, which result in this uniformity.
Additionally, it is noted that there is basic symmetry in the stress pattern in relation to the long axis (in the middle) of the finite element model of the cantilever. The reason for this stress pattern being observed is that although there are many stress waves propagating in the cantilever, including release waves from the reflections of elastic and plastic stress waves hitting a side, face, top or bottom of the cantilever, these are all symmetrical in relation to the centre of the cantilever. The limited anti-symmetrical stress patterns, in relation to the centre of the cantilever, are due to anti-symmetric waves, i.e. ringing, which like all the other stress waves propagate principally in the direction of the long axis of the cantilever.
The results for one solid element through the thickness of the cantilever are inappropriate. An improvement in results is noticed through increasing the number of solid elements through the thickness, but even at two solid elements the results are not completely appropriate. This is due to two reasons. Firstly, the higher the number of elements the better the results, which is an important requirement of this work and secondly, the bending moment through the thickness of the cantilever is important. Since solid elements are solved for values based at the middle of each element, then for one solid element the bending moment cannot be solved, for two solid elements the bending moment will be solved as a straight line. From this it can be determined that three solid elements is the minimal number of solid elements needed to be able to solve the bending moment as a parabola, or in other words with the accuracy that is being 105 sought from this work. This is based on the degrees of freedom of solid elements in LS/DYNA and MSC/NASTRAN. Of course more elements would give better bending moment characteristics for the finite element model.
Limitations in available computing resources restricted the number of solid elements to the bare minimum for the modelling of the transverse bulkhead. Therefore, all- important components of the transverse bulkhead have been modelled with three solid elements through the thickness, while the containment structure was modelled with only one solid element through the thickness.
The propagation of the stress waves throughout the entire finite element model, when run in LS/DYNA, has also been investigated. This investigation was done on two simple structures, which had either a single time-dependent shock load or multiple time- dependent shock loads applied to their top. The bases of each of these simple structures were clamped. These finite element models were modelled following the method developed above, i.e. three solid elements through the thickness and appropriate material data obtained from the compression Hopkinson Bar test series, as X-80 steel was the material used. This material data was discussed in Chapter 3.
The results from this investigation are given on the CD under the directory titled ‘Shock Test’. There are two different formats, jpg for the pictures and avi for the animated movie. The filenames for the jpg image start with either ‘Bar’ for the structure of a bar, which has an extension from one side, or ‘Yshape’ for the upside-down Y-shape structure. This is followed by ‘Single’ for the single time-dependent shock load case or ‘Multi’ for the multiple time-dependent shock load case. Finally ‘stress’ or ‘disp’ for either Von Mises Stress pattern or displacement pattern respectively. For the avi files, the filenames start with either ‘Bar’ for the structure of a bar, which has an extension from one side or ‘Yshape’ for the up-side down Y-shape structure, and is completed with either a ‘Single’ or ‘Multi’ for single or multiple time-dependent shock load cases respectively. Figures 4.3.5 and 4.3.6 are of the Bar structure for the single time- dependent shock load, giving the final von Mises Stress pattern and final displacement pattern, respectively. Similar Figures 4.3.7 and 4.3.8 give the final von Mises Stress pattern and final displacement pattern for the Y-shape structure for the single time- dependent shock load. 106
Figure 4.3.5: Final von Mises Stress pattern for the Bar structure after a single time-dependent shock load
Figure 4.3.6: Final displacement pattern for the Bar structure after a single time-dependent shock load
107
Figure 4.3.7: Final von Mises Stress pattern for the Y-Shape structure after a single time-dependent shock load
Figure 4.3.8: Final displacement pattern for the Y-Shape structure after a single time-dependent shock load
108 All the results show that the stress waves and other related effects, such as deformation, are successfully propagated throughout the entire finite element model when run in LS/DYNA. This is a successful result and as such gives confidence in the abilities of LS/DYNA to be used in this research, as a tool needed for the formation of optimised X-80 steel blast tolerant transverse bulkheads.
Finally, the investigation of solid elements with a higher p-value, i.e. more nodes associated with each solid element than the minimal eight (8), was undertaken, as there are advantages from a finite element with more nodal points, over the current solid element being used. Unfortunately, the other solid elements with a larger p-value were not supported in the system arrangement used. In particular, Hex20, Hex32 and Hex 64 were not supported in MSC/PATRAN for LS/DYNA models.
4.4. LS/DYNA modelling of the D-36 steel transverse bulkhead
The modelling methodology developed above, i.e. solid element modelling with three solid elements through the thickness; was then applied to form the finite element model of Shot 1, 4, 9, and 10. When this was run on the PC in LS/DYNA the run time was between 91-164 hours, with the final directory holding the entire model having a size of 530+ MB. Additionally, in the modelling of these blasts loaded transverse bulkheads the run was for 0.05 sec, although the blast load history was only for 0.02 sec. The extra modelling time was to permit the displacement and stresses to become almost static values. The blast histories are given in Figure 4.4.1 and 4.4.2, which are 2kg of Comp-B at 3 m in the DSTO BTR and 4kg of Comp-B at 3 m in the DSTO BTR. Shot 1 and 4 were blast tested with the 2kg of Comp-B at 3 m, while Shot 9 and 10 were blast tested with 4kg of Comp-B at 3 m.
The deformed transverse bulkhead developed hinge lines from the 3D-corners, formed by the bulkhead and containment structure, out towards the stiffeners at an angle of approximately 45 degrees. When these hinge lines reached the stiffeners they ceased to continue. The remaining plate structure of the transverse bulkhead generally deformed outwards in a parabolic form, except at and near the locations of the stiffeners, where their outward displacement was retarded.
109
The characteristics seen in the modelling deformation agrees well with the empirically observed deformation pattern. Further discussion on the accuracy of the results is presented in the sub-sections below.
Blast pressure history for 2kg of Comp-B at 3m in the DSTO BTR
1.4 1.2 1 0.8 0.6 0.4 Pressure (MPa) 0.2 0
0 0.01 0.02 0.001 0.003 0.004 0.006 0.007 0.008 0.011 0.013 0.014 0.015 0.017 0.018 Time (sec)
Pressure history at 1150mm from center Pressure history at 550mm from center
Figure 4.4.1: Blast pressure history for 2kg of Comp-B at 3m in the DSTO BTR
Blast pressure history for 4kg of Comp-B at 3m in the DSTO BTR
2.5 2 1.5 1 0.5 Pressure (MPa) 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 Time (sec)
Pressure history at 1150mm from center Pressure history at 550mm from center
Figure 4.4.2: Blast pressure history for 4kg of Comp-B at 3m in the DSTO BTR 110
4.4.1. Shot 1, 4, 9, and 10 initial observations
By comparing the maximum deformation of the finite element model results to the maximum deformation obtained from the photometric data of the deformed transverse bulkheads, the inaccuracy of the finite element model was found to be · Shot 1 8.3% · Shot 4 8.6% · Shot 9 5.0% · Shot 10 4.3% This is well within the inaccuracy range that was sought for this work.
Under the directory ‘Bulkhead Pictures’ and then the directory ‘Shot 1’ pictures of the actual Shot 1 transverse bulkhead are given for: before, filenames with a ‘b’ followed by a number in it; and after, filenames with a ‘a’ followed by a number in it. While in the directory ‘Dyna Bulkhead Models’ the jpg and avi files for finite element model results for Shot 1 are given. These files have filenames of ‘Shot 1’ followed by a number to represent that it is the same result being shown but a different angle of viewing for the avi files. While for the jpg files the filename starts with ‘Shot1’, followed by a number to represent that it is the same result being shown but at a different angle of viewing, and finally ‘stress’ or ‘disp’ which stands for either Von Mises Stress or displacement respectively. All of the jpg files are for the end time, i.e. 0.05 sec.
The references for Shots 4, 9 and 10 are the same as for Shot 1 but the number is replaced with the appropriate shot number of interest. Figures 4.4.1, 4.4.2, and 4.4.3 (covering Shot 1), Figures 4.4.4, 4.4.5, and 4.4.6 (covering Shot 4), Figures 4.4.7, 4.4.8, and 4.4.9 (covering Shot 9), and Figures 4.4.10, 4.4.11, and 4.4.12 (covering Shot 10) illustrate the actual deformation of the blasted transverse bulkhead, final von Mises pattern from the finite element results, and the final displacement pattern from the finite element results, for each shot respectively.
111
Figure 4.4.1: The actual deformed transverse bulkhead Shot 1
Figure 4.4.2: The final von Mises Stress pattern for Shot 1
112
Figure 4.4.3: The final displacement pattern for Shot 1
Figure 4.4.4: The actual deformation of Shot 4 transverse bulkhead
113
Figure 4.4.5: The final von Mises Stress pattern for Shot 4
Figure 4.4.6: The final displacement pattern for Shot 4
114
Figure 4.4.7: The actual deformation of Shot 9 after the blast test
Figure 4.4.8: The final von Mises Stress pattern for Shot 9
115
Figure 4.4.9: The final displacement pattern for Shot 9
Figure 4.4.10: The actual deformation of Shot 10
116
Figure 4.4.11: The final von Mises Stress pattern for Shot 10
Figure 4.4.12: The final displacement pattern for Shot 10
117 4.5. Comparison of the finite element data set to the photometric data set
In the sections above a basic comparison of the finite element results to the actual deformed D-36 steel bulkheads data sets were discussed. In this section a more comprehensive comparison has been made. Instead of only considering the maximum deformation values for both sets of data, the entire data sets have been reviewed. By the use of photographic metric analysis photometric deformation data sets have been obtained for the actual deformed D-36 steel blasted bulkheads, i.e. Shot 1, 4, 9, and 10. The positions of the deformation data in the two data sets are not identical, i.e. for each deformation value within the data set, which is in the x-axial direction, while its position is given in the y- and z-axial directions as shown in Figure 4.5.1. To overcome this limitation, an interpolation of the finite element data set is done to obtain finite element deformation values for all of the positions of the photometric (empirical) data set.
Origin y-axial direction, part of the position data z-axial direction, part of the position data x-axial direction, deformation value
Deformation data set entry
Figure 4.5.1: Deformation data set entry.
Sheppard Interpolation was used in this analysis because of the 3-dimensional nature of the problem. Appendix A gives the theory and explanation of the Sheppard Interpolation and the two FORTRAN computer programs that were used in this comparison. The first computer program, Model_data_maker.for, produces the displacement data from an output of MSC/PATRAN of the deformed finite element model with a force added to all the nodes of interest for the comparison. The second program, Compare.for, does the Sheppard Interpolation to the finite element data set and the comparison between both data sets.
118 From the comparison of the two deformation data sets it is noted that the finite element deformation values close to the maximum deformation value, i.e. the middle region of the bulkhead, are generally much more comparable (accuracy) to the photometric data set than those near the ends of the bulkhead. This could be for the following two reasons: 1. The Sheppard Interpolation uses values from the finite element data set within a radius of 100 mm of the photometric deformation data position. Near the ends of the bulkheads, the availability of these data points on the bulkhead’s end side of the deformation data position are limited because it is the end of the bulkhead area. This has the effect of over inflating the deformation value given to the finite element data set. 2. Areas of high slope could affect the finite element data set formed by the Sheppard Interpolated. This could occur due to more data points being on one side of the slope in relation to the photometric deformation data point than the other side, i.e. in the high slope areas near the ends of the bulkhead due to the non-uniformity within the finite element model of the deformed bulkhead.
Taking these factors into consideration, the comparison of the finite element deformation data set and the photometric data set for the entire deformed D-36 steel bulkhead is very good. The following are the results from this comparison: 1. Shot 1 has an inaccuracy between the data sets of 9.08% with a standard deviation of 6.62%. 2. Shot 4 has an inaccuracy between the data sets of 11.05% with a standard deviation of 8.25%. 3. Shot 9 has an inaccuracy between the data sets of 7.58% with a standard deviation of 5.91%. 4. Shot 10 has an inaccuracy between the data sets of 11.67% with a standard deviation of 7.05%.
Thus all the inaccuracy values, even with the addition of the standard deviations, are less than 20%. Additionally Shot 1 and 9 have inaccuracies values less than the 10% sought for, while Shot 4 and 10 inaccuracies are less than 12%.
119 Since the photometric data was recorded for the entire bulkhead, the comparison was reproduced with the photometric data folded at the horizontal mid-line. The outcome of these comparisons are given below: 1. Shot 1 has an inaccuracy between the data sets of 17.03% with a standard deviation of 11.75%. 2. Shot 4 has an inaccuracy between the data sets of 12.37% with a standard deviation of 8.94%. 3. Shot 9 has an inaccuracy between the data sets of 9.37% with a standard deviation of 7.25%. 4. Shot 10 has an inaccuracy between the data sets of 11.6% with a standard deviation of 7.22%.
It is noticeable that all the inaccuracies, except Shot 9, are larger than the initial comparison where only the bottom half of the photometric data set was used. Even with Shot 9 the difference was only in the 2nd decimal place and still had an increase in the standard deviation. This is probably due to the containment devices on top of the test bulkheads, in particular on the other side to the blast load, which is not the same as the bottom and as such is not as capable in holding the bulkhead in place. It is likely that the bulkhead deformed more at the top than at the bottom causing the higher inaccuracy for the second comparison analysis. Shot 1 has increased in inaccuracy compared to the others, which is likely to be related to the fact that after Shot 2 additional containment structural stiffeners were utilised at the top of all the remaining blasted test bulkheads. These additional stiffeners are likely to have improved the uniformities of the deformation pattern observed due to the blast load.
4.6. Conclusion
Although the comparison of results show that the inaccuracies were not less than 10%, all of the inaccuracies were less than 20%, which is acceptable and within the accuracy sought. In particular, the first comparison analysis shows that the modelling methodology used in this work is acceptable for the remaining research work.
120 The Sheppard Interpolation seems appropriate for this type of analysis, but further refinement could be used. A more heavily weighted version towards points closer to the interpolated position of the Sheppard Interpolation could overcome many of the current shortcomings. Additionally, the expansion of the radius over which data points are considered would be an improvement with some form of boundary conditions to deal with the bulkhead end problems.
Finally, run times for the bulkhead blast runs and the running of Compare.dat were often greater than 10 days. This was due to trying to obtain low inaccuracies between the finite element results and the empirical results. Therefore, for future work in this area it would be recommended that more powerful computer facilities be utilised for this work.
121
Chapter 5 Factors related to the design constraints
Abstract: The issues of stress waves and strain rates propagating through metal (X- 80 steel), and rupture failure prediction are detailed. It is noted that there is limited literature available on stress waves and the relevant strain rate propagation through metals that are coursed by a blast loaded, and in particular an explosive load that is has a similar loading to the blast load that is being considered in this research effort. More notably the thermal and pressure loads being applied to the transverse bulkhead plate, than just the response of metals to stress waves and high strain rates. More notable rupture prediction for the optimisation procedure has led to the development of a computational J-integral procedure. Although the computational J-integral procedure currently is limited, it does offer significant potential.
122 5.1. Introduction
The stress waves and strain rates that permeate a transverse bulkhead due to a blast load is a significant factor. Unfortunately, the strain rate is unknown, although it can be surmised that the strain rate due to the initial blast shock wave travelling through the thickness of the bulkhead plate would be around a magnitude of 106 - 108 sec-1, while the strain rate travelling along the bulkhead plate would be initially around a magnitude of 104 sec-1. The literature directly related to this type of events are limited, but in the section below a discussion of relevant issues is given including comments relating to theoretical work on stress wave interaction.
Rupture failure in a blast loaded transverse bulkhead is a design constraint in the optimisation procedure. To this end a method for predicting rupture failure is proposed around a computational J-integral procedure. As this computational J-integral procedure was limitedly evaluated and tested, an alternative strain to failure method is proposed.
5.2. Stress waves and strain rate in steel due to a blast load
Chapter 1 briefly covered the available literature relating to stress waves and strain rate. Most of this material was related to the scientific development of empirical, theoretical, and numerical developments about stress waves and strain rates on metals, particularly steel. Much of the work is more readily related to the forming and collision events, rather than to blast loads on structures. The exception is the material from the Ship Structural Committee (SSC), SSC-4, SSC-29, SSC-46, and SSC-76. These reports discuss the effects of blast loads on ship panels/armour. Additionally, these reports discuss the development of a standardisation testing method of materials responses to a blast load, known as the Direct Explosion Tests.
Of particular importance is Muller et al. (1949) Part II, titled “Theoretical investigation of the fracture of steel plates under explosive loading”. As the title dictates, this part investigated the “state of stress existing in a plate which is subjected to an explosive load abutting the plate”. In this investigation the following assumptions were made:
123 1. The plate behaviour to an explosive load has two phases:
a) Before changes occur in the geometry of the plate, the propagation of elastic, plastic and release waves in the plate and their reflections and interactions b) Dishing of the plate by plastic deformation.1
2. An infinite plate is assumed so that the waves radiating outwards are not reflected back in.
3. The strain rate is assumed to be 106 per second. This is much greater than is seen generally in forming and collision situations.
4. The stress-strain curve is assumed to be two straight lines. The exact value of the yield point is not critical. The results are not sensitive to yield point values at the high rates of loading. These values may be estimated in some manner or simply assumed.
5. The criteria for fracture presents difficulties because:
a) Thus far, no measurement of fracture from ordinary rates of loads have proven successful b) The extrapolation to higher rates of loading from the ordinary conditions.
These assumptions are only for the work discussed in Muller et al. (1949), and not this current research effort. It can be noted that since 1949 some of these assumptions have been relaxed, such as the stress-strain curve for high strain rates. As done in this research, empirical and numerical predictions of the stress-strain curve are now possible. Other assumptions are still valid, such as not having a definite method of determining the fracture of metals under high strain rate situations.
In Muller et al. (1949), fracture was assumed to occur when the energy density (energy per unit volume) reached the values given in the ordinary tensile test, as measured by
1 NB: Only 1 a) will be considered. 124 the area under the true stress-strain curve for the test conducted at a low rate of loading. As mentioned previously the stress-strain curve is assumed to be two straight lines. The slope of the plastic portion is obtained from an independent calculation of the velocity of the plastic wave and its relation to the slope of the stress-strain curve. It is possible to calculate the stress at which fracture occurs by knowing the area under the curve at the point of fracture, estimating the yield point, and calculating indirectly the slope of the straight-line portion of the curve.
The principal outcome of this work was the following relation
s æ L ö T ç 1 ÷ 2 lnç ÷ u C -= uupu ,2 (5.2.1.) r p èz 1 ø where s T is the tensile stress developed in the thickness direction of the plate, r p is the density of the plate, L1 is the original thickness of the plate, z 1 is the thickness of the spalled part, uu is the uncorrected velocity of the impact, and C p is the speed of the plastic wave.
uu can be corrected approximated to u , which is
æ M ö ç 2 ÷ u ç += ÷uu ,1 (5.2.2.) è M 1 ø where M 1 is the mass of the explosive charge, M 2 is the effective mass of steel plate and u is the actual velocity of detonation. Equation (5.2.1.) gives a maximum when uu is equal to C p . It is assumed that fracture will always occur if the velocity of the explosion is equal to the velocity of sound in the material.
The stress wave through the elastic part of the plate is given by
E C = , (5.2.3.) r p where E is the modulus of elasticity. In the plastic regions the velocity is given by
125 1 æ ds ö C p = ç ÷, (5.2.4.) r p è de ø which in this case becomes
E p C p = , (5.2.5.) r p with E p being the slope of AB in Figure 5.2.1.
s
s f A’ B
s o A
0 e
e o O’ e f
Figure 5.2.1: Idealised stress-strain curve.
If, as in this case, the plate has lateral restraints, then these expressions must be modified. For an assumed plane wave in the elastic region equation (5.2.1.) becomes
1 é K æ13 -u öù 2 C = ê ç ÷ú , (5.2.6.) ëê r p è1 +u øûú where K is the bulk modulus and u is the Poisson’s Ratio. For the material in the plastic state u = 1 , equation (5.2.6.) becomes 2
K C p = . (5.2.7.) r p The complete derivation of Equations (5.2.1.) and (5.2.2.) with the use of Equation (5.2.7.) is covered in Muller et. al. (1949).
Zhou and Clifton (1997) state the following:
126 & “A limiting strain rate, e m , which is not available from experiments, a value of 8x108 sec-1 or greater is chosen, primarily for the numerical purpose of avoiding the need for unreasonably small time steps at early times when the strain rate and stresses are high. These stresses relaxed in a few nanoseconds. The uncertainty in the response of the material at small strains and at shear strain rates greater than, 107 sec-1 is unavoidable at present because of the lack of experimental data in this regime. This uncertainty may have an effect on the calculated initial impact response. However, this uncertainty in the initial response of the material is not expected to play a significant role in the ductile failure which occurs much later.”
From the material on stress waves and strain rate, it can be assumed that the initial strain rate through the thickness of the loaded bulkhead plate is in the 106 - 108 sec-1 range and is a compression stress wave. This and its reflected tension stress wave have the possibility of initiation of cracks but not having any significant effect on crack propagation within the transverse bulkhead. Furthermore, these through thickness propagation stress waves, continue to go backward and forward with little or no effect on crack growth, except if they develop into longitudinal compression-tension waves that travel along the bulkhead. In this light, crack growth/propagation and the other significant effects are influenced by the outward propagating stress waves, that reflect back at the joint between the bulkhead and the deck/wall, as well as propagating through the joints. This propagation of stress waves through the joints seem to have a significant effect on the rupture behaviour of the joint and local/global structural response of the ship’s structure to the blast load.
In the next chapter, issues relating to improved joint response are investigated, in particular how to develop joints that will exhibit blast tolerant behaviour, including flexibility so that the shock load does not lead to fractures and stiffness so that the bulkhead’s deformation can be contained. In the following section, fractures and the determination of rupture under all the load cases related to this work is covered.
With consideration to the above material from the literature survey and the blast pressure history being used, it can be surmised that the strain rate for the stress waves
127 travelling along the loaded bulkhead plate is in the range of 104 sec-1. This maximum strain rate for crack propagation, permits the material data obtained from the compression Hopkinson bar tests series to supply the finite element modelling package, LS/DYNA, with the appropriate material constants.
5.3. Prediction of rupture
The Chapter 1 contribution to the literature survey on the J-integral and the other parameters related to crack propagation was brief and broad to cover all the issues/material used in this research project. For this research effort there are two principal topics of interest. These are dynamic J-integral and the determination of the J- integral from finite element analysis. In regards to the dynamic J-integral, this is a relatively new area of significant research. Nakamura et al. (1986), Zehnder et al. (1990), Bassim (1994), and Richter et al. (1999), supply methods for estimating the dynamic J-integral curve including the use of the stretch-zone width, numerical methods for approximating J-integral values, and empirical and theoretical work on the dynamic J-integral. Within this research effort, it was impractical to obtain a dynamic J-integral curve for X-80 steel, and an approximate static J-integral curve was all that could be obtained. As discussed below, a computational procedure was developed to determine the J-integral for individual solid finite elements. This computational J-integral procedure took into consideration the issues related to determining dynamic J-integrals, as mentioned in the above articles. Unfortunately this computational J-integral procedure was never tested for dynamic situations and only had limited testing for static load cases.
As mentioned in Chapter 2, a procedure was required to test for rupture. This computational procedure was required to work for static, quasi-static and dynamic load situations. The preferred method for determining crack growth was selected to be the J- integral. This was because of current developments in dynamic J-integral determination methods and the expected availability of J-integral curve data for X-80 steel. Unfortunately, this empirical data for X-80 steel ended up not being to the standard initially expected. Additionally, the J-integral is preferred over the use of strain to failure, due mainly to comments made by Jones (1993) regarding the work of Duffey
128 (1989), whereby it is incorrect to “assume that rupture occurs when the equivalent strain in a structural member reaches the rupture strain recorded in an uniaxial tensile test”, in relation to dynamic loads and/or high strain rate loads. This is due to the effect of dynamic stress concentration and modification of the stress-strain relationship at high strain rates. Even though strain to failure may be applicable to the static loads, a single J-integral analysis introduces fewer variables to the design criteria and therefore will be used for both the static and dynamic analyses.
It is necessary to have multiple J-R curves (J-integral value versus the resistance to crack growth, i.e. Da ) for different appropriate strain rates. In particular J-R curves would be required for static (10-2 sec-1 and 10-1 sec-1), quasi-static (100 sec-1 and 101 sec- 1), and dynamic (102 sec-1, 103 sec-1, 104 sec-1, 105 sec-1 and 106 sec-1) strain rates. As discussed in Chapter 1 and above there is currently a growth in research and the ability to obtain J-R curves at high strain rates. J-R curves for the last two strain rates in the dynamic load situation may not be required as the stress waves at these strain rates are inefficient in crack growth. Several J-R curves would be required per magnitude step for each of these strain rate situations. Additionally, J-R curves for parent, Heat Affected Zone (HAZ) and welded material are appropriate for the material under investigation. All of these strain rates are needed for the best possible results, although just parent data would generally suffice.
The use of the path independent parameter for characterising material toughness is well established by the work of Rice (1968) and Shih (1976). The parameter was designed to cater for elastic-plastic stress situations where the high toughness steels in naval transverse bulkheads meet the criteria. Figure 5.3.1, from Miannay (1998), shows that the J-integral characterises of the material over a broader stress range that includes elastic and elastic-plastic regimes. The loads on the naval transverse bulkhead will place it in the elastic and elastic-plastic regimes. Therefore, a path independent calculated J- integral application to determine if the naval transverse bulkhead has ruptured or not is only an extension of current practice.
Currently, the J-integral cannot be applied to complex shapes, and therefore cannot be applied to more than one component in the transverse bulkhead arrangement at once. This is because the transverse bulkhead arrangement is not a standard shape for which a 129 solution exists. Additionally, during the optimisation procedure the transverse bulkhead structural arrangement will change. The solution is then, not to apply the path- independent J-integral over the entire naval transverse bulkhead arrangement at once, but rather to the appropriate faces of the finite element bricks of interest within the model. This is possible as the shape of individual brick faces are simple and a solution can be obtained from EPRI (1981), Miannay (1998) and Tada et. al. (1973). The solid finite element bricks have dimensions between 4/3 mm by 20 mm by 20 mm to 3 mm by 20 mm by 20 mm, shown in Figure 5.3.2. The transverse bulkhead will be modelled with three solid brick elements through the thickness of the bulkhead material, as mentioned in Chapter 4.
Figure 5.3.1: Domains of deformation of a finite cracked body, as defined along the load-displacement curve and by the size of the plastic zone compared with the dimensions of the body. The parameters of interest for describing the loading and stress and strain fields are indicated for each domain, from Miannay (1998).
130 The most likely position for a crack or tear to begin is in the weld. If this tear propagates though the thickness of the weld, rupture will eventuate. As shown in Figure 5.3.3 the minimal thickness of a weld in a double weld situation is 1.5 mm for a plate 4 mm thick. It is assumed that as long as the crack only exists in one of the two welds then the redundant strength in the entire structure will be large enough for the vessel to return to port for repairs; even if the vessel is still engaged in hostilities. Therefore, the critical crack length is approximately 0.375 times the thickness of the plate.
20 mm
4/3 mm to 3 mm 20 mm Figure 5.3.2: Brick element dimensions to be used in the optimisation process.
Transverse bulkhead Bulkhead plate Double side weld joint 2 mm Stiffeners Welded joint Critical tear length, 1.5 mm Deck plate Deck
Figure 5.3.3: Double-sided welding without fillets.
In the design criteria this crack length will be reduced so to be conservative. The first reduction will be that the crack length cannot be greater than the element thickness dimension, which in the case of 4 mm thick plate is 4/3 mm. The second reduction is related to the inaccuracy in the modelling of the path-independent J-integral value. Principally this is due to the fact that the finite element processing programs, MSC/NASTRAN and LS/DYNA, will not be considering the cracks in their finite
131 element models. Sub-programs will calculate the J-integral at the completion of each load step from the nodal positions and stress data. None of this crack information will be returned to the processing programs. As a conservative estimate of a safety factor the design criteria critical crack length will be set to 75% of the finite element thickness dimension. This gives a safety factor of 3 for the permitted crack length.
The J-integral will only be calculated by using the method for a single-edge crack plate in uniform tension applied to the faces of the brick element that relate to the thickness direction of the plate. Figure 5.3.4 shows the form of the single-edge crack plate under remote uniform tension. The J-integral can be evaluated for this situation in the elastic- plastic regime by the following equation, from EPRI (1981)
2 n+1 P a a æ P ö J = f1()ae +as eoo c( )h1 ( ,n)ç ÷ , (5.3.1.) E' b b è Po ø
paF 2 where f = , aa += fr is the adjusted crack length, P is the load per unit 1 b2 e y E thickness, E'= E for plane stress and E'= for plane strain, a and n are ()1 -n 2 constants obtained from the Ramberg-Osgood material equation, s o and eo are the flow stress and strain respectively, h is a function of a and n , P = 072.1 hcs for 1 b o o
1 é a 2 ù 2 a plane stress and Po = 455.1 hcs o for the plane strain, h 1+= ( ) - ( ), ëê c ûú c
2 én -11 ùæ K ö 1 r = ç I ÷ , f = , a , b and c are shown in the figure below, y ê úç ÷ 2 bp ën +1û s o ø æ ö è 1 + ç P ÷ è Po ø
b = 2 for plane stress and b = 6for plane strain, and K1 from Miannay (1998) is
æ pa ö 2 tanç ÷ 3 P è 2b ø é æ a ö æ æ pa öö ù K1 = 1 ê +´ ç ÷ ç137.002.2752.0 -+ sinç ÷÷ ú . (5.3.2.) 2 æ pa ö è b ø è 2b ø tb cosç ÷ ëê è ø ûú è 2b ø
132 where t is the depth of the brick in relation to the face under investigation and F from Tada et. al. (1973) is
3 æ æ pa öö ()a ç137.002.2752.0 -++ sinç ÷÷ 2b æ pa ö b è è 2b øø F = tanç ÷ . (5.3.3.) pa è 2b ø æ pa ö cosç ÷ è 2b ø
Due to the equation for a single-edge crack under uniform tension the P that will be used will be the maximum value obtained from the finite element results.
P
b
a c
P
Figure 5.3.4: Single-edge cracked plate under remote uniform tension, form EPRI (1981).
The J-integral was calculated for both the parent material and weld material in the situations shown in Figure 5.3.5. It was assumed that a crack already existed, with an initial a value of 0.4 mm for the welded material and 0.01 mm for the parent plate material. At the completion of each load step (there was more than one load step per load case) the J-integral was calculated by the above equations. This calculated J- integral value was related to a J-R curve, given in Figure 5.3.6, to determine the crack extension value. This crack extension value was then used to produce the new a value, which was saved for the next time the J-integral value had to be calculated. If this new a value was greater than the critical crack length then failure was assumed. Additionally, from the J-R curve, tearing modulus analyses were performed to
133 determine if the tearing was propagating stably or unstably. If the tearing was propagating unstably then failure was assumed.
Cracks of interest
Solid finite element brick
Figure 5.3.5: Cracks that will be evaluated in the J-integral process.
J-value against Resistance (crack growth)
1.80E+06 1.60E+06 1.40E+06 1.20E+06 1.00E+06 J-R curve 8.00E+05 6.00E+05
J-integral value 4.00E+05 2.00E+05 0.00E+00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 Resistance, crack growth (mm)
Figure 5.3.6: J-R approximate curve for X-80 steel, supplied by Hrovat and Hoffman (2000)
For the static load cases, solving the J-integral procedure was simple as there was only one load step for each static load case. The dynamic air-blast load case was more 134 complex due to the propagation of the stress waves. The situation illustrated in Figure 5.3.7 shows a simple solution for this problem. Since the J-integral was calculated at the end of each time step from the nodal displacement and stress values, the time steps must be dependent on the time for a stress wave to cross the smallest dimension of the finite element brick, in consecutive time steps. The time for a stress wave to cross 4/3 mm was 2.5E-7 sec. Therefore, the time between each time step was set to 2E-7 sec and so there was 250,000 time steps for the dynamic air-blast load case, i.e. 50 msec.
There are two tearing modulus analyses, which were carried out. The first was directed at the static load cases, which utilises the J-R curve. While the second was for dynamically high strain rate load cases and investigated if the plastic zone in front of the crack tip had reached the other side of the plate that the crack was going through.
Stress Wave
(a) (b)
Figure 5.3.7: In (a) the stress wave was in the left group of elements, while in (b) it was in the right group of elements. The stress wave therefore affected the nodal stress values of the appropriate elements in the appropriate load steps.
The first tearing modulus analysis was carried out by comparing the slopes of the J-R curve at the position of the calculated J-integral value to the slope of a line joining the calculated J-integral value to the negative initial a value on the crack extension axis. The comparison was done through the following relationship, from EPRI (1981)
J ³ TT JR , (5.3.4.) for unstable crack growth. In Equation (5.3.4.),
135 E ¶J TJ = ( ) , (5.3.5.) 2 ¶a DT s o and
E dJ T = R , (5.3.6.) JR 2 da s o where the subscript DT is for total displacement held fixed and the other constants are defined above.
In the second tearing modulus analysis, if the combined length of the crack length plus the plastic zone in front of the crack tip was greater or equal to the thickness of the plate that the crack was propagating through then unstable crack growth could be assumed to follow. In other words,
+ Daa ii rp,i ³+ t p , (5.3.7.)
where ai is the initial crack length at load step i, Dai is the crack growth due to load step i, rp,i is the extent of the plastic zone ahead of the crack tip in load step i, and t p is the plate thickness through which the crack was propagating. The initial crack length and crack growth was obtained from the J-integral method discussed above, while the plate thickness was a constant value previously set. In regards to calculating the value
rp , methods were been obtained from Suresh (1998). According to Suresh (1998) the Irwin approximation was used. For mode I situation, this investigation was only for plane strain and the equation was
2 1 æ K I ö rp = ç ÷ , (5.3.8.) 3p è s y ø
where s y is the tensile flow stress and K I is the mode I stress intensity factor. While for mode II the equation is
136
2 1 æ K III ö rp = ç ÷ , (5.3.9.) è tp y ø
where t y is the shear yield stress of the material. Another approximation that could be used to calculate rp is the Dugdale model. This gives the following equation
2 p æ K I ö rp = ç ÷ . (5.3.10.) 8 è s y ø
Any of these equations would be appropriate to use in determining rp and therefore if the propagation is growing stably or not. The final selection of which equation to use would be determined through the availability of solving the new parameters and the accuracy of the results.
Figure 5.3.8, shows the fourteen computational programs used in the developed computational J-integral procedure. MSC/PATRAN, MSC/NASTRAN and LS/DYNA are commercial finite element packages, while all the other programs were developed within this research effort and are either Fortran or Perl compiled programs.
In the J-integral procedure the finite element stress values and nodal positional values are used to determine a J-value per face of the solid finite elements of interest. Only the four smallest area faces per solid finite element of interest has the J-integral solved. Due to the high computational and memory requirements only 100 elements out of the approximate 85,000 elements of the finite element model of the transverse bulkhead could be investigated with the computational resources available.
The following is an explanation of the programs within the J-integral procedure:
· MSC/PATRAN, MSC/NASTRAN, and LS/DYNA
MSC/Patran outputs *.bdf and *.key files to be run on MSC/NASTRAN and LS/DYNA respectively. From the *.bdf files Nastran_grid.dat and Nastran_position.dat files are 137 formed by cutting and pasting, similarly Dyna_grid.dat and Dyna_position.dat are formed from the *.key files. The grid files have the element numbers and their associated nodal numbers, while the position files have the nodal number and its original axial position. Furthermore, a file Element_Material.dat is formed which has a list of the element numbers to be investigated and their material properties. A material property of 1 is for parent material while 2 is for welded and heat affected material. MSC/PATRAN reads in *.op2 and d3plot files from MSC/NASTRAN and LS/DYNA respectively, to view the outputs of the responses of the load cases.
MSC/Patran
Check_sets.for
MSC/Nastran LS/Dyna
Solve_num.for Nastran_position.pm Dyna_position.pm
Nastran_stress.pm Dyna_stress.pm
Solve_stress.for Stress_dyn.dat
Check_Element.for
Face_Numbering.for
J-integral.for
Figure 5.3.8: The flow chart for the J-integral procedure
MSC/NASTRAN reads in the *.bdf file and outputs *.op2 and *.f06 files. The *.op2 file is a binary file used to show the responses due to the static load cases on MSC/PATRAN. Nastran_disp.dat and Nastran_stress.dat are formed by modifying the *.f06 file. Nastran_disp.dat gives the nodal number and the displacement in axial
138 position. Nastran_stress.dat gives the element numbers and their respective axial stress values.
LS/DYNA reads in the *.key files and outputs d3plot, elout and nodout files. The *.key file is modified by adding in element numbers and nodal numbers under investigation, which are obtained from Ele_dyn.dat and Nod_dyn.dat respectively. The d3plot file is a binary file used to show the response due to the dynamic non-linear load cases in MSC/PATRAN. There were 30 elout and nodout files for each optimisation run. The elout file gives element numbers and the axial stress values, while nodout gives the nodal numbers and the axial displacement values for each time step.
· Check_sets.for
Check_sets.for is a Fortran program which checks that the element nodal relation and the nodal position relation are the same between the input files for MSC/NASTRAN and LS/DYNA. The input files for this program are Nastran_grid.dat, Nastran_position.dat, Dyna_grid.dat and Dyna_position.dat. Grid files give the element number and their nodes, while the position files give nodal numbers and their axial position values. Output for this program is log_CS.dat and results_CS.dat, which state if everything is the same between the appropriate files or where inconsistencies have occurred.
· Solve_num.for
Solve_num.for is a Fortran program that outputs data files with element and nodal relations. This program reads in Nastran_grid.dat and Element_Material.dat, described above. The outputs are log_SN.dat, Elements.dat, element_po1.dat, element_pr1.dat, Ele_dyn.dat and Nod_dyn.dat. The log_SN.dat file gives the progress of the program and if any problems occur. The Elements.dat file gives nodes and all the elements that surround that node, while element_po1.dat and element_pr1.dat files contain the element number, its material type and the eight nodes that make them up. The last two files, Ele_dyn.dat and Nod_dyn.dat, contain all the elements and nodes that have to be outputted by LS/DYNA to solve the J-integral procedure.
139 · Nastran_position.pm
Nastran_position.pm is a Perl program that outputs the final position of the nodes of interest. This program reads in Nastran_disp.dat and Nastran_position.dat, which are described above, and outputs Position_output.dat. Position_output.dat gives the node number and its final axial position. This output file is renamed to either nodep_pr1.dat or nodep_po1.dat depending on the load case being solved.
· Nastran_stress.pm
Nastran_stress.pm is a Perl program that outputs the stress values for all of the elements of interest. In this program it reads in Nastran_stress.dat, which is described above, and outputs Stress_output.dat. Stress_output.dat contains the element number and its associated axial stress values. This output file is renamed to elements_pr.dat or elements_po.dat depending on the load case being solved.
· Dyna_position.pm
Dyna_position.pm is a Perl program that outputs at each time step the axial position of all the nodes of interest. This program reads in the Dyna_fn_nodout.dat file, all the nodout files, and the Dyna_position.dat file and outputs nodep_ay.dat and Bz.dat files. Dyna_fn_nodout.dat lists all the files of the nodout files to be used in this program, and thus permits the program to access them. The files nodout and Dyna_position.dat are described above. For nodep_ay.dat, where the y is a number between 0 and 250,000, these output files contain nodal numbers and their axial position of the node at that time step. Finally, the Bz.dat files, where the z is a number between 0 and 9, contain the file and pathname for the nodep_ay.dat files.
· Dyna_stress.pm
Dyan_stress.pm is a Perl program that outputs, at each time step, the axial stress of all the elements of interest. This program reads in Dyna_fn_elout.dat and elout files, and outputs elements_ay.dat and Az.dat files. The file Dyna_fn_elout.dat contains all the
140 filenames for all the elout files, which permits the program to open these files and process the data related to them. In elements_ay.dat files, where the y is a number between 0 and 250,000, the outputs contained in these files are the element numbers of interest and their associated axial stress values. The Az.dat files, where the z is a number between 0 and 9, contains the filename and path for the output files, elements_ay.dat.
· Solve_stress.for
Solve_stress.for is a Fortran program that outputs the axial stress values with their associated node of interest. This program reads in Elements.dat and either elements_pr.dat or elements_po.dat files, which are described above, and outputs log_SS.dat and either nodes_pr1.dat or nodes_po1.dat depending on the load case being solved for. The log_SS.dat file gives a progress report of how the program runs and if any problems were encountered. In these output files, nodes_pr1.dat and nodes_po1.dat, contain the node numbers of interest and their associated axial stress values.
· Stress_dyn.for
Stress_dyn.for is a Fortran program that outputs the axial stress values with their associated nodes of interest for each time step of the air-blast load case. This program reads in Elements.dat, elements_ay.dat and Az.dat files, which are described above, and outputs log_SD.dat, nodes_ay.dat and Cz.dat files. The log_SD.dat file gives a progress report of how the program runs and if any problems were encountered. In nodes_ay.dat files, where the y is a number between 0 and 250,000, the outputs contained in these files are the nodal numbers of interest and their associated axial stress values. The Cz.dat files, where the z is a number between 0 and 9, contains the filename and path for the output files, nodes_ay.dat.
· Check_element.for
Check_element.for is a Fortran program that checks to see if each element of interest has the same material type, and nodal relationship between the pre-air-blast load case and the post-air-blast load case. Reading in element_pr1.dat and element_po1.dat files, which are described above, and outputting log_CE.dat and resultCE.dat does this. The 141 log_CE.dat and resultCE.dat files contain a record of the progress of the program and where, if any, differences are noted between the two input files. The difference between log_CE.dat and resultCE.dat is the level of detail given.
· Face_Numbering.for
Face_Numbering.for is a Fortran program that determines the four smallest area faces per element of interest and outputs all relevant information about them. This program reads in element_pr1.dat and nodep_pr1.dat, which are described above, and outputs logFN.dat, resultsFN.dat, FN1.dat, FN2.dat, FN3.dat and FN4.dat. The logFN.dat and resultsFN.dat files contain a record of the progress of the program and if any problems occur. In the FN1.dat, FN2.dat, FN3.dat and FN4.dat files the material type of the element, the direction of the shortest side of the face, the direction of the long side of the face, and the four nodes that make up the face are contained. FN1.dat contains all the information for face one of all the elements of interest and similarly the other FN output files contain the data for their respective faces.
· J-integral.for
J-integral.for is a Fortran program that determines the crack growth due to each load case and their load steps, the final crack length, if it has exceeded the critical crack length. As well as if the crack is growing stably or unstably. This program reads in FN1.dat, FN2.dat, FN3.dat, FN4.dat, nodes_ay.dat, nodep_ay.dat, nodes_pr1.dat, nodep_pr1.dat, nodes_po1.dat, and nodep_po1.dat files, which are all described previously, further JR.dat is used. JR.dat contains the crack growth for a specific J- value, or in other words the J-R curve obtained by Hrovat (1998-2001) for BHP X-80 steel. The output of this program is log.dat and results.dat, which describes the progress of the program, and gives the maximum crack length at completion of all the load cases. Furthermore, if failure has occurred due to the crack length exceeding the critical crack length or unstable crack growth occurring, then these are recorded.
This computational J-integral procedure was evaluated against loads related to the empirical data used to obtain the approximate J-R curve for X-80 steel, and several simple load cases. From this it was determined that the situation of plane stress was 142 critical and was used from then on. Furthermore, a 4th Year project compared this procedure to empirical results. Unfortunately no real comparison could be made as shear rupture was observed at the very slow strain rates of these experiments and does not fit into the intentions of the computational J-integral procedure. However, the output results of the J-integral procedure were what were expected from the finite element input for the structural shapes and applied loads.
Although the use of the J-integral method has many advantages including permitting some crack growth before failure is assumed, compared to the strain of failure method, the availability or formation of a dynamically high strain rate J-R curve data is extremely limited at this present time. Therefore, a strain of failure method may be a simple method for testing of rupture failure. The concept is that a curve of strain of failure for tension load situations at different strain rates could be formed, shown in Figure 5.3.9. This graph would be developed from strain of failure data for tension load events obtained from static load cases, quasi-static load cases and dynamically high strain rate load cases from tests conducted on gas guns and tension split Hopkinson bar apparatus. In the analysis of the results obtained from the finite element packages, if the strain at any specific strain rate for any finite element within the model exceeds the strain of failure at that strain rate, then failure due to rupture would be assumed. Although, this method does not consider any crack growth, as a conservative method to test for rupture failure it would be reliable and easily implemented.
Strain of Failure
Strain rate (sec-1)
Figure 5.3.9: Strain of failure versus strain rate graph.
143 5.4. Conclusion
Two critical issues are addressed in this Chapter, the effect stress waves and strain rates have on metals (X-80 steel) and a method for predicting rupture. Of significance to the formation of optimised X-80 steel blast tolerant transverse bulkheads, is how to determine rupture failure at all strain rates related to such an event, as rupture failure is a constraint in the optimisation procedure. A J-integral based approach is still believed to be the best method, although this could be modified for better performances and capabilities as mentioned in Chapter 8. Since only an approximate J-R curve was obtainable for static load situations, the J-integral procedure was not implemented in the optimisation runs that have been undertaken, as discussed in Chapter 7.
144
Chapter 6 Bulkhead component investigation
Abstract: Two important structural components for the development of blast tolerant
transverse bulkheads are the joint and stiffener arrangements. The joints
need to offer flexibility so that their rupture potential is reduced, but be
stiff so to assist in the reduction of the maximum outward displacement of
the entire transverse bulkhead due to the air blast load. Since the double
skin transverse bulkhead arrangement offers the best possibilities for the
formation of blast tolerant transverse bulkheads, stiffeners between the
bulkhead plates are needed. These stiffeners need to withstand the
operational static loads, but absorb the stress/energy that passes through
them from the air blast load. In doing so the stiffeners reduce the influence
that the air blast load has on the unloaded bulkhead plate. Joint and
stiffener arrangements are investigated to meet these goals.
145 6.1. Introduction
An investigation of more capable joints and stiffeners for blast tolerant transverse bulkheads has been undertaken. Although this investigation has only been finite element based, significant progress has been made. For joint arrangements it has been clearly shown that greater flexibility is beneficial for the overall response of joints to the air blast load, but as well the response of the transverse bulkhead itself and the deck/wall that it is connected to. For the stiffener, the outcomes have not been as clear as for the joints, although this has been due in part to computational problems within the application of the finite element package, but still progress has been made. This progress has shown that stiffener designs that fail when a dynamic load is applied can reduce the overall transverse bulkhead outward displacement.
6.2. Joint structures
The joint for a transverse bulkhead is the structure between the bulkhead plate and the deck/wall. In previous DSTO blast tested transverse bulkheads, mentioned in Chapter 4, Shot 1 had no joint structure, Shot 4 and 10 had a 10 mm thick step joint structure, and Shot 9 had a T joint (also known as the admiralty T-joint) structure. These different joint structures had an effect in the overall panel deformation and rupture failure. These joint changes were done in an attempt to reduce the stress and strain level passing through the joint area. In particular the reflection of the stress wave at the weld interface between the bulkhead and the deck.
Taking the above into consideration, the joint investigation that has been undertaken used the following as design constraints:
· Dispersion of the stress waves, especially away from welded areas so that reflection of incident stress waves off them is reduced, to improve the rupture resistance of the joints · Minimise the displacement of the joint and deck due to the blast loads and stress waves, to reduce the global response that is experienced
146 · Minimise the forward displacement of the bulkhead and the outward bulging of the bulkhead, when comparing two bulkhead plates, so as to reduce the maximum displacement of the bulkhead
These are contradicting requirements, as to improve the rupture resistance of the joints, the joints need to be flexible, but to reduce the maximum bulkhead displacement the joints need to be stiff. To start this investigation, several simple joint arrangements were investigated in LS/DYNA.
The joint arrangements for this investigation were the standard/no joint arrangement (i.e. the bulkhead connected directly to the deck), step joint arrangement (i.e. where one-side of the joint is wider than the other forming a step like shape on one side), T joint arrangement (i.e. where the joint spreads out before reaching the deck), curved joint arrangement (i.e. where the joint has two separate curves one on each side of the bulkhead joining to the deck), and the inverted U joint (i.e. a semi-circle that has two connections to the deck and the bulkhead is on top). These joint arrangements were modelled as the transverse bulkheads were modelled as mentioned in Chapter 4. Additionally, in this investigation two load cases, one for a single shock load and the other a multiple shock load, were considered.
The results from this investigation are given on the CD under the directory titled ‘Initial Joint Modelling’. These results are given in jpg picture and avi movie file format. All of the filenames start with ‘Joint’, followed by one of the following: · Nothing, for the standard joint arrangement · ‘Step’, for the step joint arrangement · ‘T’, for the T joint arrangement · ‘Curve’, for the curve joint arrangement · ‘U’, for the U joint arrangement.
Then for the avi files, there is either an ‘s’ or ‘m’ for single or multiple load case respectively. While for the jpg filenames it follows with either ‘Single’ or ‘Multi’ for single or multiple load cases respectively, and then is either ‘stress’ or ‘disp’, which stands for either von Mises Stress or displacement respectively.
147
From these results it can be noted that the stress is lower for joint arrangements that have a greater connection area between the joint arrangement and the deck, and the joint arrangement and the transverse bulkhead. Additionally, if the joint arrangement is not connected to the bottom of the transverse bulkhead (i.e. the bit above the joint) the stress wave does not seem to be as pronounced within the joint arrangement and deck. Therefore, there is a potential benefit in having a joint, which has separated connections, with a separation gap between them, to the deck and connection to the transverse bulkhead, which are not on its bottom.
Following on from this, another series of simple finite element modelling was undertaken and run on LS/DYNA. This time four joint arrangements were looked at, these being no joint structure (i.e. bulkhead straight onto the deck), curved joint arrangement, the upside down U joint, and an upside down Y joint structural arrangement. In this analysis in addition to the air blast load being applied, stress loads were also applied to the bulkhead and joints that were an approximation for what could occur. These loads are given in Figures 6.2.1 to 6.2.3, where Figure 6.2.1 is the air blast load, Figure 6.2.2 is the tension and compression load applied at the top of the bulkhead, and Figure 6.2.3 is the bending load applied to the top of the bulkhead. Figure 6.2.4 shows the regions where these loads were applied.
Figure 6.2.5 shows that the no joint arrangements displace outwards much more than the other three joint arrangements. Since the outward displacement is a design constraint for the development of improved joints, this is an indication that joint enhancement is possible and could be beneficial.
On the CD under the directory ‘Four Simple Joints’, the jpeg pictures and mpeg animation are given for this part of the work. Each of the filenames start with ‘Joint’, followed by nothing if it is the standard joint, ‘C’ if it is the curve joint, ‘U’ if it is the upside down U joint, and ‘Y’ if it is the upside down Y joint. For the mpeg these filenames are then continued with ‘MPS’ for Maximum Principal Stress. While for the jpeg these filenames are then continued with either, ‘XDisp’ for the x-displacement, ‘YDisp’ for the y-displacement, ‘ZDisp’ for the z-displacement, ‘VMS’ for the von Mises Stress, ‘MPS’ for the Maximum Principal Stress, ‘VMSa’ for the von Mises 148 Strain, and ‘MPSa’ for the Maximum Principal Strain. All of the jpegs are for the end time, which was 1e-3 seconds.
Air blast load
1 0.9 0.8 0.7 0.6 0.5 Air blast load 0.4 0.3 Pressure (MPa) 0.2 0.1 0 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-04 1.00E-03 0.00E+00 Time (sec)
Figure 6.2.1: Air blast load
Compression/tension load at the top of the bulkhead
25 20 15 10 5 Compression/Tension 0 Load -5
Pressure (MPa) -10 2.00E-05 5.00E-05 7.00E-05 9.00E-05 1.10E-04 1.00E-03 -15 0.00E+00 -20 -25 Time (sec)
Figure 6.2.2: Compression and tension load
149 Bending Load at the top of the bulkhead
3
2
1
0 Bending Load
-1 Pressure (MPa) 1.00E-05 2.00E-05 4.00E-05 5.00E-05 8.00E-05 9.00E-05 1.00E-04 1.00E-03 0.00E+00 -2
-3 Time (sec)
Figure 6.2.3: Bending load
Bending load Compression and tension load
Air blast load Bulkhead
Y Joint Deck
Figure 6.2.4: Load applied to the Y joint structural arrangement
150 Outward diplacement
0.9
0.8
0.7
0.6
0.5
0.4 Z disp (mm) 0.3
0.2
0.1
0 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 8.40E-04 9.00E-04 9.60E-04
Time (sec)
Joint Joint Y Joint C Joint U
Figure 6.2.5: Outward displacement of four different joint arrangements to the combined loads
As an extension to the investigation into the joint arrangement, topology optimisation of the joint area was undertaken in ANSYS 5.6. This algorithm determined the optimal topology to meet the criteria. The contours at level 1 indicate the requirements for stiff members. The analysis is for statically applied loads. The results of these analyses are shown below and are given in the CD under the directory ‘Ansys Analysis’.
The ANSYS analysis of the joint arrangement started with the current size restriction, as given in Figure 6.2.6. Figures 6.2.7-6.2.9 show the topology optimisation outcomes for tension, compression and bending load cases. This was expanded in Figure 6.2.10 where combined load cases of tension, compression and bending were optimised and used an element size of 5 mm by 5 mm. Figure 6.2.11 shows the results of repeating the analysis in Figure 6.2.10 but with an element size of 2 mm by 2 mm. It can be observed from Figure 6.2.10 and 6.2.11 that the results are not element size dependent, but the results improved with a finer mesh.
151
It can be noted from the above that the short distance between the bulkhead connection area to the deck/wall structural connection area hinders the development of an optimum joint arrangement. Therefore, the size in the joint area of interest was increased. Initially a square of 210 mm by 210 mm was topology optimised for a combined load that was the same as above but with shear load cases also included. The shear and bending load cases were applied in each direction in these combined load cases so that symmetrical results were obtained. The results for these analyses are given in Figure 6.2.12. Figure 6.2.13 shows the new joint area of interest, which has been investigated for the combined load gives the results shown in Figure 6.2.14. Additionally, investigation of the enlarged joint area showed no significant benefit, as it generally led to overly complex joint structural arrangements.
50 mm 110 mm Bulkhead 20 mm connection area 50 mm Deck/wall structural connection area 210 mm
Figure 6.2.6: Restricted joint area of interest
Figure 6.2.7: Topology optimisation result for the tension load
152
Figure 6.2.8: Topology optimisation result for the compression load
Figure 6.2.9: Topology optimisation result for the bending load
153
Figure 6.2.10: Topology optimisation result for the combined loads
Figure 6.2.11: Topology optimisation result for the combined loads, with an element size of 2 mm by 2mm
From this ANSYS analysis it can be concluded that the optimal topology is of the curve and/or U joint structural arrangements. The requirements for blast loading will be for a flexible joint with a strong contact area to prevent rupture. It is considered this will be achieved through varying the dimensions in these optimal shapes, through runs in LS- DYNA. This ANSYS topology work carried out with static loads, was used as a guide 154 for the formation of an optimal joint, as time dependent load cases will not be undertaken within the ANSYS topology optimisation routine.
Figure 6.2.12: Topology optimisation result for the combined loads on the square
100 mm 110 mm
50 mm
150 mm
310 mm
Figure 6.2.13: The new joint area of interest
To date it can be concluded that the new joint area of interest is more appropriate than the original joint area of interest for the optimisation procedure.
The final investigation into the joint structure was undertaken using LS/DYNA, with the joint arrangement given in Figure 6.2.15. All of these joint arrangements had the loads illustrated in Figure 6.2.16 applied to them, in the method shown in Figure 6.2.17. Each of these joint test specimens had an angle iron stiffener positioned underneath the deck in the middle, while the bulkhead had a plate stiffener connecting the two bulkhead
155 plates positioned in its middle. The results for this series of analyses consider three major factors, which are shown in Figures 6.2.18 to 6.2.26, these are:
· The difference in the downward displacement between the bulkhead plate with the air blast load applied to it and the bulkhead plate that the air blast load was not applied to, gives the amount that the bulkhead has been tilted outwards. This is further analysed for the angle at the top of the bulkhead, which formed when compared to zero degrees for vertically upwards. · Maximum displacement of the bulkhead, the joint and the deck with regards to the direction of the air blast load. · The von Mises Stress, Maximum Principal Stress, von Mises Strain, Maximum Principal Strain for the entire joint test specimen.
Figure 6.2.14: Topology optimisation result for the combined loads for the new joint area of interest
From these graphs it can be noted that Joint 8 performs generally the best for the design constraints that have been set. While Joint 3 generally performs nearly as well. All joint arrangements have sufficiently low stress and strain values to not make these factors an issue. It should be noted that the responses that have been observed in this finite element modelling cannot be directly related to the global response, i.e. when these joints are part of an entire transverse bulkhead. Therefore the characteristic behaviour of the joints has been reviewed to give an idea of the best type of joint structure. 156
210mm Bulkhead 110 mm 10 mm plate 100 mm
Deck
(a) (b) (c)
110 mm 100 mm
(d) (e) (f)
110 mm 100 mm
(g) (h) (i)
Figure 6.2.15: (a) No joint arrangement, but with a 10 mm thick base plate, Joint 1 (b) Upside down Y joint with a 10 mm thick base plate, Joint 2 (c) Upside down Y joint with internal T support structure, Joint 3 (d) Upside down Y joint with internal T support structure and 10 mm thick base plate, Joint 4 (e) Upside down U joint with 10 mm thick base plate, Joint 5 (f) Upside down U joint with internal T support structure, Joint 6 (g) Upside down U joint with internal T support structure and 10 mm thick base plate, Joint 7 (h) Curve joint with 30 mm connection length at the ends, Joint 8 (i) Curve joint with internal T support structure and with 30 mm connection length at the ends, Joint 9. The above is not to scale, as the deck is 2.5 meters in length.
157
Air blast load
1 0.9 0.8 0.7 0.6 0.5 Air blast load 0.4 0.3 0.2 Pressure load (MPa) 0.1 0 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-04 1.20E-04 1.40E-04 1.60E-04 1.80E-04 2.00E-04 0.00E+00 Time (sec)
(a)
Stress loads applied to the joints
50 40 30 Top left 20 Top middle Top right 10 Left side 0 Right side Stress load (MPa) -10 -20 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-04 1.20E-04 1.40E-04 1.60E-04 1.80E-04 2.00E-04 0.00E+00 Time (sec)
(b)
Figure 6.2.16: (a) The air blast load applied onto the bulkhead and joint, (b) The stress loads applied to the top of the test specimens bulkhead, side of the bulkhead and joints
158
Left top load Mid-top load Right top load Air blast load Bulkhead Right side load Y Joint with 10 mm plate Deck
Left side load
Figure 6.2.17: Position of where the loads were applied
Difference length for the joints
1.00E-01 0.00E+00 -1.00E-01
(mm) -2.00E-01 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 0.00E+00 -3.00E-01 Difference Length -4.00E-01 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.18: Difference length for the joints
159 Angle at the top of the bulkhead
5.00E-02 0.00E+00 -5.00E-02 -1.00E-01 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 0.00E+00
Angle (degree's) -1.50E-01 -2.00E-01 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.19: Angle at the top of the bulkhead for joint test specimens
Maximum displacement of the bulkhead
1.8 1.5 1.2 0.9 0.6 0.3 0 Displacement (mm) 4.00E-05 8.00E-05 1.20E-04 1.60E-04 2.00E-04 2.40E-04 2.80E-04 3.20E-04 3.60E-04 4.00E-04 4.40E-04 4.80E-04 5.20E-04 5.60E-04 6.00E-04 0.00E+00 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.20: Maximum outwards displacement of the bulkhead
160 Maximum displacement of the joint compoment 0.4 Joint 1 0.35 0.3 Joint 2 0.25 Joint 3 0.2 Joint 4 0.15 0.1 Joint 5 0.05 Joint 6 Displacement (mm) 0 Joint 7 Joint 8 Joint 9 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 0.00E+00 Time (sec)
Figure 6.2.21: Maximum outward displacement of the joint component
Maximum displacement of the deck
0.1 Joint 1 0.09 0.08 Joint 2 0.07 0.06 Joint 3 0.05 Joint 4 0.04 0.03 Joint 5
Displacement (mm) 0.02 0.01 Joint 6 0 Joint 7 Joint 8 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 0.00E+00 Joint 9 Time (sec)
Figure 6.2.22: Maximum outward displacement of the deck
161 Maximum VMS for the entire specimen
250 200 150 100 50 VMS (MPa) 0 4.00E-05 8.00E-05 1.20E-04 1.60E-04 2.00E-04 2.40E-04 2.80E-04 3.20E-04 3.60E-04 4.00E-04 4.40E-04 4.80E-04 5.20E-04 5.60E-04 6.00E-04 0.00E+00 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.23: Maximum VMS for the entire joint specimen
Maximum MPS for the entire specimen
250 200 150 100 50 MPS (MPa) 0 6.00E-04 4.00E-05 8.00E-05 1.20E-04 1.60E-04 2.00E-04 2.40E-04 2.80E-04 3.20E-04 3.60E-04 4.00E-04 4.40E-04 4.80E-04 5.20E-04 5.60E-04 0.00E+00 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.24: Maximum MPS for the entire joint specimen
162 Maximum VMSa for the entire specimen
9.60E-04 7.20E-04 4.80E-04
VMSa 2.40E-04 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 0.00E+00 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.25: Maximum VMSa for the entire joint specimen
Maximum MPSa for the entire specimen
1.05E-03 7.50E-04 4.50E-04 MPSa 1.50E-04 -1.50E-04 4.00E-05 8.00E-05 1.20E-04 1.60E-04 2.00E-04 2.40E-04 2.80E-04 3.20E-04 3.60E-04 4.00E-04 4.40E-04 4.80E-04 5.20E-04 5.60E-04 6.00E-04 0.00E+00 Time (sec)
Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Joint 7 Joint 8 Joint 9
Figure 6.2.26: Maximum MPSa for the entire joint specimen
Interestingly, Joint 8 was the lightest joint arrangement out of all the joint arrangements considered, as shown in Table 6.2.1. The masses given in this table are for the Joint and Bulkhead component of each test specimen.
163
Table 6.2.1: Mass of the Joint and Bulkhead components of the joint arrangements
Joint Mass (kg)
1 24.42 2 33.38 3 24.84 4 35.22 5 34.26 6 24.68 7 40.58 8 21.76 9 27.05
On the CD under the directory ‘Final Joint Modelling’, the jpeg files from this work are given. All of the files start with ‘Joint’ and then a number from 1 to 9. The jpeg files then continue with ‘XDisp’ for x-displacement, ‘YDisp’ for y-displacement, ‘ZDisp’ for z-displacement, ‘VMS’ for von Mises Stress, ‘MPS’ for Maximum Principal Stress, ‘VMSa’ for von Mises Strain, and ‘MPSa’ for Maximum Principal Strain. The jpeg are suffix with either ‘eload’ for the end of the load time (2e-4 seconds), ‘0003’ for 3e-4 seconds, or ‘etime’ for the end of the run time (6e-4 seconds).
The recommendation from this work, Joint 8 arrangement, was implemented in the 4th Cycle of the optimisation runs, which are covered in the next chapter.
This work on joint structural arrangements has given some insight into possible enhancements that can be made to blast tolerant transverse bulkheads/structures. This is only an initial study and further work is required, particularly practical experiments.
6.3. Stiffener structures
It was quickly deduced that a double skin transverse bulkhead offered the best potential for blast tolerant behaviour. Therefore, along with the above investigation into the joint arrangements, an investigation into the stiffeners has also been undertaken. This has been partly induced by the results from the first optimisation cycle, where it was found that the stiffeners had not deformed or folded, as was hoped. This has led to
164 significantly higher stresses on the bulkhead plates, in particular at the positions of connections to the stiffeners.
On the CD under the directory ‘Initial Stiffener Modelling’ are the jpeg and mpeg files are given for the initial work on the stiffener structures. All the filenames have the prefix ‘Stiffener’ followed by a number 1 to 10; then either ‘Stiffener’ for images only of the stiffener structure or nothing for the entire test specimen. For the jpeg and mpeg files the suffix is either ‘ZDisp’ for the z-displacement, ‘VMS’ for von Mises Stress, ‘MPS’ for Maximum Principal Stress, and ‘VMSa’ for von Mises Strain. However, the jpeg filenames have a suffix of ‘eload’ for the end of the load time (6e-4 seconds), and ‘etime’ for the end of the run time (8e-4 seconds).
Figure 6.3.1 gives the ten stiffener arrangements used in this initial analysis. All of the test specimens had two bulkhead plates that were 600 mm by 600 mm and 6 mm thick. The bottom plate was simply supported along its boundaries, while the top plate had the first 6e-4 seconds of the 550 mm blast pressure history, given in Chapter 2, applied onto it. The outer faces of the two bulkhead plates were separated by 110 mm, i.e. leaving 98 mm for the stiffener to fit into.
In this stiffener investigation, the design constraints are as follows:
· Minimise the bottom plate outward displacement · Maximise the crushing length of the stiffener, i.e. decrease the length separating the two bulkhead plates · The maximum stress and strain must occur within the stiffener, compared to the stress and strain observed for the entrie test stiffener specimen
Figures 6.3.2 to 6.3.31 give the results from the analysis for this LS/DYNA finite element modelling. From these results it can be deduced that Stiffener 4 and Stiffener 8 arrangements offered the best potential. This was for two main reasons:
165
600 mm
4 mm plate stiffener, 4 mm plate stiffener, 600 mm with cross over with no cross over (a) (b) 7 mm 3.5 mm Cylinder part 44.9 mm 8 mm 10 mm 7 mm
45 mm 150 mm 300 mm 150 mm Solid shaft part
14 mm 7 mm 6 mm 7.1 mm (c) (d) 10 mm 4 mm 5 mm 80 mm 68 mm
5 mm 10 mm 40 mm 36 mm
6 mm 1 mm 3 mm 72 mm (e) (f) (g)
166
14 mm 40 mm 36 mm
(i) 4 mm thick corrugated stiffener 72 mm 80 mm
(h) (j)
Figure 6.3.1: (a) 4 mm plate stiffeners that cross over (3d corner), Stiffener 1 (b) 4 mm plate stiffeners that do not cross over, Stiffener 2 (c) Side view of a sliding mechanism stiffener, that is applied over the bulkhead plates as done in (a), Stiffener 3 (d) Cylindrical sliding mechanism joint that has the same dimensions as given in (c), while being positioned in the four positions shown, additionally the top view of the cylinder and solid shaft parts are given, Stiffener 4 (e) Stiffener 5 is the same as Stiffener 2 but with 5 mm by 1 mm notch on one-side at the top and bottom (f) Hollow 4 mm thick cylindrical stiffener with notches as shown that are positioned as Stiffener 4 on the bulkhead plate, Stiffener 6 (g) Hollow 4 mm thick box stiffener with notches and positions as for Stiffener 6, Stiffener 7 (h) 4 mm thick corrugated stiffener, with 7 semi-circles that have a radius of 7 mm that is applied over the bulkhead plate as Stiffener 2 has been applied, Stiffener 8 (i) 4 mm thick cylindrical stiffener that is positioned the same as Stiffener 6, Stiffener 9 (j) 4 mm thick box stiffener that is positioned the same as Stiffener 7, Stiffener 10.
· They had the greatest crushing length and as the crushing length is related to energy absorption it was believed that these two could be easy to tune to the design requirements
167 · These stiffener arrangements had the greatest value for stress and strain in the stiffener compared to their entire specimen. This should lead to failure initially in the stiffeners instead of the bulkhead plate(s)
Crushing length's for the varies stiffener arrangements
1.4 1.2 1 0.8 0.6 0.4 0.2 0 Crushing length (mm) 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec) Stiffener 1 crushing length Stiffener 2 crushing length Stiffener 3 crushing length Stiffener 4 crushing length Stiffener 5 crushing length Stiffener 6 crushing length Stiffener 7 crushing length Stiffener 8 crushing length Stiffener 9 crushing length Stiffener 10 crushing length
Figure 6.3.2: Crushing length for all of the stiffeners
Maximum bottom plate outward diplacement
0.0
-1.0
-2.0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 (mm) -3.0 Displacement -4.0 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.3: Maximum bottom plate outwards displacement
168
Maximum stiffener VMS
900 750 600 450
300(MPa) 150
Maximum VMS 0 7.80E-04 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 0.00E+00 Stiffener 1 Stiffener 2 StiffenerTime (sec) 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.4: Maximum stiffener VMS
Maximum stiffener MPS
800 600 400
(MPa) 200 0 Maximum MPS 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.5: Maximum stiffener MPS
169
Maximum stiffener VMSa
4.00E-02 3.00E-02 2.00E-02 1.00E-02 0.00E+00 Maximum VMSa 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.6: Maximum stiffener VMSa
Maximum Stiffener MPSa
2.50E-02 2.00E-02 1.50E-02 1.00E-02 5.00E-03 0.00E+00 Maximum MPSa 7.80E-04 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.7: Maximum stiffener MPSa
170
Maximum VMS for the entire specimen
1000 800 600 400 (MPa) 200 0 Maximum VMS 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.8: Maximum VMS for the entire specimen
Maximum MPS for the entire specimen
800 600 400
(MPa) 200 0 Maximum MPS 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.9: Maximum MPS for the entire specimen
171
Maximum VMSa for the entire specimen
4.00E-02 3.00E-02 2.00E-02
Strain 1.00E-02 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.10: Maximum VMSa for the entire specimen
Maximum MPSa for the entire specimen
2.50E-02 2.00E-02 1.50E-02 1.00E-02 Strain 5.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9 Stiffener 10
Figure 6.3.11: Maximum MPSa for the entire specimen
172 Stiffener 1 stresses
800 700 600 500 400 300 200 100 0 Stress values (MPa) 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.12: Stiffener 1 stresses
Stiffener 1 strains
1.20E-02 1.00E-02 8.00E-03 6.00E-03 4.00E-03
Strain values 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.13: Stiffener 1 strains
173 Stiffener 2 stresses
700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.14: Stiffener 2 stresses
Stiffener 2 strains
7.00E-03 6.00E-03 5.00E-03 4.00E-03 3.00E-03 Strain 2.00E-03 1.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.15: Stiffener 2 strains
174 Stiffener 3 stresses
900 800 700 600 500 400 300
Stress (MPa) 200 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.16: Stiffener 3 stresses
Stiffener 3 strains
3.50E-02 3.00E-02 2.50E-02 2.00E-02
Strain 1.50E-02 1.00E-02 5.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.17: Stiffener 3 strains 175 Stiffener 4 stresses
800 700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.18: Stiffener 4 stresses
Stiffener 4 strains
2.00E-02 1.50E-02 1.00E-02 Strain 5.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.19: Stiffener 4 strains
176 Stiffener 5 stresses
800 700 600 500 400 300 200 Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.20: Stiffener 5 stresses
Stiffener 5 strains
7.00E-03 6.00E-03 5.00E-03 4.00E-03 3.00E-03 Strain 2.00E-03 1.00E-03 0.00E+00 7.80E-04 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.21: Stiffener 5 strains
177 Stiffener 6 stresses
700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.22: Stiffener 6 stresses
Stiffener 6 strains
5.00E-03 4.00E-03 3.00E-03 2.00E-03 Strain 1.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPsa
Figure 6.3.23: Stiffener 6 strains
178
Stiffener 7 stresses
800 700 600 500 400 300
Stress (MPa) 200 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.24: Stiffener 7 stresses
Stiffener 7 strains
1.20E-02 1.00E-02 8.00E-03 6.00E-03
Strain 4.00E-03 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.25: Stiffener 7 strains
179 Stiffener 8 stresses
800 700 600 500 400 300
Stress (MPa) 200 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.26: Stiffener 8 stresses
Stiffener 8 strains
1.40E-02 1.20E-02 1.00E-02 8.00E-03 6.00E-03 Strain 4.00E-03 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.27: Stiffener 8 strains
180 Stiffener 9 stresses
700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.28: Stiffener 9 stresses
Stiffener 9 strains
3.00E-03 2.50E-03 2.00E-03 1.50E-03
Strain 1.00E-03 5.00E-04 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.29: Stiffener 9 strains
181 Stiffener 10 stresses
800 700 600 500 400 300 200 Sress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.30: Stiffener 10 stresses
Stiffener 10 strains
1.00E-02 9.00E-03 8.00E-03 7.00E-03 6.00E-03 5.00E-03
Strain 4.00E-03 3.00E-03 2.00E-03 1.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.31: Stiffener 10 strains
182
For completeness Table 6.3.1 gives the stiffener mass for each of these stiffener arrangements.
Table 6.3.1: Mass of the stiffener arrangements used in the initial analysis
Stiffener Mass (kg)
1 7.35 2 5.82 3 14.57 4 0.53 5 8.5 6 2.86 7 3.7 8 9.14 9 2.94 10 3.75
As stated above Stiffeners 4 and 8 show the greatest potential, but this could be related to the amount of material and type of material used in the other stiffener arrangements. These other stiffener arrangements may be able to be tuned to give as good, if not better results. As an example Stiffeners 5, 6, 7, 9, and 10 were seeking progressive dynamic buckling, but it can be assumed from the results that the thickness and strength of X-80 steel was too great for this to occur. Therefore, greater analysis of these other arrangements could be beneficial, but in the interest of developing recommendations for the optimisation cycle Stiffeners 4 and 8 are the only stiffeners for which further refinement will be carried out.
In this additional refinement ten more stiffener arrangements were going to be investigated. Unfortunately due to licensing problems and the research PC not being updated with the required software, only the first nine structural arrangements were analysed in LS/DYNA. The stiffener structural arrangements were:
· Stiffener 1, corrugated stiffener as before but with a thickness of 2 mm · Stiffener 2, corrugated stiffener as before but with a thickness of 6 mm
183 · Stiffener 3, corrugated stiffener as before but with only four semi-circles with radius of 12.25 mm and a thickness of 2 mm · Stiffener 4, corrugated stiffener as before but with only four semi-circles with radius of 12.25 mm and a thickness of 4 mm · Stiffener 5, corrugated stiffener as before but with only four semi-circles with radius of 12.25 mm and a thickness of 6 mm · Stiffener 6, is the same as Stiffener 3, but the solid shaft part had a radius of 9.1 mm, the cylindrical part had an outer radius of 10 mm and inner radius of 9 mm · Stiffener 7, is the same as Stiffener 3, but the solid shaft part had a radius of 9.6 mm, the cylindrical part had an outer radius of 10.5 mm and inner radius of 9.5 mm · Stiffener 8, is the same as Stiffener 3, but the solid shaft part had a radius of 9.1 mm, the cylindrical part had an outer radius of 9.5 mm and inner radius of 9 mm · Stiffener 9, is the same as Stiffener 3, but the solid shaft part had a radius of 9.05 mm, the cylindrical part had an outer radius of 10 mm and inner radius of 9 mm
On the CD under the directory ‘Final Stiffener Modelling’ the jpeg and mpeg files for this stiffener modelling analysis is given. All the filenames have the prefix ‘Stiffener’ followed by a number 1 to 9; then either ‘Stiffener’ for images only of the stiffener structure or nothing for the entire test specimen. For the jpeg and mpeg files the suffix is then either ‘ZDisp’ for the z-displacement, ‘VMS’ for von Mises Stress, ‘MPS’ for Maximum Principal Stress, and ‘VMSa’ for von Mises Strain. However, the jpeg filenames then have a suffix of ‘eload’ for end of the load time (6e-4 seconds), and ‘etime’ for the end of the run time (8e-4 seconds).
Figures 6.3.32 to 6.3.59 give the curves for the crushing length, maximum bottom plate displacement, the stress, and strain. From these results it can be noted that Stiffener 3 offers the best potential, its crushing length and maximum outward displacement, which is less than the maximum outward displacement observed for the previous set Stiffener 1.
184 Crushing length of the stiffeners
7.5 6 4.5 3 1.5 0 Crushing length (mm) 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.32: Crushing length of the stiffeners
Maximum outward displacement of the bottom plate
4 3 2
(mm) 1 0 Displacement 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.33: Maximum outward displacement of the bottom plate
185 Maximum stiffener VMS
1800 1350 900 450 VMS (MPa) 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.34: Maximum stiffener VMS
Maximum stiffener MPS
800 600 400 200
MPS (MPa) 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.35: Maximum stiffener MPS
186 Maximum stiffener VMSa
0.105 0.09 0.075 0.06 0.045
VMSa 0.03 0.015 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.36: Maximum stiffener VMSa
Maximum stiffener MPSa
0.081 0.0630.072 0.0450.054 0.0270.036 MPSa 0.018 0.0090 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.37: Maximum stiffener MPSa
187 Maximum VMS for the entire specimen
1720 1290 860 430 VMS (MPa) 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.38: Maximum VMS for the entire specimen
Maximum MPS for the entire specimen
810 720 630 540 450 360 270 180
MPS (MPa) 90 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.39: Maximum MPS for the entire specimen
188 Maxium VMSa for the entire specimen
0.105 0.09 0.075 0.06 0.045 MVSa 0.03 0.015 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.40: Maximum VMSa for the entire specimen
Maximum MPSa for the entire specimen
0.081 0.072 0.063 0.054 0.045 0.036
MPSa 0.027 0.018 0.009 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener 1 Stiffener 2 Stiffener 3 Stiffener 4 Stiffener 5 Stiffener 6 Stiffener 7 Stiffener 8 Stiffener 9
Figure 6.3.41: Maximum MPSa for the entire specimen
189 Stiffener 1 stresses
800 700 600 500 400 300 200 100 0 Stress values (MPa) 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.42: Stiffener 1 stresses
Stiffener 1 strains
1.20E-02 1.00E-02 8.00E-03 6.00E-03 4.00E-03
Strain values 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.43: Stiffener 1 strains
190 Stiffener 2 stresses
700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.44: Stiffener 2 stresses
Stiffener 2 strains
1.40E-02 1.20E-02 1.00E-02 8.00E-03 6.00E-03 Strain 4.00E-03 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.45: Stiffener 2 strains
191 Stiffener 3 stresses
700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.46: Stiffener 3 stresses
Stiffener 3 strains
1.40E-02 1.20E-02 1.00E-02 8.00E-03 6.00E-03 Strain 4.00E-03 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.47: Stiffener 3 strains
192 Stiffener 4 stresses
800 700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.48: Stiffener 4 stresses
Stiffener 4 strains
1.60E-02 1.40E-02 1.20E-02 1.00E-02 8.00E-03
Strain 6.00E-03 4.00E-03 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.49: Stiffener 4 strains
193 Stiffener 5 stresses
700 600 500 400 300 200
Stress (MPa) 100 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.50: Stiffener 5 stresses
Stiffener 5 strains
1.00E-02 8.00E-03 6.00E-03 4.00E-03 Strain 2.00E-03 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.51: Stiffener 5 strains
194 Stiffener 6 stresses
1600 1400 1200 1000 800 600 400 Stress (MPa) 200 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.52: Stiffener 6 stresses
Stiffener 6 strains
1.00E-01 8.00E-02 6.00E-02 4.00E-02 Strain 2.00E-02 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPsa
Figure 6.3.53: Stiffener 6 strains
195 Stiffener 7 stresses
1600 1400 1200 1000 800 600 400 Stress (MPa) 200 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.54: Stiffener 7 stresses
Stiffener 7 strains
1.00E-01 8.00E-02 6.00E-02 4.00E-02 Strain 2.00E-02 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.55: Stiffener 7 strains
196 Stiffener 8 stresses
1600 1400 1200 1000 800 600
Stress (MPa) 400 200 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.56: Stiffener 8 stresses
Stiffener 8 strains
9.00E-02 8.00E-02 7.00E-02 6.00E-02 5.00E-02 4.00E-02 Strain 3.00E-02 2.00E-02 1.00E-02 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.57: Stiffener 8 strains 197
Stiffener 9 stresses
2000 1500 1000 500 Stress (MPa) 0 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMS Entire VMS Stiffener MPS Entire MPS
Figure 6.3.58: Stiffener 9 stresses
Stiffener 9 strains
1.20E-01 1.00E-01 8.00E-02 6.00E-02 Strain 4.00E-02 2.00E-02 0.00E+00 6.00E-05 1.20E-04 1.80E-04 2.40E-04 3.00E-04 3.60E-04 4.20E-04 4.80E-04 5.40E-04 6.00E-04 6.60E-04 7.20E-04 7.80E-04 0.00E+00 Time (sec)
Stiffener VMSa Entire VMSa Stiffener MPSa Entire MPSa
Figure 6.3.59: Stiffener 9 strains
198
For the corrugated stiffener arrangements it can be noted that fewer semi-circles give better crushing performance, but the limitation of fewer semi-circles leading to larger radii can cause stiffeners to interfere with each other when crushing. An optimised corrugated stiffener for blast tolerant transverse bulkheads would probably to have fewer semi-circles and be made of aluminium, as this softer material would yield easier than X-80 steel. This would permit thicker stiffeners, so that the stiffeners could handle the static load without notable movement while still crushing when the air blast load is applied to the bulkhead.
In regards to the cylindrical sliding mechanism stiffeners (Stiffeners 6, 7, 8, and 9) they all had one stiffener that interfered with the solid shaft part and the cylindrical part. This may have only been a failing in the finite element package, LS/DYNA, where a node on one part and a face of a solid element on another part interfered with each other and caused a problem with the automatic contact surface algorithm. No matter how this occurred, it had a significant effect on the responses observed, especially the maximum stress and strain and to a lesser extent on the maximum outward displacement of the bottom plate. It is still believed that this type of stiffener arrangement offers significant advantages over the other stiffener arrangements. Not having a continuous structure connecting the two bulkhead plates means that when the stiffener tries to spring back from being crushed, as expected by Hookes Law and as observed, the discontinuity in the stiffener arrangement meant that the spring back for each part of the stiffener structure happens in both directions and the inertia force behind it is less as the top plate load is not being directly applied to the bottom plate. This effect should be beneficial in reducing the maximum outward displacement observed in the bottom plate. Unfortunately, to obtain this effect further tuning of this stiffener arrangement is required. In particular, the use of aluminium would possibly overcome some of the tuning problems, as the low yield stress would mean earlier deformation, but still permit a thicker structural arrangement so that the static loads did not cause notable movement of the bulkhead. Furthermore, the arrangement in Figure 6.3.60 may overcome the problem that was observed in this series of results.
Although the entire stiffener analysis could not be undertaken, findings from it were used in the optimisation run. In particular a corrugated stiffener arrangement was 199 implemented into the 4th optimisation cycle design. For completeness Table 6.3.2 gives the stiffener mass for all arrangements that were analysed.
~18 mm 8 mm 45 mm 53 mm
~0.5 mm ~0.5 mm ~20 mm
Figure 6.3.60: A possible improved stiffener arrangement
Table 6.3.2: Mass of the stiffener arrangements considered in this second analysis series
Stiffener Mass (kg)
1 4.61 2 13.59 3 4.61 4 9.14 5 13.59 6 0.531 7 0.585 8 0.48 9 0.527
Though these stiffeners are showing some performance improvements these results need to be further developed, which must include physical testing.
To recap this section, it should be noted that the driving issues were the attempts to attenuate the air blast load/pressure as it travelled through the stiffener structure before it reached the unloaded (bottom) plate. This is to minimise the response of this plate and thus reduce its maximum outward displacement and the possibility of the unloaded (bottom) plate rupturing. This philosophy of attenuating shock or sudden loads is not unusual and has been used for some time in the light aircraft industry, as discussed in
200 US Army (1978), Underhill and McCullough (1995), Ditter (1997), Hajela and Lee (1997), Donaldson (1999), Jaggi et al. (2000), and NASA (2000).
6.4. Conclusion
The development of improved joint and stiffener structural arrangements for blast tolerant transverse bulkhead has been covered in this chapter. Although the finite element results/analysis is interesting, an empirical investigation is required to support these findings and to build upon them. Additionally, other materials need to be considered, especially for the stiffener arrangements. Greater material properties for high strain rate situations would be beneficial in the further development of these structural components.
201
Chapter 7 Development of an optimised X-80 steel blast tolerant transverse bulkhead
Abstract: An optimisation procedure was developed for the formation of blast
tolerant transverse bulkheads. This optimisation procedure was applied to
a double skin transverse bulkhead arrangement, except for the rupture
failure criteria. Four optimisation cycles were undertaken before the
structural arrangement had altered too significantly to continue the cycles.
To finish this investigation, the previous DSTO Shot 4 and Cycle 1 of the
optimisation procedure were re-run with different air blast loads to see the
responses that occurred.
202 7.1. Introduction
An optimisation procedure was developed for the design constraints/criteria given in Chapter 2. It used surface response equations to control the cycling of the optimisation procedure that were suggested by A/Prof. Suzuki at the University of Tokyo.
This optimisation procedure was implemented on a double skin transverse bulkhead arrangement, except for the rupture failure criteria. Due to time constraints, and the introduction of additional structural modifications, the optimisation procedure was stopped at the fourth cycle.
To complete the work on transverse bulkhead responses to air blast loads, the previous DSTO Shot 4 and the optimisation procedure Cycle 1 transverse bulkhead finite element models were re-run with different air blast loads applied to them. In particular doubling of the explosive mass was compared to a tandem explosive load.
7.2. Optimisation procedure
With consideration of the design constraints given in Chapter 2, the modelling capabilities available and the material covered in previous chapters an optimisation procedure has been developed. A flow chart for this optimisation procedure is given in Figure 7.2.1. This optimisation procedure contains eight steps, which are briefly described below:
· Step 1
The plate area of the transverse bulkhead was modelled out of plate elements. The structural arrangement was optimised to the pre air blast load case, by using the shape and properties optimisation capability in MSC/NASTRAN. This has set the minimum thickness to be used throughout the optimisation procedure.
203 · Step 2
The plate area of the bulkhead was modelled out of plate elements. The structural arrangement was optimised to the air blast load case, by using the shape and properties optimisation capability in MSC/NASTRAN. This gave the structural arrangement and values for the current cycle through the optimisation procedure. The air blast load was approximated, initially by twice the average air blast load being applied and later by the surface response method outputs, given in step 8.
Step 1: Shape optimise the plate area of the transverse bulkhead for the pre air blast load case
Step 2: Shape optimise the plate area of the transverse bulkhead for the air blast load case
Step 3: Topology optimisation of the joints
Step 8: If failure occurs the pressure and Step 4: Validate the structural arrangement initial thicknesses are increased, by a for the pre air blast load case, plus obtain J- surface response method integral data sets
Step 5: Validate the structural arrangement for the air blast load case, plus obtain J- integral data sets
Step 6: Validate the structural arrangement for the post air blast load case, plus obtain J- integral data sets
Step 7 : Run the J-integral procedure to obtain the maximum predicted crack length
Optimised Blast Tolerant Transverse Bulkhead
Figure 7.2.1: The procedure for optimising the X-80 steel blast tolerant transverse bulkheads followed the solid arrows after a successfully competed step or the dashed arrow if failure occurred during this optimisation cycle
204
· Step 3
The structural forms shown in Figure 7.2.2 was used to carry out simple topology optimisation of the joints. The pressure applied was the maximum edge load from the transverse bulkhead obtained in Step 2. Specifically, on the right top third of the bulkhead in the model the maximum edge load was applied, while on the left top third of the bulkhead in the model the load on the other side from the maximum edge load was applied. The joint areas, shown in Figure 7.2.2, had separate surfaces, permitting individual properties optimisation on each of these surfaces. With consideration to the thicker surfaces obtained from this analysis the joint arrangement was developed. The joint base was a maximum length of 210 mm, which was 100 mm wider than the bulkhead arrangement, and 50 mm high. There were 5 vertical and 21 horizontal separate surface elements, along the appropriate boundaries. In the model the deck was clamped and the bulkhead part was only allowed to move +/- 10 mm in the plane of the joint.
Pj Bulkhead plate or entire structure Pj
Joints
Deck
(a) (b)
Figure 7.2.2: Initial arrangements for the topology optimisation, joint area in the thicker lined boxes
During the optimisation cycles these joint areas of interest, shown in Figure 7.2.2, were modified to permit a wider and higher joint arrangement. These developments are discussed in the next section.
205 · Step 4
The structural arrangement developed from steps 1, 2, and 3 was the finite element model out of solid elements. This was run on MSC/NASTRAN to validate the pre air blast design requirements and obtain the J-integral data sets.
· Step 5
The structural arrangement developed from Steps 1, 2, and 3 was the finite element model out of solid elements. This was run on LS/DYNA to validate the air blast design requirements and obtain the J-integral data sets.
· Step 6
The structural arrangement obtained from Step 5, i.e. the deformed transverse bulkhead due to the air blast load, had the post air blast load case applied to it and was run on MSC/NASTRAN. This validated the post air blast design requirements and obtained the J-integral data sets.
· Step 7
The J-integral procedure was run for the load step related to the pre air blast load cases, the air blast load case (~250,000 load steps) and for the post air blast load case single load step. If failure occurred in this step, i.e. rupture was predicted, or if Step 4, 5, and 6 failed then the optimisation procedure would go to Step 8. Additionally, if the transverse bulkhead structural arrangement over matched the design requirements, the optimisation procedure would go to Step 8. Otherwise if the above was satisfied, it was deduced that an optimised blast tolerant transverse bulkhead had been evolved.
· Step 8
This step controlled the cycling process of the optimisation procedure. For the initial cycles of the optimisation procedure, the structural variables and the pressure applied
206 used in Step 2 were changed manually. The initial cycles and this manual implication of these variables were continued until enough cycles had been completed to solve the surface response equation. Throughout these initial cycles the structural variables and pressure value were changed, in response to the cycle responses, so to approximate the design constraint required responses. In other words, if there was failure in Step 4, 5, 6, and/or 7 then the structural variables and pressure value were increased, while if overmatching these variables were decreased.
The surface response method, from Haftka and Gûrdal (1992), was used to obtain the new (minimal) values for these variables. In particular, the minimum thickness and the pressure applied in Step 2; additionally the pressure applied in the topology optimisation in Step 3 of the optimisation procedure was obtained from the use of surface response equations.
If in the same cycle of the optimisation procedure the same variable was obtained from more than one surface response equation, then each output was considered as the minimal value and the larger of the two was used.
Simple relationships were developed with consideration to appropriate proportionalities and the use of approximate and actual input data. An example of an approximate input was the pressure applied in Step 2, while an example of actual input was the finite element model results obtained for the maximum deformation in Step 5. The surface response equation for deformation of the transverse bulkhead to the air-blast load was
s rt j otb q =+++ deformation (7.2.1.) Pa
where s, r, o and q are constants, Pa is the pressure applied in Step 2, t j was the thickness of the joint between the bulkhead and deck, tb was the thickness of the bulkhead plate, and deformation was maximum deformation that the transverse bulkhead underwent. For the rupture there are three surface response equations. For the joint between the bulkhead and the deck the following was used
207 x y z m =+++ cl (7.2.2.) t j tb Pj
where x, y, z and m are constants, Pj was the pressure used in Step 3 of the optimisation procedure, and cl was the crack length. Between the bulkhead and the stiffeners the following equation was used
h i j k =+++ cl (7.2.3.) ts tb Pa
where h, i, j and k are constants, and ts was the stiffener thickness. For the plate material the surface response equation was
u w l =++ cl (7.2.4.) t p Pa
where u, w and l are constants and t p is the thickness of the plate. Of course these equations would change if additional structural variables where introduced. For example in the current optimisation run on the double skin transverse bulkhead structural arrangement Equation (7.2.1.) becomes
c1 c d c tb c ts c te c65432 =+++++ deformation, (7.2.5.) Pa
where c1, c2, c3, c4, c5,and c6 are constants, d is the separation distance between the two external faces of the double skin bulkhead arrangement, and te is the thickness of the edge structure, which is displayed in Figure 7.2.3.
7.3. Optimisation cycles
As mentioned in Chapter 6, the rupture prediction methods were unavailable for utilisation within this research. Therefore, in the optimisation cycles that were undertaken the above optimisation procedure was modified to where Step 7 was only the comparison of the maximum deformation/deflection obtain from Steps 4, 5, and 6 to 208 the design constraints and if failure occurred then the optimisation procedure went to Step 8. Even though a significant reduction in hard drive space requirement occurred, and the analysis was done with only the top right–hand quarter of the transverse bulkhead (due to two way symmetry), each optimisation cycle still used over 600 MB of hard drive space.
Bulkhead height, 2400 mm All structural thickness variables range between 4 mm and 20 mm Plate separation, d, between 40 mm and 110 mm
Bulkhead width, 2400 mm
Figure 7.2.3: The double skin bulkhead arrangement under investigation.
On the CD under the directory ‘Optimisation Cycles’ the jpeg files for the optimisation cycles results are given. Jpeg files are given for the results from Step 4, 5, and 6. All the filenames have the prefix ‘Cycle’ followed by a number 1 to 4, followed by ‘Step4’ for Step 4 results, ‘Step 5’ for Step 5 results, and ‘Step6’ for Step 6 results. For the jpeg files the suffix is either ‘OPD’ for the out-of-plane displacement, ‘VMS’ for Von Mises Stress, ‘MPS’ for Maximum Principal Stress, ‘VMSa’ for Von Mises Strain, and ‘MPSa’ Maximum Principal Strain. Only Step 5 images have the strain suffix.
The following covers the results and projection of the optimisation procedure:
· Cycle 1
Cycle 1 is the only cycle in which Step 1 was undertaken. In this optimisation of the transverse bulkhead the side load was 3.92 MPa, top load was 0.947 MPa, and the surface load (hydro-static) was 90 kPa. The initial plate separation, d , was 95 mm and all plate thicknesses were 6 mm. The outcome of this optimisation step was:
Separation distance = 95.2 mm
209 Bulkhead plate thickness, tb = 5.5 mm
Stiffener thickness, ts = 4.0 mm
Edge thickness, te = 5.2 mm
In Step 2 the approximate air blast load was two times the average load over the entire load history, which came out as 1.664 MPa. Using the results from Step 1 as the minimal values, a plate element finite element model was made and run through the shape optimisation algorithm in MSC/NASTRTAN. The initial plate separation distance was 109.5 mm, bulkhead plate thickness was 8 mm, stiffener thickness was 6 mm, and edge thickness was 7 mm. The outcomes from this optimisation step were:
Separation distance = 104.2 mm
Bulkhead plate thickness, tb = 5.5 mm
Stiffener thickness, ts = 4.0 mm
Edge thickness, te = 5.2 mm Maximum edge load = 6450 MPa Load across from the maximum edge load = 1380 MPa
Figure 7.3.1 gives the joint arrangement from the outcomes of Step 3.
10 mm
30 mm 20 mm 30 mm 20 mm
10 mm 20 mm
20 mm 20 mm
Figure 7.3.1: Resultant joint from Cycle 1 Step 3
210 In Step 4, the solid element transverse bulkhead took 3 hours to solve for the pre air blast loads. The outcome was a maximum displacement (out of the bulkhead plate plane) of 39.8 mm and a maximum stress of 664 MPa, just above the stiffeners. This constitutes a failure to the design criteria.
The LS/DYNA run for the solid element transverse bulkhead finite element model with the air blast load applied took 6 days to execute, i.e. Step 5. The outcomes of this was a maximum out of plane displacement of 94.8 mm on the unloaded bulkhead plate (in the top right corner area), while a displacement of 57.9 mm was observed at the centre (a corner in the finite element model) of the unloaded bulkhead plate and 150 mm on the loaded bulkhead plate. This was within the design constraints.
After moving the solid finite elements into the deformed pattern from Step 5 and applying the post air blast load, the situation was run though MSC/NASTRAN. The results for Cycle 1 Step 6 are a bulkhead maximum Von Mises Stress of 210 MPa and a maximum out of plane displacement of 2.98 mm.
This cycle had a significant failure in Step 4. Furthermore, as it was the first cycle, the optimisation procedure was repeated. It was noticed that the plate thickness generally needed to be increased and that the surface response equation was:
c 1 2.504.45.52.104 ccccc =+++++ 8.94 (7.3.1.) 664.1 2 3 4 65
· Cycle 2
Step 2 of Cycle 2 used the approximate air blast load of 8.740 MPa, or in other words two times the maximum peak pressure from the 550 mm blast pressure history. Using the results from the previous cycle as the minimal values, a plate element finite element model was made and run through the shape optimisation algorithm in MSC/NASTRTAN. The initial plate separation distance was 105 mm, bulkhead plate thickness was 7 mm, stiffener thickness was 6 mm, and edge thickness was 7 mm. The outcomes from this optimisation step were:
211 Separation distance = 110 mm
Bulkhead plate thickness, tb = 12.1 mm
Stiffener thickness, ts = 19.1 mm
Edge thickness, te = 5.2 mm Maximum edge load = 2520 MPa Load across from the maximum edge load = -825 MPa
Figure 7.3.2 gives the joint arrangement from the outcomes of Step 3.
10 mm
10 mm
20 mm
Figure 7.3.2: Resultant joint from Cycle 2 Step 3
In Step 4, the solid element transverse bulkhead was formed and the pre air blast loads were applied to it. The outcomes from this were a maximum displacement (out of the bulkhead plate plane) of 2.5 mm and a maximum principal stress of 331 MPa, in the joint/containment structure. For Von Mises stress the maximum was 303 MPa, and again this stress was positioned in the joint/containment structure.
The outcomes of Step 5 in Cycle 2 of the optimisation procedure, was a maximum out of plane displacement of 12.9 mm on the unloaded bulkhead plate (in the top right corner area), while a displacement of 5.89 mm was observed at the centre (a corner in the finite element model) of the unloaded bulkhead plate and –8.08 mm on the loaded bulkhead plate. All of these displacements were in the y-direction, the displacements in the x- and z-direction were less than 2 mm (maximum). The maximum Von Mises
212 stress on the loaded plate was 865 MPa, while on the unloaded plate it was 800 MPa. For the entire transverse bulkhead structure the maximum Von Mises stress was 1470 MPa. This occurred at a contact point between the joint and containment structure.
After moving the solid finite elements into the deformed pattern from Step 5 and applying the post air blast load, this situation was run through MSC/NASTRAN. The results for Cycle 2 Step 6 were a bulkhead maximum von Mises Stress of 99.4 MPa, positioned on the inside of the joint structure, while the maximum principal stress value of 90 MPa was positioned on the unloaded plate near the stiffeners. Additionally, the maximum out of plane displacement of 3.68 mm was observed on the unloaded plate near the centre of an entire transverse bulkhead structure.
This cycle was over designed as the design constraints were over matched. Additionally, it was noticed that the joint area of interest needed to be enlarged to offer better potential for the formation of blast tolerant joint arrangements. Finally, the surface response equation was:
c 1 2.51.191.12110 ccccc =+++++ 9.12 (7.3.2.) 8.79 2 3 4 65
· Cycle 3
Two significant changes to the structural arrangement were undertaken in this cycle of the optimisation procedure. First, the joint area of interest was enlarged, as shown in Figure 7.3.3. This joint size modification was applied to Step 3 with this new size. Secondly, as shown in Figure 7.3.4, the plate stiffeners arrangement was modified, so no 3dimensional corners were formed. This was done in an attempt to reduce the maximum stress that was being observed, by making the bulkhead structure more flexible.
In Step 2 the approximate air blast load was 6.5925 MPa. With consideration to the previous cycles of the optimisation procedure, a plate element finite element model was made and shape optimised for the approximate air blast load in MSC/NASTRAN. The initial plate separation distance was 100 mm, bulkhead plate thickness was 6 mm,
213 stiffener thickness was 6 mm, and edge thickness was 6 mm. The outcomes from this optimisation step were:
Separation distance = 105 mm
Bulkhead plate thickness, tb = 8.4 mm
Stiffener thickness, ts = 9.7 mm
Edge thickness, te = 9.7 mm Maximum edge load = 3630 MPa Load across from the maximum edge load = -2490 MPa
100 mm 110 mm 100 mm
50 mm
150 mm
310 mm
Figure 7.3.3: Enlarged joint area of interest
The outcomes for Step 4 was a maximum displacement (out of the bulkhead plate plane) of 5.81 mm and a maximum principal stress of 380 MPa, positioned on the inner side of the unloaded bulkhead plate near the joint and the vertical stiffener. The maximum von Mises stress was 383 MPa, which was at the same position as the maximum principal stress.
Figure 7.3.5 gives the joint arrangement from the outcome of Step 3.
214 800 mm Edge structure 30 mm
2400 mm Stiffener structure
60 mm
Figure 7.3.4: Cycle 3 stiffener arrangement
10 mm
10 mm
100 mm
20 mm 100 mm Figure 7.3.5: Resultant joint from Cycle 3 Step 3
The LS/DYNA run for the solid element transverse bulkhead finite element model with the air blast load ran for approximately 12 days before network programs caused it to stop. Due to lack of time this LS/DYNA run was not re-run. From the 12 days of processing the first 7 msec were solved. The following results are only based on these 7 msec. The outcomes were a maximum out of plane displacement of 146 mm on the unloaded bulkhead plate, while a displacement of 156 mm was observed at the centre (a corner in the finite element model) of the loaded bulkhead plate. Structural arrangement
215 changes seem to have been successful as the joint and containment structures had lower stresses than in previous cycles, while the maximum von Mises stress was 877 MPa.
After moving the solid finite elements into the deformed pattern from Step 5 and applying the post air blast load, it was executed using MSC/NASTRAN. The results for Cycle 3 Step 6 were a bulkhead maximum von Mises Stress of 289 MPa at the position where the loaded bulkhead plate joined the joint, and the maximum principal stress of 210 MPa at the bulkhead edge structure and in relation to the stiffeners. The maximum out of plane displacement of 6.13 mm occurred at the centre of the bulkhead.
Cycle 3 failed in the maximum displacement out of the plane. Even though Step 5 did not go for the entire 50 msec, it was appropriate to assume that the results obtained from Step 5 would be as bad if LS/DYNA had completed its run. Additionally, it was observed that a discontinuity had been introduced to the transverse bulkhead due to the stiffener arrangement modification. This was expected and had no significant disadvantages, but the stiffeners were still not folding or crushing to the level that was being sought. The surface response equation was:
c 1 7.97.94.8105 ccccc =+++++ 146 (7.3.3.) 5925.6 2 3 4 65
· Cycle 4
Due to the results obtained from the Joint and Stiffener component investigation, the transverse bulkhead structural arrangement was refined. The joint arrangement, which was used, is given in Figure 7.3.6. Furthermore, the stiffener and edge structures used the arrangement given in Figure 7.3.7, and positioned as in Figure 7.3.4.
In Step 2 the approximate air blast load was 4.992 MPa. Bulkhead plate separation was set to 110 mm. The initial plate, stiffener and edge thickness were set to 6 mm. The shape optimisation run on MSC/NASTRAN gave the following outcomes:
Bulkhead plate thickness, tb = 8.71 mm
Stiffener thickness, ts = 8.5 mm 216 Edge thickness, te = 8.77 mm
50 mm 6 mm Thickness
100 mm
50 mm 100 mm
Figure 7.3.6: Curve joint arrangement from the Joint investigation
14 mm 98 mm 6 mm Thickness Bulkhead plates
Figure 7.3.7: Corrugated stiffener (plus edge) structure, with seven corrugations with a radius of 7 mm
No stress values were recorded as Step 3 had been replaced by the results from the Joint investigation.
In Step 4, a surface load of 90 kPa was applied over the loaded bulkhead plate, plus a side load of 3.726 MPa and a top load of 0.9 MPa. The outcome of this was a maximum displacement (out of the bulkhead plate plane) of 15 mm and the maximum principal stress was 1000 MPa, at the end of the stiffener near the edge structure. Furthermore, 217 the maximum von Mises stress was 1070 MPa at the same position. Outside of this hot spot the maximum stresses were, maximum principal stress 570 MPa, and von Mises stress 500 MPa. This constitutes a failure to the design criteria.
The LS/DYNA run for the solid element transverse bulkhead finite element model with the air blast load applied had a run failure during its execution. Therefore the results are for 43 msec and not 50 msec. The outcome was a maximum out of plane displacement of 57.8 mm at the centre (a corner in the finite element model) of the unloaded bulkhead plate and 88 mm on the loaded bulkhead plate. The maximum stresses for the entire finite element model were, a maximum principal stress of 4710 MPa and a von Mises stress of 4640 MPa. Both of these occurred on the containment structure. For the bulkhead itself, its maximum stresses were, a maximum principal stress of 2720 MPa and a von Mises stress of 2930 MPa. Both of these occurred at the 3dimensional corner formed by the joint and the containment structure.
After moving the solid finite elements into the deformed pattern from Step 5 and applying the post air blast load, this situation was run though MSC/NASTRAN. The results for Cycle 4 Step 6 were a bulkhead maximum Von Mises Stress of 175 MPa and a maximum principal stress of 215 MPa. Computational error, due to a crushed element, led to incorrect stress values of 1740 MPa for Von Mises and 1550 MPa for maximum principal stress on a stiffener. Maximum out of plane displacement of 2.5 mm occurred for the loaded plate, while a displacement of 2.15 mm occurred on the unloaded plate.
This cycle did not meet all the design requirements, but did show some benefits in using the improved stiffener arrangements. Computational requirements again caused significant problems in obtaining and processing the results. The original surface response equation was:
c 1 77.85.871.8110 ccccc =+++++ 8.57 (7.3.4.) 992.4 2 3 4 65
A new surface response equation could be formed, where the number of semi-circles in the corrugated stiffeners, the radius of the semi-circles and the distance between the bulkhead and the containment structure were factors. Nevertheless, Cycle 4 of the
218 optimisation procedure introduced too many structural changes for it to be compared to previous cycles. Therefore, the optimisation procedure needed to start again. Unfortunately there was no time available to do this.
Although the optimisation procedure could not be completed, it did show that:
· Double skin transverse bulkheads offered greater range of potential to meet the design requirements than single skin transverse bulkheads · The maximum plate separation will always be sought so to give an optimised solution to the design requirements · Long run times can lead to additional computer and network problems
From this work, plus the previous Joint and Stiffener investigations, it can be concluded that an optimised blast tolerant transverse bulkhead can be formed. Furthermore, this optimised blast tolerant transverse bulkhead would have the:
· Double skin arrangement, with a plate thickness of 4-6 mm for X-80 steel · A curved or up-side down U joint, with large (70 mm) contact zones between the joint and either the bulkhead plates or the deck/wall · Stiffeners that would attenuate the shock load passing though them with some form of mechanism, such as the sliding cylinder shaft stiffener · Stiffeners likely to be fabricated out of a softer material than X-80 steel, i.e. aluminium, as this would permit thicker stiffeners to deal with the operational static loads
7.4. Additional outcomes
In an attempt to see the effect of different air blast loads, the finite element model of the previous DSTO Shot 4 (used in Chapter 4) was re-run with two different air blast loads. The original air blast load was 2 kg of Comp-B at 3 m and gave a maximum displacement of 298 mm. The new air blast loads were, 4 kg of Com-B at 3 m and two 2 kg of Comp-B at 3 m. The two 2 kg of Comp-B at 3 m was formed by repeating the 2 kg Comp-B at 3 m air blast pressure history with a separation time equal to the natural
219 harmonic of the finite element model, or in this case 0.03 sec. This led to a run time for the two 2 kg Comp-B at 3 m of 80 msec. It should be noted that this was only an approximation of a tandem blast load as the second load would be higher, due to the pressure load still in existence from the first blast.
The outcome of these additional blast loads to the previous DSTO Shot 4 were, for the 4 kg of Comp-B at 3 m the maximum displacement of 333 mm or a 11.74 % increase and for the two 2 kg of Comp-B at 3 m the maximum displacement was 298 mm or 0 % change. This showed that a larger air blast load is much more effective than a tandem air blast load.
Similarly, Cycle 1 transverse bulkhead had the 2 kg of Comp-B at 3 m and the 4 kg of Comp-B at 3 m applied to it. The results of this analysis are, for 2 kg of Comp-B at 3 m:
· For the loaded plate, a maximum displacement of 30.4 mm · For the unloaded plate, a maximum displacement of 18.7 mm and for 4 kg of Comp-B at 3 m:
· For the loaded plate, a maximum displacement of 80.2 mm · For the unloaded plate, a maximum displacement of 52.7 mm
Table 7.4.1 gives these maximum displacements, plus the values for 7 kg of Comp-B at 3 m, and the percentage of increase in the maximum displacement between these air blast events. The efficiency of larger air blast loads are clearly notable, by comparing the percentage of increase in the maximum displacement between the 7 kg, 4 kg and 2 kg explosive masses shows that the maximum displacement are more than doubled for less than a doubling in the explosive mass. It can be noted, that the increase in percentage of the maximum displacement is more effective at the lower explosive mass, 2 kg, than at the higher explosive masses. Additionally, higher explosive masses are more effective at producing displacement in the unloaded plate.
220 It can be surmised from this work that in future design criteria for blast tolerant structures, the potential highest air blast load is the critical load, generally overriding other multi-load event situations.
Table 7.4.1: The maximum displacements for Cycle 1 for different air blast loads
Maximum displacement (mm) Percentage of increase in the maximum displacement (%) 2 kg blast 4 kg blast 7 kg blast 4 kg compared 7 kg compared 7 kg compared load load load to the 2 kg to the 2 kg to the 4 kg Cycle 1 Loaded plate 30.4 80.2 150 163.8 393.4 87.0 Unloaded plate 18.7 52.7 94.8 181.8 407.0 79.9
An optimised blast tolerant transverse bulkhead needs a strong durable material, like X- 80 steel, to be used in its joint and bulkhead plates. This is so a high tolerance to rupture is possible, and so that significant displacement can occur without failure. Furthermore, a high yield stress has the benefit of maintaining elastic responses within the bulkhead plate and the joints during the air blast load event as long as possible. The joint structural arrangement needs to be such that the stress waves are dispersed and attenuated, and that the reflections of the stress waves do not act in such a way to induce failure within the welds. Therefore, large contact areas fixing the joint to the bulkhead or the deck/wall are needed, while the joints themselves needs to have a flexible structure that does not end up having its top pointing in the direction of the air blast propagation, and preferably will spring back after the air blast load has finished. Double skin transverse bulkheads have the benefit that the loaded plate can deform more and even rupture, while the unloaded bulkhead plate can still meet the design constraints. Therefore double skin transverse bulkheads have an advantage over single skin transverse bulkheads in the development of blast tolerant transverse bulkheads. The stiffener arrangement used between the two bulkhead plates need to be either a mechanism or able to form a mechanism so that the energy and the stress field travelling through the stiffener towards the unloaded bulkhead plate from the loaded bulkhead plate can be attenuated. This offers improved abilities to reduce the maximum displacement of the unloaded plate, the stress applied to this plate and in so doing the potential of rupture within the unloaded bulkhead plate. To be able to achieve these
221 types of responses, with consideration to the operational static loads, the stiffeners would preferably be constructed out of a softer material than X-80 steel, e.g. aluminium.
7.5. Conclusion
An optimisation procedure has been developed for the formation of optimised X-80 steel blast tolerant transverse bulkheads. This procedure has been applied to a double skin transverse arrangement, except for the rupture failure constraints. The optimisation procedure was suspended at the end of the fourth cycle due to time constraints and the introduction of improved joint and stiffener structural arrangements.
From the optimisation procedure and additional finite element models, it was determined that:
· Double skin transverse bulkheads offered a better potential for the development of blast tolerant structures · The bulkhead plate and joint structures benefit from stronger, more durable material in their fabrication, such as X-80 steel · The joint structural arrangement needs to be flexible and able to disperse the stress wave load · A softer material than X-80 steel should be used in the stiffener arrangement between the two bulkhead plates · The stiffener structures need to be formed so that they will collapse/fold/crush when the air blast load occurs, but be able to withstand the operational static/quasi-static loads
Additionally, it can be noted from the work on tandem explosive loads and doubling the explosive load that increasing the explosive mass has a greater effect on the increase in the maximum displacement than the use of tandem explosive loads.
222
Chapter 8 Conclusion
Abstract: An explanation on how this research project was initiated is briefly covered in the concluding Chapter. The chapter also includes a review of the work covered in the thesis and comments relating to possible follow on work.
223 8.1. Summary
This research effort was to be focussed on the formation of optimised X-80 steel blast tolerant transverse bulkheads. The development of this research was initiated through the Australian Maritime Engineering Cooperative Research Centre (AME CRC) and its partner organisations. The initial intention was to perform a series of explosive tests in the DSTO Bulkhead Test Rig (BTR) on proposed transverse bulkhead structural arrangements to support the finite element modelling work undertaken in this research effort. These tests were suspended due the AME CRC not being re-funded by the Australian Federal Government and budget constraints due to Australians involvement in East Timor. Due to the above constraints it was decided that the original focus was too broad. Hence the direction of the thesis changed and focus was based on the tools needed for the formation of optimised X-80 steel blast tolerant transverse bulkheads.
Looking into all the major factors that related to the formation of optimised blast tolerant transverse bulkheads led to a broad range of literature topics, e.g. from warship survivability to dynamic J-integrals. The amount of literature available on blast tolerant naval structures was limited due to the restricted nature of the material.
As a starting point for this research design criteria, based on operational requirements, were developed for naval blast tolerant transverse bulkheads. These operational requirements were developed for the worst case scenario.
For the numerical, finite element modelling, solutions to be of acceptable accuracy material constants of high strain situations were needed. These were obtained through a compression Hopkinson bar test series at DSTO. These material constants, derived using Cowper-Symonds constitutive model, were then used in all finite element models where X-80 steel experienced a rapid dynamic load applied to it. Through a series of developmental phases an appropriate modelling technique was developed to give accurate results for transverse bulkheads experiencing dynamic loads. This fulfilled the need to be able to model the blast loaded transverse bulkhead.
224 An important factor in rupture and to a lesser extent in the deformation of the transverse bulkhead is stress waves and their behaviour as they propagate throughout the transverse bulkhead. This is particularly important at welds where stress waves can reflect. This research has attempted to reduce the amount of stress waves propagating towards welds, either by moving welds away from direct propagation paths of the stress waves or having the structural arrangement so that the weld is supported by other structures in a way to directly counter the effect of the reflection and transmission of the stress waves through it. Two other factors considered are the interplay of different stress waves within the transverse bulkhead and high strain rates. The interplay of stress waves can give some guidance to when stress waves may initiate cracks and when stress waves will assist in crack growth. High strain rates to a greater extent have been dealt with by the material constants and the current knowledge base available within the finite element packages used in this research.
A rupture prediction technique using the J-integral was proposed. This technique currently suffers from the lack of dynamic J-R curves for X-80 steel and that the numerical solving process for the technique is external to the finite element packages. Having the numerical solving process for the J-integral rupture prediction external to the finite element packages has two disadvantages. The crack growth was not considered during the finite element run and the data storage needed. This J-integral rupture prediction process was evaluated in a 4th year project, which ended up looking at static load cases and shear failure. Not surprisingly the outcome of the comparison of the empirical results to the numerical results was poor. Additionally, a strain for failure process, which considered different strain rates, was proposed. Although this technique had the benefit of simplicity, it lacked the ability of determining crack growth.
A further rupture technique can be formulated, where a J-integral procedure is used over the entire structure initially looking for crack growth initiation. Following this crack growth initiation, a localised Crack Tip Opening Displacement (CTOD) procedure was used to determine the continuing crack growth. This methodology may have computational benefits in speed of processing the data and results, when compared to the current method.
225 The two structural components that have the greatest effect in the formation of blast tolerant transverse bulkheads are the joint and the stiffener between the two bulkhead plates. For the joint component investigation, the finite element results can not be applied directly as there is a discontinuity between the localised modelling results of only the joints and the global results for the entire transverse bulkhead. Even still it is clear that the curves and the upside down ‘U’ joint arrangements offers the greatest potential in meeting the essential joint characteristics. Specifically, the joint needs to be flexible so that the chance of rupture is reduced, but stiff so that the maximum displacement of the transverse bulkhead is reduced.
In the stiffener investigation the results obtained are comparable to the outcomes for the entire transverse bulkhead. It is clear that further tuning of the stiffener arrangements is needed to reach the full potential of these structures. From the investigation it can be determined that stiffeners designed to failure during the air blast load should be pursued. This failure could be by folding or crushing the stiffener, as is attempted in the corrugated stiffeners, or by the mechanism sliding with erosion of material at the interface surfaces, as is attempted in the cylinder shaft sliding stiffeners. In the end, the failure is used to absorb energy that is applied by the air blast load onto the loaded bulkhead plate and in doing so reduces the energy reaching the unloaded bulkhead plate. In other words, the failure of the stiffener arrangement attenuates the air blast load that reaches the unloaded bulkhead plate, and in doing so reduces the maximum displacement and the possibility of rupture in the plate.
An optimisation procedure has been proposed that meets the requirements set out in the design criteria given in Chapter 2. This optimisation procedure, minus the rupture failure criteria, was implemented on a double skin transverse bulkhead arrangement. Four cycles of the optimisation procedure were undertaken, by which time the structural arrangement had introduced significant discontinuity leading to a miss match in the surface response equation. This miss match meant that the surface response equation could not be solved using the initial cycle results and the fourth cycle results. Therefore, the development of results for the surface response equation needed to be initiated again. Due to time and computer constraints this was not possible. The structural arrangement modifications were driven by the responses observed from the transverse bulkhead when the load cases were applied to it, and additionally by the results of the 226 component investigation. Nevertheless, the responsive nature of the optimisation procedure could be seen when the approximate air blast load was modified to give a spread of surface response equations.
This research work has been published at two international conferences and one local conference. In Appendix B, the paper for the local conference Sea Australia 2000 is given. Appendix C gives the paper to the international conference Structures Under Shock and Impact loads VI (SUSI 2000). Appendix D contains the paper for the international conference Structural Failure and Plasticity (IMPLAST 2000).
As can be noted form the two international conference papers, time and computer restraints, plus the loss of the bulkhead blast test, has reduced the work that could be undertaken and finished in this research effort.
This thesis has attempted to show the main structural factors related to the formation of blast tolerant transverse bulkheads. Additionally this research has given some initial results and direction into the tools and formation of optimised blast tolerant transverse bulkheads. It is clear that for the successful development of optimised blast tolerant transverse bulkheads the following four factors need further research and development:
· Joint structural arrangement, in particular additional finite element and empirical work is needed with the ability to relate local and global results · Stiffener structural arrangement, in particular additional finite element and empirical work is needed with the ability to introduce other material and structural failure · Rupture determination and prediction methodology for all the appropriate strain rates · Formation and implementation of an optimisation procedure that includes the outcomes of the above three points and possibly the benefits of LS-OPT as mentioned in Livermore (2000)
In the light of current deployment activities, i.e. littoral warfare doctrines, the development of optimised blast tolerant transverse bulkheads is a critical activity for the
227 formation of future naval platforms. Therefore this research needs to be continued in an environment where future naval platforms are being developed and formed. As research into the development of optimised blast tolerant transverse bulkheads needs highly specialised computational and empirical equipment, the cost involved to do this project justice far surmounts the amount of money available in the present economic climate. Nevertheless, this thesis has set a precedence that future research can be based on.
228
Acknowledgements
The author would like to thank Dr. M. Chowdhury, Prof. D. Kelly, Dr. S. Cannon, Mr. R. Toman, Mr. G. Quigley, and Mr. E. Hecht for their continuing support of the author’s research program. Additionally, the author would also like to acknowledge the support and guidance from A/Prof. Suzuki at The University of Tokyo and Prof. Nurick at The University of Cape Town. Finally, this research effort would not have been possible without the Australian Maritime Engineering Cooperative Research Centre, The University of New South Wales, Defence Science and Technology Organisation, Tenix Defence Systems, Australian Maritime Technologies, BHP, and DnV.
229
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258
Appendix A Sheppard Interpolation
Abstract: A derivation of the Sheppard Interpolation that has been used in this research work is explained. Additionally, the two computer codes, written in Visual Fortran, are given.
259 A.1. Sheppard Interpolation explanation
The Sheppard Interpolation, which was obtained from Kincaid and Cheney (1996), starts with a set of points (2-dimensions or higher) and the functional values from them. For this work we have the following:
p = (y , ziii ) as the set of points of position,
f (p ) = xii as the corresponding list of deformation to the position set, where 1 £ i £ n , n is the maximum number of entries in the data set
Now select a real-value function, f , with the sole condition that:
f( ,qp ) = 0 , if and only if p = q (A.1)
As such f( , ) -= qpqp or f( , ) -= qpqp 2 . Next we assume that f is a non-negative function. Additionally, set up some cardinal function in exact analogy with the Lagrange formula in univariate approximation. From this we can obtain the following:
n vi () = Õf(), ppp j j=1 ¹ij
n v()()p = åvi p i=1 v (p) w ()p = i (A.2) i v()p
From the assumptions, set:
v (p ji ) = 0 if i ¹ j
vi (p) > 0 for all points except 1 ii +- 11 ,...,,..., pppp n
260 It follows that v(p) > 0and that wi are well defined. By the construction, w (p ) = d ijji and
n 0 w p ££ 1. Furthermore, w p = 1. Therefore, the interpolation process is: i ( ) åi=1 i ( )
n n v F = f p w = f p i (A.3) å()()ii å i v p i=1 i=1 ()
If the data sets are nonnegative, then the interpolant, F , will be nonnegative function, and if f is a constant function, then F = f . These two properties give evidence that the interpolated F inherits certain characteristics of the function being interpolated. On the other hand, if f is differentiable, then F will exhibit a flat spot at each node. This is because
wi ££ 10 and w (p ) = d ijji , so that the nodes are extreme (maximum points or minimum) points of each wi . Thus the partial derivatives of wi are zero at each node, and consequently the same is true for F .
For the situation involved with this research, the following holds;
, pp i is the finite element position data set
p j is the photometric position data set
f (pi ) is the finite element deformation data set F is the interpolated finite element deformation data set
A.2. Fortran codes
The input into this computational procedure was obtained from the bdf file from an MSC/PATRAN output. The output was from the deformed transverse bulkhead with a force vector applied to all the nodes of the inner side of the transverse bulkhead surface area. This permitted a quick and reliable way of obtaining the position vectors for all of these nodes.
Prior to using this computational procedure it was validated on continuous and discontinuous shapes. The results showed excellent ability to predict the value where significant data points
261 existed. Additionally, the problem seen in the actual utilisation of this computational procedure was not forseen in this validation and therefore not tested for specifically.
Below are the two computational codes, which are titled Make_data_model.for and Compare.for.
Make_data_model.for
! This program takes three data files from a NASTRAN input file ! and outputs a model.dat file for the comparison program. The ! two put files are Force.dat and Node.dat. It is intended that ! these files come from a LS/DYNA modelling of a transverse bulkhead ! under a blast load. This program is the first phase of the ! comparison routine to determine the accuracy of the finite ! element modelling. !************************************************************************* Program Model_maker
Implicit None
Integer I, Fl, Nl, FN(1000000), J, F1(1000000) Integer R1(1000000), GN(1000000), R2(1000000), R3(1000000) Integer R4(1000000), R5(1000000) Character*5 F(1000000), Gr(1000000) Double Precision xi(1000000), yi(1000000), zi(1000000)
!*************************************************************************** ! Force.dat and Node.dat are made from a Nastran input file, ! from MSC/Patran. !***************************************************************************
Open(unit=1, file='Force.dat', status='old') Open(unit=2, file='Node.dat', status='old') Open(unit=4, file='Model.dat', status='unknown') Open(unit=5, file='Log.dat', status='unknown')
Do 10 I=1,1000000,1 Read(1,*, end=11) F(I), F1(I), FN(I), R1(I), R2(I), R3(I), R4(I), & R5(I) Fl = Fl + 1 10 Enddo
11 Do 20 I=1,1000000,1 Read (2, *, end=21) Gr(I), GN(I), xi(I), yi(I), zi(I) Nl = Nl + 1.0 ! Print*,'GN =',GN(Nl) 20 Enddo
21 Write(5,*)'This is log file for the fortran program Model-maker.' Write(5,*)'In this log.dat the element and node numbers are give.' Write(5,*)'****************************************************'
Write(5,*)'The number of circles for the Force read is', Fl Write(5,*)'The number of circles for the Node read is', Nl
262
Write(5,*)'****************************************************'
Write(5,*)'Node numbers under consideration are.'
Do 30 I=1,Fl,1 Write(5,1000) FN(I) 1000 Format(I7) 30 Enddo
!********************************************************************************** ! Determining the position approparite nodal positional data and ! printing it to Model.dat !**********************************************************************************
Do 40 I=1,Fl,1 Do 50 J=1,Nl,1 If (FN(I).EQ.GN(J)) then Write(4,2000) xi(J), yi(J), zi(J) 2000 Format(F9.4, 5X, F9.4, 5X, F9.4) EndIf 50 Enddo 40 Enddo
Write(5,*)'******************************************************'
Write(5,*)'Program completed'
Write(5,*)'******************************************************'
Close(unit=1) Close(unit=2) Close(unit=3) Close(unit=4) Close(unit=5)
End Program
Compare.for
! This program compares the x value of two input files ! and give the average, max and min differences. ! This comparison is done by taking the x,y,z data from an input ! file called Accuate.dat. The y and z coorindates from Accurate.dat ! become the postion for evaulation of the x values. The comparison is made ! on data from Model.dat. This file has x,y,z data. The y and z coordinates ! do not much those from Accurate.dat. Therefore a Sheppard interpolation ! is used to calculate x values for Model.dat in the positions of Accurate.dat ! y and z location. !************************************************************************************ program compare
Implicit None
Integer I, Ja, Jm, J, K, M, NV(1000000), II, NNV Double Precision xa(1000000), ya(1000000), za(1000000) Double Precision ym(1000000), zm(1000000), produ, prodb Double Precision xm(1000000), xfin(1000000), zan, zbn Double Precision diff(1000000), m1, m2, m3, m4, ave, aveu
263 Double Precision prod(1000000), p1(1000000), p2, xan, vt, xbn
!************************************************************************************ ! In the D-36 blasted transverse bulkheads the Accurate.dat is from photometric ! measures, while the Model.dat is from finite element modelling results. !************************************************************************************
Open(unit=1, file='Accurate.dat', status='old') Open(unit=2, file='Model.dat', status='old') Open(unit=3, file='Results.dat', status='unknown') Open(unit=4, file='Log.dat', status='unknown')
Do 10 I=1,100000,1 Ja = Ja + 1.0 Read (1,*,end=11) xa(I),ya(I),za(I) 10 Enddo
11 Ja = Ja - 1.0
Do 20 I=1,100000,1 Jm = Jm + 1.0 Read (2,*,end=21) xm(I),ym(I),zm(I) 20 Enddo
21 Jm = Jm - 1.0
Write(3,*)'Accurate data'
Do 30 I=1,Ja,1 Write(3,120) xa(I), ya(I), za(I) 120 Format(F10.5, 10X, F10.5, 10X, F10.5) 30 Enddo
Write(3,*)'Model data'
Do 40 I=1,Jm,1 Write(3,220) xm(I), ym(I), zm(I) 220 Format(F10.5, 10X, F10.5, 10X, F10.5) 40 Enddo
!******************************************************************************* ! Sherppard Interpolation !*******************************************************************************
Do 50 J=1,Ja,1 vt = 0.0d0 II = 0 Do 60 I=1,Jm,1 p2 = 1.0d0 Do 70 K=1,Jm,1 If (I.EQ.K) then p1(K) = 1.0d0 Else p1(K) = ((ya(J)-ym(K))**2.0d0 + (za(J)-zm(K))**2.0d0) If (p1(K).GT.8100) then GOTO 75 Else II = II + 1 NV(II) = K EndIf
264 EndIf p2 = p1(K) * p2 75 Continue 70 Enddo prod(I) = p2 60 Enddo Do 80 I = 1,Jm,1 NNV = 0 Do 85 K=1,II,1 If (I.EQ.NV(K)) then NNV = 1 Endif 85 Enddo If (NNV.EQ.1) then vt = prod(I) + vt EndIf 80 Enddo zan = 0.0d0 zbn = 0.0d0 Do 90 I = 1, Jm, 1 NNV = 0 Do 95 K=1,II,1 If (I.EQ.NV(K)) then NNV = 1 Endif If (I.EQ.Jm) then NV(K) = 0 Endif 95 Enddo If (NNV.EQ.1) then zan = xm(I)*(prod(I)/vt) zbn = zan + zbn Endif 90 Enddo xfin(J) = zbn Write(4,*)'xfin =',xfin(J),'J =',J 50 Enddo
!******************************************************************************* ! Differences calculation !*******************************************************************************
Do 100 I=1,Ja,1 diff(I)=(abs(xfin(I)-xa(I))/xa(I)) * 100 100 Enddo
Write(3,*)'Computed and actual x-values for y and z postion'
Do 105 I=1,Ja,1 Write(3,150)'Interpolated x-values =', xfin(I) Write(3,150)'Actual x-value = ', xa(I) 150 Format(A, 2X, F12.3) 105 Enddo
Write(3,*)'******************************************************'
Do 110 I=1,Ja,1 aveu = aveu + diff(I) m1 = DMAX1(diff(I), m3) m2 = DMIN1(diff(I), m4)
265 m3 = m1 m4 = m2 110 Enddo
ave = aveu/Ja
Write(3,*)'Results form a Shepard Interpolation comparison of two' Write(3,*)'data sets of coordinates.' Write(3,*)'******************************************************'
Write(3,*)'The average inaccurately in percentage is'
Write(3,200) ave, '%' 200 Format(F10.2, 1X, A)
Write(3,*)'The maximum inaccurately in percentage is'
Write(3,300) m3, '%' 300 Format(F10.2, 1X, A)
Write(3,*)'The minimal inaccuractely in percentage is'
Write(3,400) m4, '%' 400 Format(F8.2, 1X, A)
Write(4,*) 'Program Completed' Close(Unit=1) Close(Unit=2) Close(Unit=3) Close(Unit=4) End Program
266
Appendix B Sea Australia 2000 paper
Abstract: A copy of the paper, ‘Benefits of using high strength thermo-mechanically controlled processed steel in future large fast ferries – Part 2: Design philosophy’, is given here. This paper was presented at the Sea Australia 2000 conference, which was held at the Convention Centre in Sydney Australia from the 1st to the 3rd of February 2000.
267 B.1. Raymond et al. (2000a)
Benefits of using high strength thermo- mechanically controlled processed steel in future large fast ferries – Part 2: Design philosophy
I. Raymond, Australian Maritime Engineering CRC - Sydney Research Core The School of Mechanical and Manufacturing Engineering The University of New South Wales, Sydney, 2052, Australia [email protected]
R. Hrovat, Australian Maritime Engineering CRC – Sydney Research Core The School of Material Science and Engineering The University of New South Wales, Sydney, 2052, Australia [email protected]
M. Chowdhury, and D. Kelly The School of Mechanical and Manufacturing Engineering The University of New South Wales, Sydney, 2052, Australia [email protected] [email protected]
ABSTRACT The potential use of X-80 steel in future large open ocean fast ferries and similar type vessels is discussed in this paper. The use of this material, over aluminium, is considered due to the likelihood of the vessel being designed to Safety Of Life At Sea (SOLAS) legislation. Additionally, the magnitude and number of large loads that such a vessel would experience compared to current fast ferries is accepted to be greater. The advantages of X-80 steel compared to aluminium are primarily greater structural fire protection, better fatigue life properties and cheaper material cost, while the disadvantages are lower corrosion resistances and additional structural weight.
Keywords: X-80 steel, fast ferries, open operation, large fast ferries.
268 1. INTRODUCTION
X-80 grade steel was initially developed in the mid-seventies for use in the pipeline industry. To this end, X-80 steel has been applied in some major pipelines around the world. The characteristics of X-80 steel are that it has a nominal yield stress of 550 MPa, an ultimate tensile strength of 720 MPa and only requires low alloy additives. The strength of the steel is obtained through a thermo-mechanical rolling process, instead of quenching or the addition of large quantities of alloys. The low alloy nature of X-80 steel means it is easier to weld compared to equivalent strength quenched and tempered high strength steels. Using the thermo-mechanical rolling process as opposed to the copper precipitation method, used in the High Strength Low Alloy (HSLA) series of steels, also makes the steel cheaper to produce. Much of the developmental work and future direction of X-grade steels, produced by BHP, is canvassed in [1].
Preliminary investigations into the potential for X-80 steel to be used in maritime structures look promising. The interests in using X-80 steel in future naval platforms and on-going research projects have been noted in [2,3]. Additionally, the use of X-80 steel in maritime structures is the subject of two postgraduate research programs at The University of New South Wales (UNSW).
This paper considers the use of X-80 steel in future large open ocean fast ferries. Designs of fast ferries into larger open ocean vessels have been developing over the past several years. The vessels developed for these types of operational scenarios will be expected to handle greater magnitudes and frequencies of these larger loads compared to what current fast ferries experience. Naval and commercial freighter operators will also require greater operational reliability than that currently required by fast ferry operators, who can divert passengers to other transport modes when the need arises. Hence, these vessels may need to be fabricated from a more durable material than aluminium, while still having thin scantlings for weight reduction and the ability to operate under these more stressful sea conditions.
2. HSLA-80 EXPERIENCE
The replacement of aluminium by a high strength steel is not a new idea. Ingalls Shipbuilding, with support from David Taylor Naval Ship Research and Development Centre, investigated the possibility of replacing the aluminium superstructure on naval combatant vessels with HSLA-80 steel [4]. This report concluded that it is possible to develop an HSLA-80 steel superstructure that would fulfil all the operational requirements that an aluminium superstructure already fulfils, but with minimum impact on weight and cost of the overall structure. Furthermore, with the use of steel over aluminium the fire resistance of the structure would be improved. A note of caution was given in relation to corrosion, in that with thicknesses reduced due to the use of HSLA-80 steel, the effects of corrosion would be likely to be more significant than in the current situation. X-80 steel shares similar material characteristics to HSLA- 80, and therefore would be expected to be able to form such a structural arrangement. The advantage with X-80 steel is that it would be cheaper [5].
269 3. INCREASING FAST FERRY OPERATIONS
In recent years the development of the fast ferry industry has headed into new fields and operational environments. The maximum size of fast ferries has increased leading to greater levels of global loads on the structure of vessels. With fast ferries going beyond 130 m in length and entering into more regular open ocean operations the consideration of global loads on structures will become more pronounced.
One of the first investigations into operating a high-speed freighter service was the 40 knot wave piercer freighter, which was based around an enlarged Incat Designs wave piercer [6,7]. Though this venture was unsuccessful, the justification for such a service, based on the just-in-time manufacturing requirements and other time-sensitive cargo, is more valid today than ever before as there are many potential routes around the world for such a service.
Noting these potential routes, the MARITECH program in the USA developed three conceptual fast transoceanic vessels [8]. These vessels were developed for the North East USA to Europe trade route, but consideration was also given to other more local trade routes. The materials of choice for these vessels were mild steel and moderate high tensile steel.
More recently the Australian Maritime Engineering Cooperative Research Centre (AME CRC), under Task C9, with support from UNSW has been investigating the possibility of a Bass Straight Fast Ferry (BSFF) [9]. The preliminary results look promising, especially for the enlarged monohull design which along with transporting passengers and their vehicles, can also handle freight. Due to the practical operational requirements, i.e. to maintain regular schedules all-year round, it is seen that this vessel is likely to be designed to SOLAS legislation.
A 60 m long, 80 passenger vessel is currently being built in Australia for Rivages Saint Martin to SOLAS legislation. This vessel is to seek exemptions from the SOLAS legislation in accordance with the High Speed Craft (HSC) code, as it will be operating in the waters off New Caledonia as a cruise vessel and will contain passenger accommodation. The effect of following SOLAS legislation was to increase the lightship weight by approximately 1%. This was due to the following · Extra anchor · Heavier anchors · Thicker glass on the windows · Heavier fire fighting sprinkler system · Fire fighting sprinkler system full of water · Double bottom forward of the engine room · Additional structural fire protection
The expansion of fast ferry concepts has not been restricted to the commercial world. In the late-eighties Ingalls Shipbuilding proposed a conceptual design for a surface effect fast sealift ship that could transport 270 5,000 short tons of payload to Europe from the USA at an average speed of 55 knots [10]. This vessel was to be fabricated out of HSLA-80 steel. In Australia, papers such as [11, 12] have pushed the case for the introduction of capabilities found in fast ferries into the Royal Australian Navy (RAN). When a potential deficiency was seen in the RAN’s capabilities, a fast ferry was considered and chosen to fulfil this gap. This led to the commissioning of HMAS Jervis Bay (shown in figure 1), an Incat 86 m long wave- piercing catamaran as a troop transporter [13].
Figure 1. HMAS Jervis Bay [14]
4. SOLAS VS HSC LEGISLATION
The HSC code was written to specific operational characteristics, that fulfil the operational requirements of the fast ferry market. This led to the conditions that an HSC vessel is never more than 4 hours from a safe harbour at operational speed while fully laden and that a shore-based rescue could be completed within 4 hours. Operations of fast ferries are generally restricted to wave heights below 4 m due to the launching of life rafts [15].
An open ocean fast ferry or other large open ocean fast commercial vessel can not afford to stop operations due to a wave height exceeding the 4m limit. Additionally, these types of vessels could not assume that support and rescue could be provided by shore based facilities. Therefore, it is assumed that such a vessel would be designed to the SOLAS code over the HSC code. Exemption, as done with the Rivages Saint Martin vessel, would be sought as per the SOLAS code on a case-by-case basis, [16,17].
5. COMPARISON OF X-80 STEEL TO ALUMINIUM
Without considering a specific vessel and operational profile, only qualitative remarks are possible in the following comparison.
5.1 Disadvantages
271 The major disadvantage of X-80 steel, when compared to aluminium, in the structure of a future large open ocean fast ferry is corrosion. To this end the following needs to be implemented · corrosion allowances in the scantling · corrosion protection paints and epoxy’s (reapplication should be done) · cathodic protection equipment
All of these lead to an increase in the weight and cost of the overall vessel when steel is used compared to aluminium. Additionally, inspections of the vessel’s structure are scheduled around the corrosion risk, which carries a cost to have undertaken. Subsequent to these inspections, repair or replacement of corroded structures may be required. The management of corrosion and fatigue in steel vessels is the subject of continuous research, which has led to repair and structural life prediction models [18].
The other major disadvantage of using steel is that the structure generally weighs more than an equivalent aluminium structure, due to the fact that the density of steel is approximately three times that of aluminium. This means for elastic analysis, where the analysis is geometry dependent, aluminium structures have a lower weight compared to an equivalent steel structure. As with the lower density of aluminium greater sectional modulus can be formed with less of an impact on the weight than occurs with the use of steel. If the analysis is elastic-plastic, where some plastic deformation is permitted in the structure due to the operational loads, the weight of the steel structure can become more comparable to that of the aluminium structure. Even not going to the elastic-plastic extreme the issue of structural weight can nearly be resolved, as covered in [4].
5.2 Advantages
The fracture performances of X-80 steel would be expected to be superior to that of aluminium. Fatigue and fracture related responses of naval aluminium structures are discussed in [19], while [20] shows some of the initial fracture data on X-80 steel. This initial data suggests that X-80 steel exhibits a strong fracture toughness. Additionally, X-80 steel and its weldments have much greater durability compared to equivalent aluminium structures. With X-80 steel having a stronger fracture toughness and being more durable than aluminium, its fatigue performance should also be better. This relates directly to the fatigue life and fatigue loads that X-80 steel structural components could handle. An important factor in the operations of a large open ocean fast ferry, as it will encounter greater load sizes in increasing numbers through its service life.
The fracture toughness directly affects the redundancy of the structure. Cracks can form from the original welding, fatigue or sudden large loads such as a blast load from a weapon. Regardless of how the crack is formed, its propagation past a critical size leads to increased risk in operating the vessel and a requirement for its repair. The superior fracture toughness of the X-80 steel would permit increased periods between consecutive inspections and in return would reduce the cost of crack maintenance.
272 Additionally, through the use of X-80 steel the crack propagation rate would be substantially reduced provided adequate design provision had been adhered to.
The reliability and maintainability of the structure will be more viable if fabricated out of X-80 steel than from aluminium. Aluminium maintenance problems in naval structures are discussed in [19], while above suggests a methodology of reducing the inspection and maintenance cost, related to crack propagation rate, for X-80 steel structures. The cost of maintaining the vessel become increasingly important in the determination of the reliability and through life cost of the vessel, especially the longer the operational life of the vessel becomes.
Another area where X-80 steel could improve the integrity of the vessel for the passengers, cargo and crew is in fire protection, i.e. heat transfer and fire containment between consecutive compartments. The fire resistance of X-80 steel is greater than aluminium. This is due to the fact that X-80 steel has a higher melting point and lower conductivity of heat compared to aluminium, a fact common to all steels and aluminium. Hence, greater fire protection insulation is needed on aluminium structures compared to steel structures to meet the International Maritime Organisation (IMO) SOLAS requirements [16, 17]. This increase in usage of fire protection insulation removes some of the weight saving gained by using aluminium in the fabrication of a fast ferry.
As shown in section 3, fast ferry concepts are beginning to enter into the realm of naval vessels. From previous experiences with aluminium in naval structures, its use is now being restricted [19]. This restriction is due to the facts that naval platforms · have a 30 year operational life · experience large global, shock and impact loads · are at risk of fire from weapon effects · must meet survivability requirements due to blast loads
Many of these requirements lend themselves to a highly durable, strong material with high fracture toughness.
X-80 steel can be purchased for approximately $1,100 per tonne, which compared to aluminium, is a considerable saving. Other advantages and disadvantages of using X-80 steel in the fabrication of future large fast ferries are covered in [20].
X-80 steel compared to mild steel has the advantage in that its yield stress is 550 MPa and its ultimate tensile stress 720 MPa. This permits its use in higher stress configurations in the design of the structure. Higher stress configurations would relate to thinner scantling and therefore a lighter structural arrangement compared to what can be produced using mild steel. Compared to quenched and tempered high strength steels, X-80’s lower carbon equivalences and alloying simplifies the welding procedure, such as reducing the requirement for pre-heat. The weldability of X-80 steel is comparable to current mild
273 steels. As previously stated, X-80 steels and HSLA-80 steels are very similar, but X-80 steel is cheaper to buy.
To obtain the full benefits of using X-80 steel in future maritime structures the optimisation of the structural arrangement should be based on elastic-plastic analysis where stable permanent deformation is permitted. This is the most probable method of obtaining the lightest structural arrangement while still having structural integrity. The addition of the corrosion allowance would have to follow. It is expected that the corrosion behaviour of X-80 steel will be similar to that of conventional ship building steels.
6. CONCLUSION
With fast ferry designs becoming larger and going into new operational environments the global loads on the structures of these vessels will increase. With these global loads increasing in magnitude and number of cycles an advantage can be gained, if not required, from a more durable and stronger material compared to the currently used aluminiums. X-80 steel could replace aluminium in such future vessels, as it can fulfil these needs without the need to go to more exotic aluminium alloys.
The proliferation of fast ferry concepts into naval platforms around the world is unlikely unless these vessels are made from steel due to past experience with aluminium and the risk of rapid high stress loads on the structure due to weapons effects. The second reason suggests that large naval platforms are to be fabricated out of steel.
ACKNOWLEDGEMENT
The authors are grateful for the assistance provided by Mr. T. Armstrong of Armstrong RD. Additionally, encouragement for this paper and the continuing research effort into X-80 steel has come from AME CRC, UNSW, Defence Science and Technology Organisation, Tenix Defence Systems, Dynamic Structures and BHP.
REFERENCE 1. Williams, J. G., Killmore, C. R., Barbaro, F. J., Meta, A., and Fletcher, L., “Modern Technology for ERW linepipe steel production (X60 to X80 and beyond), BHP Internal Report 2. Butler, J. J. L., (1996) “The suitability of X80 linepipe steel for naval applications”, DRA/SMC/CR9503103 3. Cannon, S., Gaylor, K., Goodwin, G., Jewsbury, P., Phillips, R., and Walsh, B., (1999), “Future Technologies for the next naval Surface Combatant”, Australian Naval Institute Journal
274 5. Hughes, R. K., (1997) “Innovative Ship Steels”, AME’97, Melbourne, Australia 6. Australian Shipbuilders Association and Australian Shipowners Association, (1995) The potential demand for an Australian high speed vessel cargo service, A joint study by the Australian Shipbuilders Association and Australian Shipowners Association, Department of Industry, Science and Tourism 7. P. C. Hercus, (1996) A 40 Knot Wave Piercer Freighter, INCAT Designs, Sydney 8. Sipilä, H., and Brown, A., (1997), “Application of the slender monohull to high speed container vessels”, FAST’97, pp. 247-253 9. Toman, R., Sahoo, P. K., Spkyer, R., and Stevelt, H., (1999), “Business and technical evaluation study of very high speed ships”, AME CRC IR 99/2, AME CRC Sydney Research Core and UNSW 10. Bowden, J. O., and Embry, G. D., (1989) “SFS – The 55 knot sealift ship”, Naval Engineers Journal, May, pp. 144-155 11. Williamson, A. G., (1997) “Implications for the Royal Australian Navy of very high speed marine vessels”, FAST’97, pp. 5-9 12. Babbage, R., Armstrong, T., Toman, R., and Blansjaar, J., (1997) “Military fast vessels for Australia”, FAST’97, pp. 11-20 13. Darby, A., (1999), “Military cat puts Dili just a day away”, The Sydney Morning Herald, April 27th, pp. World 9 14. Pawlenko, D., ABPH, (1999), Picture of HMAS Jervis Bay, http://www.navy.gov.au/cgi- bin/picturebook.exe?image=jb0006 15. Day, A. H., Doctors, L. J., and Armstrong, N. A., “Concept evaluation for large very-high-speed vessels”, FAST’97, pp. 65-75. 16. IMO, (1992) SOLAS, Consolidated Edition, The Bath Press 17. IMO, (1995) HSC Code, International code of safety for high-speed craft, Halstan and Co. Ltd. 18. Soares, C. G., and Garbatov, Y., “Reliability of corrosion protected and maintained ship hulls subjected to corrosion and fatigue”, Journal of Ship Research, June 1999, 43, 2, pp. 65-79. 19. Sielski, R. A., (1987) “The history of aluminum as a deckhouse material”, Naval Engineers Journal, May, pp. 165-172. 20. Hrovat. R., Raymond, I., and Hoffman, M., “Benefits of using high strength thermo-mechanically controlled processed steels in future large fast ferries – Part 1: material and fabrication considerations”, Sea Australia 2000
275
Appendix C Structures Under Shock and Impact paper
Abstract: A copy of the paper, ‘Optimisation procedure for X-80 steel blast tolerant transverse bulkheads’, is included here. This paper was presented at the Structures Under Shock and Impact conference, which was held at Cambridge, England in July 2000.
276 C.1. Raymond et al. (2000b)
Optimisation procedure for X-80 steel blast tolerant transverse bulkheads
I. Raymond1,2, M. Chowdhury2 & D. Kelly2 1Australian Maritime Engineering Cooperative Research Centre 2The School of Mechanical and Manufacturing Engineering The University of New South Wales (UNSW), Australia
Abstract
An optimisation procedure to be used to develop optimised X-80 steel blast tolerant transverse bulkheads is described. Three different structural arrangements have been investigated and optimised. This work has been stimulated by the increased interest in naval platform survivability over the past decade and the development of X-80 steel.
1. Introduction
This paper discusses an optimisation procedure for static and dynamic non-linear load cases that must satisfy the design criteria given in Raymond et al. [1] and Raymond et al. [2].
1.1 X-80 steel
X-80 grade steel was initially developed in the mid-seventies for use in the linepipe industry. The characteristics of X-80 steel is that it has a nominal yield stress of 550 MPa, an ultimate tensile strength of 720 MPa and low alloy additives. The strength of the steel is obtained through a thermo-mechanically controlled process. The low alloy nature of X-80 steel means its weldability is comparable to military grade mild steel. The developmental work and future direction of X-grade steels, produced by BHP, is canvassed in Williams et al. [3]. The interest in using X-80 steel in future naval platforms has been noted in Butler [4] and Cannon et al. [5].
1.2 Ship vulnerability
277 Often it is not the vulnerability of a ship that is discussed, but rather the ship’s survivability. Survivability is becoming an increasingly important issue in the design of future naval platforms. The increase in survivability requirements is important because of changing operational environments, recent incidents where the survivability of naval platforms have been questioned, reduction in defence budgets and shrinking of the crew sizes aboard ships. Furthermore, as stated in Chalmers [6], “currently little information on the design of bulkheads to withstand internal blast effects” exists. The transverse bulkheads aid survivability by restricting the spread of the blast load longitudinally throughout the vessel. Additionally, the transverse bulkheads are required to be at least a watertight boundary, if not an airtight boundary, against flooding, fire and/or other secondary damage effects in a post-explosion environment. Optimising the transverse bulkhead against the penetration of fragments is not considered in this optimisation procedure, as the weight penalty was not seen as justifiable. Generally, armour protection is used sparingly in naval platforms and is therefore not used on transverse bulkheads. Armour plating is usually only applied to surround vital components in the platform.
2. Optimisation procedure
The procedure used to produce optimised X-80 steel blast tolerant transverse bulkheads was developed with the obligation of meeting the design requirements and the design criteria set out in Raymond et al. [1] and Raymond et al. [2].
2.1 Design constraints
The design constraints on the transverse bulkhead were developed around a transverse bulkhead on deck 3, at about 20 m from the bow of a 120 m long warship, moving at 30 knots. The following three load cases with constraints must be satisfied in the optimisation procedure. The pre-air-blast load case consists of hydrostatic and structural loads. The hydrostatic load is 90 kPa, and is due to the transverse bulkhead being a wall of a tank. Structural loads are distributed edge loads that relate to equipment above the transverse bulkhead and bending loads on the hull. These two loads are, 22.5 MPa at the top and a side load of 93.15 MPa, respectively. The transverse bulkhead is not to deform permanently, but elastic deflections are allowed. No rupture is permitted, which will be tested by the J-integral test. The air-blast load case was developed around 150 kg of TNT equivalent explosion at 8 m from the transverse bulkhead. Using the Hopkinson scale method this relates to 7 kg Comp-B at 3 m in the Defence Science and Technology Organisation (DSTO) Bulkhead Test Rig (BTR). The pressure history data that is used in the modelling consists of two pressure readings at approximately 550 mm and 1150 mm radially outwards from the centre of the transverse bulkhead. The blast tolerant transverse bulkhead is developed to withstand this air-blast load in the DSTO BTR, and in doing so meets the requirements of 150 kg of TNT equivalent at 8 m in a real naval platform. The constraints are that no permanent 278 deformation greater than 100 mm is permitted, but due to the modelling inaccuracies the allowable maximum deformation is reduced to 80 mm. Rupture is not permitted and this condition is evaluated by the J-integral test. The post-air-blast load case only considers the flooding of the compartment, where the explosion occurred, and therefore a flooding load, which is taken to be 52 kPa on the concave side of the deformed transverse bulkhead. The transverse bulkhead is permitted to deflect a further 5 mm due to this load, and no rupture is permitted, which is investigated by the J-integral test.
2.2 J-integral test
The J-integral was chosen over the use of strain to failure due to the comments in Jones [7] regarding the work of Wierzicki et al. [8]. Jones [7] noted that it is incorrect to “assume that rupture occurs when the equivalent strain in a structural member reaches the rupture strain recorded in an uniaxial tensile test”, in relation to dynamic loads and/or high strain rate loads. Strain to failure is applicable for static load cases, but a single J-integral analysis introduces fewer variables to the optimisation procedure. The use of the path independent parameter to characterise material toughness is well established by work of Rice [9] and Shih et al. [10]. The J-integral characterises the material over a broader stress range that includes elastic and elastic-plastic regimes. The loads on the naval transverse bulkhead are in the elastic and elastic-plastic regimes. The path-independent J-integral is applied to the appropriate faces of the relevant finite element brick that make up the finite element model of the blast tolerant transverse bulkhead. The most likely position for a crack or tear to begin is in the weld between the bulkhead deck joint. If this tear propagates though the thickness of the weld in the bulkhead deck joint, rupture will eventuate. The maximum thickness of a tear in a double weld situation before rupture is assumed to occur is 0.375 times the thickness of the plate. This is because at this thickness the crack will only be in one of the two weld beads, which allows the other weld bead to maintain the joint. In the modelling and optimisation procedure this length is decreased to 0.75 times the length of the shortest axis of the finite element model face being used. This relates to a safety factor of 1/3, or a crack length of ¼ the thickness of the plate at the weld. The J-integral will be calculated using the single-edge crack plate in uniform tension applied to the faces of the brick elements that relate to the thickness direction of the plate (Figure 1). The J-integral is evaluated by using the following equation, from Kumer et al. [11]
2 n+1 P a a æ P ö (1) J = f1()ae + as eoo c( )h1( ,n)ç ÷ E' b b è Po ø
paF 2 where f = , e aa += fry is the adjusted crack length, P is the load per unit thickness, E' = E for 1 b2 plane stress and E for plane strain, a and n are constants obtained from the Ramberg-Osgood E' = 2 1-n material equation, s ( and) e are the flow stress and strain respectively, h is a function of and n , o o 1 a b 279 1 1 P =1.072 csh for plane stress and P = 1.455 csh for the plane strain, f = , é a 2 ù 2 a , o o o o 2 h 1+= ( ) - ( ) æ ö ê c ú c 1+ ç P ÷ ë û è P0 ø 2 én -11 ùæ K ö , a , b and c are shown in Figure 1, b = 2 for plane stress and b = 6for plane strain, r = ç I ÷ y ê úç ÷ bp ën +1ûè s o ø and K1 from Miannay [12] is
æpa ö 2tanç ÷ 3 (2) P è 2b ø é æ a ö æ æpa öö ù K1 = 1 ê0. +´ 2752 . ç ÷ 002 . ç137 -+ sinç ÷÷ ú 2 æpa ö è b ø è 2b ø tb cosç ÷ ëê è ø ûú è 2b ø where t is the depth of the brick to the face. F , obtained from Tada et al. [13], is
3 æ æpa öö 0. 2752 . ()a 002 . ç137 -++ sinç ÷÷ (3) 2b æpa ö b è è 2b øø F = tanç ÷ . pa è 2b ø æpa ö cosç ÷ è 2b ø
It has been shown that the material properties between the parent material and welded material are very similar due to the low heat input used in welding X-80 steel. It is assumed that the initial crack lengths are 0.01 mm for the parent material and 0.4 mm for the welded material. At the completion of each load step the J-integral is calculated using the above equations. This calculated J-integral value is related to a J-R curve to determine the crack extension value. This crack extension value is then used to produce the new a value, which is used for the next load step. If this new a value is greater than the critical crack length then failure has occurred and the modelling process is stopped. From the J-R curve a tearing modulus analysis will be performed to determine if the tearing is propagating stably or unstably. If the tearing is unstable then failure is assumed to have occurred and the evaluation is suspended. The tearing analysis follows the method given in Kumar et al. [11], which states
P
b
a c
P Figure 1: Single-edge cracked plate under remote uniform tension, from Kumar et al. [11].
(4) J ³ TT JR , for unstable crack growth. In Equation (4),
280
E ¶J (5) TJ = ( ) , 2 ¶a DT s o and
E dJ (6) T = R , JR 2 da s o where the subscript DT is for total displacement held fixed.
As previously mentioned the J-integral is calculated at the end of each load step. For the static load cases there is only one load step per load case, while for the dynamic non-linear load case it is more complex due to the propagation of the stress waves. Since the J-integral is calculated at the end of each load step from the nodal stress values, then the load steps must be dependent on time for a stress wave to pass the two closest consecutive nodes in the finite element model. The time for a stress wave to cross the smallest consecutive nodal distance in the modelling procedure being used is 2.5E-7 sec.
2.3 Working of the optimisation procedure
The optimisation procedure is illustrated in Figure 2, where the solid lines are followed at the successful completion of a stage and the dashed lines are followed if failure occurs. MSC/Nastran is used for shape and properties optimisation, as well as verifying that the static load cases meet the design requirements. LS/Dyna is used to verify the dynamic non-linear load case. Programs developed by the first author in visual Fortran conduct the J-integral test. The size of the transverse bulkhead used in the optimisation procedure is set by the size of the DSTO BTR, which is 2400 mm by 2400mm.
If failure occurs due to deformation then pressure applied in stage two of this optimisation procedure will be increased to two times the peak pressure, 8.79 MPa. If failure is repeated then the pressure is increased to four times the peak pressure, i.e. 17.58 MPa. If the failure is due to rupture, i.e. the J-integral test fails, then the thickness of the joint or the plate material will be increased from 6 mm to 8mm and then to 9.5 mm. BHP X-80 steel is currently only available in 4 mm to 9.5 mm thick sections. If failure continues after these adjustments a surface response method, from Haftka et al. [14], will be used to obtain the new values for material thickness (minimal thickness in the optimisation runs on MSC/Nastran), the pressure applied in stage two and the pressure applied in the topology optimisation in stage three of the optimisation procedure. If in the same cycle of the optimisation procedure the same variable is obtained from more than one surface response equation, then each output is considered as the minimal value and the larger of the two is then used.
281 Optimise for the pre-air-blast loads using MSC/NASTRAN. Model to consider plate elements, simply supported and only the plate area of the bulkhead.
Optimise for the air-blast load in MSC/NASTRAN. The average value of the blast pressure will be multiplied by 2, and applied to the model. The model will be of the plate area of the bulkhead and made up of plate elements. Simply supported boundary conditions will be used. The factor 2 will be changed if needed and the factor may be applied to the peak pressure value instead of the average.
Topology optimisation of the joints, using a 2D- plate model, where thickness changes are used to Increase the scaling factor deduce the topology changes. Carried out in of the air-blast pressure MSC/NASTRAN using the maximum load load, the thickness and size obtained for the joint boundary above. of the joints and apply the scaling factor applied to the
Half model of the bulkhead with the containment peak pressure. These structure and clamped boundary conditions out of increases are to be governed solid elements, to the dimensions obtain from the by the response surface method. optimisation outputs. Apply the pre-air-blast load to verify if it meets this criterion, additionally; output text data files at the completion of each load case for the J-integral procedure. Run in MSC/NASTRAN.
Use the model from the pre-air-blast verification, and apply the air-blast load and run it on LS/DYNA. This is to verify that it meets the air-blast criterion and to obtain the text data files for the J-integral procedure.
Use the finite element model obtained post the air-blast LS/DYNA run and run it on MSC/NASTRAN with the post-air-blast loads. This is to verify if it meets the post-air-blast criterion and to obtain the text data files for the J-integral procedure.
With about 250,000 text data files the J-integral program (test) will solve the J- integral to determine if rupture has occurred or not, over the entire event.
Optimised Blast Tolerant Transverse Bulkhead
Figure 2: The procedure for optimising the X-80 steel blast tolerant transverse bulkheads
Simple relationships were developed with consideration to appropriate proportionalities and the use of approximate and actual input data. An example of an approximate input is the pressure applied in stage two, while an example of actual input is the finite element model obtained results for maximum deformation. The surface response equation for deformation of the transverse bulkhead to the air-blast load is
s (7) rt j otb q =+++ deformation Pa
282 where s, r, o and q are constant, is the pressure applied in stage two, is the thickness of the joint Pa t j between the bulkhead and deck, is the thickness of the bulkhead plate, and deformation is maximum tb deformation that the transverse bulkhead undergoes. For the rupture there are three surface response equations. For the joint between the bulkhead and the deck the following is used
x y z m =+++ cl (8) t j tb Pj where x, y, z and m are constants, is the pressure used in stage three of the optimisation procedure, and Pj cl is the crack length. Between the bulkhead and the stiffeners the following equation is used
h i j k =+++ cl (9) ts tb Pa where h, i, j and k are constants, and is the stiffener thickness. For the plate material the surface ts response equation is
u w l =++ cl (10) t p Pa where u, w and l are constants and is the thickness of the plate. t p
3. Structural arrangements
The structural arrangements were chosen based on current experience at DSTO, industry and information from the literature. Furthermore, each side of the blast tolerant transverse bulkhead must have the same stiffness and strength. The thickness of all components of the transverse bulkhead can range between 4.0 mm and 9.5 mm.
3.1 Single skin transverse bulkhead arrangement
In line with the current work being done at DSTO, a single skin bulkhead arrangement will be investigated (Figure 3). With regard to the decision to have uniform stiffness and strength on each side of the transverse bulkhead plate, stiffeners are placed on both sides of the transverse bulkhead plate. There are five stiffeners on each side at a spacing of 400 mm. The stiffeners are angle bar stiffeners with a maximum web height of 80 mm and flange width of 50 mm.
3.2 Corrugated transverse bulkhead arrangement
283 From industry interest a corrugated, or wedged, bulkhead structural arrangement will be investigated (Figure 4). The corrugated bulkhead has three straps on each side to help reduce the deformation that occurs. The corrugated bulkhead has six complete corrugations in the transverse bulkhead. Through the optimisation procedure the depth of the corrugated bulkhead has a maximum set at 160 mm. The length of the parallel surface is restricted to 200 mm. The angle for the sloped surfaces will be 600 to the parallel surface. The strap width can vary between 100 mm to 200 mm.
3.3 Double-skin transverse bulkhead arrangement
(a) (b)
Figure 3: (a) Oblique and (b) top views of the single skin blast tolerant transverse bulkhead arrangement.
(a)
Slope surfaces
straps Parallel surfaces
(b)
Figure 4: (a) Top and (b) front view of the corrugated blast tolerant transverse bulkhead structural arrangement.
(b)
(a)
Figure 5: (a) Front and (b) top view of the double-skin blast tolerant transverse bulkhead structural arrangement.
From comments in Chalmers [6] and others, a double-skin transverse bulkhead structural arrangement is investigated (Figure 5). This is because the two plates and space between them increase the possibility of 284 meeting the design criteria, i.e. maximum deformation is measured from the plate, which the air-blast load is not applied to. Four girders, two vertical and two horizontal, separate the plates. This arrangement of girders was chosen because no connecting structure would be at the centre of the transverse bulkhead. In the optimisation procedure the depth of the double-skin transverse bulkhead structural arrangement is permitted to go up to 160 mm.
4. Conclusion
Currently the components of the optimisation procedure are undergoing confirmation against empirical data where possible, or tests that have been developed. Following the confirmation of the optimisation procedure, the three structural arrangements will be optimised. The latest results available at the time of the conference will be presented.
Acknowledgements
The authors would like to thank Australian Maritime Engineering Cooperative Research Centre, UNSW, DSTO, Australian Maritime Technology, Dynamic Structures, Det Norske Veritas, Lloyd’s Register of Shipping, Tenix, BHP, and the Department of Defence (Aust.) for their continuing support of this research. Furthermore, special thanks goes to A/Prof. K. Suzuki of The University of Tokyo for suggestions with regards to the surface response method and Miss K. Deeley of UNSW/Anglo-Australian Observatory.
References
[1] Raymond, I., Chowdhury, M., and Kelly, D., Design criteria for blast tolerant bulkheads, Proc. of the IMPLAST 2000, (in-prep), Australia, 2000 [2] Raymond, I., Chowdhury, M., and Kelly, D., Design criteria for X-80 steel naval blast tolerant bulkhead report, AME CRC internal report, 1999 [3] Williams, J. G., Killmore, C. R., Barbaro, F. J., Meta, A., and Fletcher, L., Modern Technology for ERW linepipe steel production (X60 to X80 and beyond), BHP Internal Report, 1996 [4] Butler, J. J. L., The suitability of X80 linepipe steel for naval applications, DRA/SMC/CR9503103, 1996 [5] Cannon, S., Gaylor, K., Goodwin, G., Jewsbury, P., Phillips, R., and Walsh, B., Future Technologies for the next naval surface combatant, Australian Naval Institute Journal, (in-prep), 1999 [6] Chalmers, D. W., Design of ship’s structures, HMSO, 1993 [7] Jones, N., Recent studies on the response of structures subjected to large impact loads, Ship Structures Symposium ’93, pp. C-1 – C-22, 1993 [8] T. Wierzicki and N. Jones (eds.), Structural Failure, John Wiley and Sons, pp. 161-192 (Duffey, T. A., Dynamic rupture of shells), 1989
285 [9] Rice, J. R. A., Path independent integral and the approximate analysis of strain concentrations by notches and cracks, Journal of Applied Mechanics, pp. 379-386, June 1968 [10] Shih, C. F., and Hutchison, J. W., Fully plastic solutions and large scale yielding estimates for plane stress crack problems, Journal of Engineering Materials and Technology, pp. 289-295, October 1976. [11] Kumar, V., German, M. D., Shih, C. F., An engineering approach for elastic-plastic fracture analysis, General Electric and EPRI, NP-1931, 1981 [12] Miannay, D. P., Fracture mechanics, Mechanical engineering series, Springer, 1998 [13] Tada, H., Paris, P. C., and Irwin, G. R., The stress analysis of cracks handbook, Del Research Corporation, Hellertown, Pennsylvania, 1973. [14] Haftka, R. T. and Gürdal, Z., Solid mechanics and its applications – Elements of structural optimisation, Kluwer Academic Publishers, 1992
286
Appendix D Structural Failure and Plasticity paper
Abstract: A copy of the paper, ‘Design criteria for blast tolerant bulkheads’, is included here. This paper was presented at the Structural Failure and Plasticity conference, which was held in Melbourne Australia from the 4th to the 6th of October 2000.
287 D.1. Raymond et al. (2000c)
Design criteria for blast tolerant bulkheads
I. Raymonda,b, M. Chowdhuryb, and D. Kellyb aThe Australian Maritime Engineering Cooperative Research Centre (AME CRC). bThe School of Mechanical and Manufacturing Engineering, The University of New South Wales (UNSW), Sydney, NSW 2052, Australia
With increasing importance being placed on survivability of naval platforms, this paper looks at a structured approach to the development of design criteria to fulfil the operational requirements of naval transverse bulkheads by using finite element modelling and a J-integral analysis. Initially the operational requirements are established, followed by the explanation of the design criteria and their implementation to X-80 steel transverse bulkheads.
1. INTRODUCTION
Survivability is becoming an increasingly important issue, and as stated in Chalmers (1993), “currently little information on the design of bulkheads to withstand internal blast effects” exists. Transverse bulkheads aid survivability by restricting the spread of the blast loads longitudinally throughout the vessel. Additionally, the transverse bulkheads are required to be at least a watertight boundary against flooding or fire in a post-explosion environment. The operational requirements are intended to ensure that if an explosion occurs inside a naval platform that the blast loads and related effects of flooding and fire are contained within the compartment that the explosion occurs in. These operational requirements have been developed into design criteria through considering safety factors and the accuracy of the finite element models.
2. OPERATIONAL REQUIREMENTS
As discussed by Williams (1990), the determination of the customers’ requirement for the product must be considered first. These are termed operational requirements.
In this paper, the operational requirements will be based around the capabilities of a transverse bulkhead on deck 3 at 19.2 m from the bow on a vessel 118 m long moving at 30 knots. This transverse
288 bulkhead will be considered as a generic worst-case naval transverse bulkhead for the operational requirements and subsequently used in the design criteria.
2.1. Pre-air-blast loads
There are two static loads that must be considered in this section. These are
a) A hydrostatic load, pH , due to the transverse bulkhead being one side of a liquid tank. The effect of sloshing will be included
b) Structural loads, pS , will cover the loads due to equipment above, and bending loads on the hull, and from such occurrences as dry-docking.
The response of the transverse bulkhead to all of these loads should be in the elastic regime and no rupture is permitted. Additionally, buckling responses will be reviewed.
2.2. Air-blast load
The air-blast load against the naval transverse bulkhead is assumed to be 150 kg of TNT equivalent explosive at 8 m. This load is comparable with the critical blast load considered by some western navies in the design of new vessels, Reese et. al. (1998) and OPNAV (1988). The response of the transverse bulkhead to this blast load will be critical in two situations. Firstly, no rupture is permitted within the transverse bulkhead structure. Secondly, a maximum permanent deformation of the transverse bulkhead will be set. This will be due to pipes penetrating through the bulkhead, equipment and walkways close to the bulkhead, and that a post-air-blast load has to be supported by the transverse bulkhead.
2.3. Post-air-blast load
The post-air-blast load is flooding of the compartment after an explosion has occurred. The deformed transverse bulkhead is required to be able to support this load without extensive deflection and no rupture in the bulkhead structure.
3. DESIGN CRITERIA
3.1. Pre-air-blast load
The hydrostatic load due to a tank is solved by the method given in BV 104 (1982), which considers the effect of sloshing. In this case the value of the hydrostatic pressure is pH = 90 kPa. The structural load comes from Chalmers (1993), where for the sides of the bulkhead it is 93.15 MPa and for
289 the top it is 22.5 MPa. These methods have built in safety factors relevant to differences between the idealised bulkhead and a fabricated bulkhead.
The hydrostatic pressure is applied as a pressure over the bulkhead plate area and the structural load is applied as a pressure field along the side and top edges of the bulkhead. The J-integral procedure will be used to confirm that no rupture occurs.
3.2. Air-blast load
The air-blast load is equivalent to, by the Hopkinson scale method, 7 kg of Comp-B at 3 m in the Defence Science and Technology Organisation (DSTO) Bulkhead Test Rig (BTR). The blast data, from Turner (1999), consists of two separate position pressure profiles of the blast. The approximate positions of the pressure gauges relative to the centre of the bulkhead are 550 mm and 1150 mm in a radially outward direction. The blast pressure profiles, shown in Figure 1, are approximation of the raw data supplied. This approximation gives the dominant feature of the blast load. The separation between the two initiation pressure values has been determined by the propagation speed of stress waves through X-80 and is discussed in Raymond et. al.(1999).
5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5
Pressure (MPa) 1.0 0.5 0.0 0.00 0.08 0.22 0.36 0.48 0.58 0.62 0.78 1.18 1.48 1.64 2.00 2.20 2.60 2.86 3.40 3.68 4.00 5.00 -0.5
Time (msec)
550 mm Blast Pressure History 1150 mm Blast Pressure History
Figure 1. Blast pressure history of 7 kg of Comp-B at 3 m in the BTR.
These two blast pressure profiles are applied to the transverse bulkhead in the finite element model as two separate transient pressure loads. Due to the high strain rate experienced in an air-blast situation, material data is required. This material data can be obtained by undertaking Hopkinson bar tests, with the use of constitutive equations such as Johnson-Cook or Cowper-Symonds (Wang and Lok (1997)) to gain general constants that can be used in the finite element modelling.
The maximum permanent deformation that can be accepted by a naval transverse bulkhead is set to 100 mm, Chalmers (1993). A safety factor is introduced, due to the modelling inaccuracy, which 290 reduces this deformation by 20% to 80 mm, Turner (1999). Rupture of the transverse bulkheads is tested by the J-integral procedure.
3.3. Post-air-blast load
The post-air-blast load that is being considered is flooding. BV 104 (1982) gives the flooding load to be 52 kPa. This is applied in the same way as the hydrostatic tank load. The deformed transverse bulkhead, due to the air-blast load, is required to maintain structural integrity due to the flooding load. The J-integral procedure will be used here to test for rupture. Structural redundancy within the vessel will absorb the structural load. As with the hydrostatic load the effect of sloshing has been covered in determining the flooding load and safety factors are built into this method.
3.4. J-integral procedure
The J-integral procedure is used to determine if rupture has occurred or not due to any of the loads mentioned above. The use of the path independent J parameter for characterising materials toughness is well established by such work as Rice (1968) and Shih (1976). The parameter was designed to cater for elastic-plastic stress situations such as high toughness steel in naval transverse bulkheads. Therefore, a path independent J-integral application to determine if the naval transverse bulkhead has ruptured or not is an extension of current practices.
The J-integral cannot be applied to the whole transverse bulkhead arrangement at once. The solution is to apply the path independent J-integral to the appropriate faces of every finite element brick of interest that makes up the finite element model. This is possible as the shape of individual brick faces is simple and a solution can be obtained from EPRI (1981), Miannay (1998) and Tada et. al. (1973). These bricks have dimensions between 1¯ mm by 20 mm by 20 mm to 3 mm by 20 mm by 20 mm. The transverse bulkhead will be modelled with three solid brick element through the thicknesses of the bulkhead material.
The most likely position for a crack or tear to begin is in the weld. If this tear propagates through the thickness of the weld, rupture will eventuate. As shown in Figure 2 the minimal thickness of a weld, in a double weld situation, is 1.5 mm for a plate 4 mm thick. It is assumed that as long as the crack only exists in one of the two welds then the redundant strength in the entire structure will be great enough for the vessel to return to port for repairs.
In the design criteria this crack length will be reduced for reasons of conservatism. The first reduction will be the crack length cannot be greater than the element thickness dimension. The second reduction is related to the inaccuracy in the modelling of the path-independent J-integral value. This is due to the fact that the finite element processing programs, MSC/NASTRAN and LS/DYNA, will not be considering the cracks in their finite element models. A sub-program will calculate the J-integral at the
291 completion of each load step from the node position and stress data. None of this crack information will be returned to the processing programs. As a conservative estimate of a safety factor the critical crack length will be set to 75% of the finite element thickness. This gives a safety factor of ¯ to the permitted crack length. The technique for determining the J-integral value will be verified against empirical results in Hrovat and Hoffman (1999).
Bulkhead plate Transverse bulkhead
Double side weld joint 2 mm Stiffeners
Critical tear length, 1.5 mm Deck plate Welded joint
Deck
Figure 2. Double-sided welding without fillets of the bulkhead plate the deck, additionally a standard transverse bulkhead is depicted.
The J-integral will be calculated using the method for a single-edge crack plate in uniform tension applied to the faces of the brick element of interest in the thickness direction of the plate. Figure 3 shows the form of the single-edge crack plate under remote uniform tension. The J-integral can be evaluated by the following equation, from EPRI (1981)
2 n+1 P a a æ P ö J = f1()ae +as eoo c( )h1 ( ,n)ç ÷ , (1) E' b b è Po ø
where a , n are the Ramsberg-Osgood parameters; s o , eo are the flow stress and strain respectively; h a ,n is a function whose values are tabulated in EPRI(1981). 1( b )
The J-integral will be calculated for both the parent and weld material. It is assumed that the initial crack length, a , will be 0.4 mm for the welded material and 0.01 mm for the parent plate material. At the completion of each load step the J-integral is calculated by the above method. This calculated J- integral value is related to a J-R curve to determine the crack extension value. This crack extension value is then used to produce the new a value, which is saved to the next time the J-integral value has to be calculated. If this new a value is greater than the critical crack length then failure is assumed and noted for review. Additionally, from the J-R curve a tearing modulus analysis will be performed to determine if the tearing is propagating stably or unstably. If the tearing is unstable then failure is assumed and the finite element evaluation is suspended. The decision of whether to base the analysis on plane stress or plane strain will be determined by the outcomes of the validation trials.
292 P
b
a c
P
Figure 3. Single-edge cracked plate under remote uniform tension, form EPRI (1981). This is one face of a brick element, where b is the thickness of the finite element.
3.5. Other relevant factors
In regards to X-80 steel plate, it is available in thickness from 4 mm up to 9 mm in intervals of 0.1mm. In the fabrication of the transverse bulkhead it is assumed that distortion is less than the thickness of the plate. This is in line with Ghose and Nappi (1994) findings.
Residual stress cannot be practically modelled, as discussed in Okumoto (1998). This is because X-80 has relatively high residual stress due to its’ manufacturing process and there is limited data on the residual stresses that form during the fabrication of an actual structure. Hence, residual stress is addressed in the following manner · The effect of residual stress on the final deformation of the transverse bulkhead due to the air- blast load is a reason why the inaccuracy of the modelling is approximately 20%. · The safety factors built into the static loads cover effects of residual stress.
4. CONCLUSION
This paper describes a structured approach to the development of design criteria for a blast tolerant naval transverse bulkhead. These design criteria will be used as the constraints in an optimisation procedure to develop optimised X-80 steel naval transverse bulkheads.
ACKNOWLEDGMENTS
The authors would like the thank Mr. Toman, Mr. Quigley, and Ms. Deeley, AME CRC, UNSW, DSTO, Tenix Defence Systems and BHP for all their continuing support.
293
REFERENCES
1. BV 104-1 “Structural analysis of the ship’s hull (strength specification)”, July 1982. 2. Chalmers, D. W., Ministry of defence – design of ship’s structures, HMSO, 1993. 3. EPRI, An engineering approach for elastic-plastic fracture analysis, General Electric company, NP- 1931, 1981. 4. Hrovat, R., Hoffman, M., AME CRC Internal Report–(in preparation), 1999. 5. Ghose, D. J. and N. S. Nappi, SSC-382, 1994. 6. Miannay, D. P. Fracture mechanics, Mechanical Engineering Series, Springer, 1998 7. Okumoto, Y., Journal of Ship Production, 14, No. 4, November 1998, pp. 277-286 8. OPNAV Instruction 9070.1, Chief of Naval Operations, Washington, 1988 9. Raymond, I., Chowdhury, M., Kelly, D., Design criteria for X-80 steel naval blast tolerant bulkheads report, AME CRC Internal report, 1999 10. Reese, R. M., Calvano, C. N., and Hopkins, T. M., Naval Engineers Journal, 100, January 1988, pp. 19-34. 11. Rice, J. R. A., Journal of Applied Mechanics, 35, June, pp. 379-386, 1968 12. Shih, C. F., and Hutchison, J. W., Journal of Engineering Materials and Technology, 98, October, pp. 289-295, 1976. 13. Tada, H., Paris, P. C., and Irwin, G. R., The stress analysis of cracks handbook, Del Research Corporation, Hellertown, Pennsylvania, 1973. 14. Turner, T., private communications, March 1999. 15. Wang, B., and Lok, T. S., 2nd Asia-Pacific Conference on Shock and Impact Loads on Structures, 1997, pp. 569-576. 16. Williams, M., Navtec’90, RINA, 1990 17. Williams, J. G., Killmore, C. R., Barbaro, F. J., Meta, A., and Fletcher, L., BHP Internal Report, 1992
294