CRASH SIMULATION OF FIBRE METAL LAMINATE FUSELAGE
A THESIS SUBMITTED TO
THE UNIVERSITY OF MANCHESTER
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY (PhD)
IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES
2014
AHMAD SUFIAN ABDULLAH
SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING
Table of Contents
Contents 2
List of Figures 6
List of Tables 9
Abstract 10
Declaration 11
Copyright Statements 12
Acknowledgement 13
Chapter 1 INTRODUCTION ...... 14 1.1. Background and Motivation ...... 14 1.2. Aim of Research ...... 16 1.3. Outline of Structure ...... 16 Chapter 2 LITERATURE REVIEW ...... 18 2.1 Crash Simulation of Aircraft ...... 18 2.1.1 Introduction of Aircraft Crash Simulation ...... 18 2.1.2 Methodology of Aircraft Crash simulation ...... 18 2.1.3 Crash Simulation of Composite Aircraft Fuselage ...... 21 2.2 Failure and Impact Response of Fibre Metal Laminate and its Constituents ...... 24 2.2.1 Introduction to Failure and Impact Response of Fibre Metal Laminate ...... 24 2.2.2 General Review on Mechanical Properties of Fibre Metal Laminate ...... 24 2.2.3 Bending and Buckling Behaviour of Fibre Metal Laminate ...... 26 2.2.4 Impact Response and Damage of Fibre Metal Laminate under Low Velocity Impact …………………………………………………………………………………………………………………..27 2.2.5 Review on Failure and Impact Response of Fibre Reinforced Composite Laminate under Low Velocity Impact ...... 30 2.2.6 Review on Failure and Impact Response of Metal under Low Velocity Impact …………………………………………………………………………………………………………………..34 2.2.7 Finite Element Modelling of Impact and Damage on Fibre Metal Laminate and Its Constituents...... 35 2.3 Summary of the Literature Review ...... 38 Chapter 3 BACKGROUND THEORY OF FIBRE METAL LAMINATE ...... 39 3.1 Introduction on Fibre Metal Laminate ...... 39 3.1.1 GLARE: A Glass Fibre Reinforced Based Fibre Metal Laminate ...... 39 3.1.2 Impact Behaviour of GLARE ...... 40 3.2 Aluminium Alloys ...... 42 3.2.1 Stress-strain Relationship of Isotropic and Homogeneous Materials ...... 42 3.2.2 Impact Behaviour of Aluminium Alloys Structure ...... 45 3.3 Fibre Reinforced Composite Laminate...... 48 3.3.1 Stress-strain Relationships of Fibre Reinforced Composite Laminate ...... 48 3.3.2 Analysis of a Composite Lamina ...... 49 3.3.3 Failure of Fibre-reinforced Composite Laminate ...... 52 3.3.4 Impact Behaviour of Fibre-Reinforced Composite Laminate under Low Velocity Impact ...... 56 Chapter 4 FINITE ELEMENT METHOD...... 59 4.1. Introduction...... 59 4.1.1. Introduction of Finite Element Method in Aircraft Crash Analysis ...... 59 4.1.2. General Description of Finite Element Method ...... 60 4.1.3. Abaqus Finite Element (FE) Software ...... 61 4.2. Nonlinear Dynamic Analysis ...... 62 4.2.1. Nonlinear Analysis of Aircraft Structure ...... 62 4.2.2. Dynamic Analysis of Aircraft Structure...... 64 4.3. Selection of Elements for Discretisation ...... 66 4.3.1. Shell element ...... 66 4.3.2. Incompatible Mode Solid Element ...... 69 4.3.3. Reduced Integration Element ...... 69 4.3.4. Hourglass Control ...... 70 4.3.5. Cohesive Element ...... 71 4.4. Material and Damage Model of Aluminium Alloy ...... 76 4.4.1. Material Model of Aluminium Alloy ...... 76 4.4.2. Damage model of Aluminium Alloy ...... 77 4.4.3. Onset of damage in Aluminium Alloy ...... 77 4.4.4. Damage Evolution of Aluminium Alloy...... 77 4.5. Material and Damage Model of Fibre-Reinforced Composite Laminate ...... 79
3
4.5.1. Material Model of Fibre-Reinforced Composite Laminate ...... 79 4.5.2. Onset of damage in Fibre-Reinforce Composite Lamina ...... 80 4.5.3. Damage Evolution of Fibre-Reinforced Composite Lamina ...... 82 4.6. Interaction and Contact Modelling ...... 85 4.7. Constraint and Connection Modelling ...... 88 4.7.1. Mesh Tie Constraints ...... 88 4.7.2. Mesh Independent Fasteners ...... 88 4.8. Computational Facilities in The University of Manchester ...... 89 Chapter 5 DEVELOPMENT OF FIBRE METAL LAMINATE FUSELAGE CRASH MODEL ...... 90 5.1. Introduction of Aircraft Crash Methodology ...... 90 5.2. Methodology of Crash Modelling of Fibre Metal Laminate Fuselage...... 91 5.3. Validation of Material and Damage Model Subjected to Impact Loading ...... 93 5.3.1. Validation of Aluminium Alloy Material and Damage Model ...... 93 5.3.2. Validation of Composite Laminate Material and Damage Model ...... 102 5.4. Validation of General Impact Modelling ...... 112 5.5. Verification of Fuselage Frame Impact Modelling ...... 119 5.5.1. Finite Element Modelling of Fuselage Frame ...... 119 5.5.2. Verification Results of Fuselage Frame Impact Model ...... 122 5.6. Development of Crash Impact FE Model of Aluminium Alloy Fuselage Section . 126 5.6.1. Geometric Information and Assumptions ...... 126 5.6.2. Discretisation of the Fuselage Section ...... 127 5.6.3. Material Assignment ...... 127 5.6.4. Impact and Contact Modelling ...... 127 5.6.5. Location of Mass ...... 128 5.7. Development of Crash Impact FE Model of GLARE Fuselage Section ...... 129 5.8. Evaluation of Acceleration Response at Floor-Level...... 130 5.8.1. Data collection and processing of the acceleration response during crash event …………………………………………………………………………………………………………………130 5.8.2. Human tolerance towards acceleration ...... 130 Chapter 6 RESULTS AND DISCUSSIONS ...... 133 6.1. Introduction...... 133 6.2. Energy Dissipation during Crash ...... 133 6.3. Structural Deformation of Fuselage Structure ...... 141 6.4. Acceleration at Floor Level ...... 150
4
Chapter 7 Conclusions and Future Work...... 153 7.1. Conclusions...... 153 7.2. Recommendation for Future Work ...... 155 References ...... 156 Appendix 1 ...... 162 Appendix 2 ...... 165
Word Count: 33,868
5
List of Figures
Figure 1 -1: A typical fibre metal laminate (Remmers 2006) ...... 15 Figure 2 -1: Variation of mechanical properties of fibre metal laminate with volume fraction of its composite, (a) elastic modulus, (b) tensile strength (Reyes & Cantwell 2000)...... 25 Figure 3 -1: Typical stress-strain curve of isotropic material (Gere & Timoshenko 1990) ..... 43 Figure 3 -2: Equivalent stress evolution versus equivalent plastic strain for different strain rates for aluminium alloy 2024-T3 (Rodríguez-Martínez et al. 2011)...... 44 Figure 3 -3.Buckling of aluminium can under axial loading (Palanivelu et al. 2011)...... 46 Figure 3 -4. Local coordinates of a lamina...... 50 Figure 3 -5 Failure modes of composite laminate (Gay and Hoa 2007)...... 52 Figure 3 -6. Sketch of crack propagation mode (Farley & Jones 1992)...... 58 Figure 4 -1. Conventional shell element and continuum shell element (Abaqus Documentation version 6.12) ...... 68 Figure 4 -2. Element deforms in hourglass mode (Westerberg 2002)...... 70 Figure 4 -3. Schematic representation of FML with interface elements (dark-grey) applied between layers (Remmers & de Borst 2001)...... 71 Figure 4 -4. Typical traction-separation response (Abaqus Documentation version 6.12).... 73 Figure 4 -5. Traction-separation response with exponential softening (Abaqus Documentation version 6.12)...... 74 Figure 4 -6. Stress-strain curve with progressive damage degradation (Abaqus Documentation version 6.12)...... 78 Figure 4 -7. A linear damage evolution based on effective plastic displacement (Abaqus Documentation version 6.12) ...... 79 Figure 4 -8. Linear damage evolution of a lamina structure(Abaqus Documentation version 6.12) ...... 84 Figure 4 -9. Hard contact pressure-overclosure relationship diagram (Abaqus Documentation version 6.12)...... 87 Figure 5 -1. Methodology of developing crash simulation of FML fuselage section ...... 92 Figure 5 -2. Mesh of aluminium alloy plate with finer mesh at the impact area ...... 96 Figure 5 -3. Different stages of the perforation process for an aluminium alloy 2024-T3 sheet, V0 4.0 m/s. (a) Localisation of deformation and onset of crack. (b) Cracks progression and formation of petals. (c) Development and bending of petals. (d) Complete passage of the impactor and petalling failure mode...... 98 Figure 5 -4. Flow stress evolution versus strain for Johnson-Cook material model ...... 100 Figure 5 -5. Impact force as a function of the impactor displacement ...... 101 Figure 5 -6 Permanent deflection of the target for FE model and experiment ...... 101 Figure 5 -7. Numerical model of the impact on composite laminate...... 104 Figure 5 -8. Impact force-time histories of impacted composite laminate ...... 107 Figure 5 -9. Impact force-displacement histories of impacted composite laminate ...... 108 Figure 5 -10. Deformation in impacted plate for FE model without adhesive...... 108 Figure 5 -11. Deformation in impacted plate for FE model with adhesive...... 109 Figure 5 -12. Energy absorption-time histories for impacted composite laminate ...... 110
6
Figure 5 -13. A quarter symmetric model of cask drop onto a rigid surface (Abaqus Documentation, 6.12) ...... 112 Figure 5 -14. Deformation of side wall of bottom containment at 5 ms, (a) axisymmetric model, (b) shell element model, (c) C3D8R element with default hourglass control model, (d) C3D8R element with enhanced hourglass control model and (e) C3D8I element model...... 116 Figure 5 -15. Crushing distance of the containment for all models ...... 117 Figure 5 -16. Plastic dissipation and elastic strain energy time histories...... 118 Figure 5 -17. Fuselage frame configuration and discretisation...... 120 Figure 5 -18. Z cross-section of fuselage frame ...... 120 Figure 5 -19. Deformation of frame (a) at time 50 ms, (b) at time 125 ms, (c) at time 175 ms ...... 123 Figure 5 -20. Crushing distance of frame with various mesh sizes...... 124 Figure 5 -21. Plastic energy dissipation of frame finite element models with various mesh sizes...... 125 Figure 5 -22. Energy balance of frame model with mesh size 32 mm...... 125 Figure 5 -23. Human coordinate system (Shanahan 2004b) ...... 131 Figure 5 -24. Acceleration crash pulse in assumed triangular pulse (Shanahan 2004)...... 132 Figure 6 -1. Energy balance within the aluminium fuselage for 10 ms-1 impact velocity crash...... 135 Figure 6 -2. Energy balance within the GLARE 5-2/1 fuselage for 10 ms-1 impact velocity crash...... 135 Figure 6 -3. Dissipation of impact energy and its distribution within the aluminium fuselage for 10 ms-1 impact velocity crash...... 136 Figure 6 -4. Dissipation of impact energy and its distribution within the FML GLARE 5-2/1 fuselage for 10 ms-1 impact velocity crash...... 137 Figure 6 -5. Energy absorbed by frame structure and its decomposition in aluminium fuselage ...... 138 Figure 6 -6. Energy absorbed by skin structure its plastic dissipation in aluminium fuselage ...... 139 Figure 6 -7. Energy absorbed by skin structure and its decomposition in GLARE 5-2/1 fuselage...... 140 Figure 6 -8. Deformation histories with plastic strain contour plot of the aluminium fuselage during crash with impact velocity 10 ms-1...... 143 Figure 6 -9. Deformation histories with plastic strain contour plot of the GLARE 5-2/1 fuselage during crash with impact velocity 10 ms-1...... 144 Figure 6 -10. Crushing distance of aluminium and GLARE 5-2/1 fuselages in 10 ms-1 impact velocity crash...... 146 Figure 6 -11. Location of plastic hinge at the bottom half of the fuselage section ...... 146 Figure 6 -12. Tensile and compressive matrix failure at composite layers in GLARE 5-2/1 skin structure at hinge location B. t = 24 ms ...... 148 Figure 6 -13. Matrix tensile failure in glass-fibre laminate (90⁰) outer lamina at t = 78 ms. 149 Figure 6 -14. Fibre tensile failure in glass-fibre laminate (0⁰) inner and outer lamina at t = 78 ms...... 149
7
Figure 6 -15. Acceleration response at passengers’ location in aluminium fuselage during 10 m/s vertical crash...... 152 Figure 6 -16. Acceleration response at passengers’ location in GLARE 5-2/1 fuselage during 10 m/s vertical crash...... 152 Figure A1-1. Schematic representation of the drop weight tower (Rodriguez-Martinez et al, 2011)...... 162 Figure A1-2. The device used to clamp the specimen (a) clamping (b) specimen support (Rodriguez-Martinez et al, 2011)...... 163 Figure A1-3. Conical striker used in the Rodriguez-Martinez’s experiment (Rodriguez- Martinez et al, 2011)...... 163
8
List of Tables
Table 3 -1 Commercially available ARALL laminates (Khan et al. 2009)...... 40 Table 3 -2 Mechanical properties of aluminium alloy 2024-T3 (Lesuer 2000; Buyuk et al. 2008) ...... 43 Table 5 -1. Material properties of 2024-T3 and 7075-T6 aluminium alloy (Lesuer 2000; Buyuk et al. 2008)...... 95 Table 5 -2. Results comparison between FE models and experimental works in terms of artificial energy percentage, maximum impact force and energy absorption...... 97 Table 5 -3. Amount of energy absorbed during impact of composite plate ...... 110 Table 5 -4. Cask drop with solid elements modelling to be verified ...... 113 Table 5 -5. Material and damage model parameters of aluminium alloy 7075-T6 (Brar et al. 2009)...... 121 Table 5 -6. Frame finite element models with various mesh sizes ...... 122 Table 5 -7. Contact surface pairs modelled within the fuselage ...... 128 Table 5 -8. Human tolerance limits (Shanahan 2004b)...... 131 Table 6 -1. Percentage of energy distribution within fuselage structure during impact ..... 137 Table A2-1. Material properties of the carbon fibre/epoxy unidirectional laminate...... 165 Table A2-2. Material properties of the interface cohesive element (Shi et al, 2012)...... 166
9
Abstract
A finite element model of fibre metal laminate (FML) fuselage was developed in order to evaluate its impact response under survivable crash event. To create a reliable crash finite element (FE) model of FML fuselage, a ‘building block approach’ is adapted. It involves a series of validation and verification tasks in order to establish reliable material and damage models, verified impact model with structural instability and large displacement and verified individual fuselage structure under crash event. This novel development methodology successfully produced an FE model to simulate crash of both aluminium alloy and FML fuselage under survivable crash event using ABAQUS/Explicit. On the other hand, this allows the author to have privilege to evaluate crashworthiness of fuselage that implements FML fuselage skin for the whole fuselage section for the first time in aircraft research field and industry. The FE models consist of a two station fuselage section with one meter longitudinal length which is based on commercial Boeing 737 aircraft. For FML fuselage, the classical aluminium alloy skin was replaced by GLARE grade 5-2/1. The impact response of both fuselages was compared to each other and the results were discussed in terms of energy dissipation, crushing distance, failure modes, failure mechanisms and acceleration response at floor-level. Overall, it was observed that FML fuselage responded similarly to aluminium alloy fuselage with some minor differences which conclusively gives great confidence to aircraft designer to use FML as fuselage skin for the whole fuselage section. In terms of crushing distance, FML fuselage skin contributed to the failure mechanisms of the fuselage section that lead to higher crushing distance than in aluminium alloy fuselage. The existence of various failure modes within FML caused slight differences from the aluminium fuselage in terms of deformation process and energy dissipation.
These complex failure modes could potentially be manipulated to produce future aircraft structure with better crashworthiness performance.
10
Declaration
No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.
11
COPYRIGHT STATEMENT
i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trademarks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in the thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant Thesis restriction declarations deposited in the University Library, The University Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in The University’s policy on Presentation of Theses
12
Acknowledgements
First and foremost, I am grateful to The God Allah S.W.T. for His continuous blessings and for allowing me to complete this thesis despite of having various challenges throughout my Ph.D journey.
I would like to express my gratitude to my research supervisor Dr. Azam Tafreshi for her advice and support during my years in The University of Manchester as a postgraduate student.
Many special thanks go to The Ministry of Education Malaysia as the main sponsor of my tuition fees and provided financial support during my research years in Manchester and also many thanks to Universiti Teknologi Mara (UiTM) for their support in various aspects.
I would like to thank to all technical staffs in The University of Manchester that may have given direct and indirect support in order for me to complete various stages of this research. Not forget to mention supportive colleagues especially those in Floor D and F of Pariser Building that always keen to help each other in completing our courses.
Finally but most importantly, thank you to my lovely wife Sakeena in which we got married during my second year of my research. Her understanding towards the challenges faced by me, her patience and supports were very much needed and tremendously appreciated. Thank you to Ali too, our beautiful one year old son, who always keep me smile and feel blessed. Thank you to my parents and sisters who keep supporting me and always be my source of motivation and inspiration.
13
Chapter 1 INTRODUCTION
1.1. Background and Motivation
The number of flights travelling across continents, countries and cities is growing rapidly year by year which is motivated by the increasing number of customers demand for air travel. In parallel, there are demands from the environmentalists and governments to cut down the fuel emission. There were few measures taken to fulfil the environmentalist and governments demand which include the research, development and manufacturing of high-performance lightweight aircraft by the aircraft manufacturers. This trend can be observed on the new released Boeing 787 Dreamliner which the lightweight composite materials are widely used for the aircraft’s main structure (Boeing). On the other side, by incorporating GLARE and other composite laminate into large proportion of the aircraft’s skin, Airbus A380 manage to cut down production and operating costs and increases the safety level of the aircraft significantly. Additionally, with the capability of carrying 560 to
660 passengers, the A380 should answer the Boeing’s 747 monopoly (Vlot et al.1999). In designing the new lightweight aircraft structure, the aircraft manufacturers cannot compromise the safety of the occupants as well as the integrity of the structure. Thus, crashworthiness of an aircraft is an important issue in designing the future lightweight aircrafts.
Crashworthiness of an aircraft can be investigated using experimental method and numerical method. Evaluating crashworthiness of an aircraft by using experimental method or crash test is expensive and it can only be executed at the end of the designing stage.
Jackson et al and Adam et al (Jackson et al. 1997; Adams & Lankarani 2010) are among the researchers that carried crashworthiness evaluation of aircraft using experimental method.
On the other side, numerical analysis and finite element analysis are more cost-effective compare to crash test. In current state of crashworthiness analysis, most of finite element
14 model for crashworthiness evaluation is verified by experiment of the same model such being implemented in several published papers by Adams et al, Meng et al, Jackson and
Fasanella and Hashemi (Adams & Lankarani 2010; Jackson & Fasanella 2005; Meng et al.
2009; Hashemi et al. 1996).
The crashworthiness of aircraft that uses fibre metal laminate (FML) as the fuselage skin is the main interest in this thesis. The idea of fibre metal laminates are by stacking metal and fibre reinforced composite layers in order to gain the superiority fatigue and fracture characteristics of fibre reinforced composite materials and to combine with the plastic behaviour and durability of the metal (Remmers 2006) A typical FML configuration is as shown in Figure 1 -1. Three main families of fibre metal laminate in aerospace industry are
ARALL, GLARE and CARALL (ECSS 2011a; ECSS 2011b). Other less commercialised FML are titanium based and magnesium based FMLs (Sinmazçelik et al. 2011). Vlot et al (Vlot et al.
1999) also anticipated that the application of FML in the entire top half of the A380’s fuselage around the passengers’ cabin and in cargo floors, cargo liners, bulkheads and flap skins of the other aircraft.
Fibre-reinforced composite
Metal
Figure 1 -1: A typical fibre metal laminate (Remmers 2006)
15
1.2. Aim of Research
The aim of the research is to evaluate the crashworthiness performance of fibre metal laminate (FML) fuselage under survivable crash event. In order to achieve this aim, a reliable crash finite element (FE) model of FML fuselage has to be developed through a series of validation and verification tasks.
1.3. Outline of Structure
This thesis consists of seven chapters with each chapter discusses relevant materials and works towards reaching the aim of research. The outline of the thesis structure is summarised as below.
Chapter 1 presents the background and motivation that produced the research objective.
Chapter 2 presents the literature review on relevant materials mainly on crash simulation of aircraft structure and impact response of fibre metal laminate and its constituents.
Chapter 3 presents the background theories on mechanical response of aluminium alloy and composite laminate in order to establish firm understanding on the mechanical response of fibre metal laminate.
Chapter 4 presents the finite element method in modelling various material and structural behaviour in order to establish the foundation of modelling crash simulation of fibre metal laminate fuselage
Chapter 5 presents the methodology and its process in developing a reliable crash model of fibre metal laminate fuselage. This includes the results of the validation and verification works.
Chapter 6 presents the results of crash simulation of aluminium alloy fuselage and fibre metal laminate fuselage. This chapter also discusses the impact response, failure
16 mechanisms and crashworthiness of fibre metal laminate fuselage in comparison to aluminium alloy fuselage.
Chapter 7 concludes the research work presented in this thesis and future recommendation works are outlined.
17
Chapter 2 LITERATURE REVIEW
2.1 Crash Simulation of Aircraft
2.1.1 Introduction of Aircraft Crash Simulation
The concept of crash survivability of aircrafts has been established over 50 years ago.
However, its implementation into operational aircraft has been remarkably slow until U.S
Army committed to improve the crash survivability of its helicopters during the conflict in
South East Asia (Xue et al. 2014). The NASA Langley research centre is one of the earliest crash testing facilities which was originally built for simulating lunar landing. Numbers of crash test on aircrafts and rotorcrafts have been performed there. Their main objective was to improve crashworthiness by analysing the dynamic response of aircraft structure, seats and occupants during crash events (Jackson et al. 2004).
Due to the complexity of the dynamic response of aircraft structure and its expensive crash tests, computational simulations have been developed and quickly become an effective tool (Xue et al. 2014). In 1995, the validation of numerical simulation was identified as one of the key technology that needs to be extensively developed to enhance research on crashworthiness (Noor and Carden 1993).
2.1.2 Methodology of Aircraft Crash simulation
Implementation of numerical methods in crashworthiness research enables researchers to evaluate the impact behaviour of aircraft structures during crash events and to evaluate a new crashworthy design approaches with relatively lower cost (Xue et al. 2014).
Throughout the years, several numerical software codes that specifically and non- specifically developed for crash simulation of air transports have been established and implemented including LS-Dyna, KRASH, MSC.Dytran and Abaqus (Jackson & Fasanella
2005)(Fasanella & Jackson 2000)(Meng et al. 2009).
18
As early as 1980, Pifko and Winter (Pifko & WInter 1980) outlined the computational formulations and methods for crash simulations in DYCAST program and discussed the use of that formulation in finite element solution of crash analysis of automobile and on helicopter cockpits. They described that the implementation of computational nonlinear dynamic analysis on crash of vehicle is a complex and challenging task. It requires the user of crash simulation code to clearly understand the underlying theories so that the model created is reliable. The users are also required to exercise their engineering judgement in order to interpret results meaningfully.
In 1996, Hashemi et al (Hashemi et al. 1996) presented a modelling verification methodology of an aircraft subfloor fuselage component under survivable impact condition. The FE crash simulation of that particular component was modelled and analysed by PAM-CRASH FE code. To verify the reliability of the FE model, results from FE analysis is compared with dynamic test in terms of failure mechanisms. The verified FE model then is used as an established baseline model for the parametric studies.
Throughout this modelling process, they concluded that an established FE modelling approach at aircraft’s component level is an effective method to verify the full-scale finite element modelling of aircraft crash simulation. This method is simply the ‘building block’ approach that typically used in the design and certification of aerospace structures.
Building block approach is a method that consists of tests on increasingly complex structure in order to develop design allowable and to account structural details. It can be adopted to develop verified full-scale aircraft crash simulation as suggested by Kindervater et al
(Kindervater et al. 2011). Several other authors also used building block approach including
Heimbs in which he verified the FE model at coupon and structural element levels before simulate the crash of full-scale composite aircraft (Hashemi & Walton 2006; Kindervater et al. 2011; Heimbs et al. 2013).
19
In 2002, Kumakura (Kumakura 2002) and his colleagues developed a crash simulation of YS-
11A aircraft using LS-Dyna3D as part of the project on structural crashworthiness of aircraft by NAL Structures and Materials Research Center. The computer model consisted of small- scaled under-floor fuselage structures that crash vertically onto a rigid impact surface. The impact response was compared with a vertical drop test of a fuselage section from a YS-
11A aircraft. The simulation results fairly correlate with test in terms of deformation of the under-floor fuselage structure. In 2013, Feng et al (Feng et al. 2013) al also modelled only the under-floor section of the fuselage that consists of fuselage frame, fuselage skin below the cabin floor, floor beams, floor panels, stringers and struts. This simplification is based on assumption that deformation during crash mainly occurred in the fuselage sub-floor structure. This simplification method is attractive in terms of reducing computational cost, but it need to be implemented with caution under certain impact condition such as a crash on a non-symmetry impact surface or inclining roll angle. Besides, under higher velocity crash, the stress wave propagation would play a significant role on the impact behaviour. In
2001, Fasanella et al (Fasanella & Jackson 2001) modelled a crash simulation of a fuselage section of Boeing 737 with a relatively rigid auxiliary fuel tank beneath the occupant’s floor.
Adams and Lankarani (Adams & Lankarani 2010) and Tan et al (Tan et al. 2012) also separately simulated the crash of the same structure. The FE models in their works consist of a full circle of fuselage section, unlike models simulated by Kumakura (Kumakura 2002) and Feng et al (Feng et al. 2013). The impact responses being investigated in the simulations are the acceleration at passengers’ floor, the failure mechanism and the deformation of the structure. These results were compared with the drop test of Boeing
737 fuselage section with the same configuration which was run and analysed by
Abromowitz et al earlier in year 2000 (Abromowitz et al. 2000).
All the papers reviewed above have mainly focused on the crash simulation of in-service real aircraft. There are also crash simulations of future aircrafts performed by a few
20 researchers. The objective of their work is to propose new design concepts for aircrafts that have better crashworthiness performance. These concepts include having new form of lower fuselage floor, incorporating energy absorbing sub-floor structure also using composite-foam sandwich materials as the fuselage skin (Jackson et al. 1997; Jackson 2001;
Fasanella et al. 2002; Bisagni 2003; Meng et al. 2009). As their crash simulations could not be validated by the experimental drop tests, the methodology to verify their respective crash simulations have been the key aspects in validating their models.
2.1.3 Crash Simulation of Composite Aircraft Fuselage
Aluminium alloys are the most commonly used materials for the construction of aircraft fuselages. They are capable of absorbing large amount of energy through plastic deformation during crash event. However, due to their high specific strength and high specific stiffness ratios, composites have gradually replaced aluminium alloys in the aerospace industry. Obviously, composites have different mechanical properties and characteristics. It is generally brittle in nature, unlike aluminium alloys. Thus, composite’s capability in absorbing energy during crash becomes a new issue for researchers and air transport designers (Wiggenraad et al. 2001). Therefore, the crashworthiness of composite fuselage structures has been studied by many academics and aerospace designers in recent years as reviewed below. However, crash simulations of aircraft structure that related to composite are based on new design concept aircraft. They are simulated as part of the design process in order to achieve new design concept with better crashworthiness performance.
In 1997, Jackson et al (Jackson et al. 1997) simulated the crash performance of a 1/5-scale aircraft model that had energy absorbing capabilities fuselage skin, floor and sub-floor structure. The fuselage skin and floor were made of composite laminate with polyurethane foam core meanwhile the energy absorbing sub-floor structure was made of Rohacell foam.
21
The fuselage skin was made of fibre reinforced laminated composite with various fibre orientations but they are modelled as a homogenous material. In terms of deformation and acceleration at passenger’s floor level, the results of their scaled numerical model agreed well with a crash test of full-scale model. In 2002, Fasanella and Jackson simulated the full scale model of the same design concept fuselage.
In 2001, Wiggenraad et al (Wiggenraad et al. 2001) simulated crash event of a new design concept for a composite sub-floor. The new design concept consisted of under-floor composite fuselage frame and energy-absorber sine-wave beams. However it was proven that this new concept did not improve crashworthiness unless certain adjustments were made. In 2013, Feng et al (Feng et al. 2013) numerically studied the effect of composite ply number and composite ply angle on crashworthiness of aircraft subfloor structure in which its fuselage skin was made of composite. They concluded that composite skin ply numbers and ply angles have a great influence on the crashworthiness of a composite fuselage and these can be tailored for better crashworthiness. However, the modelling technique and verification for the composite structure was not informed in their crash simulations.
For the ease of modelling and analysis of crash events, in some of the papers reviewed, laminated composites were modelled as isotropic and homogeneous materials. This technique requires a coupon test in order to obtain the material properties and failure strains of the laminate. This technique is also known as macro-level approach. Another technique in modelling laminated composites is meso-level approach in which each lamina is modelled as a unidirectional fibre composite. It is obvious that the latter is computationally more expensive but its implementation in crash simulation of composite aircraft enables the researcher to capture more accurate failure mechanisms and failure modes. Besides, the capability to capture the failure mechanisms may also significantly affect the evaluation of energy absorbance within composite fuselage structure. In the end,
22 it depends on the understanding of the global impact response of the aircraft and objective of the analysis in choosing the best modelling approach to model the composite laminate.
23
2.2 Failure and Impact Response of Fibre Metal Laminate and its
Constituents
2.2.1 Introduction to Failure and Impact Response of Fibre Metal Laminate
The concept of fibre metal laminates (FML) is to combine metal and fibre reinforced composite layers in order to improve certain mechanical properties of the material that to be used in engineering applications especially in aerospace industry. Three most common families of FML in aerospace industry are ARALL, GLARE and CARE (CARALL), defined by their fibre-reinforce laminate’s constituent. Improved damage tolerance and superior impact properties are among the main advantages benefited from FMLs compare to their parents’ materials. Within these two decades, various studies were reported investigating the failure mechanics and impact response of FML. Understanding of failure and impact response of FML in aerospace application is essential as aerospace structure is always exposed to impact conditions.
2.2.2 General Review on Mechanical Properties of Fibre Metal Laminate
Discussion on failure and impact response of fibre metal laminate (FML) fairly requires general understanding of the mechanical properties of fibre metal laminate. Obviously mechanical property of FML depends on the mechanical properties of its constituents.
As early as 1994, Wu et al (Wu et al. 1994) investigated the effect of specimen size and geometry on the mechanical properties of FML. Based on tension tests on various FML specimens with various size and geometry, he proved that these parameters do not affect the elastic modulus, yield stress and ultimate tensile strength of FML. In year 2000, Reyes and Cantwell (Reyes & Cantwell 2000) carried a general study on the mechanical properties of FML based on glass-fibre reinforced polypropylene. They observed that by increasing the volume fraction of composite will cause the FML to have higher ultimate strength but lower elastic modulus as shown in Figure 2 -1.
24
(a) 80
70
60 50 40 30
20 Tensile Modulus (GPa) Modulus Tensile 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Volume fraction of composite
(b) 600
500
400
300
200
Tensile strength (MPa) strength Tensile 100
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Volume fraction of composite
Figure 2 -1: Variation of mechanical properties of fibre metal laminate with volume fraction of its composite,
(a) elastic modulus, (b) tensile strength (Reyes & Cantwell 2000).
Kawai et al (Kawai & Hachinohe 2002) in his study on fatigue property of GLARE observed that the high strength properties of aluminium alloy enhanced the specific stiffness and strength of GLARE in the fibre direction. In the same paper, Kawai et al also stated that fibre bridging mechanism in GLARE impedes the growth and propagation of cracks in the aluminium alloy under tensile loading conditions. The presence of fibre bridging mechanism in GLARE is also reported by Hagenbeek (Hagenbeek 2005) and previously proven by Marissen (Marissen 1988) in his study on fatigue crack growth in ARALL.
25
In 2006, Cocchieri et al (Cocchieri et al. 2006) discussed the interlaminar shear strength of
FML which depends on the adhesion between fibres and matrix and adhesion between metal and composite laminate. Several researchers are reported of making use of single cantilever beam test (SCB) and three and five point bending test to determine the interlaminar shear strength of FML (Reyes & Cantwell 2000; Khalili et al. 2005).
2.2.3 Bending and Buckling Behaviour of Fibre Metal Laminate
Bending and buckling are one of the failure modes of fibre metal laminate (FML). In year
2005, Khalili et al (Khalili et al. 2005) studied the bending of various FML configurations and compared with monolithic metals and fibre-reinforced composite laminate. He stated in his paper that bending strength and stiffness of FML would not increase by placing aluminium alloy away from the neutral axis. Additionally he observed that the use of aluminium in FML would cause higher deflection in bending compare to FML that use steel. He also observed that in bending, the failure that may occur is either delamination alone or combination of delamination and tensile failure that starts from the external layers.
In year 2001, Remmers et al (Remmers & de Borst 2001) studied the delamination buckling of GLARE and he represented the mechanism of the failure in which the failure starts with initial delamination, followed by local buckling, then growth of delamination until failure.
Mesoscopic-level numerical model was developed by him based on mechanism he presented and cohesive element was used to model the delamination. He concluded that buckling of FML cannot be predicted by elastic buckling analysis due to the presence of buckling delamination and plastic deformation within the aluminium alloy layer. This conclusion is also supported by Bi et al (Bi et al. 2014) in his study on buckling and post- buckling of FML.
26
2.2.4 Impact Response and Damage of Fibre Metal Laminate under Low Velocity
Impact
Sinmazçelik et al (Sinmazçelik et al. 2011) in his review on test methods on Fibre Metal
Laminate (FML) categorised impact test on FML into three; low velocity, high velocity and blast loading impact tests. In this thesis, review are only made on impact response and damage of FML under low velocity impact as the main work in this thesis is limited to velocity impact ranging between 1 and 20 ms-1. Recently in 2014, Chai and Manikandan
(Chai & Manikandan 2014) reviewed low velocity impact response of FML and he classified various parameters that influence impact response of FML into two main groups; material- based parameters and geometry-based parameters. Materials based parameters include types of metals, types of fibre-reinforced composite, lay-up configuration and constituent’s volume fraction.
Impact test is not the only methodology in investigating impact response of FML. A number of researchers developed finite element modelling of dynamic impact and damage for FML due to several advantages including capability to analyse barely visible impact damage
(BVID) in composite, capability to quantify the degradation of the materials, inexpensive and quicker method compare to experiment. Thus, impact response and damage analysis of FML that carried by numerical studies are also reviewed and discussed in this section.
Moriniere et al (Morinière et al. 2013) in his paper discussed the failure mechanisms of
GLARE that make it a superior impact resistance. When subjected to lateral impact loading, the composite laminate core that has higher bending stiffness than aluminium modifies the flexural deformation profile of the aluminium alloy. As a result, the crack initiation of the aluminium is delayed. In the same time the impacted aluminium layer would dampen the impact on the composite laminate core. Meanwhile the outer non-impacted aluminium
27 layer delays the delamination growth. These mechanisms results in damage being contained in the vicinity of the impacted zone.
In 2002, Laliberte et al (Laliberté et al. 2002) studied the low velocity impact response of
FML via experiment and numerical method. It is observed that delamination plays insignificant role in absorbing impact energy under localised lateral impact condition unlike under bending and buckling as discussed previously. Thus it is up to the understanding of the impact event in order to determine either or not to incorporate delamination if to model impact response of FML. Obviously incorporating delamination model will increase computational cost especially when involving large models.
All studies on FML impact response discussed above are mainly based on vertical drop weight impact. In 2005, Khalili et al (Khalili et al. 2005) investigated the impact response of
FML via Charpy impact test. In fact it is observed that Khalili et al is the only author that studied dyanic impact behaviour of FML by not using the vertical drop weight impact that produces much localised impact area. In his paper, Khalili et al observed that energy per unit area required to fracture for GLARE with unidirectional fibre orientation is 5% lower than its parent glass fibre composite due to the deficiency of aluminium layers in tolerating tensile loads.
2.2.4.1 Effect of Metal/Composite Volume Fraction on Impact Response of Fibre
Metal Laminate
From 1991 to 1997, Vlot and his colleagues studied the impact properties and impact damage of FML. In one of his study of impact damage on various FML, he observed that increasing the volume fraction of glass-fibre reinforced laminate in GLARE will increase the damage resistance. It also increases the minimum cracking energy at low velocity and high velocity impact higher than its monolithic constituent aluminium alloy. Besides the contribution of high stiffness of the composite laminate, the improvement in impact
28 resistance is because the presence of delamination. Delamination causes the FML to be loaded in a more efficient membrane manner, unlike monolithic metal that dominated by bending deformation (Vlot 1993; Vlot 1996; Vlot & Krull 1997).
2.2.4.2 Effect of Metal Type on Impact Response of Fibre Metal Laminate
In 2009, Liu and Liaw (Liu & Liaw 2009) studied the impact resistance of different FML families and grades including GLARE1, 2 and 3. Aluminium alloy 2024-T3 is the metal used in all GLAREs except in GLARE 1 that utilises stronger aluminium alloy 7475-T6. Due to tougher and slightly stiffer properties of 2024-T3, GLARE 2 and 3 has better impact resistance than GLARE 1. In their study, the failure mechanism is observed to start from indention around the impact area. Then delamination is induced between the outer non- impacted aluminium and its adjacent fibre-reinforced laminate followed by the non- impacted aluminium crack. In higher energy impact, the aluminium crack will be followed by severe damage in the fibre-reinforced laminate layers. Global bending during impact causes the FML to suffer more damage at the non-impacted side.
Several other researchers are reported to investigate other metal such as magnesium and titanium as potential replacement of aluminium in FML due to their superior properties that aluminium alloys does not have. However magnesium and titanium based FML were proven not as good as aluminium based FML in terms of impact resistance. Details on their works can be referred at respective references (Cortés & Cantwell 2005; Nakatani et al.
2011).
2.2.4.3 Effect of Stacking Sequence on Impact Response of Fibre Metal Laminate
Several researchers are reported to compare the damage resistance between various grades of GLARE under low velocity impact which their full work can be referred in their respective papers (Lalibert 2005; Wu et al. 2007; Liu & Liaw 2009). From their works, it can be concluded that GLARE 5 shows the best damage resistance as smaller damage observed
29 and less impact energy is absorbed. Meanwhile GLARE 3-3/2 perform better than GLARE
1,2-3/2 in terms of damage resistance. This observation is simply resulted by the higher volume fraction of fibre-reinforced laminate in GLARE 5. The other reason of having GLARE
5 as the best damage resistance is because of the use of cross-ply composite as studied later by Yaghoubi et al (Seyed Yaghoubi et al. 2011).
In 2011, Yaghoubi et al (Seyed Yaghoubi et al. 2011) did parametric studies on impact response of GLARE 5-3/2 by varying the stacking sequence of the composite laminate which includes cross-ply, unidirectional, angle-ply and quasi-isotropic orientations. He observed that quasi-isotropic orientation (0⁰/45⁰/90⁰) provides highest stiffness thus results in good impact resistance with low permanent deflection and conversely unidirectional orientation (0⁰4) gives the worse impact resistance.
Fan et al (2011) in his numerical modelling of FML under low velocity impact discussed the effect of FML laminate sequence and composite thickness on impact resistance. Changing the laminate sequence from 2/1 to 3/2 resulted in increase in perforation energy. Several other authors that investigate the effect of laminate sequence also provided the same observation which can be referred in their papers respectively (Sadighi et al. 2012;
Morinière et al. 2013).
2.2.5 Review on Failure and Impact Response of Fibre Reinforced Composite
Laminate under Low Velocity Impact
Failure in fibre-reinforced composite laminate and its impact response significantly affect the failure and impact response of fibre metal laminate (FML) as presented in previous section. Good understanding on the failure mechanisms and failure modes of fibre- reinforced composite is required in analysing impact response of FML. Besides, the available literature on failure and impact response of FML mostly is based on drop weight impact that has very localised contact area. Literature on failure and response of FML
30 under dynamic axial loading is non-existence and only limited number of researchers studied on buckling and bending response of FML as reported previously. Thus general review is made on literatures that discuss the failure and impact response of the constituents of FML. This section is on failure and impact response of fibre-reinforced composite and the next section is on metal.
In general, scientific studies on impact response of composite can be classified into two main categories. The first one is lateral impact which the impact occurs in the direction of the composite thickness (Robinson & Davies 1992)(Kim et al. 1997)(Aslan et al. 2003)(Shyr
& Pan 2003). The second one is axial impact which the impact occurs in the direction of the length of the composite(Robinson et al. 1997; Farley & Jones 1992; Bisagni 2009).
In 1992, Robinson and Davies (Robinson & Davies 1992)studied a lateral low velocity impact on composite and examined the effect of impactor’s mass on the impact response of various woven fibre-reinforced composite laminate. They observed that the impact damage is a function of impact energy alone and independent from mass or velocity of the impactor. Two approaches were introduced by them on predicting energy absorbed through damage process by the specimen. The first one is simply by subtracting the elastic energy at maximum impact force from the incident impact energy and the second one is by integrating the force-time history. Further discussion on reliability of these encouraging approaches can be referred in their paper (Robinson and Davies, 1992).
Aslan et al in 2003 (Aslan et al. 2003) experimentally and numerically studied the response of rectangular E-glass/epoxy laminate (0⁰/90⁰/90⁰/0⁰)s under low velocity lateral impact.
Numerically, it is observed that the out-of-plane stresses are significantly smaller than the in-plane stresses but they may lead to delamination within the laminate. Meanwhile the maximum stress in fibre direction is larger than in its in-plane orthogonal direction because the flexural wave moves faster in the fibre direction as explained by them. They also
31 observed that larger delamination occurs at the outer non-impacted layer due to bending stresses compare to the upper impacted layers (Aslan et al. 2003). Shyr and Pan (Shyr &
Pan 2003) in studying impact resistance and damage for various E-glass reinforced composite also reported the same observation on the delamination location which is due to bending stresses at the non-impacted layers. In the same paper, they also observed that fibre fracture dominates the impact failure in thick laminate meanwhile delamination plays a major role in thinner laminate.
As most of the impact response investigations were carried numerically on a flat composite plate, Kim et al (Kim et al. 1997) observed that failure coupling between matrix cracking and delamination occur in curved composite laminate under low velocity impact loading.
They also observed that as curvature of laminate increases, the delaminated area is also widens under the same impact energy.
Impact response of composite laminate under axial loading is studied by several authors. In
1992, Farley and Jones (Farley & Jones 1992) studied the crushing characteristics of composite tubes which they described the response is complex due to interactions of various failure mechanisms that control the crushing process. They explicitly described three unique crushing modes of composite tube under axial loading are; transverse shearing, lamina bending and local buckling which were controlled by various failure mechanisms. The failure mechanisms that involved in determining the failure mode might be combination of delamination, lamina bundle fracture, matrix fracture and fibre fracture.
In 2009, Bisagni (Bisagni 2009) also studied on axial impact on composite tube and discussed the failure mode of the tube. Despite of using different terms for the composite collapse mode such as socking mode, tearing mode and splaying mode, the fundamental concept of the failure mode are just the same as described by Farley and Jones (Farley &
Jones 1992).
32
Robinson et al (Robinson et al. 1997) studied the parameters affecting the crashworthiness of composite material structure under axial, bending and combined loading. He observed that composite material do not undergo plastic deformation like metal due to its brittle nature of both fibres and matrix. The parameters that affect the energy absorption capabilities of composite include the materials of the composite, structural geometry and loading condition
One of the failure mechanisms that consistently appear in discussing impact response of composite is delamination. Delamination is also the main failure mechanism of composite under buckling mode. In 1993, Jih and Sun (Jih & Sun 1993) studied delamination as an impact response of composite under low velocity impact and they concluded that delamination could be predicted by using the static interlaminar fracture toughness.
In 1993, Shaw and Shen (Shaw & Shen 1993) studied dynamic buckling of a composite circular cylindrical shell that geometrically imperfect. He observed that the sensitivity of critical load over size of imperfection under dynamic load increases significantly compare to under static loading. Delaminated composite is also a type of imperfection that control buckling of composite. In 2006, Tafreshi studied delamination buckling in composite cylindrical shells under combined axial compression and external pressure by using finite element method. Critical load does not decrease by the existence of very small area of delamination but the critical load is sensitive to the location of the delamination in the case of larger area of delamination. The critical load is observed to be very small when the delamination moves closer to the free surface of the composite laminate. Besides, stacking sequence of laminate also plays significant role on critical buckling, thus there are stacking sequence that can be tailored to favour higher resistance on buckling (Tafreshi 2006).
33
2.2.6 Review on Failure and Impact Response of Metal under Low Velocity
Impact
In 2000, Karagiozova (Karagiozova & Jones 2000) studied the dynamic effects on buckling and energy absorption of steel and aluminium cylindrical shells. He revealed that a shell that subjected to axial impact is both mass and velocity sensitive. The inertia characteristics and material properties of the shell would determine the patterns of the axial stress wave propagation resulting different type of dynamic buckling. His studies continue in 2001
(Karagiozova & Norman Jones 2001; Karagiozova & N Jones 2001) on the same topic gives a good insight on mechanism of buckling initiation in a transient mode where combination of plastic and elastic stress wave speed and propagation determined the type and shape of the buckling. In his numerical studies on dynamic impact, Karagiozova and Jones
(Karagiozova & N Jones 2001; Karagiozova & Jones 2002; Karagiozova & Norman Jones
2001) observed that dynamic effects are larger in strain-rate sensitive material compare to the one with less sensitivity. The effects include initial instability pattern, energy absorption during the deformation process and the deformation shapes.
In 2004, Marais et (Marais et al. 2004) al studied two material models that incorporate strain-rate plasticity model which are Cowper-Symonds and Johnson-Cook model. He tested these two material models by compare them with experimental results. He concluded that the selection of correct parameter values for both constitutive models is vital in obtaining good correlation with experimental results. Earlier in 2000, Lesuer (Lesuer
2000) studied the dynamic effect on Johnson-Cook material model and failure model in which he suggested a new material and failure parameter values to be implemented for high strain rate impact analysis. With the new parameters provided by Lesuer, Buyuk and
Loikkanen (Buyuk et al. 2008) studied the effect of different Johnson-Cook parameters including the original material parameters provided by Johnson and his colleagues (Johnson
1983; Johnson & Cook 1985). He concluded that it is necessary to recalibrate the Johnson-
34
Cook parameters to obtain a better consistency between simulations. For implementation of Johnson-Cook model in low velocity impact regime, Mohotti et al (Mohotti et al. 2013) tested the model for low impact velocity ranging between 9.02 to 13.20 ms-1. Results from the numerical model that used Johnson-Cook material and failure models correlate well with experimental results but has a small time lag observed in its deflection-time histories.
2.2.7 Finite Element Modelling of Impact and Damage on Fibre Metal Laminate
and Its Constituents
2.2.7.1 Plane stress assumption and choice of element
In 2014, Chai and Manikandan (Chai & Manikandan 2014) et al reviewed works on low velocity impact response of fibre metal laminate (FML) and concluded that a full unambiguous continuum finite element model with appropriate interface elements is required to simulate impact response of FML. In the same year, Morinière et al (Morinière et al. 2014) also highlighted that plane stress assumption in composite failure criterion within FML impact response model is invalid and he suggested full three-dimensional composite failure criterion is used instead. There is a number or researchers that implement full three-dimensional composite failure in their impact models. The development of their FE impact model of composite can be referred in their respective papers (Seo et al. 2010; Donadon et al. 2008; Tita et al. 2008; Lee & Huang 2003). All of them concluded that model with full three-dimensional material and damage model produced very good correlations with experimental results in almost all aspects. Important to be mentioned that in modelling impact response of composite laminate, plane stress material and failure model still produced reasonable results as proved by Seo et al (Seo et al. 2010). This claim is also supported initially by Hashagen in 1995 (Hashagen et al. 1995) in which solid-like shell element that implement plane stress analysis is capable of computing laminate structure behaviour and its consequences. In Abaqus FE code, solid-
35 like shell element is known as continuum shell element (Abaqus Documentation, version
6.10). Other researchers that also implemented plane stress failure criterion for composite and FML also proved that their results correlate well up to certain degree with experimental results (Sadighi et al. 2012; Song et al. 2010; Fan et al. 2011; Seo et al. 2010;
Zhu & Joyce 2012). With all due respect, understanding of the impact mechanics of particular impact event is essential in order to determine the requirement of full three- dimensional material and damage model for composite constituent in FML. Localised impact event is the most likely case to implement full three-dimensional model as the impact occurs in through thickness direction, meanwhile impact condition that might cause buckling and bending as the main responses could adequately modelled with plane stress assumption in its composite constituents. It is obvious that by upgrading plane stress model to full three-dimensional model will cause increase in computational cost.
In modelling metal constituent of the FML, eight nodes solid element is mainly used by researchers including Zhu and Joyce (Zhu & Joyce 2012), Seo et al (Seo et al. 2010) and Fan et al (Fan et al. 2011). Buyuk and Loikkanen (Buyuk et al. 2008) and Kay (Kay 2003) that studied impact behaviour of aluminium alloy 2024-T3 also discretized the metal plate using solid element in which produced results that well correlate with experiment.
Computational efficiency in their finite element models is achieved by implementing reduced integration solid element with suitable hourglass control without compromising the accuracy of the results.
2.2.7.2 Interface layer for delamination model
In 2004, Linde (Linde et al. 2004) et al develop an FE model of the inter rivet buckling behaviour in a stiffened FML fuselage shell. He described that delamination is not expected only to occur between metal and composite surfaces, but it is also likely to occur within the composite layers themselves.
36
Morinière et al (Morinière et al. 2014) claimed that delamination in low velocity localised impact event has lower contribution compare to high velocity localised impact event and it is proven by Laliberte et al (Laliberté et al. 2002)in his comparative study between FML impact model with and without delamination. This claim is valid for localised impact event but invalid for impact event in the axial direction that may cause buckling. Earlier in 2001,
Remmers (Remmers & de Borst 2001) presented that buckling delamination is the main failure mode in FML buckling. Thus the impact condition on FML should determine the significance of modelling interface layer between layers.
37
2.3 Summary of the Literature Review
The importance of evaluating crashworthiness of fibre metal laminate (FML) fuselage has been discussed previously. In the early work in the literature review, it is proven that numerical modelling is progressively becoming a practical method in evaluating crashworthiness of an aircraft. The capability of computational facilities nowadays makes numerical modelling less expensive and more efficient than crash test in evaluating crashworthiness of an aircraft. In addition to the non-existence crash test of FML fuselage, a fully computational development of reliable numerical model of FML fuselage are taking place in this thesis. In order to do this, it is suggested by several authors that building block approach that mainly used in aircraft design industry can be adapted into pure computational modelling of aircraft crash numerical model. This building block adaptation is well explained in Chapter 5. It involves validation of material and damage model of both aluminium alloy and composite laminate, validation of impact modelling that causes large displacement and instability and verification of a fuselage frame under impact condition.
This adaptation technique is modelled based on the understanding obtained from the mechanical and impact properties of fibre metal laminates and its constituents. Papers reviewed suggested several material models that suit impact and damage for aluminium and composite laminate which is valuable in modelling reliable numerical model of FML fuselage. The discussion on the necessity of modelling interface layer within composite laminate concluded that the author has to exercise its engineering judgement based on the general structure of interest, impact condition and anticipation on the failure mechanisms of the FML structure.
38
Chapter 3 BACKGROUND THEORY OF FIBRE METAL LAMINATE
3.1 Introduction on Fibre Metal Laminate
Fibre metal laminates (FML) are made of a combination of fibre reinforced laminated composites and thin layers of metals. These hybrid materials provide superior mechanical properties compared to the polymer matrix composites or aluminium alloys. FMLs have better tolerance to fatigue crack growth and impact damage especially for aircraft applications. Different combinations of metal alloys and composite laminates produce different families of FMLs. The most common types of FMLs are Glass Reinforced
Aluminium Laminate (GLARE), Aramid Reinforced Aluminium Laminate (ARALL) and Carbon
Reinforced Aluminium Laminate (CARALL). This chapter reviews and discusses the material properties, constitutive equations and impact characteristics of aluminium alloys, fibre reinforced laminated composites and GLARE.
3.1.1 GLARE: A Glass Fibre Reinforced Based Fibre Metal Laminate
GLARE is a glass fibre reinforced aluminium laminate which is commercialized in six different grades as shown in Table 3-1. Composite in GLARE is all based on advanced unidirectional glass fibres which are embedded within epoxy FM94 adhesive with a nominal fibre volume fraction of 60% (Cocchieri et al. 2006; Sadighi et al. 2012). Metal in GLARE is aluminium alloy 2024-T3 except for GLARE 1 that uses aluminium alloy 7475-T761. Prepreg is stacked symmetrically in GLARE except for GLARE 3 and GLARE 6. In standard practice, a coding system is used to specify GLARE and other FML. For example GLARE 2B-4/3-0.4 is a
GLARE 2B (Table 3-1) that has four layers of aluminium with 0.4 mm thick each and three
90⁰/90⁰ prepreg layers (Cocchieri et al. 2006).
GLARE that has already been used to construct the top half fuselage skin in Airbus A380 has a potential to be used as bottom half of the fuselage skin in the near future as it has excellent impact resistance (Sinmazçelik et al. 2011). In fact it is being evaluated for use as
39 cockpit crown, forward bulkheads and leading edges in which they are the area that require most excellent impact resistance material (Asundi & Choi 1997).
In comparison to ARALL, GLARE has advantages in terms of higher tensile strength, higher compressive strength, higher failure strain, superior impact resistance and does not absorb moisture. However GLARE has higher specific weight and lower stiffness than ARALL.
Grade Sub Metal Metal Fibre Prepeg Characteristics type thickness layer orientation (mm) (mm) in each fibre layer (⁰)
GLARE 1 - 7475- 0.3-0.4 0.266 0/0 Fatigue, strength, T761 yield stress
GLARE 2 GLARE 2024-T3 0.2-0.5 0.266 0/0 Fatigue, strength 2A
GLARE 2024-T3 0.2-0.5 0.266 90/90 Fatigue, strength 2B
GLARE 3 - 2024-T3 0.2-0.5 0.266 0/90 Fatigue, impact
GLARE 4 GLARE 2024-T3 0.2-0.5 0.266 0/90/0 Fatigue, strength, 4A in 0⁰ direction
GLARE 2024-T3 0.2-0.5 0.266 90/0/90 Fatigue, strength, 4B in 90⁰ direction
GLARE 5 - 2024-T3 0.2-0.5 0.266 0/90/90/0 Impact, shear, off- axis properties
GLARE 6 GLARE 2024-T3 0.2-0.5 0.266 +45/-45 Shear, off-axis 6A properties
GLARE 2024-T3 0.2-0.5 0.266 -45/+45 Shear, off-axis 6B properties
Table 3 -1 Commercially available ARALL laminates (Khan et al. 2009).
3.1.2 Impact Behaviour of GLARE
Extensive review on impact behaviour of FML has been presented in Chapter 2 and it is conclusive that mechanical property and impact response of fibre metal laminate (FML)
40 depends on the mechanical properties and impact response of the constituents itself. In addition to the impact response of FML’s constituent as the basis, the interaction between their impact response to each other including various failure mechanisms and modes have to be taken into account.
41
3.2 Aluminium Alloys
Aluminium alloys have been used in aircraft industry since World War One and they still remain one of the most important materials in aerospace industry. Aluminium alloy is an isotropic and homogeneous material where by definition the material properties are independent of direction.
3.2.1 Stress-strain Relationship of Isotropic and Homogeneous Materials
The stress-strains relations for a linear elastic, isotropic and homogeneous material can be written as
(3.1)
where and , E and are the stress tensor, strain tensor, Young’s Modulus and
Poisson’s ratio, respectively. The above equation can also be written in matrix form as,
(3.2) where is called the stiffness matrix. As shown in equation 3.1, only two material properties or elastic constants are required to form the stiffness matrix of a homogeneous and isotropic material. The stress-strain relations can also be written in terms of the compliance matrix (S) where
(3.3)
or
42
Similar to other metal, aluminium alloy exhibits elastic-plastic behaviour in which it undergoes irreversible plastic strain when the stress within the material reaches yield stress, . The stress-strain curve that illustrates elastic-plastic behaviour of a typical aluminium alloy bar subject to static loading is shown in Figure 3 -1. Beyond yield stress the plastic deformation occurs with strain hardening up to ultimate tensile strength (UTS).
Beyond UTS, the strain softens until fracture or total fail. Aluminium alloy 2024-T3 that used in GLARE also follows the same stress-strain behaviour. Mechanical properties of aluminium alloy 2024-T3 are tabulated in Table 3-2.
Stress, UTS
E
0 Strain,
Figure 3 -1: Typical stress-strain curve of isotropic material (Gere & Timoshenko 1990)
Density, ρ (kg/m3) 2700
Melting temperature, Tm (Kelvin) 775 Elastic properties Young’s modulus, E (GPa) 73.1 ν 0.33
Yield stress, (MPa) 345 Ultimate tensile strength, UTS 483
Failure strain, 0.18
Table 3 -2 Mechanical properties of aluminium alloy 2024-T3 (Lesuer 2000; Buyuk et al. 2008)
43
Metallic material can be sensitive or insensitive to the strain-rate when subject to loading and this sensitivity depends on the type of alloy. The stress-strain relationships of a strain- rate sensitive material under static loading cannot accurately predict the stress-strain relationships of the same material when is subject to impact loading (Rodríguez-Martínez et al. 2011). Figure 3 -2 shows the stress-strain curves of aluminium alloy 2024-T3 for subjected to loading with three different strain rates. It is observed that strain rate affect the yield stress, hardening and ultimate tensile strength of the material.
600
500
400
300
200
0.01s-1 Equivalent stress (MPa)stress Equivalent 100 10s-1 100s-1 0 0.00 0.05 0.10 0.15 0.20 Equivalent plastic strain
Figure 3 -2: Equivalent stress evolution versus equivalent plastic strain for different strain rates for aluminium alloy 2024-T3 (Rodríguez-Martínez et al. 2011).
Stress-strain curves under different strain rate can be obtained by tensile test carried on the strain rate desired. Several models are available to estimate the strain response of metal under various loading rate including Johnson-Cook material model that contain the estimation of rate-dependent yield stress and rate-dependent hardening as in Equation 3.4 to 3.5 (Johnson & Cook 1983; Abaqus Documentation version 6.12). In a non-thermo- coupled analysis, the homologous temperature so the final term consists of the
44 homologous temperature will be equal to 1. So the expression can be rewritten without the final term as in Equation 3.5.
(3.4)
(3.5)
where , , , and are material properties of the aluminium alloy, is equivalent
plastic strain, is equivalent plastic strain rate, is reference strain rate and is homologous temperature.
3.2.2 Impact Behaviour of Aluminium Alloys Structure
An aluminium alloy structure which is subjected to axial impact may fail due to buckling when the impact load exceeds its dynamic critical buckling load. Figure 3 -3 shows aluminium alloy structure that fail under axial impact loading due to buckling. The critical buckling load of an aluminium alloy structure under dynamic impact mainly depends on its material properties, mass, the impact velocity and most importantly the impact energy.
These parameters determine the patterns of the axial stress wave propagation which result in different type of buckling modes. The axial stress wave can be divided into elastic stress wave and plastic stress wave. The above parameters also affect the energy absorption of the aluminium alloy structure during impact. The aluminium alloy structure which is subject to axial impact may experience elastic-plastic deformation only or may crack as well. As mentioned earlier, this mainly depends on the geometry of the structure, its material properties, impact energy and impact velocity (Karagiozova et al. 2000; Karagiozova &
Jones 2000; Karagiozova & Jones 2001a, Hooputra et al 2004).
45
Figure 3 -3.Buckling of aluminium can under axial loading (Palanivelu et al. 2011).
An aluminium alloy plate subjected to the lateral low velocity impact may be subjected to indention damage or perforation. Again, this mainly depends on the plate’s material properties, the impact energy and the impact velocity. The plate that exhibits indention initially experiences localised plastic deformation, with or without cracks. If perforation occurs, it usually starts with a local plastic deformation. Thus cracks initiate and then followed by crack propagations (Rodriguez-Martinez et al. 2011).
Crack or fracture in aluminium alloy in any type of impact loading may occur due to stresses within the aluminium alloy that surpass its critical limit. The stresses could be tensile stress or shear stress. Tensile failure or fracture occurs due to nucleation growth and coalescence voids within the structure. Meanwhile shear fracture is caused by shear band localisation (Abaqus Documentation version 6.12). Johnson-Cook failure criterion is one of the ductile fracture criterions as expressed in Equation 3.6.
(3.6)
where is the equivalent plastic strain at failure, are failure parameters measured at or below the transition temperature, , p is the pressure stress, q is
the Mises stress. is the plastic strain rate and is the reference strain rate (Johnson &
Cook 1985; Abaqus Documentation version 6.12).
46
Damage mechanics would determine the effect of damage on the stiffness of the damaged material up to its total failure condition. The strain response in damaged material is generally defined by Equation 3.7
(3.7)
where the damage variable represents the damage within the material point which controlled by stiffness degradation rules based on fracture mechanics. The damage variable may have values between 0 to 1 in which denotes that the material has totally damaged; leaving no residual stiffness and that element is removed from the global finite element equation of the body problem.
47
3.3 Fibre Reinforced Composite Laminate
Fibre reinforced laminates are composite materials that have strong continuous or non- continuous fibres surrounded by a weaker material called matrix. The most common types of fibre materials are glass, aramid (Kevlar), carbon, boron and silicon carbide. Meanwhile matrix materials could be grouped into three categories; polymer matrix such as thermoplastic resins, ceramic matrix such as carbon and metallic matrix such as aluminium alloys. Fibres and matrix are bonded during a manufacturing process called curing (Gay &
Hoa 2007).
3.3.1 Stress-strain Relationships of Fibre Reinforced Composite Laminate
Unlike aluminium alloy, composite materials are anisotropic in nature which make composite to have 21 independent engineering constants in its stress-strain relationship as expressed in Equation 3.8.
(3.8)
where is the stiffness matrix ( ). The stress and strain tensors are symmetric, and since the stress-strain relations in linear elasticity can be derived from a strain energy density function, the following symmetries hold for linear elastic materials
for .
An orthotropic material has two orthogonal planes of symmetry. Therefore, only 9 independent engineering constants are required to construct the material’s stiffness matrix. Stress-strain relations for a linear elastic orthotropic material can be as expressed
(Gay & Hoa, 2007).
48
(3.9)
As shown, there is no interaction between normal stresses , , and shear strains
, , . Similarly there is no interaction between shear stresses and normal strains.
The stress-strain relationships of orthotropic composite laminates can also be expressed in terms of the compliance matrix (Gay & Hoa, 2007),
(3.10)
or
(3.11)
with
, ,
3.3.2 Analysis of a Composite Lamina
A unit block of a composite laminated structure is a lamina. Superposition of a number of laminas or layers made of unidirectional layers form a composite laminate. A lamina is very thin in relation to its transverse dimensions and it is usually considered to be in plane stress
49 state when subjected to in-plane loadings. Figure 3 -4 illustrates the local coordinates of lamina under state of plane stress analysis.
2 y
1 x
Direction of fibres Figure 3 -4. Local coordinates of a lamina
Under this plane stress state, is assumed to be zero. The stress-strain relationships are now expressed as in equation 3.12 to 3.17 which reduces the independent constants to only four (Gay & Hoa, 2007). The stress-strain relationship of an orthotropic composite lamina in terms of stiffness coefficients is;
(3.12)
(3.13)
with
, , (3.14)
, ,
and its compliance;
(3.15)
50
(3.16)
, , (3.17)
, ,
All expressions defining stress and strain relationship are in local 1,2 directions of the lamina. If the local direction is not coincident with global axis, transformation matrix must be applied such that;
and (3.18)
(3.19) where
(3.20)
with and with is the angle between the local axis and global axis.
Finally forming the relation between global stresses and strains as
(3.21) with is global stiffness matrix of the composite lamina where
(3.22)
Subscripts and in Equation 3.18 to 3.21 indicate the global axis and local axis respectively.
51
3.3.3 Failure of Fibre-reinforced Composite Laminate
Fibre-reinforced composite laminates experience different types of failure such as fibre rupture, matrix rupture and delamination. Figure 3 -5 illustrates schematically main modes of damage when the loads exceed the critical limits.
Figure 3 -5 Failure modes of composite laminate (Gay and Hoa 2007).
In composite design, various failure criteria have been proposed by several researchers in order to predict the onset of composite laminate failure. The most popular failure criteria are the Hashin’s criterion Puck’s criterion, Tsai-Hill criterion, Chang and Chang’s criterion, maximum stress criterion and maximum strain criterion. Hashin’s failure criterion has been used by many researchers and it is one of the most reliable methods to predict the strength of laminated composites (Sun & Tao 1998). In this thesis, Hashin’s failure criterion (Hashin
& Rotem 1973; Hashin 1980) is employed and both three-dimensional and two-dimensional or plane stress cases are presented.
Hashin’s failure criterion was originally developed for unidirectional fibre-reinforced laminate. Even though a three-dimensional failure criterion is available, but it is limited to the scope of unidirectional laminates (Hashin and Rotem 1973; Hashin 1980). The criterion
52 is based on two failure mechanisms which are associated with failure in fibre and failure in matrix, distinguishing in both cases between tension and compression. Two sets of Hashin’s failure criterion are presented here; one with a plane stress assumption and the second one is three-dimensional failure criterion.
3.3.3.1 Hashin’s Failure Criterion under State of Plane Stress
Failure mechanisms of fibre are governed by the longitudinal stress with reference to the fibre orientation. Meanwhile failure mechanisms of matrix are governed by the transversal and tangential stresses to the fibre. Failure is said to occur or damage is initiated at any failure mode if the failure criterion of that failure mode is equal or greater than one
(Abaqus Documentation version 6.12). It must be noted that the original Hashin’s failure criterion based on his paper in 1998 for compressive fibre mode is a non-quadratic expression. Modification to quadratic term in fibre compressive mode possibly due to maximum stress criterion would underestimate the strength of the laminate.
For failure in tensile fibre mode ( ),
(3.23)
For failure in compressive fibre mode ( ),
(3.24)
For failure in tensile matrix mode ( ),
(3.25)
For failure in tensile matrix mode ( ),
(3.26)
53 where XT, XC, YC, YT, S12, S23 and are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength, longitudinal shear strength, transverse shear strength in 2-3 direction and coefficient that determines the contribution of the shear stress to the fibre tensile failure criterion, respectively. is a function that describes the failure criterion.
3.3.3.2 Three-Dimensional Hashin’s Failure Criterion
Three-dimensional Hashin’s failure criterion is based on Hashin’s work in 1980. The same basis as Hashin’s failure criterion under plane stress state is used where two separate failure mechanisms are described in both tensile and compressive stress states. The additional term that does not appear in failure criterion under plane stress state is the transverse shear strength of 1-3 direction, .
For failure in tensile fibre mode ( ),
(3.27)
For failure in compressive fibre mode ( ),
(3.28)
For failure in tensile matrix mode ( ),
(3.29)
For failure in tensile matrix mode ( ),
(3.30)
54
3.3.3.3 Delamination of Fibre-Reinforced Composite Laminate
Delamination or interlaminar crack occurs when the lamina that form the laminate structure separate from each other due to interlaminar shear stresses. It may also be triggered by matrix cracking close to the surface of the laminas with different fibre orientation or close to a matrix rich area between two plies. Composite structures that fail under buckling mode always suffer delamination. Composite structure may also suffer delamination at the outer layers that experiences tensile stress gradient along its thickness when subjected to bending. Delamination in composite laminate is also part of the failure mechanisms that control the failure mode when a composite laminate structure is axially crushed. In laminate and delamination analysis, the surface where the delamination can occur is always referred as interface layer.
Delamination degrades the stiffness and strength of laminate, alters the damping coefficient in impact and can cause local buckling if compression load is applied. The analysis of delamination in composite laminate is divided into two steps; delamination initiation and delamination propagation.
A stressed based quadratic failure criterion for delamination initiation is expressed in equation 3.31 (Brewer & Lagace 1988; Zhou & Sun 1990).
(3.31)
where in the above equations is tensile strength in the thickness direction at the interface layer, is interlaminar shear strength in the direction at the interface layer and is interlaminar shear strength in the direction at the interface layer.
Stresses in Equation 3.31 are the average interlaminar stresses defined as in Equation 3.32 where is the thickness of the interface layer.
55
(3.32)
In analysing delamination propagation, fracture mechanics is always used as this approach may avoids difficulties caused by stress singularity at crack point. Delamination growth is mainly controlled by the properties of the matrix (Farley & Jones; 1992).
3.3.4 Impact Behaviour of Fibre-Reinforced Composite Laminate under Low
Velocity Impact
Impact behaviour of fibre-reinforced composite laminate is mainly analysed under two categories. The first one is lateral impact onto the laminate by drop weight alike and the second one is dynamic axial crushing. Both analyses involve analysing the impact damage, failure mechanisms, failure modes and energy absorption due to the damage process.
3.3.4.1 Lateral Impact
Under lateral impact on composite laminate, out-of-plane stresses are significantly smaller than in-plane stress even though the impact is in the thickness direction. In the same time, maximum stress in fibre-direction is always larger than in its in-plane orthogonal direction because the flexural wave moves faster in the fibre direction compare to the other direction (Aslan et al, 2003). Failure in composite laminate under low velocity lateral impact can be caused fibre fracture or matrix fracture or delamination or combination of them.
Thick and thin composite laminates response differently under lateral loading. In thick laminate, impact failure is always dominated by fibre fracture meanwhile in thin laminate, delamination plays a major role in the impact failure. High bending stiffness in thick laminate causes high out-of-plane stresses within the localised impacted area thus causes high indention effect which results the fibre fracture dominate the impact damage in thick laminate. In thin laminate, low bending stiffness causes the high bending or tensile stress at the outer layer (non-impacted). This high in-plane tensile stress causes matrix cracking at the surface of the outer lamina and may trigger delamination at that surface. The impact
56 response of thin laminate is almost like an efficient membrane response especially in the presence of delamination. Due to this, researcher that model impact response of laminate that consists of unidirectional laminas always simply consider the composite laminate as a combination of lamina under plane stress state but with incorporation of interface layer modelling in order to take into account the delamination.
3.3.4.2 Axial Impact
Impact response of composite laminate under axial crushing exhibits complex response due to the interaction of various failure mechanisms. Three crushing modes of composite laminate tube under dynamic axial loading are; i. Transverse shearing mode
Failure mechanisms that control transverse shearing mode are interlaminar crack growth and lamina bundle fracture. Interlaminar crack growth or delamination can occur as opening mode (Mode I) or as forward shear mode (Mode II) as illustrated in Figure 3 -6. Its growth is mainly controlled by the properties of the matrix, but in the same time circumferentially oriented fibre can have a major influence. Then the delaminated lamina or laminates are subjected to the bending force, causing the lamina bundles to fracture once the stress at the tensile side of the bended bundle exceeds its strength.
57
Figure 3 -6. Sketch of crack propagation mode (Farley & Jones 1992).
ii. Lamina bending crushing mode
The failure mechanisms that control this failure mode is almost the same as in transverse shearing mode except that when the lamina bends, the transverse shear crack does not take place but the bending keep its progress and interlaminar crack progressively propagate. Besides interlaminar crack, energy is absorbed due to friction work between the loading surface and crushing surface of the composite. Thus it is important to take into account the contribution of friction work in modelling such failure mode. iii. Local buckling crushing mode
This mode is controlled by yielding of matrix or combination of both matrix and fibres.
58
Chapter 4 FINITE ELEMENT METHOD
4.1. Introduction
4.1.1. Introduction of Finite Element Method in Aircraft Crash Analysis
Finite element method is a numerical technique for finding approximate solutions to boundary value problems for differential equations. Since the basic idea is to find the solution of a complex problem by replacing it with a simpler one, the solution will be an approximation rather than the exact one. The region of the problem to be solved is discretised to many small interconnected subregions which are called as finite elements. By assuming approximate solutions of each finite element, conditions of overall equilibrium of the region are derived. In this study, region of the problem is referred to aircraft structure such as fuselage frames, fuselage skin, stringers and floor beams.
Originally, finite element method was developed for the aircraft structure’s analysis either on component level, structural level, section level or full-scale fuselage level. Substantial amount of static and dynamic analyses have been carried using finite element method either by researchers or aircraft designers (Hashemi et al. 1996; Hashemi & Walton 2000;
Fasanella and Jackson 2000; Jackson & Fasanella 2005; Meng et al. 2009). One of the departments in aircraft structural analysis benefited from finite element method is aircraft crash analysis in order to analyse the impact response of the aircraft including structural integrity of the aircraft, collapse mechanisms and crashworthiness. In the emergence of new materials for aircraft structure such as composites and fibre metal laminate (FML), the impact response of the aircraft especially in terms of crashworthiness becomes new issue for the aircraft designers. Impact test might provide extensive data on impact response under crash but it is limited to a number of impact conditions only. Additionally, impact test is very expensive. The use of finite element method enables researchers to analyse crash of aircraft not just with lower cost but with almost unlimited impact conditions can
59 be simulated. In order to simulate aircraft crash, certain methodology must be developed in order to obtain reliable crash simulation results. This might includes material characterisation and modelling verifications. Methodology and verification process of crash simulation model for fibre metal laminate (FML) fuselage is presented in the next chapter.
This chapter discusses about finite element method and its background theory used in developing crash simulation of FML fuselage section.
4.1.2. General Description of Finite Element Method
A structure to be analysed by finite element method has to be discretised to form interconnected finite elements in which the connections between elements occurs at specified joints call nodes. Field variables at the nodes are the unknowns to be solved from the finite element problems which are generally in the form of matrix equations. Once the unknowns at the nodes are solved, the field variables inside the elements are approximated by a simple function called interpolation models. As a result, the field variables throughout the assemblage of elements or the whole region will be known.
Generally, solving a continuum problem by the finite element method is an orderly step by step process. The step by step process is described below (Rao 1999).
Step 1: Discretization of the structure
Step 2: Selection of a proper interpolation model or displacement model
Step 3: Formation of element stiffness matrix
Step 4: Formation of global stiffness matrix and load vector
Step 5: Solution of the unknown nodal displacements
Step 6: Computation of element strains and stresses
Step 7: Post-processing
60
These steps are carried carefully throughout the process in developing a finite element model of fibre metal laminate (FML) fuselage section. While using commercial finite element (FE) code software, these steps are not necessarily distinctive because they could be mixed between them while the user select the type of elements to be used, the formulations used to control the section of elements, the material models, type of analysis and many more. For in-depth understanding on these six steps, one can refer to text books that discuss about finite element model from the fundamentals to specific analysis
(Zienkiewicz & Taylor 1991a; Zienkiewicz & Taylor 1991b; Rao 1999).
In general, a finite element equation system is form for the body region to be analysed as
(4.1)
, and denote the load vectors, stiffness matrix and displacement vectors of the complete structural body or system. The finite element equation is solved by various methods depends on the body problem and type of analysis.
4.1.3. Abaqus Finite Element (FE) Software
All finite element modelling and analysis in this thesis is done in Abaqus/Explicit version
6.10 and 6.12 but all the final results of the FML crash simulation are solved in version 6.12.
Abaqus/Explicit is used in order to take advantage its capabilities in solving nonlinear transient analysis and its computational efficiency. The analysis was carried successfully even though there were challenges in terms of computational stability in explicit solver which may cause the solution to diverge and terminated immaturely. The author used both
CAE and keyword modelling (input files) for pre-processing and fully used CAE for post- processing.
61
4.2. Nonlinear Dynamic Analysis
4.2.1. Nonlinear Analysis of Aircraft Structure
In many practical engineering problems including fuselage deformation in crash analysis, the linearity of the problems does not preserved. In structural analysis, the nonlinearity of the problem exists might be due to either by the nonlinearity of the constitutive relations or by the nonlinearity of the structure geometry. Both nonlinearities exist in crash simulation of fibre metal laminate (FML) fuselage. Fuselage section that made of FML consists of aluminium alloy that will undergo plastic deformation when the stresses surpass its yield criterion. Due to this, nonlinear constitutive relations are considered in the metallic part of the fuselage structure. Meanwhile nonlinearity of the structure geometry occurs in this study when the fuselage structure undergoes large displacement and structure instability.
4.2.1.1. Plasticity Analysis
In nonlinear plasticity analysis, the stress-strain relationship within the material is expressed in incremental form. The nonlinearity requires the stress-strain relationship and both local and global finite element equation to be solved and satisfied incrementally
(Zienkiewicz & Taylor 1991b). The constitutive stress-strain relationship in nonlinear plastic analysis is in form of
(4.2)
where is the nonlinear stiffness matrix. Incremental strain is decomposed into incremental elastic strain, and incremental plastic strain as expressed in Equation
4.3.
(4.3)
62
To solve the finite element equation of plastic analysis, first one needs to solve the incremental stress in Equation 4.2. There are several methods to solve the equation.
Method that used by Abaqus FE code is by solving few related equations with the constitutive stress-strain equations using backward Euler method and central difference operator (Abaqus Documentation version 6.12). Following the incremental procedure of the stress-strain constitutive equation, the finite element equation (Equation 4.1) for the plasticity analysis is also in incremental form and solved by applying incremental load
(Zienkiewicz & Taylor 1991b).
4.2.1.2. Geometrically Nonlinear Analysis
In aircraft crash analysis, the structure might undergo large displacements and strains such as deformation due to instability of the structure. Large displacement or deformation can occur even the elastic limits are still not exceeded. Geometry nonlinearity must be considered in aircraft crash analysis. In crash simulation of FML fuselage, geometric nonlinearity is combined with material nonlinearity.
In geometrical nonlinear analysis, the stress-strain constitutive equation is linear but the strain-displacement relationship is non-linear unlike strain-displacement relationship in ordinary linear stress-strain analysis. Besides that, geometrical nonlinear analysis equations are in incremental form, similar to equations in plastic analysis. If the analysis is a combination of geometrical nonlinear and plastic analysis, the linear stress-strain constitutive equation is replaced with the nonlinear stress-strain equation as in plasticity analysis (Zienkiewicz & Taylor 1991b).
Once the finite element equation for the geometrically nonlinear analysis is formed, the same procedure as plasticity analysis is used to solve the equation.
63
4.2.2. Dynamic Analysis of Aircraft Structure
Aircraft crash analysis is a nonlinear dynamic analysis problem which is a time-dependent or transient process. Such nonlinear analysis can be solved either implicitly or explicitly in
Abaqus FE code. In implicit analysis (Abaqus/Standard), the problems are solved by iterating the nonlinear equations at every increment in order to solve them. It solves the equilibrium state of the whole problem domain at every increment. As it iterates at every increment, implicit procedure can be performed relatively at fewer number of time increments compare to explicit procedure but it has a large set of linear equations to be solved. On the other hand, explicit procedure solves the problem without iterations by explicitly advancing the kinematic state of the body problem from the previous increment.
Due to this, it requires a large number of small time increments, but relatively inexpensive as it does not have to solve large number of linear equations as in implicit (Zienkiewicz &
Taylor 1991b, Abaqus Documentation version 6.12).
Explicit procedure is efficient for problem that involves wave propagation. Besides, it is very attractive in terms of computational cost as it requires less disk space and memory and it solves dynamic problems quicker than implicit procedure for the same simulation. This is because implicit procedure has to store and solve large amount of linear equations within each iteration. With all due respect, explicit procedure is used in this project in simulating crash of fibre metal laminate (FML) fuselage.
The key element in explicit dynamic analysis in Abaqus/Explicit is the implementation of an explicit integration rule and the use of diagonal element mass matrices. The finite element equation of dynamic is based on the dynamic equation of motion of a body thus the field problems in dynamic equation are not just in form of stresses, strains and displacements but also in form of velocities and accelerations. This equation of motion is integrated using the explicit central difference integration rule. Explicit procedure is conditionally stable due
64 to the use of central difference operator, unlike implicit procedure that unconditionally stable. The stability is controlled by introducing small amount of damping which reduces the stable time increment. The time increment scheme in Abaqus/Explicit is automatic thus it will automatically determine the stable time increment for the solution to proceed successfully (Abaqus Documentation version 6.12; Zienkiewicz & Taylor 1991b).
65
4.3. Selection of Elements for Discretisation
There are few considerations need to be made in order to select the proper element in discretising the structure of the problems. The considerations include type of analysis, the geometry of the structure, the dimension of the problem and the application of the structure within the problem. Computational efficiency and cost would also become the reason of one to choose a specific type of element to discretise the problem. For example, in aircraft fuselage section, the structure consists of fuselage frames, stringers and floor beams that act as the main stiffeners of the fuselage section which can be represented as sets of beams. The fuselage skin alone is like a massive cylindrical shell structure.
Meanwhile the interface layer in between composite laminate and aluminium alloy within
FML acts as the adhesive between these two layers. Thus suitable element has to be selected to model all those structures.
4.3.1. Shell element
Shell element is used to model a three dimensional body structure which its thickness is significantly smaller than the other dimensions. It is actually an improvisation of the flat or plate element that originally developed to analyse flat plate. Plate is a flat structure that subjected to bending. Meanwhile shell is an extension of plate by initially forming the middle plane to a singly or doubly curved surface in which its stress resultant parallel to middle plane now have components normal to the surface (Zienkiewicz & Taylor 1991b).
Shell element is categorized as structural element in finite element analysis as it possesses common configuration in many physical structures and bodies.
4.3.1.1. Thin and Thick Shell Theories
Shell element formulation could be based on Kirchhoff thin shell theory or Reissner-Mindlin thick shell theory. Both theories have a mutual basic assumption which is the middle plane of the shell remains plane during and after deformation.
66
For thin shell theory, two additional assumptions are made as the basis of the theory. The assumptions are the normal of the middle plane remain normal to the middle plane and the thickness of the shell does not change during and after deformation (Timoshenko &
Woinowsky-Krieger 1959). As a result, there is no transverse shear deformation in thin shell theory. This type of shell element is suitable for structure that has thickness less than 1/15 of the characteristic length of the structure and the transverse shear deformation can be neglected (Abaqus Documentation version 6.12).
Meanwhile in thick shell theory, the two additional assumptions are not incorporated so the shell can have transverse shear deformation. There will be stress gradient across the shell thickness and the thickness of the shell may change. This element is suitable for thick shell structure in which the transverse shear stress and deformation are essential in capturing the structure’s response accurately (Abaqus Documentation version 6.12).
4.3.1.2. Conventional Shell Element and Continuum Shell Element
Two types of shell element are available which are conventional shell element which the body is discretised as a reference surface and continuum shell element which the body is discretised as three-dimensional body. Figure 4 -1 illustrates conventional shell element and continuum shell element. Conventional shell element is specified at the reference surface in which its thickness does not appear in its geometry but defined in the constitutive equation that define its section behaviour. It has both rotational and displacement degree of freedom at each node. Meanwhile continuum shell element discretised the whole geometry where its thickness depends on the defined geometry. Its nodes have only displacement degree of freedom.
67
Figure 4 -1. Conventional shell element and continuum shell element (Abaqus Documentation version 6.12)
In this thesis, both conventional and continuum shell elements that are categorised as general-purpose shell elements where they use thick shell theory as the thickness increases and use thin shell theory as the thickness decreases. Kirchhoff constraint is applied in their formulation in which the constraint becomes fully effective when the thickness is very thin and gradually released up to full thick shell theory as the thickness increases. The use of such shell element is capable of providing robust and accurate solution for many applications (Abaqus Documentation version 6.12).
Interpolation model in an element is used to interpolate the field variables output at its node to the space within its element. Interpolation model within shell element can be linear or polynomial (Rao 1999). In Abaqus, only linear and quadratic interpolation formulations are available for shell elements and there is only linear interpolation formulation available for explicit analysis. The number of nodes within an element shall describe the interpolation model used within an element. An element that uses linear interpolation formulation has only corner nodes and it should not have middle node at any of its edge. Consequently, a linear quadrilateral conventional and continuum shell element has four and eight nodes within their element respectively.
68
4.3.2. Incompatible Mode Solid Element
In finite element model of fuselage section, the fuselage skin can be modelled either by shell element or continuum element. It is adequate to use shell element if the fuselage skin is a single layer metallic material such as aluminium alloy. In a case of fuselage skin made of fibre metal laminates (FML) which consisted of at least two aluminium alloy layer and few layers of glass fibre composite laminate, it is more suitable to use continuum elements to discretise the structure. The interactions between lamina by using interface layers and the requirement of stresses continuity between them suggest that continuum element is more suitable. Solid continuum element is the most suitable element to model the aluminium alloy layer because it is modelled as elastic-plastic material, gets involve with contact and might undergoes large deformation during the analysis.
Incompatible mode solid element is a fully integrated first-order solid element in which incompatible mode is being incorporated in its formulation in order to improve its bending behaviour. The incompatible mode is responsible to eliminate the parasitic shear stresses.
Parasitic shear stresses are the stresses and artificial stiffening due to Poisson’s effect that cause ordinary first-order solid element to have stiff response towards bending. The use of incompatible mode in first order solid element requires incorporation of internal degree of freedom which causes this element more expensive than ordinary fully integrated solid element. However, it is favourable as it can produce results as good as second order fully integrated solid element (Abaqus Documentation version 6.12).
4.3.3. Reduced Integration Element
Integration point is the location where the integration evaluates various values including the stiffness matrix of the element. In fully integrated element, there are four integration points meanwhile in reduced integration element there is only one integration point. The field output calculated from these integration points than extrapolated within the element.
69
Intuitively, fully integrated element should produce more accurate results. However fully integrated element may suffer shear locking and in the same time reduced integration element may suffer hourglassing. By incorporating proper hourglassing control, accurate results can be obtained by using reduced integration element which sometimes better than its full integration element.
4.3.4. Hourglass Control
Most of the reduced integration element has only integration point being placed at the centroid of the element. Under certain condition, nodes that form the shape of the element may have displacement but the integration point at the centroid registers no energy and no straining. This zero-energy mode caused a phenomenon called hourglassing which finally leads to inaccurate results. Figure 4 -2 shows the deformation of the element in an hourglassing mode with the integration point experience no displacement or straining.
Figure 4 -2. Element deforms in hourglass mode (Westerberg 2002).
Hourglass control is introduced to prevent hourglassing problem within reduced integration element. This is done by adding a small artificial stiffness that associated with the zero- energy deformation. Several hourglass control formulations are available in Abaqus FE to suppress hourglass modes. Enhanced hourglass control is the best approach as it can produce good results with coarse mesh, provides increased resistance to hourglassing for nonlinear materials and works well with reduced integration shell element in both in-plane
70 and out-of-plane bending. This approach is actually a refinement of pure stiffness method in which the stiffness coefficients are based on the enhanced assumed strain method
(Abaqus Documentation version 6.12). The pure stiffness method is based on Kelvin viscoelastic approach defined as in Equation 4.4.
(4.4) where is the hourglass mode magnitude, is the force conjugate to , is the scaling factors and is the hourglass stiffness. So in enhanced hourglass control, the scaling factors is removed but the formulation would alter the hourglass stiffness based on its enhanced assumed strain method.
4.3.5. Cohesive Element
Interface layer has to be modelled in between FML layers. Interface layer can be represented by cohesive element (Linde et al. 2004). It is a special type element in Abaqus designated to model discontinuities like adhesives and interfacial layers in composite.
Figure 4 -3 illustrates a schematic representation of a finite element model of FML with cohesive element (dark-grey) being applied between layers.
Figure 4 -3. Schematic representation of FML with interface elements (dark-grey) applied between layers (Remmers & de Borst 2001).
71
Interface layer in FML is very thin and its thickness is relatively negligible to the thickness of the FML. So traction-separation constitutive approach to model the mechanical constitutive response of the cohesive element is implemented. This approach is simply an application of fracture mechanics in which amount of energy to create a new surface is being considered and it can be applied in three-dimensional problems (Abaqus
Documentation version 6.12).
4.3.5.1. Mechanical Constitutive Response of Traction-Separation Cohesive Element
The traction-separation model assumes initially linear elastic behaviour followed by damage initiation and damage evolution. The elastic constitutive matrix that relates the nominal stresses to the nominal strains governs the elastic behaviour of the cohesive element. To ensure that the nominal strain is equal to the separation, the constitutive thickness is set to be equal to 1.0. It must be reminded that constitutive thickness in this model is not the same with the actual thickness of the interface layer which is typically equal or close to zero (Abaqus Documentation version 6.12). The nominal stress vector consists of three components; the normal stress , shear traction on 1-local direction and shear traction in 2-local direction . The elastic behaviour then is written as
(4.5)
where
, and (4.6)
, , .
72 with , and are the corresponding separations and is the original thickness of the cohesive element. Figure 4 -4 illustrates typical traction-separation response with failure mechanisms in a cohesive element.
Figure 4 -4. Typical traction-separation response (Abaqus Documentation version 6.12)
4.3.5.2. Damage of Traction-Separation Cohesive Element
Damage initiation of interface layer is determined by the damage criterion. Several option of damage criterion for cohesive element is available in Abaqus. Quadratic nominal stress criterion assumes damage is initiated when a quadratic interaction function involving all nominal stress component ratios reaches a value of one. The quadratic nominal stress criterion is adapted from Brewer & Lagace (1988) and Zhou & Sun (1990) as in equation
3.31 and rewritten as in Equation 4.7.
(4.7)
where , , are the normal and two transverse shear tractions, , , are the normal and two transverse shear strengths and the symbol denotes that a pure compressive deformation or stress state does not initiate damage.
73
In order to fully model the damage of cohesive element, damage evolution model has to be incorporated to describe the propagation of the damage through degradation of the material stiffness corresponds to the damage initiation that has been satisfied.
Damage evolution is defined based on the fracture energy or amount of energy being dissipated due to the damage process (Abaqus Documentation version 6.12). Fracture energy is the area under the traction-separation curve as shown in Figure 4.5. Figure 4.5 illustrates the traction-separation response with exponential damage model. The term exponential mentioned indicates that the material softening occurs exponentially once the
material point passes the effective separation at damage initiation, as shown in Figure
4 -5. Meanwhile is the effective separation at total failure.
Figure 4 -5. Traction-separation response with exponential softening (Abaqus Documentation version 6.12).
Evolution of damage variable in exponential softening is expressed as in Equation 4.8 where and are effective traction and displacement respectively and is elastic strain energy at damage initiation (Abaqus Documentation version 6.12).
(4.8)
74
Fracture energy is defined separately for each traction components, but it can be modelled as mixed mode in which the deformation fields are dependent proportionally with all the traction components. The power law fracture criterion defines that failure under mixed- mode conditions is governed by a power law interaction of the energies required to cause failure in each individual traction mode. The criterion is expressed as
(4.9)
where , , are the work done by the tractions and their conjugate relative
displacements and , , are the fracture energies of each mode (Abaqus
Documentation version 6.12). In this criterion, the power of the law is 2.
75
4.4. Material and Damage Model of Aluminium Alloy
This section presents the material and damage model of the aluminium alloy used in modelling the metallic part of the FML fuselage. Some of the constitutive equations have been presented in previous chapter so it will not be rewritten here but reference of the equation number will be given. Material and damage properties of both aluminium alloy
2024-T3 and 7075-T6 are presented in Chapter 5 while specifically discussing on validation of their material models.
4.4.1. Material Model of Aluminium Alloy
Aluminium alloy fuselage structure is modelled as an elastic-plastic material. The elastic part of the model is described as isotropic elastic which possess only two elastic constants;
Young’s modulus and Poisson’s ratio. The constitutive three-dimensional stress-strain relationship that governs the elastic response of the aluminium alloy is expressed in
Equation 3.2.
The plastic response that defines the yielding and hardening of aluminium alloy is modelled using Johnson-Cook plasticity model as expressed in Equation 3.5. Johnson-Cook plasticity model is capable of determining the rate dependent yield stress and rate dependent hardening so it is very suitable to model the aluminium alloy under impact loading. It is also very suitable for high strain rate deformation modelling (Abaqus Documentation version
6.12). Four material parameters are required to use this plasticity model which can be obtained by sets of material test. These parameters for aluminium alloy 2024-T3 and 7075-
T6 that used in FML fuselage section are available in several published papers. The numerical solution procedure of plasticity is as described in section 4.2.1.1 on plasticity analysis.
76
4.4.2. Damage model of Aluminium Alloy
Failure onset, damage evolution and the total failure are used to model damage and failure in aluminium alloy. This damage models are suitable for both quasi-static and dynamic conditions. Following is the description of the damage initiation model to determine the onset of failure or damage in aluminium alloy. The damage evolution that describes the progression of the initiated damage and the total failure in which the element’s stiffness has fully degraded are also described.
4.4.3. Onset of damage in Aluminium Alloy
The onset of damage in Aluminium Alloy is determined by a special ductile criterion named
Johnson-Cook criterion. The criterion determines the equivalent plastic strain at the onset of damage as expressed in Equation 3.6 and rewritten as Equation 4.10 by removing the thermo-coupled term in the equation.
(4.10)
This criterion is a function of plastic strain rate , stress triaxiality and parameters to
. p is the pressure stress, q is the Mises stress which are measured at the instantaneous time meanwhile the to are failure parameters obtained from experiment. These parameters for aluminium alloy 2024-T3 and 7075-T6 that used in FML fuselage section are available in several published papers (Lesuer, 2000; Murat Buyuk, Matti Loikkanen 2008).
4.4.4. Damage Evolution of Aluminium Alloy
Damage evolution defines the stiffness degradation of the material in which the damage has initiated based on the Johnson-Cook failure criterion. Figure 4 -6 illustrates the typical stress-strain curve of aluminium alloy with progressive damage and stiffness degradation.
The softening curve is controlled by the damage evolution model. The dash line is simply the path of the straining if damage evolution is not modelled. The stiffness of the material
77 is degraded and controlled by the damage parameter . Effective plastic displacement is introduced once damage is initiated with
(4.11) where is the characteristic length of an element. In a first-order solid element, is simply the length of a line across that element. is used to form a new stress-displacement relationship in order to evaluate damage, as the use of ordinary stress-strain relationship can no longer accurately present the behaviour of the material once damage occurs
(Abaqus Documentation, version 6.12). Figure 4 -7 illustrates the linear damage-effective
plastic displacement relationship where is the effective plastic displacement at total failure. The damage-effective plastic displacement follows this relationship
(4.12)
Figure 4 -6. Stress-strain curve with progressive damage degradation (Abaqus Documentation version 6.12).
78
Figure 4 -7. A linear damage evolution based on effective plastic displacement (Abaqus Documentation version 6.12)
4.5. Material and Damage Model of Fibre-Reinforced Composite
Laminate
This section presents the material and damage model of the fibre-reinforce composite laminate used in modelling the composite laminate part of the FML fuselage. Some of the constitutive equations have been presented in previous chapter so it will not be rewritten here but reference of the equation number will be given.
4.5.1. Material Model of Fibre-Reinforced Composite Laminate
Fibre-reinforce composite laminate alloy fuselage structure is modelled as elastic material with damage model incorporated at lamina level. Plasticity is not modelled as this material is brittle in nature. Modelling the material response at lamina level allow us to represent each lamina as in a state of plane stress, thus there is only five elastic constants in its stress-strain constitutive equation. The plane stress-strain relationship is expressed previously in Equation 3.13 and its compliance form as in Equation 3.15. The through thickness response of the laminate is modelled by stacking each lamina and incorporating interface layer in between.
79
4.5.2. Onset of damage in Fibre-Reinforce Composite Lamina
Failure onset, damage evolution and the total failure are used to model damage and failure in fibre-reinforced composite laminate. Again, damage model is incorporated at lamina level same as how the undamaged mechanical response is modelled. Damage through thickness is represented by the damage of the cohesive element as the interface layer which has been discussed in section 4.3.5 . Following is the description of the damage initiation model to determine the onset of damage, the damage evolution that describes the progression of the initiated damage and the total failure in which the element’s stiffness has fully degraded in composite laminate.
In general, damage in the lamina degrades the stiffness of the material and it modifies the constitutive elastic stress-strain relationship as in Equation 4.14 (Abaqus Documentation version 6.12).
(4.13) with
(4.14)
where , is the current damage state of fiber, is the current damage state of the matrix and is the current damage state of shear damage.
Onset of damage in fibre-reinforce composite lamina is based on Hashin’s failure criterion.
The criterion differentiates four failure modes; fibre mode in tension, fibre mode in compression, matrix mode in tension and matrix mode in compression (Hashin & Rotem
1973; Hashin 1980). It is a stress based failure criterion in which the effective stress is used to express the failure surface. Effective stress is the stress acting over the area that efficiently resists the stress. The material that resists the stress within the lamina might
80 have been damaged by other failure mode. So the undamaged part within the damaged material is presented as the area left to resists the stress applied. Equation 4.15 expresses the relationship of stresses and the effective stresses.
(4.15) where is the effective stress, is the true stress and is the damage operator in which
(4.16)
with
,
,
Shear damage is in the function of all other damage mode that occurring within the lamina (Abaqus Documentation version 6.12). The Hashin’s failure criterion for each mode is presented in Equation 3.23 to 3.26. With all the stress components are replaced with their effective stresses respectively, the damage initiation criterion is rewritten as in
Equation 4.17 to 4.20 below. It should be noted that the criterion used here assumes plane stress state following that the plane stress state is assumed in the stress-strain constitutive equation of the lamina.
For failure in tensile fibre mode ( ),
(4.17)
81
For failure in compressive fibre mode ( ),
(4.18)
For failure in tensile matrix mode ( ),
(4.19)
For failure in tensile matrix mode ( ),
(4.20)
In the above equations
where XT, XC, YC, YT, S12, S23 and are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength, longitudinal shear strength, transverse shear strength in 2-3 direction and coefficient that determines the contribution of the shear stress to the fibre tensile failure criterion, respectively. F is a function that describes the failure criterion.
4.5.3. Damage Evolution of Fibre-Reinforced Composite Lamina
Similar to damage evolution in aluminium alloy, stress-displacement relationship is established to avoid mesh-dependency problem during softening if using ordinary stress- strain relationship. The equivalent displacement and stress are defined for each failure mode gives
For failure in tensile fibre mode ( ),
(4.21)
(4.22)
82
For failure in compressive fibre mode ( ),
(4.23)
(4.24)
For failure in tensile matrix mode ( ),
(4.25)
(4.26)
For failure in tensile matrix mode ( ),
(4.27)
(4.28)
Symbol in above equations indicate that for every as . Once the damage has initiated, the following expression define the damage of each failure mode
(Abaqus Documentation version 6.12).
(4.29)
where is the equivalent displacement at damage initiation for particular mode and is the equivalent displacement at total failure for that particular mode. Damage evolution of each mode is independent to each other unlike damage evolution in cohesive element that exhibit mixed mode damage. Figure 4 -8 illustrates the equivalent stress-equivalent displacement relationship with linear softening represented by line AC. If damage material is unload back to origin state such from point B to 0, the same path will be followed back to point B and then continue with the softening. Area under the curve is the energy required
83 to cause a total damage to a material point. So the fracture energy of each mode is specified which will then determine the equivalent displacement at failure at each mode.
The fracture energy can be related to strain to failure as in Equation 4.30 to 4.33 (Shi et al.
2012) in which strain to failure is material parameters that can be determined through material tests.
(4.30)
(4.31)
(4.32)
(4.33)
where , , , are fracture energy of each mode and are strain at total failure of each mode with subscript represents fibre tensile mode, fibre compression mode, matrix tensile mode and matrix compression mode respectively.
Figure 4 -8. Linear damage evolution of a lamina structure(Abaqus Documentation version 6.12)
84
4.6. Interaction and Contact Modelling
General contact algorithm in Abaqus/Explicit is used in this study. It only has few restrictions in its algorithm compare to contact pair algorithm. This advantage makes it very suitable for crash analysis of FML fuselage which involves complex interaction within various bodies. General contact also allows the use of element based surface in order to model surface erosion during analysis. Thus the faces of any failed element will be removed from the contact domain which means the contact domain evolves during the analysis.
General contact algorithm is enforced with penalty constraint enforcement.
For computing efficiency, the pair of the surfaces involve in the contact are defined. This includes the two adjacent layer surfaces in FML fuselage skin that separated by cohesive elements so that contact will occur once the cohesive element in between has failed and deleted. If contact and interaction are not defined between these adjacent layers, the structure would not exhibit proper structural response including excessive element distortion and surface penetration. As a result, the job analysis might be terminated or diverging results are produced. In this thesis, any possible contact surface was predicted by observing results of crash tests and crash simulation of Boeing 737 fuselage section previously done by other authors. Besides, the author himself makes an attempt to anticipate any other possible contact surface. If the anticipated contact surfaces never make any contact during the simulation, it would not affect the results of the simulation except adding some computation time due to the contact algorithm within the software package. The details of the possible contact surfaces are discussed in Chapter 5.
General contact algorithm refers to interaction property between surfaces in order to model the tangential behaviour and normal behaviour. Tangential behaviour is defined by friction formulation meanwhile normal behaviour is defined by contact pressure- overclosure relationship (Abaqus Documentation version 6.12).
85
The classical isotropic Coulomb friction model is used as the friction formulation. The model assumes that no relative motion occurs if the equivalent frictional stress is less than the critical stress, in which the critical stress is proportional to the contact pressure as in Equation 4.34.
(4.34) where is the friction coefficient. The equivalent frictional stress is defined as
(4.35) where it is a function of transmitted shear forces across the interacting surfaces.
The contact pressure-overclosure relationship governs the motion of the interacting surfaces in the contact domain. In this work, hard contact pressure-overclosure relationship is enforced. Figure 4 -9 shows the hard contact pressure-overclosure relationship. The relationship defines that when the contact pressure between surfaces reduces to zero, the surfaces will separate and when the clearance between the surfaces becomes zero, the surfaces will come into contact. Any contact pressure can be transmitted between the contacted surfaces during contact. Meanwhile Transfer of tensile stress across the contact interface is not allowed in this model (Abaqus Documentation version 6.12).
86
Figure 4 -9. Hard contact pressure-overclosure relationship diagram (Abaqus Documentation version 6.12).
87
4.7. Constraint and Connection Modelling
Fuselage section is an assemblage of few structures that connected either by adhesive, fasteners and spot welds. Finite element allows modelling such connection with various approaches such as applying constraint between two parts or fastens the two parts with additional connecting elements. Two main concepts in such modelling are constraints and connections.
4.7.1. Mesh Tie Constraints
Mesh tie constraint is one of the constraining approaches that dependent to the mesh of the constrained bodies. Constraint means that it eliminate degrees of freedom of a group of nodes called slave nodes and couple their motion to the motion of master nodes. The constraint bonds the two surfaces through their nodes permanently even though the element of the surface has fully degraded due to material failure.
4.7.2. Mesh Independent Fasteners
Mesh independent fasteners are independent from the mesh of the connected bodies. It can be used to model spot welds, rivets and adhesive and failure model can be incorporated within its formulation. Connector elements defined within the fasteners definition provide point-to-point connection between two or more surfaces. Mesh independent fasteners provide distributing coupling constraint in which the distribution weight between the two surfaces can be controlled.
88
4.8. Computational Facilities in The University of Manchester
Abaqus FE code version 6.10 and 6.12 has been used to solve all the finite element models related to this thesis. Three main computing facilities that contributed to the finite element analysis of this research are:
1. Personal desktop with Abaqus 6.10 and 6.10 licensed to The University of
Manchester
2. Condor or previously known as Epsilon; a high throughput computing (HTC) owned
and managed by Engineering and Physical Science Faculty of The University of
Manchester. The maximum number of processor can be used for a job is 4 cores
with 4 to 8GB RAM for each core.
3. Computer Shared Facilities (CSF): A cluster of machines that include Intel and AMD
processors with various specs that owned by The University of Manchester.
Mechanical, Aerospace and Civil Engineering School in total can submit up to 288
cores in the multiple nodes that connected with Infiniband at one time.
89
Chapter 5 DEVELOPMENT OF FIBRE METAL LAMINATE FUSELAGE CRASH MODEL
5.1. Introduction of Aircraft Crash Methodology
Crash simulations of aircraft have been carried by many researchers mainly for the purpose of investigating the impact response. Various methodologies they used to ensure the results produced from their simulations are reliable. Several researchers used ‘building block’ approach to develop a fuselage section crash model. Building block approach is a typical approach in design and certification of aerospace structure. It involves step-by-step tests from coupon test for material characterization, followed by structural element tests, then components and finally the full scale fuselage structure. This approach is adapted to finite element modelling by following the same step-by-step procedure but with fully computational works or combination of both computations and tests (Hashemi and
Walton, 2000; Kindervater, 2011; Heimbs et al, 2013). Other methodology is by simulating crash of a scaled fuselage model accompanied by validations from a scaled fuselage test in which the results of the scaled fuselage test have been pre-correlate with a full scale fuselage test (Jackson et al, 1997). Scaling effects are being considered in order to produce reliable results. Modelling method by simulating only a section of the aircraft is a popular method. This method is always applicable if the impact condition is limited to vertical impact only which is a component of the impact direction in a real aircraft crash. Subjected by a vertical impact loading, aircraft is always sectioned into the area that the researchers are interested in such as fuselage section that contain three rows of passengers’ seats.
Based on the simulation objectives, some researchers assumed that the aircraft crash response only dominated by the fuselage structure underneath the floor level, thus only structure below the floor are modelled and investigated (Kumakura et al, 2002; Feng et al,
2013)..
90
5.2. Methodology of Crash Modelling of Fibre Metal Laminate
Fuselage
As the development of fibre metal laminate (FML) fuselage crash simulation is fully computational work, verification and validations of the model at material modelling level, failure mechanisms level and structural response level are essential. These verification and validation works are incorporated into the building block approach thus making it as the main frame of the development methodology. Fully verified and validated model at each level should produce a reliable full scale FML fuselage crash model. Crash simulation of FML fuselage in this thesis is limited to the vertical component of the impact due to the size and complexity of the model especially in its material level. Combined with the one of the objective of the thesis which is to evaluate crashworthiness, only a fuselage section with two rows of passengers’ seats is modelled. Figure 5 -1 summarise the methodology adopted in developing the crash simulation of FML fuselage.
Development of crash simulation of FML fuselage starts with validation of material and damage modelling for materials used in FML fuselage. Materials used in FML fuselage in this thesis are classified into two which are aluminium alloy and fibre-reinforced composite laminate. In modelling fibre-reinforced composite laminate, adhesive material is also modelled to represent the interface layer between laminas. Material and damage model for both categories are validated as the preliminary work and presented in section 5.3. The development process continues with the verification of impact model that possesses dynamic instability and large displacement which is presented in section 5.4. The last stage before modelling the full scale fuselage section is the verification of the main individual structure of the fuselage section as presented in section 5.6. The main individual structure being verified is the fuselage frame. Finally, the verified and validated models at every
91 level, the structures are assembled to form a full-scale fuselage section and ready for its crash simulation and analysis.
Figure 5 -1. Methodology of developing crash simulation of FML fuselage section
92
5.3. Validation of Material and Damage Model Subjected to Impact
Loading
Fibre metal laminate (FML) fuselage section consists of three categories of material which are aluminium alloy that exhibits elastic-plastic response, composite laminate that exhibits elastic-brittle response and balsa wood that only exhibits elastic response. Fuselage structures that are made of aluminium alloy are metallic part of the FML fuselage skin, fuselage frames, floor beams, longitudinal stringers and seat tracks. Meanwhile composite laminate is the constituent of the FML fuselage skin. The balsa wood with elastic response only is used as the floor panel but its material model is not necessary as it is assumed that it is not actively involved in the global impact response of the fuselage section. In fact some of the researchers did not model the floor panel in its aircraft crash simulation model
(Meng et al, 2009; Yu et al, 2013). Following section discusses about validation model of material and damage model for aluminium alloy and composite laminate.
5.3.1. Validation of Aluminium Alloy Material and Damage Model
The geometry and material of the fuselage section in this thesis is based on commercial aircraft Boeing 737. The only difference is that the FML fuselage uses FML material instead of aluminium alloy alone in the real Boeing 737. Boeing 737 uses aluminium 7075-T6 for its fuselage frames, floor beams, stringers and seat tracks and aluminium alloy 2024-T3 for its fuselage skin. In GLARE FML fuselage skin, the metallic constituent is also 2024-T3 aluminium alloy. The material and damage model for both are the same in which they exhibit elastic-plastic response and undergo damage once the criterion is satisfied followed by damage progression up to total failure.
Validation of material and damage model is carried by subjecting an FE plate model made of this material with a rigid impactor under low velocity impact. The impact loading and the plate structure of this FE model is based on an experimental work done by Rodriguez-
93
Martinez who was originally studying a 2024-T3 aluminium alloy plate under thermo- mechanical impact loading (Rodriguez-Martinez et al, 2011). The results of the experimental work under room temperature are then compared to the results from the FE model. The Rodriguez-Martinez’s experimental set-up is shown in Appendix 1.
Material and Damage Model Formulation
The elastic response of aluminium alloy is based on the stress-strain constitutive equation of isotropic material in Equation 3.1, Chapter 3. Two engineering constants are required,
Young’s modulus, and Poisson’s ratio, . The yield stress and plastic hardening model with strain-rate dependent is modelled by using Johnson-Cook plastic model as expressed in Equation 3.5, Chapter 3 and failure criterion of the alloy is prediction by Johnson-Cook damage model as in Equation 4.10, Chapter 4. The material properties including parameters that required for Johnson-Cook plasticity and damage model are tabulated in
Table 5 -1 for both 2024-T3 and 7075-T6 aluminium alloy. However, only FE plate model with 2024-T3 aluminium alloy only is being modelled in this thesis. Meanwhile aluminium alloy 7075-T6 will be used for few structural parts once the fuselage section has been assembled, Section 5.6 and 5.7.
94
Parameter Notation 2024-T3 7075-T6 Density (kg/m3) ρ 2700 2810 Young’s modulus (MPa) 70000 71700 Poisson’s ratio 0.33 0.33
Strain failure 0.18 0.11 Plasticity parameters of Johnson-Cook Plasticity Model Static yield stress (MPa) 369 546 Strain hardening modulus (MPa) 684 678 Strain hardening exponent 0.73 0.71 Strain rate coefficient 0.0083 0.024 Damage parameters of Johnson-Cook Damage Model
0.112 -0.068
0.123 0.451
-1.5 -0.952
0.007 0.036
Table 5 -1. Material properties of 2024-T3 and 7075-T6 aluminium alloy (Lesuer 2000; Buyuk et al. 2008).
5.3.1.1. Finite Element Model under Low-Velocity Impact for Aluminium Alloy 2024-
T3
The model consists of an aluminium alloy plate with thickness of mm and size of A =
80 x 80 mm2. As the plate is clamped at all sides in the experimental set up, all degree of freedom for nodes at all edges in the numerical model are set to zero. The plate is impacted by a discrete rigid impactor that has conical shape at impact velocity 4 m/s. The larger diameter of the striker is 20 mm, radius of nose is 3 mm and angle of its conical nose is 18⁰. Total mass of the stiker, Mtotal is 18.787 kg.
The meshing of the plate is shown in Figure 5 -2. Mesh of aluminium alloy plate with finer mesh at the impact area where the mesh is finer at the impacted area. The geometry of the plate is meshed by a reduced integration linear solid element C3D8R. Four elements are defined across the plate’s thickness.
95
Figure 5 -2. Mesh of aluminium alloy plate with finer mesh at the impact area
5.3.1.2. Validation on Model with Various Hourglass Controls
Preliminary, five cases using different hourglass control option are analysed. The first case uses enhanced hourglass control option; the second uses relax stiffness hourglass control option; and the rests are pure stiffness, pure viscous and combined stiffness and viscous hourglass control options.
Table 5-2 shows that model with viscous hourglass control has the lowest value of artificial strain energy meanwhile model with enhanced hourglass control has the highest. Amount of artificial strain energy observed from any numerical model is directly associated with constraints used to remove singular modes including hourglass control (Abaqus
Documentation, version 6.12). It is recommended that the artificial strain energy (ALLAE) is less or equal to 2% from the total internal energy (ALLIE) but overall the artificial strain energy for all numerical model is still low (below than 5%).
96
Model with different Artificial strain Maximum impact Energy absorbed,
Hourglass Control energy, ALLAE (%) force (kN) Et (J) Experiment (Rodriguez- - 3.75 14.64 (10%) Martinez) Enhanced 4.103% 3.57303 10.105 Relax stiffness 0.696% 2.99191 9.192 Stiffness 2.611% 3.33666 9.395 Viscous 0.265% 2.49626 9.127 Combined 1.313% 3.08959 9.239
* All values are evaluated at failure time tf
Table 5 -2. Results comparison between FE models and experimental works in terms of artificial energy percentage, maximum impact force and energy absorption.
Numerical model with enhanced hourglass control has maximum impact force closest to experiment results. Model with viscous hourglass control is the worst, 33% lower than experiment results. Meanwhile in term of amount of energy absorbed, Et at failure time, tf indicates that model with enhanced hourglass control produced the best results when compare to experiment results followed by stiffness, combined, relax stiffness and viscous hourglass control models. Failure time, tf is the time when the impact force is maximum,
where . Overall, energy absorbed, Et predicted by all numerical model is still
lower than the energy absorbed recorded from the experiment. Based on these observations, the rest of the results are analysed from FE model with enhanced hourglass control.
5.3.1.3. Results Correlation
Sequence of images of the perforation and failure process is shown in Figure 5 -3. A dishing phase is found at the beginning of the loading process that involves both elastic and plastic deflection of the plate as can be seen in Figure 5 -3a. Subsequently, strain localises on the contact surface which leads to the onset of cracks. From this point on, high circumferential strains caused by the passage of the striker lead to radial crack propagation as can be seen
97 in Figure 5 -3b. Figure 5 -3c-d illustrates a number of symmetric petals are formed and bent until complete perforation of the target.
(a) (b)
(c) (d)
Figure 5 -3. Different stages of the perforation process for an aluminium alloy 2024-T3 sheet, V0 4.0 m/s. (a) Localisation of deformation and onset of crack. (b) Cracks progression and formation of petals. (c) Development and bending of petals. (d) Complete passage of the impactor and petalling failure mode.
Next is to compare energy absorbed, by the target from the first contact up to the failure time, . In the experiment by Rodriguez-Martinez, energy absorbed is expressed by
Equation 5.1
(5.1)
98 where is residual velocity at failure time. Numerically, energy absorbed by the target is simply evaluated by subtracting the kinetic energy of the striker at failure time from the impact energy. It is understood that the process of strain localisation and subsequent plastic instabilities are responsible for the target collapse during impact (Rodriguez-
Martinez, 2011). Most of the energy is dissipated through these plastic works. The FE model under predicted the energy absorbed by the 2024-T3 plate by 21%. This behaviour is well explained by the comparative stress-strain curves between experimental results
(Rodriguez-Martinez, 2011) and Johnson Cook material model as shown in Figure 5.4. The comparison is made for 100 s-1 strain rate. Strain rate in FE model is evaluated by dividing
the equivalent plastic strain at failure, 0.18 by the failure time, tf which is 1.62 ms (Fan
-1 et al, 2011) resulting 111 s strain rate. Failure time, tf is the time when the impact force
reaches its maximum value or in which is the displacement of the impactor
(Rodríguez-Martínez et al. 2011). Plastic flow exhibited in experiment is higher than plastic flow in Johnson-Cook plastic model as shown in Figure 5 -4 which indicates that the ‘real’ aluminium alloy absorbed more energy per unit volume compared to Johnson-Cook plastic model. So the energy absorbed by material based on stress-strain curve from experiment is higher than by material modelled by Johnson-Cook for the similar yielding and straining.
This explains why FE model under predict the energy absorption by the aluminium plate subjected to impact loading. Energy absorbed per unit volume, is the area under the stress strain curve (Rodriguez-Martinez et al, 2011) as expressed in Equation 5.2.
(5.2)
99
600
500
400
300
200
Equivalent stress (MPa) stress Equivalent Experiment 100 FE material model
0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Equivalent plastic strain
Figure 5 -4. Flow stress evolution versus strain for Johnson-Cook material model
Impact force versus striker displacement is examined up to 15 ms where the whole body of the striker has perforated through the aluminium alloy plate. Figure 5 -5 shows that FE model correlates well with experiment in terms of maximum impact force. However, the predicted maximum impact occurred at lower striker displacement compare to experiment.
In terms of permanent deflection of the plate, FE model predicted higher deflection than experiment by 20% as illustrated in Figure 5 -6.
5.3.1.4. Conclusion on the Validation Work on Material and Damage Model of
Aluminium Alloy
Despite of having highest artificial strain energy within the model which was greater than recommended 2% value, enhanced hourglass control method provide the best results compared with experimental results in terms of the force evolution and energy absorbed during impact. Artificial strain energy to total internal energy ratio of 4% is still considered low and relatively being compromised as its results correlate well with experiment.
100
Overall, FE material and damage model predicted well the impact response and damage process of aluminium alloy where it starts with strain localisation at the impacted area, crack onset, progress of perforation and petalling. It is observed that the material strain rate is in magnitude of 100 s-1 when impacted by impactor under 4 m/s impact velocity.
However, FE models under predicted the amount of energy dissipated through damage by
21%.
5,000 4,500 Experiment 4,000 FE model 3,500 3,000 2,500
Force (N) Force 2,000 1,500 1,000 500 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Striker displacement (mm)
Figure 5 -5. Impact force as a function of the impactor displacement
Target length, Lt (mm) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0 -0.5 -1
-1.5
-2 (mm) -2.5
-3 experiment -3.5 FE Model
Permanent deflection on the targetthe on deflection Permanent -4
Figure 5 -6 Permanent deflection of the target for FE model and experiment
101
5.3.2. Validation of Composite Laminate Material and Damage Model
Composite laminate within the FML fuselage skin consists of unidirectional composite lamina stacked and bonded in an orderly orientation. Validation of material and damage model for composite is carried by subjecting an FE plate model made of fibre-reinforce composite laminate with a rigid impactor under low velocity impact. The impact loading and the composite laminate structure of this model is based on experimental work and FE model developed by Shi et al (2011) who was investigating impact response of composite laminate subjected to low velocity impact (Shi et al, 2011). Then the results from this FE model are compared to experiment and FE model produced by Shi et al (2011).
In Shi et al (2011) work, he investigated the impact response of a carbon fibre composite laminate. Even though carbon fibre composite laminate is not used in this thesis, but the response of this material as a laminate consists of orderly stacked fibre-reinforced unidirectional lamina should possess the same characteristic with the one made of glass- fibre that used in GLARE FML. Thus it assumed that this work is adequate to validate the material and damage model of fibre reinforced composite laminate. The only difference between carbon-based and fibre-based reinforced composite laminate is the value of their material properties.
5.3.2.1. Material and Damage Model Formulation
The composite laminate is modelled as a compilation of individual laminas in which interface layer is incorporate between each laminas in order the lamina to interact with each other and to form continuities along the thickness direction as previously illustrated in
Figure 4.3, Chapter 4. Effectively, two separate material and damage models are used to model the individual lamina and the interface layer or we call it as adhesive. Theoretically, the adhesive between unidirectional lamina is the matrix of the composite itself in which that bonding was formed during curing. However a richer matrix composition is formed at
102 the surface plane between adjacent laminas with different fibre orientation, effectively being regarded as adhesive or interface layer. Thus the material properties of the adhesive are actually the material properties of the matrix of the lamina itself. i. Composite lamina
Composite lamina exhibits elastic-brittle mechanical response which is based on the stress- strain constitutive orthotropic material in Equation 3.12 to 3.17 in Chapter 3. This stress- strain relationship considers a state of plane stress. Only four engineering constants required to model the mechanical response of the undamaged lamina respectively Young’s modulus in the direction of fibre , Young’s modulus in the direction orthogonal to the fibre , the Poisson’s ratio and the in-plane shear modulus .
No plasticity is modelled due to the elastic-brittle nature of composite lamina. Damage is initiated once the lamina stress condition satisfies the failure criterion. Failure criterion of the composite lamina is Hashin’s failure criterion that defines criteria for each failure mode separately; fibre tensile, fibre compressive, matrix tensile and matrix compressive as explain in section 3.3.3. The plane stress Hashin’s failure criterion is used as expressed in
Equation 3.23 to 3.26. However the effect of the damage from other mode to the damage initiation of other mode does exist via relationship in Equation 4.13 to 4.16. The damage evolution of composite lamina as discussed in section 4.5.3 is modelled with a linear stiffness degradation with fracture energy of each failure mode determines the equivalent displacement at total failure. The material properties of carbon fibre reinforced composite laminate in this validation work are tabulated in Appendix 2. ii. Adhesive (Interface layer)
Adhesive between lamina is modelled using a special-purposed element regarded as cohesive element in Abaqus which is governed by a linear mechanical constitutive traction-
103 separation relationship as in Equation 4.5 to 4.6 in Chapter 4. Damage initiation is based on quadratic nominal stress criterion (Equation 4.7). Mixed-mode damage between all traction components are used with power law is used to interact the fracture energy for each mode as expressed previously in Equation 4.8. The power of the law used is 2 and the damage evolution response is exponential. The material properties of the adhesive in carbon fibre reinforced composite laminate in this validation work are tabulated in Appendix 2.
5.3.2.2. Finite Element Model under Low-Velocity Impact for Fibre-Reinforced
Composite Laminate
The impact target is made of 2 mm composite plate consisted of eight plies with a ply thickness of 0.25 mm in the stacking sequence [0,90]2s. Diameter of the composite laminate plate is 75 mm with all displacement and rotational degree of freedom at all nodes of the edge is set equal to zero in order to have a clamped boundary condition. The impactor has hemispherical head of 15 mm in diameter and its weight is 2 kg. The impactor hits the target with impact velocity of 3.834 ms-1 resulting in impact energy of 14.7 J. Figure 5 -7 illustrates the geometry of the model and the boundary condition at the edge of the plate.
mm
mm
z Fixed edge x y
Figure 5 -7. Numerical model of the impact on composite laminate.
104
In this validation task, two different models are developed, one with cohesive element and the other without cohesive element. The purpose of modelling two techniques is to investigate the significance of adhesive layer as delamination model in modelling impact response of composite laminate.
Continuum shell element, SC8R is used to model the unidirectional lamina. Cohesive element, COH3D8 is used to model the interface layer with its geometrical thickness of
0.001 mm. As mentioned previously, geometrical thickness is not the constitutive thickness used in the traction-separation constitutive equation. The computing time is reduced by introducing different mesh size/density in different regions of the FE model; higher density mesh at the impacted zone as can be seen in Figure 5 -7. The degradation parameters were set as maximum and failed elements were removed from the FE model once the failure criteria are satisfied.
5.3.2.3. Results Correlation
Impact force and energy versus time curves from finite element model in this validation model is compared to Shi’s experimental and numerical work in order to assess the accuracy of the proposed model. i. Impact force
In Figure 5 -8 shows the force-time histories for the 14.7 J impact test.. In general the impact force time histories start with vibration induced by initial contact between the striker and the composite laminate. Then the impact force will increase up to the peak value which when the damage within the laminate is initiated. The striker then bounces upward and the load is reduced to zero. All finite element models in this study follow this general impact force time histories pattern.
105
The maximum force recorded in Shi’s experiment and his finite element model are 4605 N and 3917 N respectively. Finite element models without and with adhesive developed for validation estimated maximum force of 6359 N and 4663 N respectively. Easily notified that finite element model with adhesive estimated more accurate results than the FE model without adhesive. In FE model without adhesive, it overestimates the strength between the composite lamina or actually the composite lamina will never delaminate. Effectively, this model is stiffer than FE model with adhesive. Meanwhile in FE model with adhesive, delamination failure provides additional energy dissipation mechanism thus decreasing the striker’s deceleration and maximum impact forces on the composite laminate. As a result, it is predictable that FE without adhesive causes higher maximum impact force compare to the experiment and FE models with adhesive.
After the peak load is reached and the striker starts to rebound, the numerical results take longer time to reach zero compare to experimental results except for FE model without adhesive. As mentioned by Shi et al (2011), this phenomenon might occur due to contact forces between delaminated plies after the cohesive elements have been removed from the simulation as the composite plate returns to its original shape. However, Shi’s explanation should not be the case in this validation models because the impact force output is obtained from the impact surface pairs which is between impactor and the composite laminate.
The impact force-time results in Figure 5 -8 are then translated into force-displacement curves shown in Figure 5 -9. In the initial phase of the impact event, there is similar slope until the maximum impact force reached. It is the same case as force-time curves where FE model without adhesive estimated relatively higher maximum force impact compare to the rest of FE models predictions and experiment results. However, all numerical models predicted smaller or zero indention when the contact force has reduced to zero compared
106 to experimental results. This is simply due to the linearity of the material in FE model in which in experiment, the composite possessed little inelastic strain which caused permanent deformation. FE model without adhesive predicted that the composite plate returns to its initial pre-impact state which indicates that there is no permanent displacement except some elements are deleted as they have fully degraded. Figure 5 -10 and Figure 5 -11 show impacted composite plates and their cross-section of the FE mode.
For FE model without adhesive, it shows no permanent deflection and few elements are deleted due to material failure. FE model with adhesive shows the existence of delamination. The delamination causes the lamina to undergo large displacement and have more elements to fail compare to FE model without adhesive, thus gives more damping and absorbs more impact energy.
7,000 6,500 Experiment (Shi) 6,000 5,500 FE model (Shi) 5,000 FE model with no adhesive 4,500 FE model with adhesive 4,000 3,500
3,000 Force (N) Force 2,500 2,000 1,500 1,000 500 0 0 1 2 3 4 5 6 Time (ms)
Figure 5 -8. Impact force-time histories of impacted composite laminate
107
6,500 6,000 5,500 5,000 4,500
4,000 3,500 3,000
Force (N) Force 2,500 2,000 1,500 1,000 500 0 0 1 2 3 4 5 6 7 Displacement (mm)
experiment FE model (Shi) FE model with no adhesive FE model with adhesive
Figure 5 -9. Impact force-displacement histories of impacted composite laminate
Figure 5 -10. Deformation in impacted plate for FE model without adhesive.
108
Figure 5 -11. Deformation in impacted plate for FE model with adhesive.
ii. Impact energy
The impact energy of the striker is transferred to the composite laminate once contact is made. Figure 5 -12 illustrates the energy absorption-time histories. During the impact event, part of the energy is absorbed by composite laminate in the form of elastic energy which will not cause any permanent deformation, while a larger amount of energy is dissipated through damage in the composite lamina, delamination and friction between contact surfaces. Once the striker’s velocity reaches zero, the elastic energy stored in the laminate will be transferred back to the striker causing it to rebound in opposite direction.
FE models predicted that the impact energy are transferred to the composite laminate at higher rate compare to experiment results and to FE model developed by Shi.
FE model without adhesive quickly lose its energy as large amount of it that has been absorbed initially were transferred back to the striker. The composite laminate absorbed the initial kinetic energy mainly as elastic energy. Only little of them were absorbed which caused the intra-lamina damage in the composite laminate. The rest of the model absorbed
109 more energy than FE model without adhesive as the energy was also dissipated through delamination. Table 5.3 presents the amount of energy absorbed by the laminate and its prediction from numerical models. FE model with adhesive predicts better in terms of energy absorption compare to other models including model developed by Shi himself.
16 15 14 13 12 11
10 9 8
7 Energy (J) Energy 6 5 4 Experiment (Shi et al) 3 FE model (Shi) 2 FE model without adhesive 1 FE model with adhesive 0 0 1 2 3 4 5 6 time (ms)
Figure 5 -12. Energy absorption-time histories for impacted composite laminate
Impact energy (J) Absorbed energy FE model without FE model with Experiment (J) FE by Shi (J) interface layer (J) interface layer (J) 14.7 9.52 9.08 5.67 9.49
Table 5 -3. Amount of energy absorbed during impact of composite plate
5.3.2.4. Conclusion on the Validation Work on Material and Damage Model of Fibre-
Reinforced Composite Laminate
FE model without adhesive experiences highest impact energy than the rest of the FE model. This is because delamination as one of the main energy dissipation mode is not modelled. So the impact energy is mainly absorbed by elastic strain and only small portion
110 of the impact energy is absorbed by intralaminar damage which causes under-prediction of energy absorption. In strength-sense, FE model of composite laminate without adhesive will overestimate the strength of the laminate especially if delamination mode is one of its main energy absorption in that particular impact condition.
Results of FE model with adhesive correlates well with experiment results in terms of impact force between the contacted surfaces. It predicts the maximum impact force and the duration of the impact force close to experiment.
As a conclusion, the material model used in this work is able to predict the impact response and damage of fibre-reinforced composite laminate. The incorporation of cohesive element as interface layer which is used to model delamination improve the material and damage response of the laminate under impact loading as it provide better prediction in terms of failure mechanisms and energy dissipation mechanisms.
111
5.4. Validation of General Impact Modelling
This section is to validate a general impact modelling that involves geometrically nonlinear response of the structure due instability and large deformation. Validation of finite element model of dynamic buckling of structure made of isotropic element suits this objective.
The validation task involves modelling of a non-modified and modified finite element model of cask drop analysis using axisymmetric solid element, shell element and three- dimensional solid element which. This impact model is based on one of the impact model example in Abaqus Documentations (version 6.12). The configuration of the cask drop analysis is as shown in Figure 5 -13.
Figure 5 -13. A quarter symmetric model of cask drop onto a rigid surface (Abaqus Documentation, 6.12)
Example of cask drop with foam impact limiter in Abaqus Documentation is based on
Sauve’s work (Sauve et al, 1993). A containment cask is partially filled with fluid and a foam
112 impact limiter as illustrated in Figure 5 -13. The drop impact onto a rigid surface is modelled by assigning the whole cask including the water and foam in it with initial velocity, V0 of
13.35 m/s which equivalent to the same cask being dropped from a height of 9.09 meter.
The dropping is this case is not modelled by impacting the cask onto a rigid surface but it is modelled by setting zero degree of freedom (ENCASTRE) to all nodes at the containment base.
Contact conditions are defined for interaction between the fluid and the inside part of the upper compartment and for interaction between foam impact limiter and the inside of the bottom compartment of the cask. Self contact is also defined in the structure. The examples in Abaqus Manual present the results of model using axisymmetric shell element
(SAX1) and three-dimensional shell element (S4R) for the side wall of the containment.
Three models using solid element are also simulated in this test in order to verify the reliability of solid element in modelling impact by comparing to the results of axisymmetric shell element model and shell element model provided by the manual. These three solid element model parameters are listed in Table 5.4.
Model Element used to model side wall of the Hourglass control containment 1 Reduced integration solid element, C3D8R Relax stiffness (default) 2 Reduced integration solid element, C3D8R Enhanced 3 Incompatible mode solid element, C3D8I -
Table 5 -4. Cask drop with solid elements modelling to be verified
For this particular validation work, the field of interest is to analyse the deformation of the side wall of the lower containment, the displacement of the steel that separate the fluid and the foam and the energy balance during the impact. Figure 5 -14 shows the deformation shape of the side wall of bottom containment which is the rounded part for all models at 5 ms. The bottom wall buckled in a similar way for all models except solid
113 element with default hourglass control model which exhibits stiff response. The deformation shape for incompatible mode solid element model is totally similar to axisymmetric model as C3D8I element has good bending behaviour. Meanwhile model with enhanced hourglass control solid element buckled with smaller deflection compare to both axisymmetric model and shell element model. As nodes of shell element have rotational degree of freedom, it is expected that the buckled wall contains hinged deflection between each element affected within model with shell elements.
114
(a) (b)
(c) (d)
115
(e)
Figure 5 -14. Deformation of side wall of bottom containment at 5 ms, (a) axisymmetric model, (b) shell element model, (c) C3D8R element with default hourglass control model, (d) C3D8R element with enhanced hourglass control model and (e) C3D8I element model.
Displacement of the bottom side wall is measured at dotted location in Figure 5 -14a for all models. Displacement at this location represents crushing distance of the structure during impact. Figure 5 -15 illustrates the crushing distance histories of all models meanwhile
Figure 5 -16 illustrates the elastic strain energy and energy dissipated through plastic dissipation during impact. Crushing time history and final crushing distance of incompatible mode element model correlates well with results from Abaqus example. The results correlation is consistent with the deformation shape and magnitude of deflection of the side wall by referring to Figure 5 -14.
The amount of energy dissipated through plastic deformation for all models correlates well with axisymmetric model with the largest difference of 7.5% by solid element with default hourglass control model. Incompatible mode element model differs with axisymmetric model with 5% meanwhile enhanced hourglass control solid element gives the best correlation with axisymmetric model in terms of plastic energy dissipation.
116
In terms of crushing distance and plastic energy dissipation, incompatible mode element is seen as better option to model isotropic element that undergoes crushing due to impact compare to enhanced hourglass control solid element. This is due to good bending capability of incompatible mode element. Meanwhile enhanced hourglass control solid element C3D8R comes second possibly because part of the impact energy is dissipated through its artificial strain energy due to hourglassing control. There is no hourglassing in full integrated incompatible mode element C3D8I.
40 35
30 25 20
15 Displacement Displacement (mm) 10 5 0 0 5 10 15 20 25 Time (ms) axisymmetric model shell element model solid element with default hourglass control model solid element with enhanced hourglass control model incompatible mode solid element model
Figure 5 -15. Crushing distance of the containment for all models
117
25
20
15
Energy (kJ)Energy 10
5
0 0 5 10 15 20 25 Time (ms) ALLPD - axisymmetric model ALLPD - shell element model ALLPD - default hourglass control solid element model ALLPD - enhanced hourglass control solid element model ALLPD - incompatible mode solid element model ALLSE - axisymmetric model ALLSE - shell element model ALLSE - default hourglass control solid element model ALLSE - enhanced hourglass control solid element model ALLSE - incompatible mode solid element model
Figure 5 -16. Plastic dissipation and elastic strain energy time histories
118
5.5. Verification of Fuselage Frame Impact Modelling
Fuselage frames are the main structure in an aircraft fuselage section that keep the shape of the fuselage structure and hold the weights of the aircrafts body section. As fuselage frame is the main source of strength within the fuselage section, reliable finite element modelling of fuselage frame is essential in order to simulate crash of aircraft fuselage.
5.5.1. Finite Element Modelling of Fuselage Frame
Verification of fuselage frame under crash event is essential in developing crash simulation of full-scale fuselage section. A semi-monocoque frame based on Boeing 737’s frame geometry is discretised as shown in Figure 5 -17. The upper outer radius and lower outer radius of the frame are 1.88 meter and 1.80 meter. Details of the frame’s geometry are obtained from Boeing Company website and Niu’s textbook (Boeing Website; Niu 1988).
Frame is made of aluminium alloy 7075-T6 which is stiffer then aluminium alloy 2024-T3 used for fuselage skin. Density of AA 7075-T6 is 2934.07 kg/m3 with Young’s modulus of
71.7 GPa and Poisson’s ratio of 0.33. Full material properties and damage parameters of aluminium alloy 7075-T6 used in this model are provided in Table 5-5. Plastic hardening and damage of AA 7075-T6 are defined by Johnson-Cook material and damage models, the one that has been validated in section 5.3.1.
119
Figure 5 -17. Fuselage frame configuration and discretisation.
Figure 5 -18. Z cross-section of fuselage frame
120
Parameter Notation Hardening parameters Static yield stress [MPa] A 546 Strain hardening modulus [MPa] B 678 Strain hardening exponent n 0.71 Strain rate coeeficient C 0.024 Thermal softening exponent m 1.56
Melting temperature [K] 750 Damage parameters
-0.068
0.451 -0.952
0.036
0.697
Table 5 -5. Material and damage model parameters of aluminium alloy 7075-T6 (Brar et al. 2009).
Shell element S4R with enhanced hourglass control is used for the entire fuselage frame.
Mass element is modelled at two locations as highlighted as red dots in Figure 5 -17 in order to replicate the weight of floor beam. Red dots are a simplified location of where the floor beam is attached to the frame. In order to avoid deflection in longitudinal z-direction, inner flange of the frame is restrained from moving into z-direction. In full fuselage section, fuselage frames are restrained to move in z-direction by the stringers and the rigid fixes.
Initial velocity of 9 m/s is defined at all nodes of the frame causing to have 3.5 kJ of impact energy onto a rigid impact surface. General contact that implements penalty contact method is used to define contact between frame and rigid surface. Self-contact on frame structure is also defined. Friction coefficient of 0.15 is set between frame and rigid surface.
Element is set to be deleted if its damage degradation reaches maximum value, Dmax = 1.
Energy balance during impact is the main output to be analysed in order to check the reliability of the models. Meanwhile the crushing distance of the frame which is measured
121 at location that is highlighted with black dot in Figure 5 -17 is also analysed. Three finite element models with three different mesh sizes are modelled as described in Table 5-6.
Model Mean Characteristic length (Element size) Number of elements frame_64 64 mm 734 frame_32 32 mm 2018 frame_20 20 mm 3899
Table 5 -6. Frame finite element models with various mesh sizes
5.5.2. Verification Results of Fuselage Frame Impact Model
Figure 5 -19 shows the deformation at time 50 ms which the bottom of the fuselage started to buckle in upward direction. Another major buckling occurred at two locations which geometrically symmetric to each other at impact time 125 ms as shown in Figure 5 -19b.
Figure 5 -19c shows the deformation of the frame just before it rebounded in upward direction due to elastic strain stored within the structure. All these major buckling produced permanent plastic strain that dissipated most of the impact energy beside the elastic strain energy that causes the frame to rebound. This deformation mode corresponds to the buckling verification of isotropic structure made of shell element discussed previously.
122
(a)
(b)
(c)
Figure 5 -19. Deformation of frame (a) at time 50 ms, (b) at time 125 ms, (c) at time 175 ms
123
Crushing distance of the frame is illustrated in Figure 5 -20. All models with various mesh sizes have almost similar crushing pattern. Displacement of model with most refine mesh is
1.237 meter which the difference with model with coarsest mesh is only 1%. The displacement is only analysed up to 225 ms as the frame rebounded right after that and the impact force has reduced to zero.
1.40
1.20
1.00
0.80
0.60
0.40 Crushing distance 64 mm Crushing distance distance Crushing (meter) Crushing distance 32 mm 0.20 Crushing distance 20 mm 0.00 0 20 40 60 80 100 120 140 160 180 200 220 240 Time (ms)
Figure 5 -20. Crushing distance of frame with various mesh sizes.
Figure 5 -21 shows plastic energy dissipation of models with various mesh sizes. Mesh convergence is observed when mesh size is reduced from 32 mm to 20 mm with energy dissipated through plastic strain is 1.7 kJ. Energy balance of finite element model with element size 32 mm is further shown in Figure 5 -22 which indicates consistency of kinetic energy loss with plastic strain energy dissipation and elastic strain energy stored.
124
2500 ALLPD 64 mm ALLPD 32 mm 2000 ALLPD 20 mm
1500
ALLPD ALLPD (J) 1000
500
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 5 -21. Plastic energy dissipation of frame finite element models with various mesh sizes.
4000
3500 ALLKE ALLPD 3000 ALLSE
2500
2000 Energy (J)Energy 1500
1000
500
0 0 20 40 60 80 100 120 140 160 180 200 220 Time (ms)
Figure 5 -22. Energy balance of frame model with mesh size 32 mm.
125
5.6. Development of Crash Impact FE Model of Aluminium Alloy
Fuselage Section
5.6.1. Geometric Information and Assumptions
The fuselage section is based on commercial Boeing 737 fuselage. The front fuselage section with no cargo door and auxiliary fuel tank was modelled. The geometry measurements of the fuselage section were obtained from the technical data owned by
Boeing Company. The cross-section of the fuselage is a double-lob structure with lower lob and upper lob radius of 1.8 meter and 1.88 meter respectively. Only two fuselage stations were modelled with a total longitudinal length of 1.016 meter which includes two window cutouts at both sides.
The fuselage section consist of three fuselage frames, a cylindrical fuselage skin with windows cutouts, three floor beams, floor panel, seat tracks and longitudinal stringers. The same fuselage frame model that has been verified in section 5.5.2 was used in this model.
The cylindrical fuselage skin is attached to the fuselage frames by mesh tie constraint.
Meanwhile longitudinal stringers are fastened to fuselage skin using mesh independent fastener. There is no failure being modelled in joints that formed by both mesh tie and mesh independent fastener. The rest of the joints to assemble all structures into a complete fuselage section is also modelled by mesh tie constraints. The impact surface where the fuselage section will impacted onto is modelled as rigid impact surface. Thus no deformation would occur at the impact surface. Another simplification is that seats and occupants were modelled by point mass element. These assumptions and simplifications are necessary to keep the model simple without compromising the reliability of the results
(Adams and Lankarani, 2003).
Development of model is performed by Abaqus. The fuselage section is discretized, assigned with proper elements and material models. Contact is defined between bottom
126 part of the fuselage and the rigid impact surface. Contact is also defined in between fuselage structures that may come into contact.
5.6.2. Discretisation of the Fuselage Section
The verified fuselage frame was modelled by shell element, S4R with enhanced hourglass control. Meanwhile the aluminium alloy 2024-T3 fuselage skin was modelled by incompatible mode solid element, C3D8I. This element was chosen based on the verification of impact modelling of isotropic structure in section 5.4. Meanwhile seat tracks were modelled by beam elements, B31. The rest of the structures were discretised by shell elemet S4R including stringers, floor beams and floor panels.
5.6.3. Material Assignment
All structures in aluminium alloy fuselage section are made of aluminium alloy 7075-T6 except fuselage skin and floor panel. Fuselage skin is made of aluminium alloy 2024-T3 meanwhile floor panel is made of balsa wood that only possessed elastic response.
5.6.4. Impact and Contact Modelling
General contact algorithm was used to model contact between fuselage section and the rigid impact surface. Contact between structures within fuselage was also modelled using general contact algorithm. All nodes within the fuselage structure were given initial velocity
10 ms-1 in downward direction in order to simulate the impact velocity of the fuselage.
Gravitational force was also assigned to the fuselage structure. Friction coefficient of 0.15 was assigned between fuselage and the rigid impact surface. Table 5-7 shows the possible contact surfaces and pairs during the crash of the fuselage.
127
Pair Surface 1 Surface 2 1 Ground (Rigid impact surface) Fuselage skin (outer and inner) 2 Ground (Rigid impact surface) Fuselage frame 3 Fuselage frame (bottom half) Floor beams 4 Fuselage frame (bottom half) Floor panels 5 Fuselage frame (bottom half) Seat tracks 6 Fuselage skin (bottom half) Floor beams 7 Fuselage skin (bottom half) Floor panels 8 Fuselage skin (bottom half) Seat tracks 9 Longitudinal stringers Floor beams 10 Longitudinal stringers Floor panels 11 Longitudinal stringers Seat tracks 12 Longitudinal stringers Fuselage skin 13 Fuselage frame Fuselage Frame (self-contact) 14 Fuselage skin Fuselage skin (self-contact)
Table 5 -7. Contact surface pairs modelled within the fuselage
5.6.5. Location of Mass
Mass element is modelled to represent the mass of the seats and the passengers. This fuselage model has six seats in a row which three at each side. 100 kg is specified for the total mass of a passenger and a seat. Thus in total 300 kg seats with passengers at each side. These mass is distributed between two seat tracks at each side where each seat tracks supports 150 kg. The 150 kg mass is further distributed at nodes within a single seat track.
128
5.7. Development of Crash Impact FE Model of GLARE Fuselage
Section
The only difference between aluminium alloy fuselage section and GLARE fuselage section is the modelling of their fuselage skin. This section discuss the development of the GLARE fuselage skin meanwhile the rest of the fuselage structure were modelled with the same technique as discussed in section 5.6.
GLARE fuselage skin is made of GLARE grade 5-2/1 which has two outer layer of aluminium alloy 2024-T3 and four layers of unidirectional glass-fibre reinforce lamina with stacking orientation of 0⁰/90⁰/90⁰/0⁰.
The aluminium alloy 2024-T3 is modelled by incompatible model solid element C3D8I and
Johnson-Cook plastic and damage model. Meanwhile the laminate is modelled by continuum shell element, SC8R with Hashin’s failure criterion to model the damage initiation. Interface layer is incorporated in between layers including in between lamina and aluminium alloy. All the constituents within GLARE are modelled based on the validated and verified models in previous section. However, maximum material degradation of composite laminate is set as 0.99 and no element deletion is modelled. The reason of not modelling element deletion at maximum degradation is to ensure that the elements of the laminate did not distorted excessively due to complex contact interaction between lamina, cohesive element and aluminium alloy within the GLARE skin.
129
5.8. Evaluation of Acceleration Response at Floor-Level
5.8.1. Data collection and processing of the acceleration response during crash event
Acceleration response of the fuselage during crash was evaluated at two nodes for both fuselages; the node at the outer right seat track and at the inner right seat track. This is to represent the acceleration response experienced by the passengers seating inside the fuselage cabin during crash. As the fuselage section is geometrically symmetry, only acceleration at the right side was evaluated. The acceleration response on the left side is assumed to be mirror image response of the right side. Noises in the acceleration-time history data were filtered with a 60 Hz low pass filter using Matlab. Cutoff frequency 60 Hz was applied as it is the cutoff frequency that commonly used by aircraft crash researchers in analysing acceleration response including Adams and Lankarani (Adams & Lankarani
2010). The filtered response has pulse duration that match the apparent pulse duration of the unfiltered acceleration response.
5.8.2. Human tolerance towards acceleration
The acceleration responses experienced by the passengers in crash analysis of aluminium alloy and fibre metal laminate fuselage are analysed based on the human tolerance towards acceleration. Two factors of human tolerance towards abrupt acceleration
(Shanahan 2004a) are evaluated; magnitude of the acceleration and direction of the acceleration.
Due to the different tolerance level in different direction, the acceleration tolerance level of human is described in term of coordinate axes which comprises of magnitude and direction as in Figure 5 -23 and Table 5 -8. In vertical crash test or crash simulation, only headward and tailward acceleration direction is considered.
130
Figure 5 -23. Human coordinate system (Shanahan 2004b)
Table 5 -8. Human tolerance limits (Shanahan 2004b).
Table 5 -8 shows the summary of tolerance level of human towards acceleration in their respective directions for 0.1 second crash pulse. In general, human can tolerate better towards shorter crash pulse of the same acceleration magnitude. The acceleration tolerance level in this table is specified in terms of G, where 1 G is the gravitational acceleration at sea level which is 9.81 m/s2.
Acceleration-time history of a crash may consist of pulses with very complex shapes. For practical purposes, the crash pulse is considered as triangular in shape as suggested by
Shanahan (Shanahan 2004b) as in Figure 5 -24. The maximum acceleration experienced is
131 denoted by the peak of the pulse and the average acceleration of the pulse is one-half of the peak acceleration.
Figure 5 -24. Acceleration crash pulse in assumed triangular pulse (Shanahan 2004).
132
Chapter 6 RESULTS AND DISCUSSIONS
6.1. Introduction
The crash simulation was carried on two types of fuselage section models. The first model was fuselage section that made of aluminium alloy fuselage skin representing the original
Boeing 737 fuselage section. The second model was fuselage section that made of the fibre metal laminate (FML) GLARE 5-2/1 fuselage skin. Beside the fuselage skin, all other structures within fuselage with FML fuselage skin are the same with the fuselage with aluminium alloy fuselage skin. From now on in Chapter 6, fuselage section with aluminium alloy fuselage skin is simply referred as aluminium fuselage meanwhile fuselage section with fibre metal laminate (FML) GLARE 5-2/1 fuselage skin is simply referred as GLARE 5-
2/1 fuselage.
Two main objectives to be achieved in this chapter are to analyse the impact response of
GLARE 5-2/1 fuselage and how impact response of GLARE 5-2/1 fuselage differs from the aluminium fuselage during crash event. Discussion on these results should develop understanding on failure and deformation, energy dissipation and acceleration response at floor level within future FML fuselage during survivable crash event.
6.2. Energy Dissipation during Crash
Aluminium fuselage and GLARE 5-2/1 fuselage were both executed with at 10 ms-1 in their vertical direction. The duration of the simulation was 180 ms. With 10 ms-1 impact velocity, the impact energy of aluminium fuselage and GLARE 5-2/1 fuselage was 35.41 kJ and 39.05 kJ respectively. The mass difference is due to the difference in the mass of their fuselage skin alone. Apparently, GLARE 5-2/1 fuselage in this thesis is 5.8% heavier than the aluminium fuselage. Worth to mention that GLARE 5-2/1 could have different specific mass
133 depends on the thickness of the aluminium alloy layer as commercially it varies between
0.2 to 0.5 mm.
During crash, fuselage structure absorbs the impact energy and distributed among the structural components such as fuselage frames, fuselage floor, fuselage skin, seat tracks and stringers. Analysing the percentage of energy transferred to and dissipated through the structural components should gives understanding on energy dissipation mode within the aircraft structure. With this technique, the energy absorption capability of GLARE 5-2/1 fuselage skin can be evaluated.
Figure 6 -1 and Figure 6 -2 show the energy balance of aluminium and GLARE 5-2/1 fuselage crash simulations under velocity impact 10 ms-1. Both energy balances show similar characteristic in terms of their energy dissipation. The energy is absorbed by the fuselages initially by their elastic response and then followed by plastic deformation that dominates energy dissipation in both fuselages. Energy dissipated through material damage is almost negligible in both fuselages but it is too early to conclude that damage material model can be neglected in modelling aircraft crash simulation under this impact velocity. As can be seen in Figure 6.1 and 6.2, the total kinetic energy do not reach zero after declining gradually due to plastic deformation and elastic strain energy within the first 150 ms in both fuselages. Beyond 180 ms, all major deformation would have been completed and the fuselage has started to bounce upward due to elastic strain energy stored in the structure especially within the frames.
134
40 Total kinetic energy Plastic dissipation 35 Elastic strain energy Damage dissipation 30
25
20
Energy (kJ) Energy 15
10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -1. Energy balance within the aluminium fuselage for 10 ms-1 impact velocity crash.
40 Total kinetic energy 35 Plastic dissipation Elastic strain energy 30 Damage dissipation
25
20
Energy (kJ) Energy 15
10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -2. Energy balance within the GLARE 5-2/1 fuselage for 10 ms-1 impact velocity crash.
Figure 6 -3 and Figure 6 -4 show the distribution of impact energy within the main aluminium fuselage structure and GLARE 5-2/1 fuselage structure respectively meanwhile
135
Table 6 -1 summarises the percentage of energy distributed within fuselage structures.
Frame structure absorbs highest percentage of the impact energy in both fuselage with
54.91% for aluminium fuselage and 59.50% for GLARE 5-2/1 fuselage. Frame structure in fuselage is designed not just to maintain the shape of the fuselage, but it is also designed to have a strong structure in order to protect the occupants in the fuselage space. Thus it is desirable and expected to see that it absorbs the most of the impact energy in form of elastic strain energy, plastic strain deformation and damage in both type of fuselage.
Total kinetic energy Total energy dissipated Frames (energy distribution) 40 Skin (energy distribution) Floor beams (energy distribution) 35 Stringers (energy distribution)
30
25
20
Energy (kJ) Energy 15
10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -3.Dissipation of impact energy and its distribution within the aluminium fuselage for 10 ms-1 impact velocity crash.
136
Total kinetic energy Total energy dissipation Frames (energy distribution) Skin (energy distribution) Floor beam (energy distribution) 40 Stringer (energy distribution) 35
30
25
20
Energy (kJ) Energy 15
10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -4. Dissipation of impact energy and its distribution within the FML GLARE 5-2/1 fuselage for 10 ms-1 impact velocity crash.
% of energy distribution at maximum total energy dissipation Aluminium GLARE 5-2/1 Structure fuselage fuselage Frame 54.91% 59.50% Skin 14.23% 24.15% Stringer 13.08% 4.61% Floor beam 12.17% 9.21% Seat tracks 0.49% 0.49%
Table 6 -1. Percentage of energy distribution within fuselage structure during impact
Figure 6 -5 shows the decomposition of energy distributed to frame in aluminium fuselage.
Great amount of the energy dissipated through plastic deformation in which it significantly reduces the energy within the fuselage. Effectively, frame structure in aluminium fuselage dissipates 52.9% of the impact energy through plastic deformation. Small amount of the
137 absorbed energy is in the form of elastic strain energy that gives the frame some recoverable deformation at the end of the crash. Energy dissipated through material damage is very small and almost negligible in aluminium fuselage, only in range of 6 mJ.
This suggests that frame in aluminium fuselage can be modelled without incorporating damage model for such impact condition. Orderly after frame, energy distribution within aluminium fuselage structure is followed by skin, stringer and floor beam with each of them absorbed energy in between 12.17 to 14.23% only. The rest of the energy is distributed within seat tracks and floor panels.
25 Energy absorbed
Plastic dissipation 20
15
Energy (kJ) Energy 10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -5. Energy absorbed by frame structure and its decomposition in aluminium fuselage
Figure 6 -6 shows the energy dissipated through plastic strain and amount of energy absorbed by skin structure in aluminium fuselage. 57% of the energy absorbed by the skin in aluminium fuselage is dissipated through plastic deformation. Effectively, skin structure dissipates the impact energy of the whole fuselage structure through plastic deformation by 9.8%.
138
25 Energy absorbed Plastic dissipation 20
15
Energy (kJ) Energy 10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -6. Energy absorbed by skin structure its plastic dissipation in aluminium fuselage
In GLARE 5-2/1 fuselage, higher percentage of energy is absorbed by skin structure compare to energy absorbed by skin in aluminium fuselage as shown in Figure 6 -7 and
Table 6.1. Skin structure in GLARE 5-2/1 fuselage dissipates impact energy by 9.49% and
0.22% through plastic dissipation and damage due to material degradation respectively.
With total energy dissipated of 9.71% of the impact energy through its skin, this made the
GLARE 5-2/1 skin structure is as effective as aluminium alloy skin in terms of energy absorption during impact. However, this is not conclusive in terms of improvement on crashworthiness as acceleration at passengers’ level and global deformation must be taken into account as well.
139
25
Energy absorbed Elastic strain energy 20 Plastic dissipation Damage dissipation
15
Energy (J) Energy 10
5
0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -7. Energy absorbed by skin structure and its decomposition in GLARE 5-2/1 fuselage.
140
6.3. Structural Deformation of Fuselage Structure
Analysing the deformation should give more understanding on the failure mechanisms and failure modes of the fuselage structure during crash. By reflecting the deformation behaviour with the energy balance, the impact behaviour of GLARE 5-2/1 fuselage section during crash can be established. First of all, deformation of frame structure is analysed as the main structure that absorbed the impact energy and sustain the shape of the fuselage.
After that, we will discuss on the deformation of the fuselage skin structure. Figure 6 -8 and
Figure 6 -9 show the deformation or crushing process of the aluminium and GLARE 5-2/1 fuselage during crash respectively. The deformation histories are shown in selected time steps up to 180 ms.
In aluminium fuselage, the plastic strain localisation started at the bottom impacted frame structure due to impact force reaction. This exerted large lateral force and caused the frame at the bottom to have bending response. Another two locations possessed localised plastic strain as early as 10 ms in the frame at the inner side that has non-smooth circular shape. The immediate plastic strain response shown in the deformation history is also supported by the energy balance diagram in Figure 6.1 where energy was quickly dissipated by plastic straining immediately after impact. Around 10 ms, the localised plastic strain at the bottom of frame started to buckle upward as the inertia of the fuselage section provided a compressive force along the frame circumference and the reaction force at the impacted side guided the direction of the deflection. The buckling progressed and caused large plastic deformation at the bottom part of the frame between 20 to 150 ms. This large plastic deformation within this period also can be observed in the energy balance of frame during impact in Figure 6 -5. During this period, the frame at the bottom is also observed to be twisted at the high localised strain locations mentioned earlier. The non-symmetry cross-section of the z-shaped frame caused instability at that area which finally caused the
141 deflections. At 85 ms, the buckled frames made contact with and exerted impact force to the floor beams which caused the floor beams displaced in upward direction and experienced plastic deformation at the impacted area. The contact between the frames and the floor beams continued up to 180 ms and as a result, seat tracks that attached to floor beam experienced plastic deformation as well. For crash simulation of aluminium fuselage, the fuselage structure started to bounce upward at 148 ms as the elastic strain energy within the fuselage section was released into kinetic energy meanwhile it occurred at impact time 151 ms for GLARE 5-2/1 fuselage. As mentioned earlier, all major deformation would have been completed once the impact time reached 180 ms and the fuselage has started to bounce upward due to the release of the elastic strain energy stored in the structure especially within the frames.
Deformation history of frames in GLARE 5-2/1 fuselage exhibits the same character as in aluminium fuselage as shown in Figure 6 -9 in terms of deformation process and the deformation shapes. One observable difference is that the third fuselage frame at the back deflected upward higher than the frame in aluminium fuselage as can be seen in both fuselage, for example in Figure 6 -8 at time 50 ms for aluminium fuselage. The frame deflection is due to the non-symmetry cross-section of the frame about the fuselage vertical plane as shown in Chapter 5. Supposedly, such deflection is minimal in real full body fuselage due to the continuation of the fuselage frame, skin and stringers along the fuselage length. As no additional stiffener was modelled around the open ends of the fuselage section FE model, such deflection is inevitable. It is believed that the deflection played a minor role in terms of the crushing of the bottom of the fuselage and the response experience at the passenger’s floor level. However, the difference in deflection magnitude at the top of the frame between aluminium fuselage and GLARE 5-2/1 fuselage is assumed to be the couple effect of impact energy distribution between frames and skin. The ratio of energy distributed between frame and skin in aluminium fuselage and GLARE 5-2/1
142 fuselage is around 3.9:1 and 2.5:1 respectively. The deformation of the frame far from the impacted area which mainly depends on the stress wave propagation might be affected by the deformation of skin at the top which also mainly depends on the same mechanisms.
Thus the difference of stiffness and strength of the two skins effected the deformation at the top part of the fuselage section.
Figure 6 -8. Deformation histories with plastic strain contour plot of the aluminium fuselage during crash with impact velocity 10 ms-1.
143
Figure 6 -9. Deformation histories with plastic strain contour plot of the GLARE 5-2/1 fuselage during crash with impact velocity 10 ms-1.
Material in frame did not degrade up to the total failure in both aluminium and GLARE 5-
2/1 fuselage as there was no element deletion occurred. However there were few elements deleted in stringer for both fuselages. The elements deleted in both fuselages were at different location but both occurred at area that fastened to the fuselage frames.
The skin of the fuselage is constrained to the frames and stringers. The modelling used does not allow the skin to detach from the frames and stringers. However skin still may detach if the element at the connection point itself is deleted due to material degradation.
144
With this assumption in the constraint modelling, skin structure is expected to follow the deformation of the more dominant frame structure during crash event. Figure 6 -10 shows the crushing distance time history meanwhile Figure 6 -11 shows the deformation shape of fuselage skin for both aluminium and GLARE 5-2/1 fuselages at impact time 180 ms. The same buckling deformation and plastic hinge as frames occurred at the bottom part of the fuselage. Plastic hinges at the side bottom frame did not occur in skin structure as that hinges occurred at the inner side of the frames as shown earlier in Figure 6 -8. Even though the deformation of both skins was alike in general view, the response and damage within the GLARE 5-2/1 skin structure must be studied. Worth to mention that although frames were the dominant structure in responding to the impact force, but the bottom part of the fuselage skin was the main structure that transferred the impact force from the rigid impact surface to the frames through the thickness of the skin
Observation on deformation of the fuselage structure continues by analysing the crushing distance of the fuselage. Figure 6 -10 shows that GLARE 5-2/1 fuselage possessed larger crushing distance than aluminium fuselage by 6.27 cm. The crushing distance was mainly determined by the large bending and rotation that occurred at the plastic hinges within the frames and skin as shown in Figure 6 -11. Although the difference is relatively small, it is our interest to investigate how it happened.
145
1.0
0.9
0.8
0.7
0.6
0.5
0.4
Crushing distance (m) distance Crushing 0.3
0.2 Aluminium fuselage 10 m/s 0.1 GLARE 5-2/1 fuselage 10 m/s 0.0 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -10. Crushing distance of aluminium and GLARE 5-2/1 fuselages in 10 ms-1 impact velocity crash.
A
B
C
Figure 6 -11. Location of plastic hinge at the bottom half of the fuselage section
As crushing distance was mainly determined by the magnitude of the rotation and bending at the plastic hinges, attempts are made to find the cause of the magnitude change
146 between aluminium fuselage and GLARE 5-2/1. As the frames for both fuselages were the same in every sense, the bending stiffness and critical buckling load of the skin at plastic hinges location could be the source of differences.
Plastic hinges occurred in skin because skin and frames are tied together thus skin that attached to frames would deform according to deformation of frames. In the same time, the stiffness and strength in skin structure provided some resistance to the deformation that taking place at the proximity of the tied frame. Figure 6 -12 shows damage that occurred within composite laminate in GLARE 5-2/1 skin structure at hinge location B at 24 ms. Element in red indicates that the composite material has reached its maximum damage, either in matrix tensile mode or matrix compressive mode. As the material stiffness of the skin degraded especially along the line of hinge location B, the damaged skin gave minimal resistance towards deflection progression due to bending in frames.
However there is no failure in fibre mode at hinge location B at that impact time. Figure
6 -13 shows the matrix tensile failure in the outer lamina at step time 78 ms where the frames buckling and bending were progressing. At hinge location A, B and C, it is observed that the outer and inner 0⁰ laminas were damaged in their fibre tensile mode as shown in
Figure 6 -14. Based on these observations, it is understood that the material stiffness degradation in various failure modes within GLARE 5-2/1 contributed to the crushing process of the GLARE 5-2/1 fuselage during crash.
Critical loading for buckling is sensitive to delamination especially delamination that occur further from the composite of FML surface. However, there was no total material degradation within adhesive layer observed, thus there was no delamination occurred in this crash analysis that can contribute to the failure mechanisms of the GLARE 5-2/1 fuselage during crash under 10 ms-1 velocity impact.
147
0⁰ fibre orientation, inner layer 90⁰ fibre orientation, inner layer
Outer layer (90⁰) Outer layer (0⁰) Figure 6 -12. Tensile and compressive matrix failure at composite layers in GLARE 5-2/1 skin structure at hinge location B. t = 24 ms
148
Figure 6 -13. Matrix tensile failure in glass-fibre laminate (90⁰) outer lamina at t = 78 ms.
Inner lamina (0⁰) Outer lamina (0⁰)
Figure 6 -14. Fibre tensile failure in glass-fibre laminate (0⁰) inner and outer lamina at t = 78 ms.
149
6.4. Acceleration at Floor Level
One of the main crashworthiness evaluations of aircraft is the acceleration experienced by the passengers or occupants during crash event. The acceleration-time histories were measured at two locations on the seat tracks; the outer right seat track and the inner right seat track. The acceleration-time histories were filtered with 60 Hz low pass filter as discussed in previous chapter. The peak acceleration on headward and tailward direction for both locations were used to compare with the amount of acceleration that human can tolerate in order to evaluate the survivability of the passengers during crash.
Figure 6 -15 shows the acceleration-time histories at the outer and inner right seat tracks of the aluminium fuselage. Both acceleration responses started with headward direction
(eyeballs down) and then followed by tailward direction (eyeballs up) and continued with this cycle until the impact energy was dissipated through plastic deformation and through global change of velocity due to elastic energy released within the structure. Headward peak acceleration at the outer right seat track of aluminium fuselage was 24.31 G which occurred as early as 8 ms of the impact time. Meanwhile tailward peak acceleration of
19.24 G occurred at 162 ms impact time. However, both headward and tailward peak accelerations at inner right seat track were larger than the peak accelerations at outer right seat track with 43.37 G and 42.02 G respectively. High headward peak acceleration
(eyeballs down) at inner right seat track occurred right after the buckled bottom part of the fuselage frame made contact with the floor beam as can be seen in Figure 6 -8 (t = 100ms).
By comparing these peak acceleration values to the tolerable values by human, headward acceleration pulse at the outer right seat track was the only value lower than the tolerable value, i.e.: uninjured passenger. The rest of the peak acceleration values indicated that the passengers in both outer and inner seat tracks may have suffered severe injury during the crash. However, in real crash event, the passengers are well restrained by safety belt,
150 seated on cushioned seats and the seats themselves may have structures that capable of absorbing some of the impact energy. Thus, the acceleration response of the passengers in real event should be lower than shown in Figure 6 -15. To put things into perspective, the magnitude of the peak acceleration experienced by passengers during aircraft crash which was carried by Adams and Lankarani (Adams & Lankarani 2003) was used for comparison.
In Adams and Lankarani’s work, acceleration response was measured at seat tracks for both experimental crash test and crash simulation, similar to the measurement’s location in this thesis. Similar fuselage section B737 was used in Adams and Lankarani’s but with lower impact velocity of 9 ms-1. The peak acceleration measured at the inner seat track in Adams and Lankarani’s work was 38 G which is comparable to peak acceleration measured in this thesis in terms of order of magnitude. Even though the acceleration values evaluated in this thesis are incapable of determining exactly whether or not the passengers will sustain severe injury (restrain and seat were not modelled), their order of magnitudes are very valuable in which they will be compared to the acceleration response in a GLARE 5-2/1 fuselage crash event.
Figure 6 -16 shows the acceleration response of both outer and inner seat tracks of GLARE
5-2/1 fuselage. At outer seat track, both headward and tailward peak acceleration values were larger than peak acceleration values in aluminium fuselage. Contrarily, peak acceleration at the inner seat track in GLARE 5-2/1 fuselage was smaller than in aluminium fuselage for both headward and tailward directions. This difference might be due to the differences in crushing distance and failure mechanisms at the plastic hinges and buckled structures between aluminium and GLARE 5-2/1 fuselage. Overall, the peak acceleration responses for both fuselages exhibited similar magnitude which indicates that the crashworthiness performance in terms of acceleration experience by passengers in GLARE
5-2/1 fuselage is in the same order with the original aluminium fuselage.
151
outer right aluminium 50 inner right aluminium 43.47 40
30 24.31
20
10
0
-10 Acceleration (G) Acceleration -20 -19.24 -30
-40 -42.02 -50 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -15. Acceleration response at passengers’ location in aluminium fuselage during 10 m/s vertical crash.
outer right fml 50 inner right fml 40 32.44 30 29.49
20
10
0
-10 Acceleration (G) Acceleration -20
-30 -29.21
-40 -40.66
-50 0 20 40 60 80 100 120 140 160 180 Time (ms)
Figure 6 -16. Acceleration response at passengers’ location in GLARE 5-2/1 fuselage during 10 m/s vertical crash.
152
Chapter 7 Conclusions and Future Work
7.1. Conclusions
Crash simulation of fibre metal laminate (FML) fuselage went through a series of development process. The development of FML fuselage FE crash model includes the establishment of material and damage model for all FML’s material constituents, validation of the material and damage models, verification of impact model with buckling failure and large displacement and verification of frame FE model. This long development process was continued by assembling all the validated and verified works to form a reliable FML fuselage crash model.
The aim of the research was to develop a reliable FE crash model of fibre metal laminate
(FML) fuselage and to evaluate the crashworthiness of this new future aircraft. A building block approach which was originally and only previously used in aircraft design industry was adapted in order to fully computationally develop a reliable FE model of aircraft crash.
The success in adapting this approach is one of the novel achievements and contributions in this field of research. Throughout the process of developing FML fuselage via building block approach, various modelling techniques were performed in order to model a reliable impact response of aluminium alloy, composite laminate and fibre metal laminate especially when subjected to axial impact condition. It is learnt that there are few critical aspects to be considered in modelling the impact response of FML. Conclusively, first aspect is to develop a reliable material model for each of the constituents that suit the desired impact condition. Secondly, one needs to understand the failure mechanisms of
FML under various impact conditions so that an efficient FE models can be develop. Thirdly, consideration of how the constituents of FML interact with each other in response to impact enables one to correctly model the failure of FML structure. With all due respect, capability to exercise these three aspects was another achievement in this research.
153
However, the greatest and novel finding in this research was to be able to analyse the impact response of FML fuselage under survivable impact condition by pure computational work. By comparing the impact response of FML fuselage to the original Boeing 737 aluminium fuselage, few key findings were concluded. During impact, FML fuselage skin affected the impact response of the main fuselage structure which is the fuselage frame especially in terms of crushing process of the bottom part of the fuselage. The damage in laminate played a significant role in the failure mechanisms of the fuselage subfloor structure. There was no delamination observed within the FML fuselage which may suggest that delamination model could be ignored by eliminating the need of cohesive element as interface layers in modelling crash analysis of FML fuselage under low velocity impact. In terms of acceleration responses experienced by passengers which were measured at the seat tracks, FML fuselage exhibited the same order of peak acceleration compared to the aluminium fuselage.
Overall, the response of the FML fuselage based on presented observations indicates that its crashworthiness performance have the same order and magnitude as the aluminium fuselage. This finding gives great confidence to aircraft designer to use FML as the fuselage skin for the whole fuselage instead of being used as the top fuselage skin only as implemented in Airbus A380. This conclusive crashworthiness performance of FML fuselage when compared to aluminium fuselage is essential and also a novel contribution into the research field of an aircraft crash.
154
7.2. Recommendation for Future Work
Enormous amount spent in developing the reliable crash model of FML fuselage left the author little time to study further on the impact response of FML fuselage. The first and foremost future work is to process the acceleration data in order to evaluate thoroughly the crashworthiness of the FML fuselage. Other future works recommended by the author are:
a. Crash simulation of FML fuselage without delamination model incorporated within the
FML fuselage skin.
b. Parametric studies on impact response of FML fuselage under various impact
conditions.
c. Parametric studies on impact response of FML fuselage based on different grades of
GLARE.
d. Parametric studies on impact response of FML fuselage on various roll angles of impact
surface.
155
References
1. Abaqus Documentation, Version 6.12, Dassault Systemes Simulia Corp. 2. Abromowitz, A., Smith, T.G. & Vu, D.T., 2000. Vertical Drop Test of a Narrow- Body Transport Fuselage Section With a Conformable Auxiliary Fuel Tank Onboard. 3. Adams, A. & Lankarani, H.M., 2010. A modern aerospace modeling approach for evaluation of aircraft fuselage crashworthiness, pp.37–41. 4. Aslan, Z., Karakuzu, R. & Okutan, B., 2003. The response of laminated composite plates under low-velocity impact loading. Composite Structures, 59(1), pp.119–127. 5. Asundi, A. & Choi, A.Y.N., 1997. Materials Processing Technology Fiber Metal Laminates : An Advanced Material for Future Aircraft. 6. Bi, R. et al., 2014. Buckling and postbuckling analysis of elasto-plastic fiber metal laminates. Acta Mechanica Solida Sinica, 27(1), pp.73–84. Bisagni, C., 2003. Development of a crashworthy subfloor concept for a commuter aircraft. , 39(2), pp.2– 5. 7. Bisagni, C., 2009. Experimental investigation of the collapse modes and energy absorption characteristics of composite tubes. International Journal of Crashworthiness, 14(4), pp.365–378. 8. Brar, N.S. et al., 2009. CONSTITUTIVE MODEL CONSTANTS FOR Al7075-T651 and Al7075-T6. , 945(1), pp.945–948. 9. Brewer, J.C. and Lagace, P.A., 1988 "Quadratic Stress Criterion for Initiation of Delamination", Journal of Composite Materials, Vol. 22, pp. 1141-1155. 10. Buyuk, M., Loikkanen, M. & Kan, C.-D. (Steven), 2008. Explicit Finite Element Analysis of 2024-T3 / T351 Aluminum Material Under Impact Loading for Airplane Engine Containment and Fragment Shielding. 11. Chai, G.B. & Manikandan, P., 2014. Low velocity impact response of fibre-metal laminates – A review. Composite Structures, 107, pp.363–381. 12. Cocchieri, E.B. et al., 2006. A Review on the Development and Properties of Continuous Fiber / epoxy / aluminum Hybrid Composites for Aircraft Structures 2 . The Production of Metal / laminate Hybrid Composites. , 9(3), pp.247–256. 13. Cortés, P. & Cantwell, W.J., 2005. The fracture properties of a fibre–metal laminate based on magnesium alloy. Composites Part B: Engineering, 37(2-3), pp.163–170. 14. Donadon, M.V. et al., 2008. A progressive failure model for composite laminates subjected to low velocity impact damage. Computers & Structures, 86(11-12), pp.1232– 1252. 15. ECSS, 2011a. Space engineering, Structural Materials Handbook - Part 5. 16. ECSS, 2011b. Space engineering, Structural Materials Handbook - Part 7. 17. Fan, J., Guan, Z.W. & Cantwell, W.J., 2011. Numerical modelling of perforation failure in fibre metal laminates subjected to low velocity impact loading. Composite Structures, 93(9), pp.2430–2436. 18. Farley, G.L. & Jones, R.M., 1992. Crushing Characteristics of Continuous Fiber- Reinforced Composite Tubes. Journal of Composite Materials, 26(1), pp.37–50. 19. Fasanella, E.L. & Jackson, K.E., 2001. Crash Simulation of a Boeing 737 Fuselage Section Vertical Drop Test.
156
20. Fasanella, E.L. & Jackson, K.E., 2000. Impact Testing and Simulation of a Crashworthy Composite Fuselage Section with Energy-Absorbing Seats and Dummies US Army Research Laboratory , Vehicle Technology Directorate. 21. Fasanella, E.L., Jackson, K.E. & Lyle, K.H., 2002. Finite Element Simulation of a Full-Scale Crash Test of a Composite Helicopter. Journal of the American Helicopter Society, 47(3), p.156. 22. Feng, Z. et al., 2013. Research on effects of composite skin on crashworthiness of composite fuselage section. International Journal of Crashworthiness, 18(5), pp.459– 464. 23. Gay, D. & Hoa, S. V., 2007. Composite Materials: Design and Applications Second Edi., CRC Press. 24. Gere, J.M. & Timoshenko, S., 1990. Mechanics of Materials, PWS-KENT Publications. 25. Hagenbeek, M., 2005. Characterisation of Fibre Metal Laminates under Thermo- mechanical Loadings 26. Hashagen, F. et al., 1995. Finite element procedure for modelling fibre metal laminates. Composite Structures, 32(1-4), pp.255–264. 27. Hashemi, S.M.R., Sadeghi, M.M. & Walton, A., 1996. Modelling verification of an airframe section and comparisons with impact test. International Journal of Crashworthiness, 1(1), pp.11–20. 28. Hashemi, S.M.R. & Walton, A.C., 2006. A systematic approach to aircraft crashworthiness and impact surface material models. , 214, pp.265–280. 29. Hashin, Z., 1980. Failure Criteria for Unidirectional Fiber Composites , 47(June 1980), pp.329–334. 30. Hashin, Z. & Rotem, a., 1973. A Fatigue Failure Criterion for Fiber Reinforced Materials. Journal of Composite Materials, 7(4), pp.448–464. 31. Heimbs, S. et al., 2013. Dynamic testing and modelling of composite fuselage frames and fasteners for aircraft crash simulations. International Journal of Crashworthiness, 18(4), pp.406–422. 32. Hooputra, H., Gese, H., Dell, H., Werner, H., 2004. A comprehensive failure model for crashworthiness simulation of aluminium extrusions, International Journal of Crashworthiness, 9:5, 449-464. 33. simulation of aluminium extrusions, International Journal of Crashworthiness, 9:5, 449- 464 34. Jackson, K.E. et al., 2004. A History of Full-Scale Aircraft and Rotorcraft Crash Testing and Simulation at NASA Langley Research Center. 35. Jackson, K.E., 2001. Impact Testing and Simulation of a Crashworthy Composite Fuselage Concept. International Journal of Crashworthiness, 6(1), pp.107–122. 36. Jackson, K.E. & Fasanella, E.L., 2005. Crash simulation of a vertical drop test of a commuter-class aircraft. International Journal of Crashworthiness, 10(2), pp.173–182. 37. Jackson, K.E., Fasanella, E.L. & Kellas, S., 1997. Crash simulation of a 1/5-scale model composite fuselage concept. , pp.1–14. 38. Jih, C.J. & Sun, C.T., 1993. Prediction of Delamination in Composite Laminates Subjected to Low Velocity Impact. Journal of Composite Materials, 27(7), pp.684–701.
157
39. Johnson, G.R. & Cook, W.H, 1983. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures.pdf. In Seventh International Symposium on Ballistics,. 40. Johnson, G.R. & Cook, W.H., 1985. FRACTURE CHARACTERISTICS OF THREE METALS SUBJECTED TO VARIOUS STRAINS , STRAIN RATES , TEMPERATURES AND PRESSURES. , 21(I). 41. Karagiozova , D., Alves, M., Jones, M., 2000. Inertia effects in axisymmetrically deformed cylindrical shells under axial impact. International Journal of Impact Engineering, 24, 1083-1115. 42. Karagiozova, D. & Jones, N., 2001. Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact. Thin-Walled Structures, 39(7), pp.583–610. 43. Karagiozova, D. & Jones, N., 2000. Dynamic elastic–plastic buckling of circular cylindrical shells under axial impact. International Journal of Solids and Structures, 37(14), pp.2005–2034. 44. Karagiozova, D. & Jones, N., 2001. Influence of stress waves on the dynamic progressive and dynamic plastic buckling of cylindrical shells. , 38, pp.6723–6749. 45. Karagiozova, D. & Jones, N., 2002. On dynamic buckling phenomena in axially loaded elastic–plastic cylindrical shells. International Journal of Non-Linear Mechanics, 37(7), pp.1223–1238. 46. Kawai, M. & Hachinohe, A., 2002. Two-stress level fatigue of unidirectional fiber – metal hybrid composite : GLARE 2. , 24, pp.567–580. 47. Kay, G., 2003. Failure Modeling of Titanium 6Al-4V and Aluminum 2024-T3 With the Johnson-Cook Material Model, 48. Khalili, S.M.R., Mittal, R.K. & Kalibar, S.G., 2005. A study of the mechanical properties of steel/aluminium/GRP laminates. Materials Science and Engineering: A, 412(1-2), pp.137–140. 49. Khan, S.U., Alderliesten, R.C. & Benedictus, R., 2009. Post-stretching induced stress redistribution in Fibre Metal Laminates for increased fatigue crack growth resistance. Composites Science and Technology, 69(3-4), pp.396–405. 50. Kim, S.J., Goo, N.S. & Kim, T.W., 1997. THE EFFECT OF CURVATURE ON THE DYNAMIC RESPONSE AND IMPACT-INDUCED DAMAGE IN COMPOSITE LAMINATES. , 51, pp.763– 773. 51. Kindervater, C. et al., 2011. Validation of Crashworthiness Simulation and Design Methods by Testing of a Scaled Composite Helicopter Frame Section. 52. Kumakura, I.K., 2002. Vertical Drop Test of a Transport Fuselage Section. , pp.69–72. 53. Lalibert, J.F., 2005. Impact Damage in Fiber Metal Laminates , Part 1 : Experiment. , 43(11). 54. Laliberté, J., Poon, C. & Straznicky, P. V, 2002. NUMERICAL MODELLING OF LOW- VELOCITY IMPACT DAMAGE IN FIBRE-METAL-LAMINATES. , pp.1–10. 55. Lee, Y. & Huang, C.-H., 2003. Ultimate strength and failure process of composite laminated plates subjected to low-velocity impact. 56. Lesuer, D.R., 2000. Experimental Investigations of Material Models for Ti-6Al-4V Titanium and 2024-T3 Aluminum. 57. Linde, P. et al., 2004. Modelling and Simulation of Fibre Metal Laminates. , pp.421–439.
158
58. Liu, Y. & Liaw, B., 2009. Effects of Constituents and Lay-up Configuration on Drop- Weight Tests of Fiber-Metal Laminates. Applied Composite Materials, 17(1), pp.43–62. 59. Marais, S.T. et al., 2004. Material testing at high strain rate using the split Hopkinson pressure bar. , 1(July), pp.319–338. 60. Marissen, R., 1988. Fatigue crack growth in ARALL A hybrid aluminium-aramid composite material Crack growth mechanisms and quantitative predictions of the crack growth rates. 61. Meng, F.X., Zhou, Q. & Yang, J.L., 2009. Improvement of crashworthiness behaviour for simplified structural models of aircraft fuselage. International Journal of Crashworthiness, 14(1), pp.83–97. 62. Mohotti, D. et al., 2013. Out-of-plane impact resistance of aluminium plates subjected to low velocity impacts. Materials & Design, 50, pp.413–426. 63. Morinière, F.D., Alderliesten, R.C. & Benedictus, R., 2013. Low-velocity impact energy partition in GLARE. Mechanics of Materials, 66, pp.59–68. 64. Morinière, F.D., Alderliesten, R.C. & Benedictus, R., 2014. Modelling of impact damage and dynamics in fibre-metal laminates – A review. International Journal of Impact Engineering, 67, pp.27–38. 65. Nakatani, H. et al., 2011. Damage characterization of titanium/GFRP hybrid laminates subjected to low-velocity impact. Composites Part A: Applied Science and Manufacturing, 42(7), pp.772–781. 66. Niu, M.C.Y., 1988. Airframe structural design, practical design information and data on aircraft structures, Conmilit Press Ltd. 67. Noor, A., and Carden, H.D., 1993. Computational Methods for Crashworthiness. In NASA Conference Publication 3223. 68. Palanivelu, S. et al., 2011. Low velocity axial impact crushing performance of empty recyclable metal beverage cans. International Journal of Impact Engineering, 38(7), pp.622–636. 69. Pifko, A.B. & WInter, R., 1980. Theory and application of finite element analysis to structural crash simulation. 70. Rao, S.S., 1999. The Finite Element Method in Engineering Third Edit., Butterworth- Heinemann. 71. Remmers, J.J.. & de Borst, R., 2001. Delamination buckling of fibre–metal laminates. Composites Science and Technology, 61(15), pp.2207–2213. 72. Remmers, J.J.Co., 2006. Discontinuities in materials and structures. 73. Reyes, G. V & Cantwell, W.J., 2000. The mechanical properties of fibre-metal laminates based on glass fibre reinforced polypropylene. , 60, pp.2–6. 74. Robinson, A.G.M.M., Ioannidis, D.E.M.G.A.D.M.B. & Carruthersb, J., 1997. Review Crashworthy capability of composite material structures p. , 37, pp.109–134. 75. Robinson, P. & Davies, G. a. O., 1992. Impactor mass and specimen geometry effects in low velocity impact of laminated composites. International Journal of Impact Engineering, 12(2), pp.189–207. 76. Rodríguez-Martínez, J. a., Rusinek, a. & Arias, a., 2011. Thermo-viscoplastic behaviour of 2024-T3 aluminium sheets subjected to low velocity perforation at different temperatures. Thin-Walled Structures, 49(7), pp.819–832.
159
77. Sadighi, M., Alderliesten, R.C. & Benedictus, R., 2012. Impact resistance of fiber-metal laminates: A review. International Journal of Impact Engineering, 49, pp.77–90. 78. Seo, H. et al., 2010. Numerical Simulation of Glass-Fiber-Reinforced Aluminum Laminates with Diverse Impact Damage. AIAA Journal, 48(3), pp.676–687. 79. Seyed Yaghoubi, a., Liu, Y. & Liaw, B., 2011. Stacking Sequence and Geometrical Effects on Low-Velocity Impact Behaviors of GLARE 5 (3/2) Fiber-Metal Laminates. Journal of Thermoplastic Composite Materials, 25(2), pp.223–247. 80. Shaw, D. & Shen, Y.L., 1993. DYNAMIC BUCKLING OF AN IMPERFECT COMPOSITE CIRCULAR CYLINDRICAL SHELL. , 48(3). 81. Shanahan D. F.(2004). Basic principles of crashworthiness, RTO HFM Lecture Series on “Pathological Aspects and Associated Biodynamics in Aircraft Accident Investigation”, 28-29 October 2004, Madrid, RTO-EN-HFM-113. 82. Shanahan D. F.(2004). Human Tolerance and Crash Survivability, RTO HFM Lecture Series on “Pathological Aspects and Associated Biodynamics in Aircraft Accident Investigation”, 28-29 October 2004, Madrid, RTO-EN-HFM-113. 83. Shi, Y., Swait, T. & Soutis, C., 2012. Modelling damage evolution in composite laminates subjected to low velocity impact. Composite Structures, 94(9), pp.2902–2913. 84. Shyr, T.-W. & Pan, Y.-H., 2003. Impact resistance and damage characteristics of composite laminates. Composite Structures, 62(2), pp.193–203. 85. Sinmazçelik, T. et al., 2011. A review: Fibre metal laminates, background, bonding types and applied test methods. Materials & Design, 32(7), pp.3671–3685. 86. Song, S.H. et al., 2010. Experimental and Numerical Investigation on Impact Performance of Carbon Reinforced Aluminum Laminates. Journal of Materials Science & Technology, 26(4), pp.327–332. 87. Sun, C.T. & Tao, J., 1998. PREDICTION OF FAILURE ENVELOPES AND STRESS / STRAIN BEHAVIOUR OF COMPOSITE LAMINATES *. , 3538(97). 88. Tafreshi, A., 2006. Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure. Composite Structures, 72(4), pp.401–418. 89. Tan, T. et al., 2012. Development of Computational Models for Simulating Full-Scale Crash Tests of Aircraft Fuselage and Components. 90. Timoshenko, S., Winowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-Hill 91. Tita, V., de Carvalho, J. & Vandepitte, D., 2008. Failure analysis of low velocity impact on thin composite laminates: Experimental and numerical approaches. Composite Structures, 83(4), pp.413–428. 92. Vlot, A., 1993. IMPACT PROPERTIES OF FIBRE METAL. , 3, pp.911–927. 93. Vlot, A., 1996. Pergamon IMPACT LOADING ON FIBRE METAL LAMINATES simplified Von K ~ rmfin equations and also found in the work of Shivakumar et al . [ 5 ],. , 18(3), pp.291–307. 94. Vlot, A. & Krull, M., 1997. Impact Damage Resistance of Various Fibre Metal Laminates. , 7(1 997). 95. Vlot, A., Vogelesang, L.B. & Vries, T.J. De, 1999. Towards application of fibre metal laminates in large aircraft. , pp.558–570. 96. Westerberg, C., 2002, Finite element simulation of crash testing of self-piercing rivet joints, peel specimen, Master Dissertation.
160
97. Wiggenraad, J.F.M., Santoro, D. & Lepage, F., 2001. Development of a crashworthy composite fuselage concept for a commuter aircraft Development of a crashworthy composite fuselage concept for a commuter aircraft. 98. Wu, G., Yang, J.-M. & Hahn, H.T., 2007. The impact properties and damage tolerance and of bi-directionally reinforced fiber metal laminates. Journal of Materials Science, 42(3), pp.948–957. 99. Wu, H.F. et al., 1994. Use of rule of mixtures and metal volume fraction for mechanical property predictions of fibre-reinforced aluminium laminates. Journal of Materials Science, 29(17), pp.4583–4591. 100. Xue, P. et al., 2014. Crashworthiness Study of a Civil Aircraft Fuselage Section. , pp.1– 13. 101. Zhou, S.G., Sun, C.T., 1990, Failure analysis of composite laminate with free edge, Journal of Composite Technology and Research, 12(2), pp.91-97. 102. Zhu, X.-K. & Joyce, J. a., 2012. Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization. Engineering Fracture Mechanics, 85, pp.1–46. 103. Zienkiewicz, O.C. & Taylor, R.L., 1991a. The Finite Element Method, Fourth Edition, Volume 1, Basic Formulation and Linear Problems, McGraw-Hill. 104. Zienkiewicz, O.C. & Taylor, R.L., 1991b. The Finite Element Method, Fourth Edition, Volume 2, Solid and Fluid Mechanics, Dynamic and Non-linearity, McGraw-Hill.
161
Appendix 1
Experimental set-up for low velocity perforation test by Rodriguez-Martinez
Rodriguez-Martinez studied a low velocity perforation tests on AA 2024-T3 thin plates at two different initial temperatures 213 K and 288 K by conducting it using a drop test tower.
This configuration allows a perpendicular impact on the specimen with controllable impact velocity, V0 by adjusting the height from which the striker is dropped.
Figure A1-1. Schematic representation of the drop weight tower (Rodriguez-Martinez et al, 2011)
In Rodriguez-Martinez experiment, several impact velocities were chosen including 4 m/s which will be modelled numerically in this paper. The specimens have thickness of h = 1
2 mm and size of At = 100x100 mm . They were clamped by screws that were symmetrically
2 fixed all around its active surface of Af = 80 x 80 mm .
162
Figure A1-2. The device used to clamp the specimen (a) clamping (b) specimen support (Rodriguez-
Martinez et al, 2011)
The steel striker has conical shape as shown in Fig. 3. The larger diameter of the striker is
20 mm, radius of nose is 3 mm and angle of its conical nose is 18⁰. Mass of the striker is
Mp=0.105 kg but it is attached to the instrumented bar of the drop weigh tower and to additional mass giving its accumulative mass 0.866 kg and 18.787 kg. The Mtotal = 18.787 is known as effective mass.
Figure A1-3. Conical striker used in the Rodriguez-Martinez’s experiment (Rodriguez-Martinez et al,
2011)
The set-up allows to record impact forces history within 16 ms impact duration with acquisition frequency of 250 kHz. The time dependent velocity V(t) and displacement δs(t) of the striker are calculated by integration from the impact force history.
; (A1-1)
(A1-2)
163
(A1-3)
In above equation, a(t) is the deceleration of the striker during perforation.
164
Appendix 2
Density, ρ (tonne/mm3) 1600 x 10-12
Elastic properties
E1 153 GPa
E2 = E1 10.3 Gpa
ν12 = ν13 0.3
ν23 0.4
G12 = G13 6 GPa
G23 3.7 GPa
Strength
XT 2537 MPa
XC 1580 MPa
YT 82 MPa
YC 236 MPa
S12 90 MPa
S23 40 MPa
In plane fracture toughness
91.6 kJ/m2
79.9 kJ/m2
0.22 kJ/m2
1.1 kJ/m2
Table A2-1: Material properties of the carbon fibre/epoxy unidirectional laminate (Shi et al, 2012)
165
Density, ρ (tonne/mm3) 1200 x 10-12
Elastic properties
E 1373.3 MPa
G 493.3 MPa
Failure stresses
62.3 MPa
92.3 MPa
92.3 Mpa
Fracture energies
Gn 0.28 N/mm
Gs 0.79 N/mm
Gt 0.79 N/mm
Table A2-2. Material properties of the interface cohesive element (Shi et al, 2012)
166