A Study of Welded Built-Up Beams Made from Titanium and A

A STUDY OF WELDED BUILT-UP BEAMS MADE FROM TITANIUM AND A

TITANIUM ALLOY

A Thesis

Presented to

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Narendra Babu Poondla

May, 2010 A STUDY OF WELDED BUILT-UP BEAMS MADE FROM TITANIUM AND A

TITANIUM ALLOY

Narendra Babu Poondla

Thesis

Approved: Accepted:

______Advisor Department Chair Dr. Anil Patnaik Dr. Wieslaw K. Binienda

______Co-Advisor Dean of the College Dr. T.S. Srivatsan Dr. George K. Haritos

______Committee Member Dean of the Graduate School Dr. Craig Menzemer Dr. George R. Newkome

______Date

ABSTRACT

Titanium is well recognized as a modern and high performance metal that is much stronger and lighter than the most widely used steels in the industry. There is a growing need to reduce the part weight, cost and lead time, while concurrently facilitating enhanced performance of structural parts made from titanium and titanium alloys.

Structural components made from titanium have the advantage of high strength-to-weight ratio, and high stiffness-to-weight ratio. Owing to good resistance to corrosion and superior ballistic properties, titanium is used in several defense applications. This thesis presents a summary of the research conducted on welded built-up titanium beams so as to eventually facilitate the design, fabrication, and implementation of titanium in large structural members.

An alternative to machining a structural component from thick plates or billets is to fabricate beams using the built-up concept. Rolled plates and sheets of titanium alloys can be cut to size and welded together to fabricate a built-up structural component. The primary objective of this project is to investigate structural performance of built-up welded beams fabricated from commercially pure (Grade 2) titanium and a common alloy

(Ti-6Al-4V) under both static and fatigue loading conditions. Six welded built-up titanium beams were fabricated and tested to experimentally and theoretically evaluate

iii structural performance. Analysis and design approaches for static and fatigue performance of built-up beams were also studied and it is clearly demonstrated that it is feasible to fabricate large built-up titanium beams by welding parts together using

GMAW-P welding process. The welds produced by this method were found to be sound and without any visible cracks. The study also revealed that there is no deleterious influence of welding on structural performance of the built-up welded beams of commercially pure titanium and Ti-6Al-4V titanium alloy.

With suitable modifications to the current AISC steel design specifications a preliminary design methodology was developed for the titanium beams. The failure loads, deflections and strains of welded built-up titanium beams are predictable to a reasonably good level of accuracy. The test beams also demonstrated significant reserve strength and ductility following yielding. The deflection curves and the load versus strain relationships obtained from the test results demonstrate a reasonably close match between the theoretical predictions and experimental test results up until the elastic limit of the material. The fatigue tests conducted for this research revealed that the welded built-up beams made from the commercially pure titanium have better life than those made from the Ti-6Al-4V. However additional work is required to develop further insight into the fatigue behavior of welded built-up titanium beams.

Finally the proposed welded built-up beam approach is anticipated to be a cost effective alternative to fabricating large structural elements and members by machining of the parts from thick plates or billets.

ACKNOWLEDGEMENTS

I am heartily thankful to my advisor, Dr. Anil Patnaik, whose encouragement and guidance has helped me to accomplish an in depth understanding in every step of my research. He has been a constant source of great inspiration for me to do my research in the field of Welded built-up titanium beams. I am also very thankful to my committee members, Dr. T.S Srivatsan and Dr. Craig Menzemer for their invaluable suggestions and corrections and also for being on my committee.

Also, I would like to thank my family and friends for their continued love and support.

TABLE OF CONTENTS

Page

LIST OF TABLES ...... x

LIST OF FIGURES ...... xi

CHAPTER

I. INTRODUCTION ...... 1

1.1 Background ...... 1

1.2 Research Motivation and Significance ...... 3

1.3 Concept of Built-Up Welded Beams ...... 4

1.4 GMAW-P: A New Welding Technology Developed at Picatinny Arsenal (NJ)...... 5

1.5 Objectives ...... 6

1.6 Thesis Outline ...... 7

II. LITERATURE REVIEW ...... 9

2.1 Titanium Alloys ...... 12

2.2 Structural Applications of Titanium and Its Alloys ...... 18

2.3 Titanium Applications for Architectural and Other Engineering Structures ...... 23

2.4 Summary of Commercial Available Titanium and its Alloys ...... 26

III. PROCUREMENT AND TESTING OF MATERIALS ...... 28

3.1 Commercially Pure Titanium ...... 28

3.2 Ti-6Al-4V ...... 30

3.3 Experimental Procedures...... 31

3.4 Results and Discussion ...... 34

3.5 Hardness Tests...... 38

3.6 Concluding Comments ...... 43

3.7 Summary ...... 45

IV. THEORETICAL ANALYSIS OF BEAMS USING THE MATERIAL PROPERTIES OF Ti ALLOYS………………………………………………………………………...46

4.1 Design Specifications...... 46

4.2 Review of Steel Design Specifications for Potential Application in the Design of Titanium Built-Up Beams………………………………………………………….49

4.3 Discussion ...... 74

V. DESIGN OF TEST BEAMS USING COMMERCIALLY PURE TITANIUM AND Ti ALLOYS……………………………………………………………………………..76

5.1 The Design Basis ...... 77

5.2 Material Properties ...... 77

5.3 Section Properties ...... 78

5.4 Design Procedure ...... 81

5.5 Summary ...... 84

VI FABRICATION OF TEST BEAMS ...... 85

6.1 Preparation of Parts for the Test Beams ...... 86

6.2 Machining of Parts for the Test Beams...... 87

6.3 Fixture for Welding the Test Beams ...... 89

vii

6.4 Welding of Test Beams ...... 90

6.5 Test Beams ...... 94

6.6 Summary ...... 95

VII STATIC BEND TESTS OF TITANIUM ALLOY BEAMS ...... 96

7.1 Test Set-Up ...... 96

7.2 Instrumentation ...... 99

7.3 Test procedure ...... 102

7.4 Test Results ...... 102

7.5 The Load versus Deflection Curves ...... 110

7.6 The Load versus Strain Relation ...... 113

7.7 Summary ...... 119

VIII FATIGUE TESTS OF TITANIUM ALLOY BEAMS ...... 120

8.1 Test Set-Up and Instrumentation ...... 120

8.2 Test Procedure ...... 123

8.3 Stress Ratios and Loads for Fatigue Tests ...... 124

8.4 Summary ...... 135

IX ANALYSIS OF TEST RESULTS ...... 136

9.1 Tensile Deformation, Fracture behavior, Influence of Material Composition on Microstructural Development, and Hardness ...... 137

9.2 Static Bend Tests of welded Built-Up Titanium Beams ...... 137

9.3 Fatigue Tests of welded Built-Up Titanium Beams ...... 139

9.4 Summary ...... 139

X CONCLUSIONS ...... 140

viii

10.1 Tensile Deformation, Fracture behavior, Influence of Material Composition on Microstructural Development, and Hardness ...... 140

10.2 Welded Built-Up Titanium Beams ...... 143

REFERENCES ...... 146

APPENDICES ...... 150

APPENDIX A LIST OF NOTATIONS ...... 151

APPENDIX B IMAGE GALLERY OF ARCHITECTURAL APPLICATIONS OF TITANIUM ...... 169

LIST OF TABLES

Table Page

1: Details of CP Ti (Gr. 2)……………………………………………………………….29

2: Nominal expected chemical composition of Ti-6Al-4V (in weight percent)…………30

3: A compilation of microhardness test data made on the two materials Ti-6Al-4V alloy and commercially pure titanium (Grade 2)…………………………………….39

4: A compilation of macrohardness test data made on the two materialsTi-6Al-4V alloy and commercially pure titanium (Grade 2)……………………………………..39

5: Plate Thickness for Different Elements of Test Beams (in Inches)…………………..78

6: Summary of Test Beam Design……………………………………………………….84

7: Details of Welds Made for Different Test Beams…………………………………….92

8: Procedure Qualification Record……………………………………………………….93

9: Maximum and minimum loads applied to the test specimens for fatigue tests……...124

10: Summary of Failure Loads and Predicted Strengths……………………………….138

LIST OF FIGURES

Figure Page

1: Applications of titanium in the United States (as on 2006)…………………………….2

2: Welded steel plate girders in a typical highway bridge……………………………...... 4

3: The concept of the titanium built-up welded beam…………………………………….6

4: Typical shear test beam and their failure modes (3-bay and 5-bay) respectively……..20

5: Titanium Drip Shield for Yucca Mountain Repository……………………………….22

6: Titanium Aluminide Subelement……………………………………………………...23

7: CP Ti Plates as Received……………………………………………………………...30

8: Optical micrographs showing the key micro-constituents in the Ti-6Al-4V alloy at three different magnifications………………………………………………...35

9: Optical micrographs showing the key micro-constituents in the CP (Grade 2) titanium at three different magnifications……………………………………………..36

10: Influence of test specimen orientation on engineering stress versus engineering strain curve of Ti-6Al-4V alloy…………………………………………37

11: A profile showing the hardness values across the length of annealed commercially pure (Grade 2) titanium: (a) Microhardness and (b) Macrohardness………………..41

12: A profile showing the hardness values across the length of fully annealed Ti-6Al-4V alloy: (a) Microhardness and (b) Macrohardness………………………..42

13: Bar graph depicting the average microhardness and macrohardness values of the commercially pure (Grade 2) and Ti-6Al-4V alloy………………………………….43

14: Energy of Distortion Yield Criterion for Plane Stress………………………………61

15: Buckling of Plate Girder Web Resulting from Shear Alone………………………...66

16: Effect of Aspect Ratio on K…………………………………………………………73

17: Effect of Aspect Ratio on K…………………………………………………………74

18: Details of Ti-6Al-4V Beams B1 and B2 (with Grooves)…………………………....79

19: Details of Ti-6Al-4V Beam B3 (Without Grooves)…………………………………79

20: Details of CP Ti (Gr. 2) Beams B4 and B5 (with Grooves)………………………....80

21: Details of CP Ti (Gr. 2) Beam B6 (Without Grooves)………………………………81

22: Three Plate Assembly for a Typical Built-up Section……………………………….87

23: Test Beam Elements after Edge Preparation and Grooving…………………………87

24: CNC Machine for Machining Large Parts…………………………………………...88

25: CNC Machine for Machining Small Parts…………………………………………...88

26: Carbide End Mill Bits………………………………………………………………..89

27: General View of Fixturing for Tack Welding of Test Beams……………………….89

28: General View of Fixture for Welding Test Beams…………………………………..91

29: Close-up View of the Fixture………………………………………………………...91

30: A Typical Tack Welded Titanium Test Beam……………………………………….94

31 (a): Typical Test Beam Fit……………………………………………………………94

31 (b): Fully Welded Titanium Test Beams……………………………………………..95

32: Test set-up for Static Bend Test of Beams…………………………………………..98

33: Close-up View of the beam test set-up………………………………………………99

34: Side View of Lateral Support………………………………………………………100

xii

35: Loading Fixture……………………………………………………………………..100

36: Strain Gage Layout…………………………………………………………………101

37: Strain Gage Fixing and Strain Gages attached to Web……………………………..101

38: Failure Mode of Commercially Pure Gr. 2 Titanium Beam (B4) by Web Shear Buckling…………………………………………………………………………….103

39: Failure Mode of Commercially Pure Gr. 2 Titanium Beam (B4) by Web Shear Buckling as Captured in DIC ARAMIS System (Strain Contours are Shown)…….104

40: Final Failure Mode of Commercially Pure Gr. 2 Titanium Beam (B4)……………105

41: Failure by Web Shear Buckling of Beam B5………………………………………106

42: Failure Mode of Beam B1 (Ti-6Al-4V) by Excessive Deflection………………….108

43: Failure of Beam B1 (Ti-6Al-4V) as Captured in DIC System……………………..108

44: Failed Beam B1 (Ti-6Al-4V) after Unloading and Removal from the Test Set-up..109

45: Compression Flange (Top Flange) Local Buckling of Beam B1 (Ti-6Al-4V)……..109

46: Load-Deflection Curve of Beam B1 (Ti-6Al-4V)………………………………….110

47: Load-Deflection Curve of Beam B4 (Commercially Pure Gr. 2 Titanium)………..112

48: Load-Deflection Curve of Beam B5 (Commercially Pure Gr. 2 Titanium) after Fatigue Test…………………………………………………………………………112

49: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Top Flange outside Strains……………………………………………………….....113

50: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Top Flange inside Strains…………………………………………………………...114

51: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Bottom Flange outside Strains……………………………………………………..114

52: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Web Strains (45 Degrees)…………………………………………………………..115

53: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Web Strains (135 Degrees)………………………………………………………….115

xiii

54: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Top Flange Outside Strains……….116

55: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Top Flange Inside Strains………...117

56: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Bottom Flange Outside Strains…...117

57: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Web Strains (45 Degrees)………...118

58: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Web Strains (135 Degrees)……….118

59: Test Setup for Fatigue Tests………………………………………………………..122

60: Test Setup for Fatigue Tests………………………………………………………..122

61: Typical Load-Time History for Beam B5 – CP Gr. 2 Titanium (Stage 3)…………126

62: Typical Deflection-Time History for Beam B5 – CP Gr. 2 Titanium (Stage 3)……126

63: Typical Load-Time History for Beam B6 – CP Gr. 2 Titanium (Stage 2)…………128

64: Typical Deflection-Time History for Beam B6 – CP Gr. 2 Titanium (Stage 2)……129

65: Typical Load-Time History for Beam B2 – Ti-6Al-4V……………………………129

66: Typical Deflection-Time History for Beam B2 – Ti-6Al-4V………………………130

67: Typical Load-Time History for Beam B3 – Ti-6Al-4V……………………………130

68: Typical Deflection-Time History for Beam B3 – Ti-6Al-4V………………………131

69: Overall Failure Model of Beam B2 (Ti-6Al-4V)…………………………………..132

70: Failure Model of Beam B2 (Ti-6Al-4V)……………………………………………133

71: Failure Initiation at the Bottom Flange of Beam B2 (Ti-6Al-4V)………………….133

72: Overall Failure Model of Beam B3 (Ti-6Al-4V)………………………………….134

73: Failure Mode of Beam B3 (Ti-6Al-4V)……………………………………………135

xiv

CHAPTER I

INTRODUCTION

1.1. Background

There is a growing need to reduce part weight, cost and lead time, while concurrently facilitating enhanced performance of structural parts made from the newer and emerging generation of titanium alloys. An overview of the alloys that are suitable for use in performance-critical aerospace and a few other non-aerospace applications to include corrosion protection, armor, orthopedic, and sports equipment were presented and discussed in a recent paper [1]. Titanium is recognized as a high performance metal in the present industry because of its two most attractive properties, corrosion resistance and superior ballistic properties. Titanium is frequently chosen as one of the main candidates for aircraft structural parts and components of aircraft engines due to its high strength-to- weight ratio [E/ρ], and high stiffness-to-weight ratio [E/ρ]. A summary of titanium applications in the United States in year 2006 is shown in Figure 1. This figure is based on the data presented by Moiseyev [2]. The figure demonstrates that the use of titanium and its alloys is mostly confined to airframe structures, defense hardware, and the like that are performance critical, and not necessarily cost critical.

Commercial Aircraft Jet Engines 16 Military Aircraft Jet 1 31 Engines

7 Commerical Airframes Military Airframes 10

Space Rockets 15 20 Helicopters and Armaments

Figure 1: Applications of titanium in the United States (as of 2006)

A one-to-one substitution of steel with titanium is not possible based on just mechanical properties because titanium will always work out to be expensive. The cost of the titanium is about 50 to 75 times to that of steel on per pound basis and also the technology is not ready for direct implementation of titanium in large structures and performance critical applications.

In addition to this, there are no proper design guidelines (like AISC Steel design) available to design the structural components. One of the main reasons for the high cost is that titanium is not often found in high concentrations or in the pure state, and therefore, needs complicated multistage processing to bring it to a stage where it can be put to use in structural applications.

1.2. Research Motivation and Significance

It is clear that the “key” structural applications of titanium have been confined to performance-critical structures such as defense hardware and airframe structures. There certainly does exist an immediate need to do the following: (i) develop structural design methodologies and specifications, and (ii) bring forth innovative manufacturing and fabricating techniques with the purpose of producing, promoting and proliferating the use of cost effective titanium structures for a spectrum of applications. This thesis presents a summary of recent research conducted at The University of Akron on built-up welded beams so as to eventually facilitate the design, fabrication, and implementation of larger structural members. A comprehensive report on this project was submitted to the US

Army (Picatinny Arsenal) and Defense Metals Technology Center (North Canton, OH).

For further details please see reference 8. a. The most noticeable downside of utilizing monolithic titanium is the cost and lead-

time associated with its procurement, and machining. b. The costs associated with high grade titanium forgings are presently in the order of

$35 to $75 per pound with a lead time of 12 months or more. Machining of

monolithic airframe fittings from thick section forgings or plates has a few

disadvantages including some issues related to safety. c. An alternative to machining is to fabricate beams using the built-up concept, which

is proposed in this research. Large amount of the current and emerging Ti alloy

sheets is currently available in the titanium market, which will result in reduced

lead time. If structural components can be fabricated using the built-up approach,

there can be a noticeable reduction in both lead time and cost primarily because of

the reduced cost of using thin sheets and plates of titanium to make large structural

components that satisfy the structural performance standards that are comparable

with the performance standards of those structural parts that are machined from

thick elements.

1.3. Concept of Built-Up Welded Beams

An alternative method to machining a structural component from thick plates or billets is to fabricate beams using the built-up concept. Rolled plates and sheets of titanium alloys can be cut to size and welded together to fabricate a built-up structural component. The concept of fabricating built-up steel beams (known as plate girders) from thin-walled plate elements is not new for highway bridges [3]. Riveted, bolted and/or welded plate girders have been widely used since the beginning of 1950‟s. A typical I shaped built-up steel girder is shown in Figure 2.

Figure 2: Welded steel plate girders in a typical highway bridge

1.4. GMAW-P: A New Welding Technology Developed at Picatinny Arsenal (NJ)

With notable strides made in the domain of welding technology for titanium and its alloys, it is now possible to weld titanium plates to make built-up structural components. For example, the US Army‟s division at Picatinny Arsenal (NJ) has developed a Pulsed Gas Metal Arc Welding process (referred to henceforth in this report as GMAW-P), which involved a careful modification of the existing practices so as to be applicable to titanium and its alloys [4-6]. The linear weld speeds can be up to ten times faster than the corresponding speeds of tungsten inert gas (TIG) or gas tungsten arc welding (GTAW) processes. Also, the number of passes can be reduced by a factor of three. The new process developed by the US Army division at Picatinny Arsenal uses

100% helium shielding gas that facilitates good penetration capability and a double pulse template. The welding of titanium is standardized in a recently released welding specification put forth by the American Welding Society (AWS). This specification is referred to AWS D1.9/D1.9M [7]. It is therefore feasible to make welded built-up beams with titanium plates as shown in Figure 3.

Figure 3: The concept of the titanium built-up welded beam

1.5. Objectives

The primary objective of this thesis is to describe the results of a recent investigation on structural performance of built-up welded beams of commercially pure

(Grade 2) titanium and a common titanium alloy under both static and fatigue loading conditions. The secondary objectives were three-fold:

 To evaluate the feasibility of fabricating commercially pure titanium (Grade 2) and

Ti-6Al-4V built-up beams to produce high strength, low weight, corrosion resistant

and low cost structural beams for the purpose of applications in the defense sector.

 To experimentally and theoretically evaluate Ti alloy beams fabricated and tested

under both static and fatigue loading.

 To develop analysis and design approaches for static and fatigue performance of

built-up beams made from both commercially pure titanium and a common titanium

alloy.

1.6. Thesis Outline

This thesis comprises both analytical and experimental research components that were performed at The University of Akron. This thesis is organized into the following chapters.

Chapter 2 Literature Review

Chapter 3 Procurement of Materials

Chapter 4 Theoretical Analysis of Beams Using the Material Properties of Ti Alloys

Chapter 5 Design of Beams Using Ti Alloys

Chapter 6 Fabrication of Ti Alloy Test Beams

Chapter 7 Static Bend Tests of Ti Alloy Beams

Chapter 8 Fatigue Tests of Ti Alloy Beams

Chapter 9 Analysis of Test Results

Chapter 10 Conclusions

CHAPTER II

LITERATURE REVIEW

Titanium mostly known as the “wonder metal” was found in 1791 by a British mineralogist and chemist, William Gregor. Four years later, a Berlin chemist, Martin

Heinrich Klaproth, independently isolated titanium oxide from a Hungarian mineral, known as rutile. Titanium is not actually a rare substance as it ranks as the ninth most plentiful element and the fourth most abundant structural metal in the earth crust exceeded only by aluminum, iron and magnesium. Unfortunately titanium is not found in pure state. Titanium usually occurs in mineral sands containing ilmenite (FeTiO3), found in Ilmen Mountains of Russia, or rutile (TiO2), from the beach sands in Australia, India and Mexico.

It took more than 100 years before Mathew Albert Hunter was able to isolate the metal 1910 by heating the titanium tetrachloride (Ticl4) with sodium in a steel bomb.

Finally, Wilhelm Justin Kroll from Luxemburg, who is recognized as the father of the titanium industry, produced significant amounts of titanium by combining Ticl4 with calcium in 1932. At the U.S bureau of mines, he demonstrated that titanium could be extracted commercially by reducing Ticl4 by changing the reducing agent from calcium to magnesium. In 1948, the DuPont Company was the first to produce titanium commercially. The prime consumer of titanium and its alloys is aerospace industry and

9 the other consumers gaining importance include architecture, chemical processing, medicine, marine and offshore, sports and leisure and transportation industry.

Some significant facts or important advantages offered by titanium and its alloys include

[41]:

 The density of titanium is only about 60% of that of steel or nickel based super

alloys

 The tensile strength of titanium and its alloys can be comparable to that of lower

strength martensitic stainless steel and is better than that of austenitic or ferrite

stainless steels.

 The commercial alloys of titanium are useful at temperatures to about 538oC to

595oC.

 The cost of titanium is approximately four times that of stainless steel and is

comparable to that of super alloys.

 Titanium is exceptionally corrosion resistant in most aqueous and chemical

environments.

 Titanium can be forged or wrought by standard techniques.

 Titanium can be joined by means of fusion, welding, brazing, adhesives, diffusion

bonding, and fasteners.

 Titanium is castable, with injection casting being the preferred method.

However, titanium now has accumulated experience of some 50 years of modern industrial practice and design applications to support its use. Much of the use has come in military applications and aircraft applications. Unfortunately the current titanium

10 production system is extremely labor and capital intensive. Titanium is expensive only because the current process of refining the ore metal is a multistep, high temperature batch process.

Since 1950‟s, titanium and its alloys were used by orthopedic surgeons when the surgeons began to use titanium made plates, screws, and pins for operative treatment of broken bones. In fact, the first paper on titanium was published in 1951 with the title

“Titanium, a metal for surgery”. The technological knowledge of how to manufacture products from titanium in the 1950‟s was probably available only in two countries, Soviet

Union and USA. In the mid 1950‟s titanium was already first used in automotive industry. The turbine-driven, experimental vehicle of General Motors, the Titanium

Firebird II, had an outer skin completely manufactured from titanium. Since then, titanium has become a constant objective to penetrate into the mass market of the automotive industry.

The first alloys, including today‟s most popular Ti-6Al-4V, were developed in the late 1940‟s in the United States. Titanium was first used in the chemical industry in

1960‟s, initially and mainly for applications involving control of processes with oxidizing chloride environments. Today, it is also used for other aggressive media including acetic and nitric acids, wet bromine and acetone.

In the 1970‟s and 1980‟s, the Russian navy operated submarines that were the first with a hull completely manufactured from titanium which offers exceptional corrosion resistance both in seawater and in sour hydrocarbons. Titanium has been the preferred material for use in marine technology particularly in petroleum and gas exploration in saline environments. Apart from corrosion resistance, the high strength and low specific

11 weight of titanium compared to high-strength steels are also deciding factors for the choice of titanium in offshore services. Today, a large number of titanium alloys have paved the way of light metals to vastly expand into many industrial applications.

A more recent field of application for titanium is in architecture. Since the 1980s, titanium has been increasingly used as exterior and interior cladding material for roofing, curtain walls, column covers, soffits, fascias, canopies, protective cladding for piers, artwork, sculptures, plaques, and monuments. In 1997, the Guggenheim Museum in

Bilbao, Spain, opened- probably the most spectacular “titanium building” so far.

In golf, the prime objective is to drive the golf ball as far as possible. In the mid

1990‟s, the first metal made from titanium alloys came into market and have become quite popular since then. As in the case of golf, for any kind of sport where balls have to be hit fast and far, weight savings is of advantage. Frames of tennis racquets and baseball bats are also made from titanium. Titanium golf club shafts, tennis racquet frames, pool cue shafts and even bicycle frames are currently fabricated using alloys such as Ti-3Al-

2.5V. This alloy has the properties needed for sports applications like low modulus of elasticity, damage tolerance, good strength-to-weight ratio and overall good corrosion resistance.

2.1 Titanium Alloys

The titanium and its alloys are being widely used in the aerospace industry and also in the automobile industry.

2.1.1 Selection of Titanium for Aerospace Applications

With a documented density of 4.5g/cm3, titanium alloys are about half the weight of the conventional steel and can compete with competing nickel-base alloys. This noticeable physical property, i.e., density, in combination with excellent corrosion resistance makes the alloys of titanium a favorite in the aerospace sector. The earliest titanium alloys were developed in the United States during the early 1940s and following sustained research and development efforts, alloy Ti-6Al-4V emerged and gradually grew in stature to be the most popular alloy, which was widely chosen and used for aerospace and other performance-critical applications spanning both the defense and civilian sectors. Due to its excellent properties like high specific strength (σ/ρ), stiffness, corrosion resistance, good erosion resistance in environments spanning a range of aggressiveness, acceptable mechanical properties at elevated temperature coupled with the ability to withstand and function at elevated temperatures, the alloys of titanium have gradually found varied use in aerospace and other space-related applications.

The need to reduce costs while concurrently not compromising on the growing demand for maximization of component performance has motivated manufacturers of end components to adopt a life cycle approach to material selection for the purposes of design. Besides, the need for a healthy combination of good mechanical properties, other factors like cost, machinability, castability and weldability are also important and must be considered in the selection and use of a titanium alloy for a performance specific application.

The noticeable advantage of weight reduction arising from the use of titanium and other competing materials has been the topic of interest that is continuously encouraged by the aero-space industries primarily because of the higher savings in cost coupled with an increased load carrying capacity. For example, once the fuel consumption of the commercial aircraft, a BOEING 747, is reduced by about 10%, the payload can be increased by up to 10 tons. Additionally, a decrease in weight means the intrinsic ability to use smaller and lighter engines, wings and other support structures, which would ultimately lead to huge savings.

Generally, savings in weight is the primary factor for a steady, yet noticeable, increase in the selection and use of titanium alloys for fuselage applications during the last 4 decades. For example, approximately 9% of the structural weight of the commercial aircraft, a BOEING 777, is made from the use of alloys of titanium. The other areas where titanium alloys have been chosen for use include the following [13]:

(i) To prevent the propagation of fatigue cracks in aircraft fuselages by placing thin narrow rings around the aluminum fuselage.

(ii) Use of Ti-3Al-2.5V for hydraulic tubing in aircrafts has resulted in a weight

reduction of up to 40% compared to tubes that are made of steel.

(iii) Commercial pure titanium is used where high corrosion resistance is required

coupled with moderate strengths. Aircraft floors surrounding onboard kitchens

and toilets are the areas where emphasis and importance of the corrosive

environment comes into picture.

(iv) The piping system for de-icing equipment is manufactured from unalloyed

titanium.

(v) For other important parts, such as, aircraft landing gear and cockpit windows have

been constructed from forged titanium despite its huge cost.

Compared with the aircrafts manufactured for use in the civil commercial sector, the usage of alloys of titanium in military aircraft is noticeably higher. This has been attributed to a significantly larger mechanical and thermal loadings associated with higher speeds. The alloys of titanium account for 30-50% of the weight of a modern fighter jet. Most of this weight can be found in the engine bay of an aircraft where temperatures are so high that aluminum and its alloys cannot be used as a viable alternative.

The key difference in the selection and use of titanium alloys in commercial aircraft market compared to the military aircraft market is that overall cost effectiveness is important for commercial aircraft, while high performance requirements govern their selection and use for the military aircraft. The noticeably high machining loss that is typical of titanium forgings has created a need for an effective optimization of the forging processes.

Very few materials like aerospace hydraulic fluid are detrimental by way of corrosion to the alloys of titanium, which are generally resistant to both local and global corrosion. At elevated temperatures, the hydraulic fluid tends to form an acid that promotes hydrogen embrittlement of the component.

Furthermore, due to the high cost-low payload criteria of space vehicles, reduction in weight can result in noticeable cost savings in all space-related applications.

This makes the alloys of titanium a potentially viable candidate that is chosen and used extensively for the fuel and satellite tanks. A healthy synergism of the high strength of

15 titanium, low weight and long term chemical compatibility with fuel does certainly provide the metal an edge over conventional high-strength steels.

2.1.2 Selection and Use of Titanium for Automotive Production

The noticeable advantages of significant weight reduction and functional improvements have led to the use of alternative materials in the automotive industry with the use of aluminum and magnesium alloys since the 1930‟s. Alloys based on iron, aluminum and magnesium are generally used for structural applications where as the metals like copper, lead, tin and chrome are put to use for a few minor applications.

Other materials like the nickel-base alloys, although suitable for structural applications, have the drawback of their high cost as an impediment in their selection and use in the commercial automotive industry.

Since the initiation of industrial production of pure titanium and its alloy counterparts in the early 1950‟s, automobile manufacturers have shown increased interest in them due to their high elastic energy absorption and corrosion resistance properties.

However, the high cost of the material has been largely responsible in part for its failure from being an extensively preferred, chosen and used material for non-performance- critical applications spanning the automotive industry.

If a component is to be designed for maximum fatigue strength pure titanium and its alloys were found to be superior to other contending materials. However, it was not a viable choice if the component of interest is designed for optimized stiffness primarily because of its comparatively low Young‟s modulus. As the body of an automobile is

16 designed for a healthy combination of tension stiffness, bending stiffness and even torsion stiffness, the applications of titanium and its alloy counterparts are often limited to chasis and power train components. Along with the high material cost of titanium, the actual cost associated with manufacture of the component is higher when titanium is the material chosen.

Another application of titanium is for valve springs, which are widely used in racing cars. The use of titanium for these parts when combined with conventional steel valves did lead to a noticeable reduction of weight up to 40%. The weight reduction was

70% when valves made from the TiAl intermetallic were used [9].

In armored military vehicles, the selection and use of titanium was justified by its properties of light weight construction, high specific strength (σ / ρ) and good corrosion resistance. An example of such usage is the application of single melted Ti-6Al-4V in the

American M2A battle tanks for track chain protection and turret armor [9].

Through the years increased and growing use of titanium has made noticeable the fact that joining technology is one of the most difficult technical production problems.

Though cold joining methods like lock seaming and flaring are widely used, welding is still problematic since it requires a careful consideration of issues associated with a necessity for reverse shielding the weld seam using a suitable gas cover, such as, argon.

On account of the high cost involved, a suitable alternative must be found that will reduce the use of reverse shielding gas in the design phase and the number of welds should be minimized.

Thus, in more recent years the use of titanium and its alloys have come a long way in the automobile industry. However, there is no denying that their scope for selection and use is strictly limited to specialized components and applications. With continued efforts in the area of research being carried out coupled with an increased emphasis on the selection and use of titanium in automotive production, it is anticipated that the metal will become an important structural materials in the automotive industry in the years ahead.

2.2 Structural Applications of Titanium and Its Alloys

While there have been several structural applications such as airframe structures in defense and civil sector, extensive literature search revealed that the research conducted has largely remained proprietary and/or unpublished. Some of the commercial structural grade titanium alloys that are available in market are summarized by strength in

Table A2 of Appendix 1A. There are very few publications describing truly large scale structural applications of titanium and its alloys [1, 2]. Those limited publications are briefly reviewed in this section.

2.2.1 Picatinny Blast Shield

The first of its kind, the Picatinny Blast Shield (PBS) was designed and fabricated to satisfy the US Army requirement for survivability upgrades on marine light tactical vehicles. Voted as one of the US Army‟s “Top Ten Greatest Innovations” for 2007, PBS

18 kits are lightweight modular units that can be retrofitted to the existing attaching points in less than 30 minutes in a battle field environment. Other similar successes in structural applications of titanium and the US Army interests in using titanium are described in other papers by Luckowski. The US Army projects the demand for titanium and its alloys to be over quarter million pounds for such applications.

2.2.2 Intermediate Shear Beam Development for Boeing SST [42]

A comprehensive research program was initiated by Boeing for the development of titanium intermediate diagonal tension-field shear beam analysis and design methods necessary to support Boeing SST [42]. Detailed studies were done on the structural efficiency of intermediate diagonal tension-field shear beams and theoretical analysis of post buckled plates. The initial tests consisted of four titanium cantilever beams that were loaded in shear, shear plus axial tension, and shear plus axial compression. These tests showed the failure trends in the stiffeners and the webs of the test specimens. The study reported that the beam strengths were decreased by 4% to 12% by adding axial compression load approximately equal to the shear load on the beam, or increased by approximately 7% upon adding axial tension load.

Without any attempts to account for combined loading, the test results varied from 22% to 88% above the predicted strengths. For the titanium beams, linear extrapolations of the aluminum web and stiffener strength prediction methods were used.

Reduced shear head countersunk titanium rivets were used to attach the stiffeners to the webs, and premature failure of some of the panels occurred due to rivet pull-out. Based

19 on the analysis of stiffener and web strain gage data, the ultimate strengths of the beams were believed to be nearly reached. It was reported that the failure might have occurred at loads close to the observed load even if the rivets had not failed.

Analysis and tests indicated that improvements are possible in the structural efficiency of intermediate tension field shear beams. Detailed studies and tests indicated that these types of beams are limited in application and conservative, and also in need of improvement in providing more efficient designs. Although this treatment deals only with static strength, it was recognized that the design of shear beams and other structures are strongly influenced by fatigue conditions. Improvements in design, static strength, stress analysis and deflection analysis were identified as the future research needs in order to permit the development of a meaningful fatigue analysis of intermediate shear beams.

Figure 4: Typical shear test beam and their failure modes (3-bay and 5-bay) respectively

[42]

2.2.3 Titanium Drip Shield for Yucca Mountain Repository [9]

An engineered barrier system (EBS) was proposed for the high level radioactive waste repository at Yucca Mountains (Nevada, USA) which is a combination of titanium

20 and Ni-Cr-Mo alloy waste package (WP). While the waste package (WP) being the primary barrier for radionuclide release (see Figure 5), the drip shield was believed to divert potential seeping water and rock fall impingements from the waste package.

Titanium drip shield is primarily needed to act as a protection to the waste package from seeping drips that could lead to crevice corrosion. Titanium was considered to be used in the drip shield under the Yucca Mountains where Grade-7 was proposed for the shell and

Grades 28 and 29 were proposed for the support members.

The selection of titanium alloy for the fabrication of the drip shield is because of its exceptional resistance to the aqueous corrosion. However, titanium alloys are susceptible to hydrogen-induced corrosion (HIC). Simulations published elsewhere were used to predict the drip shield lifetimes, and to investigate the effects of the hydrogen absorption efficiency. The assessment of drip shield performance in a nuclear waste repository requires predictions over a long-time (10,000 to 100,000 years) based on experimental data collected over a short time.

The failure of the drip shield is controlled by the environment, the corrosion rate, the material properties and the hydrogen absorption efficiency which depends on the properties of the oxide film on the alloy surface. However, the drip shield approach has been recently abandoned because of the cost and political considerations coupled with lack of assurance from the technical community on the long term protection provided by the proposed titanium drip shield.

Figure 5: Titanium Drip Shield for Yucca Mountain Repository

2.2.4 NASA‟s Titanium Aluminide Subelements [10,11]

An international team led by NASA Glenn Research Center successfully fabricated and tested the largest titanium aluminide (γTiAl) sheet structure [10,11]. The research work mainly focused on evaluating wrought titanium aluminide (γTiAl) as a viable material for high-speed civil transportation exhaust nozzle. The γTiAl sheet structure was fabricated for benchmark testing in three-point bending. The subelement dimensions were 33 in x 5 in x 3 in. The structural integrity of the γTiAl sheet subelement was evaluated by conducting a room temperature three-point static bend test

(Figure 6). The maximum deflection to span ratio obtained in the tests was approximately

1 in 400 at first yield. The subelement specimen failed at a load that is 93% greater than the predicted load. The subelement was reported to have failed at the center shear clip edge within the stress concentration area. Post test finite element analysis using the observed load showed that the stress at failure location was 520 MPa (75 ksi). Since this is within 5% of the γTiAl sheet‟s ultimate tensile strength of 550 MPa (80 ksi), the

22 fabrication process of hot forming and brazing was reported not to have affected structural load carrying.

Figure 6: Titanium Aluminide Subelement [11]

2.3 Titanium Applications for Architectural and Other Engineering Structures

Normal engineering structures that are used in Civil Engineering are overly cost prohibitive. Therefore, titanium and its alloys are not materials of choice for such structures. However, there have been several trials in the area of non-defense applications of titanium and its alloys.

Titanium is 100% recyclable because it does not degrade during service.

Therefore, on a life-cycle basis, titanium is one of the most competitive of all architectural metals. Aesthetics aside, the high resistance to corrosion is the prime reason to select titanium for architectural applications. Commercially pure titanium (mostly

Grade 1) is used in such applications, allowing wall thicknesses typically ranging from as thin as 0.4 to 1 mm.

A more recent field of application for titanium is in architecture and buildings.

Since the 1980s, titanium has been increasingly used as exterior and interior cladding material for roofing, window frames, ventilators, curtain walls, column covers, soffits,

23 fascias, canopies, protective cladding for piers, artwork, sculptures, plaques, and monuments. These are the types of applications made from titanium alloys that are cited in the open literature. These components are expected to last at least 100 years.

An advantage of titanium is its low coefficient of thermal expansion, which is only half that of stainless steel and only one-third of aluminum. This favors titanium over other metals for structures that have a lot of glass or concrete because these materials also have a low coefficient of thermal expansion. For a metal, titanium is an excellent insulator. Its thermal conductivity is only one tenth of that of aluminum, increasing a building‟s energy efficiency. Particularly in cases where architects are restricted to metal structures, titanium proves to be a very energy-efficient material with a positive impact on the building‟s economy.

Abu Dhabi airport is among the world‟s first to consider using titanium in large scale structural applications [12]. Due to high specific strength, titanium beams were significantly smaller than steel beams giving architects extended freedom in design and realization of their aesthetic visions. Most of these large mobile structures can only be realized because of the reduced weight of titanium. Low weight means that large areas of roofing can be supported by less massive structures, with corresponding cost savings.

Examples of impressive structures made of titanium include the roof of the Naya Temple in Fukui, the Fukuoka Dome, the Miyazaki Ocean Dome, the International Conference

Building in Tokyo, the Shimane Prefecture art Museum in Matsue, Japan, the futuristic curtain wall of the Showa-Kan building in Kudan, Tokyo, and the Glasgow Museum of

Science with its adjacent IMAX theatre, as well as the roof of the Titanium Dome.

The Parthenon on the Acropolis of Athens, Greece was built in the 5th century

B.C. Since 1975, the Acropolis Restoration Project team, headed by a Greek architect

Manolis Korres, started the restoration of the Parthenon and surrounding structures. Non- corrosive titanium rods were used to hold the thousands of fragmented marble stones together. Titanium rods were also used to strengthen the structure‟s foundations [13].

In 1997, the Guggenheim Museum in Bilbao, Spain, opened- probably the most spectacular “titanium building” so far. U.S. architect Frank Gehry designed the museum with thin sheets of titanium. The titanium scales not only provided striking appearance, but also reflect heat away from the building, thereby protecting the priceless collection of artwork inside [14].

Addition of Frederic C. Hamilton Building doubled the size of the Denver Art

Museum in 2006. The new building is constructed with 2740 ton steel superstructure, which is an interwoven cluster of leaning braced frames and trusses. Over 3100 pieces of steel are contained by 20 sloping planes, including a 194-foot prow, which extends 167 feet over the street and looms 100 feet above the ground. None of the planes are parallel or perpendicular to any other plane – adding to the design and construction challenges.

The complicated trusses were all clad in titanium skin cladding [15].

The National Centre for the Performing Arts, formerly known as the National

Grand Theater [16], and colloquially described as The Egg, is an opera house in Beijing,

China. The Centre, an ellipsoid dome of titanium and glass surrounded by an artificial lake, seats 6,500 people in three halls and is 200,000 m² in size. It was designed by

French architect Paul Andreu. Construction of the theater started in December 2001 and the inaugural concert was held in December 2007.

A new anti-corrosion system that uses titanium-clad steel plates has been developed and applied to the splash and tidal zones of the steel piers on the Trans-Tokyo

Bay bridge. The 4-mm thick steel plates, clad with 1 mm thick titanium are welded to the steel piers. To investigate the durability of this method, steel pipes 60 cm in diameter were protected by this method, exposed to a marine environment, and monitored for five years. No corrosion of the titanium clad steel plate was observed after five years, showing that the method has sufficient long-term durability.

The above are some of the known applications of titanium and its alloys in Civil

Engineering structures. However, it is believed that widespread applications of titanium are highly unlikely in the near future in the area of Civil Engineering structures due to the exorbitant costs involved in the usage of the metal. An image gallery of architectural applications of titanium and its alloys is given in Appendix 1B.

2.4 Summary of Commercial Available Titanium and its Alloys

Extensive product search was conducted to prepare a comprehensive database of readily available new alloys of titanium that have the potential for use in applications of interest to the DoD. All the relevant properties and product data are summarized for titanium and its Ti alloys in Table A1 in Appendix 1A. The listed alloys are classified into equivalent ASTM grades based on the best judgment. Of particular interest to this research are the longitudinal and transverse mechanical properties which are summarized in Table A2 in the Appendix 1A. Several other alloys are also listed in the International

Titanium Associate software “Database of Titanium Properties CD-ROM” .This reference source presents numeric values for the physical and mechanical properties of approximately 60 different commercially important titanium alloys.

CHAPTER III

PROCUREMENT AND TESTING OF MATERIALS

From the literature review presented in Chapter 2, two titanium alloys were selected. One is commercially pure titanium (Grade 2) and the other is titanium alloy Ti-

6Al-4V. The materials that were selected in this study were investigated for characterization of the microstructure, hardness, and mechanical properties. The results of the study are presented in this section.

3.1 Commercially Pure Titanium

Commercially Pure Titanium was supplied by TICO Titanium (Wixom, MI). The quantities supplied by TICO are shown in Figure 7 and were as follows:

i. Plate 0.375″ TK X 3.00″ wide X 36.00″ Long six pieces

ii. Sheet 0.125″ TK X 4.00″ wide X 36.00″ Long three pieces

The edges of the plates and sheets were sheared. The chemical composition of the plates was provided by the supplier and is as shown in Table 1 along with other details.

Table 1: Details of CP Ti (Gr. 2)

Description 0.375″ Thick Plate 0.125″ Thick Sheet Specification ASTM B-265-06/ASME ASTM B-265-07/ASME SB- SB-265-A06 GR. 2 EN 265-7/ASTM F-67-06 GR.2 10024:2004 Type 3.1 EN 10204:2004 Type 3.1

Chemical Composition  Fe Iron 0.13 0.08  Oxygen 0.16 0.1  N Nitrogen 0.002 0.0105  C Carbon 0.012 0.014

 Residual Element  Residual Element (Each) (Each) less than 0.10 less than 0.10

 Residual Element  Residual Element (Total) (Total) less than 0.40 less than 0.4

 Final Product  Final Product Hydrogen Hydrogen 0.0032 11/10 PPM

 Titanium Remainder  Titanium Remainder

Average Tensile Strength, 73,500 70,250 psi Yield 0.2% Offset 52,100 49,500 Elongation % 33 25.75 RA % 59 Anneal Condition Yes 1370F, HGA 3 to 11 Min Guided Bend Test Pass

Figure 7: CP Ti Plates as Received

3.2 Ti-6Al-4V

Allegheny Technologies ATI Wah Chang (Albany, OR) supplied six pieces of Ti-

6Al-4V to the following dimensions:

 Plate 0.25″ TK X 12.00″ wide X 36.00″ Long six pieces

The material supplied by ATI Wah Chang is a commercial titanium alloy, and therefore, the chemical composition is proprietary to the supplier. From published literature for similar titanium alloys, the chemical composition is expected to be as shown in Table 2.

Table 2: Nominal expected chemical composition of Ti-6Al-4V (in weight percent)

Material Ti Al N V C Fe H O

Ti-6Al-4V 90.0 6.0 0.05 4.0 0.1 0.4 0.02 0.20

3.3 Experimental Procedures

The various experimental procedures like sample preparation and initial microstructural characterization and mechanical testing was done.

3.3.1 Sample Preparation

The tensile tests were conducted on both the longitudinal and transverse oriented test specimens that were precision machined from both the longitudinal and transverse orientation of the as-provided annealed plate stock. The longitudinal specimens were machined with the major stress axis parallel to the rolling direction of the Ti-6Al-4V alloy and CP (Grade 2) titanium plates, while the transverse specimens were machined with the major stress axis perpendicular to the rolling direction of the two plates. The cylindrical test specimen conformed well to the specifications outlined in the standard

ASTM E-8 and had threaded ends. At the gage section, the test specimens measured 3 mm in diameter and 12.5 mm in length. To minimize the effects and/or contributions from surface irregularities and finish, final surface preparation was achieved by mechanically polishing the gage section of the machined test specimens with progressively finer grades of silicon carbide impregnated emery paper (320 grit, 400 grit and 600 grit) to remove all circumferential scratches and any residual machine marks.

2.3.2 Initial Microstructure Characterization

An initial characterization of the microstructure of the as-provided material was done using a low magnification optical microscope. Samples were cut from the as- received stock of the commercially pure (Grade 2) and Ti-6Al-4V titanium alloy and mounted in bakelite. The mounted samples were then wet ground on progressively finer grades of silicon carbide impregnated emery paper using copious amounts of water both as a lubricant and as a coolant. Subsequently, the ground samples were mechanically polished using five-micron diamond solution. Fine polishing to a perfect mirror-like finish of the surface of each titanium material was achieved using one-micron diamond solution as the lubricant. The polished samples were subsequently etched using a reagent that is a solution mixture of 5-ml of nitric acid (HNO3), 10 ml of hydrofluoric acid (HF) and 85 ml of water (H2O). The polished and etched surface of the samples of CP (Grade

2) and Ti-6Al-4V alloy was observed in an optical microscope and photographed using bright field illumination technique.

2.3.3 Mechanical Testing

Uniaxial tensile tests were performed on a fully-automated, closed-loop servo- hydraulic mechanical test machine [INSTRON-8500 Plus] using a 100 kN load cell. The tests were conducted at room temperature (300 K) and in the laboratory air (Relative

Humidity of 55 pct) environment. The test specimens were deformed at a constant strain rate of 0.0001/sec. An axial 12.5-mm gage length clip-on type extensometer was

32 attached to the test specimen at the gage section using rubber bands. The stress and strain measurements, parallel to the load line, and the resultant mechanical properties, such as, stiffness, strength (yield strength and ultimate tensile strength), failure stress and ductility

(strain-to-failure) was provided as a computer output by the control unit of the test machine.

2.3.4 Hardness Testing

A basic mechanical property of a material is its hardness. The hardness test is an important and widely used test for the purpose of quickly evaluating the mechanical properties of monolithic metals, their alloy counterparts, and even composite materials based on metal matrices. Hardness can be defined as the resistance offered by the material to indentation, i.e., permanent deformation and cracking [17]. A direct measurement of hardness is a simple and useful technique for characterizing the base-line mechanical properties while concurrently investigating and establishing the role and contribution of intrinsic microstructural constituents. The hardness test is simple, easy and can be essentially categorized as being non-destructive [18]. In this study, the

Vickers (HV) micro-hardness measurements were made on a Suntech microhardness tester using an indentation load of 200 grams, a dwell time of 11 seconds, with the aid of a Vickers tool indenter. The indenter (made of diamond) has a square-base pyramidal geometry with an included angle of 136 degrees. The indenter rests for a specified length of time on the polished surface of the test specimen. The machine makes an indent, or impression, on the sample surface whose diagonal size was measured using a low

33 magnification optical microscope. The area of the impression is directly proportional to the load used and a load independent hardness number can be found. The Vickers hardness number (HV) is the ratio of applied load to the surface area of the indent.

2 According to the Vicker‟s prescription HV = 1.8544 P/d . At least four indents were made across the polished surface of each test specimen of the commercially pure titanium

(Grade 2) and Ti-6Al-4V alloy, and the result is reported as the average value in units of kg/mm2.

The macrohardness measurements (RC) were made on a Rockwell hardness machine using an indentation load of 140 Kgf, a minor load of 10 Kgf, 120 degree diamond cone, a dwell time of 10 seconds and the value read on the „C‟ scale. The macrohardness tests were also done on the polished surface of each titanium alloy test specimen.

3.4 Results and Discussion

The microstructure of an alloy is an important factor that determines its mechanical properties to include tensile properties, fracture toughness, fatigue resistance and resultant fracture behavior. The optical microstructure of the Ti-6Al-4V alloy is shown in Figure 8 and of the CP (Grade 2) in Figure 9 at three different magnifications.

These figures reveal that the as-received, undeformed microstructure of the two chosen materials to be slightly different. The difference is primarily in the volume fraction, morphology, size, and distribution of the intrinsic micro-constituents in the microstructure.

The following figure shows the key microstructure constituents of the titanium alloy Ti-

6Al-4V at three different magnifications.

(a) (b)

100 µm 50 µm

(c)

20 µm

Figure 8: Optical micrographs showing the key micro-constituents in the Ti-6Al-4V alloy at three different magnifications.

The following figure shows the key microstructure constituents of the Commercially Pure

Titanium at three different magnifications.

(a) (b)

100 µm 50 µm

(c)

20 µm

Figure 9: Optical micrographs showing the key micro-constituents in the CP (Grade 2) titanium at three different magnifications.

(i) Low magnification observation of the microstructure of the high purity CP (Grade

2) titanium essentially revealed the primary alpha (α) grains to be intermingled with small yet noticeable pockets of the beta (β) grains. High magnification observation revealed very fine alpha (α) phase lamellae located within the beta (β) grain (Figure 9b).

(ii) Observations of the Ti-6Al-4V alloy over a range of magnifications spanning very low to high magnification revealed a duplex microstructure consisting of the near equiaxed alpha (α) and transformed beta (β) phases.

At equivalent high magnification (500 X), the differences in intrinsic microstructural constituents of the two alloys, i.e. CP (Grade 2) and Ti-6Al-4V, is shown in Figures 8c and 9c bringing out clearly the size, morphology, volume fraction and distribution of the alpha (α) and beta (β) phases.

1400 Ti-6Al-4V L - LONGITUDINAL 1200 T- TRANSVERSE

1000

800

600 L T

400

200

ENGINEERING STRESS (Mpa) STRESS ENGINEERING

0 0 5 10 15 20 ENGINEERING STRAIN ( %)

Figure 10: Influence of test specimen orientation on engineering stress versus engineering strain curve of Ti-6Al-4V alloy

3.5 Hardness Tests

Two samples of commercially pure (Grade 2) and two samples of alloy Ti-6Al-

4V were examined for microhardness and macrohardness measurements. The results of the microhardness and macrohardness tests are summarized in Table 3 and Table 4.

The Vickers microhardness measurements (Table 3) show a marginal variation in microhardness taken through a cross-section of the specimens of both the commercially pure (Grade 2) and Ti-6Al-4V alloy. This can be ascribed to intrinsic microstructural contributions, namely, the presence of both the soft alpha and hard beta phases. Further, it is seen that the hardness values when plotted reveal marginal spatial variability with an average value of 200 kg/mm2 for the commercially pure (Grade 2) titanium and 330 kg/mm2 for the Ti-6Al-4V alloy. This suggests that the commercially produced and annealed Ti-6Al-4V alloy is noticeably harder than the commercially pure counterpart.

The measurements were made with accuracy and precision across the center of each sample that was mounted in bakelite in order to gather detailed information pertaining to the spatial variability of hardness while concurrently minimizing contributions from location of the indent. The measurements provide an idea of how the presence of both the alpha and beta phases contributes to hardness of the titanium material and the intrinsic influence of processing-related artifacts resulting in a concurrent weakening effect. The presence of processing-related artifacts, if any, such as, (a) fine microscopic pores and voids, and (b) fine microscopic cracks, when intercepted by the pyramidal indenter will tend to cause a net decrease in the value of measured microhardness of the test sample of the chosen material.

Table 3: A compilation of microhardness test data made on the two materials Ti-6Al-4V alloy and commercially pure titanium (Grade 2) Alloy Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Average

Vickers Sample 2A 340.41 325.20 332.72 334.61 340.46 334.68 hardness Ti-6Al-4V

Rc 25 27 - 30 25 26.75 Vickers Sample 2B 330.88 342.44 332.74 327.11 338.51 334.36 hardness Ti-6Al-4V Rc 28 25 25 27 28 26.6 Vickers Sample 1A 213.59 195.36 193.65 193.67 200.58 199.37 hardness CP Grade 2 Rc ------Vickers Sample 1B 175.59 178.58 167.21 169.26 193.67 176.82 hardness CP Grade 2 Rc ------

Table 4: A compilation of macrohardness test data made on the two materialsTi-6Al-4V alloy and commercially pure titanium (Grade 2)

Alloy Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Average

Vickers Sample 2A 286 286 302 279 286 287.8 hardness Ti-6Al-4V

Rc 28 28 30 27 28 28.2 Vickers Sample 2B 286 294 310 279 286 291 hardness Ti-6Al-4V Rc 28 29 31 27 28 28.6 Vickers Sample 1A 260 260 272 254 260 261.2 hardness CP Grade 2 Rc 24 24 26 23 24 24.2 Vickers Sample 1B 260 266 279 254 260 263.8 hardness CP Grade 2 Rc 24 25 27 23 24 24.6

The macrohardness values (Table 3), based on the Rockwell C scale, across the length of a machined test specimen gave an average value of 260 kg/mm2 for the commercially pure titanium (Grade 2) and 290 kg/mm2 for the Ti-6Al-4V alloy. The micro-hardness values were marginally lower than the macrohardness value across the length of the test specimen for the commercially pure titanium (Grade 2), as shown in

Figure 11. However, for the Ti-6Al-4V alloy the microhardness (average value: 330 kg/mm2) is noticeably higher than the corresponding macrohardness value (average: 290 kg/mm2), as shown in Figure 12. The observed lower value of the macrohardness of the

Ti-6Al-4V alloy when compared to its microhardness can be ascribed to the presence of a population of processing-related artifacts. The average values of both the microhardness and macrohardness measurements for the commercially pure (Grade 2) and Ti-6Al-4V alloy, are compared in the bar graph shown in Figure 13. The bar graph representation reveals the intrinsic influence of microstructural effects on both microhardness, i.e., local hardness, and macrohardness, i.e., global hardness, of the two materials.

The following graphs show the difference between the micro-hardness and macrohardness of the commercially pure titanium.

Microhardness

) 250 2 (Kg/mm v H -

200 Vickers Hardness Vickers

150 0 1 2 3 4 5 6 Maesurment Number

Macrohardness

300 2) (Kg/mm

v 250 H -

200 Vickers Hardness Vickers 150 0 1 2 3 4 5 6 Measurement Number

Figure 11: A profile showing the hardness values across the length of annealed commercially pure (Grade 2) titanium: (a) Microhardness and (b) Macrohardness

The following graphs show the difference between the micro-hardness and macrohardness of the commercially pure titanium.

Microhardness 400 ) 2 (kg/mm

v 350 H -

300 Vickers Hardness Vickers

250 0 1 2 3 4 5 6 Measurment Number

Macrohardness 350 ) 2 (Kg/mm v H - 300 Vickers Hardness Vickers 250 0 1 2 3 4 5 6

Measurement Number

Figure 12: A profile showing the hardness values across the length of fully annealed Ti-6Al-4V alloy: (a) Microhardness and (b) Macrohardness

400 Microhardness Macrohardness

350 )

2 300

250

(Kg/mm

H - 200

150

Vickers Vickers Hardness 100

0 CP Grade-2 Ti-6Al-4V

Figure 13: Bar graph depicting the average microhardness and macrohardness values of the commercially pure (Grade 2) and Ti-6Al-4V alloy

3.6 Concluding Comments

A study of the influence of material composition on microstructural development and hardness of Ti-6Al-4V and commercially pure titanium (Grade 2) both in the annealed condition provides the following key findings:

(i) The as-received commercially pure (Grade 2) in the annealed condition essentially

revealed the primary alpha (α) grains intermingled with small pockets of the beta

(β) grains. High magnification observation revealed clearly the alpha (α) phase

lamellae located well within the beta (β) grain.

(ii) The Ti-6Al-4V alloy exhibited a duplex microstructure consisting of the near

equiaxed alpha (α) and the transformed beta (β) phases. The primary near

equiaxed shaped alpha (α) grains was well distributed in a lamellar matrix with

transformed beta.

(iii) The Ti-6Al-4V alloy has an elastic modulus of 125 GPa, while the Commercially

pure (CP: Grade 2) titanium has an average elastic modulus of 115 GPa, both in the

longitudinal orientation of the as-provided annealed plates.

(iv) The yield strength and tensile strength of the Ti-6Al-4V alloy are marginally lower

in the longitudinal orientation than the transverse orientation. The ultimate tensile

strength is only marginally higher than the yield strength indicating the tendency for

strain hardening beyond yield to be low.

(v) The yield strength and ultimate tensile strength of CP (Grade 2) is noticeably higher

in the longitudinal orientation than in the transverse orientation. In both

orientations the tensile strength is higher than the yield strength indicating the

occurrence of noticeable work hardening beyond yield.

(vi) The Ti-6Al-4V alloy in the annealed condition has acceptable ductility quantified in

terms of elongation-to-failure and reduction-in-area in both the longitudinal and

transverse orientations. The ductility, i.e., elongation-to-failure and reduction-in-

area, of the CP (Grade 2) is noticeably higher in both the longitudinal and

transverse orientations when compared to the alloy (Ti-6Al-4V) counterpart in

conformance with the lower strength of this material when compared to the alloy in

both the longitudinal and transverse orientations. Tensile fracture of the Ti-6Al-4V

alloy was macroscopically rough and essentially normal to the far field stress axis

for the longitudinal orientation and cup-and-cone morphology for the transverse

orientation. However, microscopically, the surface was rough and covered with a

population of macroscopic and fine microscopic cracks, voids of varying size, a

population of shallow dimples of varying size and shape, features reminiscent of

locally brittle and ductile failure mechanisms.

(vii) The microhardness and macrohardness measurements were consistent through the

sheet specimen for the two materials. The microhardness and macrohardness data

reveals the Ti-6Al-4V alloy to be harder than the commercially pure (Grade 2)

counterpart.

(viii) The observed lower value of the macrohardness of the Ti-6Al-4V, can be ascribed

to the presence of a population of processing-related artifacts and the hard beta-

phase. However, for the commercially pure titanium counterpart the macrohardness

was marginally higher than the microhardness resulting from the presence of a large

volume fraction of the soft alpha phase.

3.7 Summary

In this Chapter, the microstructure, hardness, and mechanical properties were studied and are presented. The mechanical properties developed in this chapter were used for subsequent chapters in the design of test beams and analysis of test results.

CHAPTER IV

THEORETICAL ANALYSIS OF BEAMS USING THE MATERIAL PROPERTIES

OF Ti ALLOYS

4.1 Design Specifications

Design of metal structures has matured into a sound fundamental science over the last fifty years. The three of the major sources for design of metallic structures are the

Military Handbook (MIL-HDBK-5H), the American Institute of Steel Construction

(ANSI/AISC 360-05), and the Aluminum Design Manual [25].

4.1.1 Military Handbook MIL-HDBK-5 [23]

Primarily developed for aerospace vehicle structures, MIL-HDBK-5H is a very useful resource for a variety of metallic materials and alloys. The intention of the document is to primarily act as a source of design allowables of metallic materials and elements (primarily fasteners) that are widely used in the design of aerospace structures

[23]. The data provided in MIL-HDBK-5H are acceptable to the Air Force, the Navy, the

Army, and the Federal Aviation Administration. The latest version of the handbook was released in 1998 and it appears that no further revision of the handbook is released yet.

MIL-HDBK-5H specifications are based on elastic behavior of metallic materials and structural members. The following elastic bending stress equation is normally used for design within the elastic range of structural members:

fb = My/I = M/Z (1)

Bending stresses due to loads are required to be determined for service loads that are anticipated on the structure using Eq. (1), and allowable bending stresses are determined based on a predefined level of allowable stress (usually about 66.7% of the yield stress of the material).

Similar design equations are available in the handbook for other actions such as shear, direct tension and axial compression. Eq. (1) is valid in the elastic range of behavior for compact sections that are not subject to instability. Thin walled structural elements will be subjected to failure through instability that was classified in the handbook as (1) primary or (2) local. Most of the discussion on failures resulting from elastic or plastic instability given in the handbook is confined to column (compression) members. Any treatment of failures from combined actions is referred to more advanced methods that are published in the open literature. The specifications for design of beams refer to the methods given in old references published in 1947 and 1957 [26, 27].

There is only a brief mention of built-up beams in MIL-HDBK-5H Section

2.8.1.2 where it is mentioned that “built-up beams usually fail because of local failures of the component parts. In welded steel tube beams, the allowable tensile stresses should be reduced properly for the effects of welding”.

4.1.2 AISC Steel Design Specifications [24]

Developed as a consensus document, AISC Steel Manual and the specifications

(ANSI/AISC 360-05) contained in the manual are based on (a) past successful usage, (b) the current state of knowledge, and (c) established industry practices. The AISC specifications were first published in 1923 and are widely used around the world as the leading standard for steel structural member design.

Idealized bilinear elastic-plastic stress-strain behavior of steel is considered in the derivation of beam design equations provided in the AISC specifications. The design equations consider the ultimate strength of the member at failure. The beam design approach is twofold: (1) the strength limit state at failure using factored load effects, and

(2) the serviceability limit state within the elastic range. The AISC specifications deal with welded built-up members in great detail including the post-buckling gain of shear strength for thin slender webs that are normally used in plate girders. The main basis for the derivation of design equations in this thesis is the steel design specifications given in

AISC Steel Construction Manual.

4.1.3 Aluminum Design Manual [25]

Aluminum structures have a shorter history of applications than steel. The first aluminum structure was built in 1930 [25]. The first aluminum specification was published in 1967. The relevant design recommendations for aluminum structures and members are published in the Aluminum Design Manual. One of the major differences

48 between the equations for beam design given in the aluminum design manual and those given in steel design manual is the inclusion of the strength reduction effect of heat affected zones for welded aluminum built-up structures. Design methods for welded built-up steel structural members do not include such strength adjustment. The extent of residual stresses is well established for steel structures and the design equations were calibrated to include the effects of residual stresses due to both hot rolling for plates or sheets and due to welding [24].

4.2 Review of Steel Design Specifications for Potential Application in the Design of

Titanium Built-Up Beams

A thorough review was performed of the current design methodologies given in

MIL-HDBK-5H, AISC Steel Construction Manual and the Aluminum Design Manual for the design of metallic structures. From the review, it was found that the steel design specifications of AISC [43] were closest to the current-state-of-the-art for the design of metallic built-up structural members [28-37, 43]. Therefore, from here on, steel design specifications are presented and adopted for application to built-up structural members with the material properties of titanium and its alloys.

4.2.1 Failure Modes of Welded Built-Up Beams

Beams have parts (regions) that are subjected to tension and compression at the same time. Welded built-up beams subjected to transverse loading that predominantly

49 causes bending moment and shear force due to flexural bending of the member can fail in following modes:

(a) Tearing initiated by tensile yielding and failure in the tension flange by excessive

tensile stresses

(b) Squashing initiated by compression yielding and failure in the compression flange

by excessive compressive stress

element that falls within the compression region of the section)

(d) Compression flange (member) out-of-plane buckling by deflection that is lateral

to the axis of the compression flange (also known as lateral torsional buckling)

(e) Shear failure characterized either by shear yielding of the web cross section or

shear buckling of the shear panel

(f) Other local web failures such as bearing failure or web buckling near loading or

support points

(g) Weld failures in the welds that join the web with the flanges leading to failure in

shear or due to pre-existing cracks (i.e., micro-cracks formed during welding)

The design of a welded built-up beam requires the design engineers to determine:

(i) Moment strength

(ii) Shear Strength

(iii) Web compression buckling and yield strength at supports and loading points

(iv) Stiffener details at the supports and the loading points

(v) Weld strength at the web-flange welds

Each of the above design aspects are discussed in the following section.

4.2.2 Brief Explanation of Elastic Plate Buckling [28-30]

Since rolled shapes as well as built-up shapes are composed of thin plate elements, the member strength of the section based on its slenderness ratio can only be achieved if the plate elements do not buckle locally under loading. Local buckling of plate elements can cause premature failure of the entire section, or at least, it will cause stresses to become non-uniform and reduce the overall strength. The basic theory of elastic stability of plates is well developed [28-30] and the theoretical elastic critical buckling stress for a plate is given as:

휋2퐸 퐹 = 퐾 (2) 푐푟 12 1−휇 2 푏/푡 2

Where K is the plate buckling coefficient and depends on the type of stress, edge support conditions, aspect ratio (a/b), plate thickness (t), modulus of elasticity (E) and Poisson‟s ratio (μ).

1 푎 푏 2 퐾 = + 푚 (3) 푚 푏 푎

Where a/b is the aspect ratio defined by the length to width ratio, and m is the number of half sine waves that occur in the x-direction at buckling. While the poisson‟s ratio of steel and titanium are somewhat equal, the difference in the values of modulus of elasticity for the two materials will result in vastly different values of critical buckling stresses for two plates with identical dimensions that are made from the two materials.

4.2.3 Moment Strength

The specifications presented in this section are mainly for doubly symmetric hot rolled I-shaped sections and welded built-up beams with small web slenderness ratio:

h E  5.70 t w Fyf

Where, the web slenderness ratio is defined as the ratio of height of the web (h) to the thickness of the web plate (tw).

Four limit states of failure need to be considered for the determination of moment strength:

(a) Yielding

(b) Lateral torsional buckling (LTB) – applicable to major axis bending only

(d) Web local buckling (WLB)

Smallest moment strength of a beam from the above four limit states is considered as the moment strength of the beam.

Concept of Compact, Non-Compact and Slender behavior

Compact Behavior: Entire section has yielded, all stresses are equal to Fy

Non-Compact Behavior: Behavior in between compact and slender conditions

A part of the section has stresses equal to Fy and the rest of the section has stresses less than Fy

Slender Behavior: All stresses within the section are less than Fy

4.2.3.1 Flange Local Buckling

Local buckling occurs when a compression element of the cross-section buckles under load before it reaches the yield stress of the material. Because buckling occurs at a stress lower than the yield stress, the shape is not capable of reaching the plastic moment strength. Thus, the strength of member is less than Mp, the plastic moment strength of the section. The plastic moment of the section is defined as the maximum moment strength that can be developed when the compression region of the section is fully plasticized to reach compressive yield stress while at the same time the tension region of the section reaches tensile yield stress. Table B4.1 of the AISC specification [24] provides the limiting slenderness values, λp for compression flanges and webs in order to insure that the full plastic moment strength can be reached. When both the compression flange and web meet these criteria, the member is classified as compact. If either element does not meet the criteria, the shape cannot be classified as being compact and the nominal moment strength must be suitably reduced to less than below Mp.

For the compression flange of an I-shaped section, the slenderness limits are,

퐸 퐸 휆푝 = 0.38 ; 휆푟 = 1.0 퐹푦 퐹푦

These limits were derived as follows:

The general expression for finding the slenderness limits from the elastic buckling equation is given as

푏 2 퐾휋2 퐸 = 2 푡 12(1 − 휇 ) 퐹푐푟

For the limiting width/thickness ratio (λr), critical stress after the adjustment for the residual stresses is:

Fcr = Fy – Fr = 0.7Fy (Approximately)

Fcr is the critical stress, Fy is the yield stress, and Fr is the residual stress.

For outstanding flange elements, K is approximately equal to 0.7 from AISC manual [47

- Pg 16.1-265] and µ = 0.3.

푏 2 0.7 ∗ 3.142 퐸 퐸 휆푟 = = 2) = 0.902 푡 12(1 − 0.3 0.7퐹푦 퐹푦

푏 퐸 푏 퐸 휆푟 = = 0.95 ≅ 휆푟 = = 1.0 푡 퐹푦 푡 퐹푦

For the width/thickness limit λp to achieve plastic deformation, K = 0.425 (least value).

푏 0.425 ∗ 휋2 퐸

= 2 푡 12(1 − 0.3 ) 퐹푦

푏 퐸 = 0.62 푡 퐹푦

Since residual stress effects disappear in the plastic range and material imperfections have less effect, K = 0.425 is an overly severe limitation. The strain at onset of strain

54 hardening is 15-20 times εy and that amount of plastic strain is not necessary even for achieving the plastic moment strength. The compact section limits are intended to achieve compression plastic strain about 7-9 times εy, about one-half the strain necessary to reach the strain hardening. Thus, the compression limit was adopted to be,

푏 퐸 휆푝 = = 0.38 푡 퐹푦

4.2.3.2 Web Local Buckling

Where buckling is taken as the design basis in the design of webs, the maximum stress in the web should not exceed the buckling stress divided by a factor of safety. The geometric parameters that determine the buckling of web are web thickness (t), the web height (h), which is the clear distance between the flanges, and the spacing (a) of transverse stiffeners.

For the web to be compact, the slenderness limits are,

퐸 퐸 휆푝 = 3.76 ; 휆푟 = 5.7 퐹푦 퐹푦

For limiting the width/thickness ratio (λr), residual stresses are to be considered with K =

23.9 [29],

푏 23.9 × 휋2 퐸

휆푟 = = 2 푡 12 1 − 0.3 0.7퐹푦

푏 퐸 퐸 휆푟 = = 5.54 ≅ 5.7 푡 퐹푦 퐹푦

For the width/thickness limit λp to achieve plastic deformation, K = 13.8,

푏 13.8 × 휋2 퐸

휆푝 = = 2 푡 12 1 − 0.3 퐹푦

푏 퐸 휆푝 = = 3.76 푡 퐹푦

4.2.3.3 Lateral Torsional Buckling

To ensure that a beam cross-section can develop its full plastic moment strength without buckling, LTB limits the slenderness to,

퐿푏 퐸 ≤ 1.76 푟푦 퐹푦

Where, Lb = unbraced length of the compression flange

ry = radius of gyration for the shape about the y-axis

The practical application of this limitation is to use the unbraced length alone. This results in a requirement for attaining full plastic moment strength.

퐸 퐿푏 ≤ 퐿푝 = 1.76푟푦 퐹푦

56 where, Lp = maximum unbraced length that would permit the shape to reach its plastic moment strength

A beam buckles elastically if the actual stress in the member does not exceed Fy at any point. Because all hot rolled shapes have built-in residual stresses, there is a practical limit to the usefulness of this elastic LTB equation. According to specification, only 0.7Fy is available to resist bending moment elastically, this establishes a limit for the elastic moment MrLTB = 0.7FySx.

In this equation, Sx is the elastic section modulus. This permits the determination of a limiting unbraced length Lr, beyond which the member buckles elastically.

퐸 퐽푐 0.7퐹 푆 ℎ 2 푦 푥 표 퐿푟 = 1.95푟푡푠 1 + 1 + 6.76 0.7퐹푦 푆푥 ℎ표 퐸 퐽푐

The derivation of the above limits is shown below,

The differential equation of the lateral torsional buckling for obtaining the slenderness limits is given by,

휋 휋퐸 2 푀 = 퐶 퐼 + 퐸퐼 퐺퐽 푐푟 퐿 퐿 푤 푦 푦

Where, E = Modulus of Elasticity of Steel =29,000 ksi G = Shear Modulus of Steel = 11,200 ksi

2 Cw = Warping torsional constant = Ifh /2

Iy = Moment of Inertia about weak axis

1 J = Torsional constant = 2푏푡 3 + ℎ푡 3 3 푓 푤

Lateral supports need to be provided at locations where the plastic moment Mp is expected to occur and the distances between lateral support points is relatively small.

Therefore, the term involving torsional rigidity GJ may be neglected.

휋 휋퐸 2 푀 = 퐶 퐼 푐푟 퐿 퐿 푤 푦

For the width/thickness limit Lp to achieve plastic deformation,

푀푐푟 = 푀푝 = 푍푥 퐹푦

휋 휋퐸 2 푍 퐹 = 퐶 퐼 푥 푦 퐿 퐿 푤 푦

휋2퐸 퐼 ℎ2 푦 푍푥 퐹푦 = 2 퐼푦 퐿푏 4

퐿 2 휋2퐸 ℎ 푏 = 퐼푦 푍푥 퐹푦 2

퐿 퐴ℎ 휋2퐸 푏 = 푟푦 푍푥 2퐹푦

Upper limit for the above equation is obtained by assuming perfect elasto-plastic steel

퐴ℎ without residual stresses. Taking a conservative low value of 1.5 for 푍푥

2 퐿푏 휋 × 1.5 퐸 = 푟푦 2 퐹푦

퐿푏 퐸 = 2.71 푟푦 퐹푦

Experimental data reported elsewhere [43] showed that a lower limit is necessary to achieve adequate rotation capacity R. Thus,

퐿푏 퐸 = 1.76 푟푦 퐹푦

For limiting the width/thickness ratio (Lr/ry), residual stresses are to be considered.

Mr is the moment strength available for service loads when extreme fiber reaches the yield stress Fyf (including the residual stress),

푀푟 = 퐹푦푓 − 퐹푟 푆푥

The length Lr is obtained by equating the maximum elastic moment strength Mr to the elastic lateral torsional buckling strength Mcr.

휋 휋퐸 2 푀 = 퐶 퐼 + 퐸퐼 퐺퐽 = 퐹 − 퐹 푆 푐푟 퐿 퐿 푤 푦 푦 푦푓 푟 푥

On solving, we get,

퐸 퐽푐 0.7퐹 푆 ℎ 2 푦 푥 표 퐿푟 = 1.95푟푡푠 1 + 1 + 6.76 0.7퐹푦 푆푥 ℎ표 퐸 퐽푐

4.2.4 Shear Strength

As long as the web is stable, that is, instability resulting from shear stress or a combination of shear and bending stress cannot occur. The shear strength (Vn) of the section is based on overall shear yielding of the web. Thus,

Vn = τy .Aw

Where τy = shear yield stress of the web

Aw = area of the web = d.tw

According to the “energy of distortion” theory, the shear yield stress τy equals the tension-compression yield stress Fy divided by √3 when shear stress acts alone

1 i.e; τ = 퐹 τy = 0.58 Fy ≈ 0.6 Fy 푦 3 푦

The nominal shear strength is obtained by Vn = 0.6 Fyw Aw

Where Fyw = yield stress of the web

Aw = area of the web

4.2.4.1 Energy of Distortion (Yield Criterion)

The most commonly accepted theory gives the uniaxial yield stress in terms of the three principal stresses. The yield criterion may be stated

1 휎 2 = [(휎 − 휎 )2 + (휎 − 휎 )2 + (휎 − 휎 )2 ] 푦 2 1 2 1 2 3 1

Where 휎1, 휎2, 휎3 are tensile or compression stresses that act in the three principal directions and 휎푦 is the “yield stress” that may be compared with the uniaxial value Fy.

For most structural design situations, one of the principal stresses is either zero or small enough to be neglected because of plain strain effects in thin wall sections. Hence, the above equation reduces to

2 2 2 휎푦 = 휎1 + 휎2 − 휎1휎2 (Neglecting third direction)

When stresses on thin plates are involved, the principal stress acting transverse to the plane of the plate is usually zero (at least to the first order approximation). Flexural stresses on beams assume zero principal stress perpendicular to the plane of bending.

Figure 14: Energy of Distortion Yield Criterion for Plane Stress [43]

4.2.4.2 Shear Yield Stress

The yield point for pure shear can be determined from a stress-strain curve with shear loading, or if the multiaxial yield criterion is known, that relationship can be used.

Pure shear occurs on 45 degree planes to the principal planes when σ2 = -σ1 and the shear stress τ = σ1, Substituting σ2 = -σ1 in the above equation

2 2 2 2 휎푦 = 휎1 + (−휎1) − 휎1 −휎1 = 3휎1

2 2 휎푦 = 3휏

This indicates that the yield condition for shear stress acting alone is,

휎푦 휏푦 = = 0.58휎푦 3

4.2.5 Slenderness limits for shear

The nominal shear strength, Vn, of unstiffened or stiffened webs, according to the limit state of shear yielding and shear buckling is

푉푛 = 0.6퐹푦 퐴푤 퐶푣

4.2.5.1 Elastic buckling Under Pure Shear

The elastic buckling stress for any plate is given by the elastic plate buckling equation as given below.

휋2 퐸 퐹푐푟 = 퐾. ℎ 2 2 12 1 − 휇 푡

Considering the case of pure shear the above equation can be written as(using τcr for Fcr and Kv for K)

휋2 퐸 휏푐푟 = 퐾푣. ℎ 2 2 12 1 − 휇 푡

5.34 푎 Where 퐾 = 4.0 + 푎 for ≤ 1 푣 ( )2 ℎ ℎ

4.0 푎 퐾 = 5.34 + 푎 for ≥ 1 푣 ( )2 ℎ ℎ

For practical purposes and without loss of accuracy, these equations have been simplified as

5.0 퐾 = 5.0 + 푣 푎 2

ℎ

For use in design equations, the above equation has been put into non-dimensional form defining Cv as the ratio of τcr (shear stress at buckling) to shear yield stress τy.

2 휏푐푟 퐾푣휋 퐸 퐶푣 = = 휏 ℎ 2 푦 휏 12 1 − 휇2 푦 푡

2 퐾푣휋 퐸 퐶푣 = ℎ 2 2 0.6퐹푦푤 12 1 − 휇 푡

Substituting 휇 = 0.3 in the above equation

2 퐾푣휋 퐸 퐶푣 = ℎ 2 2 0.6 × 12 × 1 − 0.3 퐹푦푤 푡

1.51 퐾푣퐸 퐶푣 = ℎ 2 (푡) 퐹푦푤

4.2.5.2 Inelastic Buckling under Pure Shear

As in all stability situations, residual stresses and imperfections cause in-elastic buckling as critical stresses approach yield stress. A transition curve for inelastic buckling was derived based on curve fitting and using test results. In the transition zone between elastic buckling and yielding,

휏푐푟 = 휏푝푟표푝 .푙𝑖푚𝑖푡 × 휏푐푟(𝑖푑푒푎푙 푒푙푎푠푡𝑖푐 )

It has been suggested to take the proportional limit as 80 percent of the yield stress of the web [34].

Therefore, the proportional limit is taken as 0.8 τy, higher than for compression in flanges, because the effect of residual stresses is less

휏 1.51 × 퐾 퐸 퐶 = 푐푟 = 0.8 × 푣 푣 휏 2 푦 ℎ 퐹 푡푤 푦푤

퐾 퐸 1.10 푣 퐹푦푤 퐶푣 = ℎ 푡푤

If 퐶푣 ≤ 0.8 then the first of the above equations is used and,

If 퐶푣 ≥ 0.8 then the second of the above equations is used.

ℎ The slenderness limits are obtained for , corresponding to Cv = 1.0 (i.e; the web yields 푡푤

ℎ in shear and no buckling occurs). The above equation may be solved for when Cv= 1.0 푡푤

ℎ 퐾푣퐸 = 1.10 푡푤 퐹푦푤

ℎ When does not exceed the value from the above equation, the nominal shear strength 푡푤

푉푛 = 0.6퐹푦 퐴푤

ℎ The relationship that divides elastic and inelastic buckling may be obtained by taking 푡푤

Cv = 0.8

퐾 퐸 1.10 푣 퐹푦푤 0.8 = ℎ 푡푤

ℎ 퐾푣퐸 = 1.37 푡푤 퐹푦푤

Figure 15: Buckling of Plate Girder Web Resulting from Shear Alone [43]

4.2.5.3 Buckling of Rectangular Plates Under the action of Shear

Consider a simply supported rectangular plate submitted to the action of shearing forces Nxy uniformly distributed along the edges.

In calculating the critical value of shearing stresses τcr at which buckling of plates occurs, the strain energy method is used. The deflection surface of the buckled plate is given by the expression in the form of a double series.

∞ ∞ 푚휋푥 푛휋푦 푤 = 푎 푠𝑖푛 푠𝑖푛 푚푛 푎 푏 푚=1 푛=1

The strain energy of bending of the buckled plate is given by the following expression.

∞ ∞ 2 퐷 휋4푎푏 푚2 푛2 ∆푉 = 푎2 + 2 4 푚푛 푎2 푏2 푚=1 푛=1

The work done by the external forces is,

푎 푏 휕푤 휕푤 ∆푇 = −푁푥푦 푑푥 푑푦 0 0 휕푥 휕푦

Substituting the expression for the deflection surface in the above equation, we get:

푎 푚휋푥 푝휋푥 sin 푐표푠 푑푥 = 0 , 𝑖푓 푚 ± 푝 𝑖푠 푎푛 푒푣푒푛 푛푢푚푏푒푟 0 푎 푎

푎 푚휋푥 푝휋푥 2푎 푚 sin cos 푑푥 = 2 2 , 𝑖푓 푚 ± 푝 𝑖푠 푎푛 표푑푑 푛푢푚푏푒푟 0 푎 푎 휋 푚 − 푝

We obtain,

푚푛푝푞 ∆푇 = −8푁 푎 푎 푥푦 푚푛 푝푞 푚2 − 푝2 (푞2 − 푛2) 푞푝푛푚

In which m,n,p,q are such integers that m±p and n±q are odd numbers

Now, Equating the work produced by the external forces to strain energy, the critical value of shearing forces is obtained,

푚2휋2 푛2휋2 ∞ ∞ 푎2 ( + )2 푎푏퐷 푚=1 푛=1 푚푛 푎2 푏2 푁푥푦 = − 푚푛푝푞 64 푎 푎 푞푝푛푚 푚푛 푝푞 푚2 − 푝2 (푞2 − 푛2)

Now, It is necessary to select such a system of constants amn and apq as to make Nxy a minimum. By equating the derivatives of the above equation with respect to each of the coefficients amn to zero, we obtain a system of homogeneous linear equations in amn.

This system can be divided into two groups, one containing constants amn for which m+n are odd numbers, and the other for which m+n are even numbers. The second group of equations gives the smallest value for (Nxy)cr.

Using notations, we can write this group of equations in the following matrix form

푎 휋2 휋2퐷 훽 = ; 휆 = − 2 푏 32훽 푏 ℎ. 휏푐푟

a11 a22 a13 a31 a33 a42 = 0

휆(1 + 훽2)2 4/9 0 0 0 8/45 = 0 훽2

16휆(1 + 훽2)2 4/9 -4/5 -4/5 36/25 0 = 0 훽2

휆 1 + 9훽2 2 0 -4/5 0 0 -24/75 = 0 훽2

휆 9 + 훽2 2 0 -4/5 0 0 24/21 = 0 훽2

휆 9 + 9훽2 2 0 36/25 0 0 -72/35 = 0 훽2

휆 16 + 4훽2 2 8/45 0 -24/75 24/21 -72/35 = 0 훽2

Now, To obtain τcr the determinant of the above equations is to be equated to zero.

Limiting to two equations with two constants a11 and a22 and equating the determinant of the equations to zero, we get:

휆 1 + 훽2 2 4 훽2 9 = 0 4 16휆 1 + 훽2 2 9 훽2

16휆2 1 + 훽2 4 16 − = 0 훽4 81

1 훽4 휆2 = . 81 (1 + 훽2)4

1 훽2 휆 = ± 9 (1 + 훽2)2

Now, From the above notation we have

휋2 휋2퐷 휆 = − 2 32훽 푏 ℎ. 휏푐푟

휋2 휋2퐷 ±9(1 + 훽2)2 휏 = − . . 푐푟 32훽 푏2ℎ 훽2

9휋2 (1 + 훽2)2 휋2퐷 휏 = ± . . 푐푟 32훽 훽3 푏2ℎ

This approximation is not sufficiently accurate since the error is about 15 percent for square plates and increases as the ratio of a/b increases. To get more satisfactory

69 approximation, a large number of equations in the system must be considered. By taking five equations and equating the determinant to zero, we obtain:

2 2 훽4 81 81 1 + 훽2 81 1 + 훽2 휆2 = 1 + + + 81(1 + 훽2)4 625 25 1 + 9훽2 25 9 + 훽2

Using the above notation,

휋2 휋2퐷 휆 = − 2 32훽 푏 ℎ. 휏푐푟

훽2 81 81 1 + 훽2 2 81 1 + 훽2 2 휋2 휋2퐷

± 2 2 1 + + 2 + 2 = − 2 9 1 + 훽 625 25 1 + 9훽 25 9 + 훽 32훽 푏 ℎ. 휏푐푟

9휋2 (1 + 훽2)2 휋2퐷 1 휏 = . . . 푐푟 32훽 훽3 푏2ℎ 81 81 1 + 훽2 2 81 1 + 훽2 2 1 + + + 625 25 1 + 9훽2 25 9 + 훽2

For a square plate, we have a = b

푎 훽 = = 1 푏

휋2퐷 휏 = 9.4 푐푟 푏2ℎ

In general, the expression can be written as

휋2퐷 휏 = 퐾. 푐푟 푏2ℎ

Here, the error of approximation is less than 1 percent. The above equation gives satisfactory approximation for K, if the shape of the plate does not differ much from a square, say a/b ≤ 1.5.

For larger values of the ratio a/b, a large number of equations of the system must be considered. To get more accurate results, for a long narrow plate, a limiting case of an infinitely large plate with simply supported edges may be considered.

An approximate solution of the problem is obtained by taking the deflection surface of the plate by the following expression,

휋푦 휋 푤 = 퐴 푠𝑖푛 sin 푥 − 훼푦 푏 푠

This expression gives zero deflection for y=0 ; y=b and also for which (x-αy) is a multiple of s. Here, s represents the length of the half waves of the buckled plate and the factor α is the slope of the nodal lines. The equation for the strain energy of bending of the buckled plate is given by:

2 2 1 휕2푤 휕2푤 휕2푤 휕2푤 휕2푤 푉 = 퐷 + − 2(1 − 휗) − − 푑푥 푑푦 2 휕푥2 휕푦2 휕푥2 휕푦2 휕푥휕푦

Work done by the external forces during buckling is given by

푎 푏 휕푤 휕푤 ∆푇 = −푁푥푦 푑푥 푑푦 0 0 휕푥 휕푦

Now, Substituting the equation of the deflection surface of the buckled plate in the equation for strain energy of bending of buckled plate and also in the equation for the work done by external forces and equating these two quantities, we obtain:

휋2퐷 푠2 푏2 휏 = 6훼2 + 2 + + 1 + 훼2 2 푐푟 2훼푏2ℎ 푏2 푠2

The smallest value for τcr is obtained by taking

1 푠 = 푏 1 + 훼2 푎푛푑 훼 = 2

2 휋2퐷 휏 = 3+2+1.5+1.5 푐푟 2 푏2ℎ

휋2퐷 휏 = 5.65 푐푟 푏2ℎ

The exact solution of the problem for an infinitely long strip with simply supported edges gives

휋2퐷 휏 = 5.35 푐푟 푏2ℎ

The combination of pure shear with a uniform longitudinal compression or tension σx was also studied and the corresponding values of K are given by the curve [29]. It is seen that any compressive stress reduces the stability of a plate subjected to shear, while any tension increases this stability.

For σx = 0 the value K = 8.98 is obtained from the curve.

The error of approximate solution in this case is about 6 ½ percent. Having the exact value for K in for an infinitely long plate and a very accurate value of K is obtained by a parabolic curve given by the equation

푏 2 퐾 = 5.35 + 4 푎

25 20 15 K 10 5 0 0 0.5 1 1.5 2 2.5 b/a

Figure 16: Effect of Aspect Ratio on K

It is seen that for longer plates, the values of K given in the table are always above the curve.

The buckling of an infinitely long plate under uniform shear has been solved for the case of clamped edges and the following value found for the critical stress:

휋2퐷 휏 = 8.98 푐푟 푏2ℎ

The case of combined shearing and bending stresses is also studied [29] and has been investigated in the case of a plate with simply supported edges by taking the deflection surface and using the energy method.

Figure 17: Effect of Aspect Ratio on K [43]

4.3 Discussion

From Sections 4.1 and 4.2, it is clear that the moment strength and shear strength equations of AISC specifications [24] are based on elastic buckling behavior of plates with adjustments to the equation made based on post-elastic behavior and curve fitting of test results. The scope this thesis is limited in nature, and therefore, it was not practical to develop many test data points with a range of variables. Until a comprehensive study of welded built-up beam behavior of members fabricated from titanium and its alloys is conducted, it might be hard to make firm design recommendations. However, in the

74 interim, it is recommended that the welded built-up steel beam design equations be used with appropriate adjustments to incorporate the differences between the material properties of steel and those of titanium and its alloys. This is the approach taken in this thesis.

CHAPTER V

DESIGN OF TEST BEAMS USING COMMERCIALLY PURE TITANIUM AND Ti

ALLOYS

Based on the results of chapters 3 and 4, suitable test beams were designed with the materials procured for the project. The test beams are simply supported and loaded at the third points. Welded built-up I-beams with one top flange and one bottom flange welded to the web were designed for experimental validation. The test beams were designed both by elastic method and by plastic method. The plastic methods of design assume a bilinear stress-strain curve for the commercially pure titanium and the Ti alloy used in this study. This assumption is realistic because significant plasticity is demonstrated and the material behavior is non-linear after the linear material behavior, as presented in Chapter 3 on materials. The beam flanges and the web were designed to prevent local plate buckling, and lateral torsional buckling so that the test beams would fail by material yielding in the compression flange or tension flange. Web stiffeners were provided at the location of the loading points and the support points. Beam designs were finalized for fabrication of test beams based on the approach presented in this chapter.

The span of each of the test beams was 24 inches, and total depth of each beam was 4.25 inch to 4.75 inch depending on whether or not grooves are provided. Three beams each of CP titanium and Ti-6Al-4V (for a total of six beams) were designed and they are

numbered as B1, B2, B3 for the Ti-6Al-4V alloy and B4, B5, B6 for the CP Titanium.

Grooves were provided on web and flange plates of beams B1 and B2, and on flange plates of B4 and B5. Beams B3 and B6 did not have any grooves. Where provided, the grooves were 1/16th inch (0.0625 inch) in depth, and were wide enough to snugly accommodate the thickness of the mating part.

5.1 The Design Basis

The beams were designed using the AISC approach [38] that was presented in

Chapter 4 with the required adjustments to suit the material properties of CP titanium and the titanium alloy used in this project. The details of the design calculations are presented in the Appendix 1B.

5.2 Material Properties

The two alloys, primarily considered for this study are Commercially Pure

Titanium (Grade-2) and Ti-6Al-4V alloy. The modulus of elasticity of 18,000 ksi was used for the design of Ti-6Al-4V test beams, and 15,560 ksi was used for the design of

CP titanium test beams. The yield strength used in the design for Ti-6Al-4V test beams was 137 ksi, while that of CP titanium beams was 62.6 ksi. These properties were adopted from the test results presented in Chapter 2 and they correspond to the longitudinal direction of the beam axis.

5.3 Section Properties

Three welded built-up I-Section beams were fabricated using Ti-6Al-4V and three test beams were fabricated using Commercially Pure Titanium. The actual thickness of the flange and web elements of the test beams are shown in Table 5.

Table 5: Plate Thickness for Different Elements of Test Beams (in Inches)

Element / Alloy Ti-6Al-4V Commercially Pure Titanium

Thickness of Flanges 0.267 0.395

Web thickness 0.267 0.125

Fastener thickness 0.25 0.25

The dimensional details of the four kinds of beams are shown in Figures 18 to 21. The details of Ti-6Al-4V beams (B1 and B2) are shown in Figure 18. These two beams have grooves machined in the flanges and the web to receive the ends of the mating parts. The overall depth of B1 and B2 was 4.4 inch. Beam B3 had no grooves machined in the elements. The overall depth of the beam section was 4.53 inch. Other details of the beam are shown in Figure 19.

Figure 18: Details of Ti-6Al-4V Beams B1 and B2 (with Grooves)

Figure 19: Details of Ti-6Al-4V Beam B3 (Without Grooves)

Beams B4 and B5 were fabricated with Commercially Pure Titanium. The flange elements of these two beams were provided with grooves. The webs were not provided with grooves because the web plates were ⅛ inch thick and therefore, cannot accommodate two grooves of 1/16 th inch depth (one groove on each face of the web) without consuming the total thickness of the plate. The dimensional details of Beam B6 in inches are given in Figure 21. This beam did not have any grooves.

Figure 20: Details of CP Ti (Gr. 2) Beams B4 and B5 (with Grooves)

Figure 21: Details of CP Ti (Gr. 2) Beam B6 (Without Grooves)

5.4 Design Procedure

The unbraced length of the beam le was determined based on the support condition of the compression flange. The support conditions of the beam test setup are simple supports with both vertical translation and rotation restrained. The compression flange is laterally supported at the beam ends. The slenderness (h/tw) of the beam was

퐸 then determined, and it should be less than 5.7 where E and Fy are the elastic 퐹푦 modulus and yield stress of the beam respectively. If the slenderness value is greater than

퐸 the value of 5.7 then it should be designed as a plate girder. In this project, all the 퐹푦 beams were designed so that the web slenderness falls within this limit.

5.4.1 Moment Strength

The various limit states like yielding, LTB, FLB, WLB were determined and the limiting moment of resistance (MR) of the beam was determined based on the least value of all the above limit states. In order to find the above limit states their corresponding slenderness limits were determined first. Based on these values, the beam is classified to be in the plastic (compact), inelastic (non-compact) or elastic (slender) zones of behavior.

The corresponding moment equations are applied to obtain the limiting moment of resistance (Mn) . The slenderness limits for the above limit states are given below:

1. Flange Local Buckling:

퐸 퐸 휆푝 = 0.38 ; 휆푟 = 1.0 퐹푦 퐹푦

2. Lateral Torsional Buckling:

2 퐸 퐸 퐽푐 0.7퐹푦 푆푥 ℎ표 퐿푝 = 1.76푟푦 ; 퐿푟 = 1.95푟푡푠 1 + 1 + 6.76 퐹푦 0.7퐹푦 푆푥 ℎ표 퐸 퐽푐

3. Web Local Buckling:

퐸 퐸 휆푝 = 3.76 ; 휆푟 = 5.7 퐹푦 퐹푦

5.4.2 Shear Strength

Shear failure of beam with transverse web stiffeners occurs in three stages. First, pure shear is developed in the unbuckled web, then a diagonal tension field action is

82 developed if the web is slender and shear buckling is initiated. Finally, plastic hinges develop in the flanges which cause the collapse of the beam to occur in shear. The shear strength of the beam is obtained by 푉푛 = 0.6퐹푦 퐴푤 퐶푣 where the factor Cv is dependent on the web slenderness limits related to shear strength. Based on the slenderness limits, the beam falls in three different categories (i) plastic, (ii) inelastic, and (iii) elastic zones, and the corresponding Cv equation is used to determine the Cv value. The limiting slenderness ratios for the shear strength are given below.

퐾푣퐸 퐾푣퐸 휆푝 = 1.10 ; 휆푟 = 1.37 퐹푦푤 퐹푦푤

5.4.3 Load Carrying Capacity

A typical four point bending test set up is shown below.

Once the moment strength and shear strength are obtained, the maximum load carrying capacity of the beam is determined from the above loading condition.

5.5 Summary

From the design calculations presented in this chapter, the following failure loads and failure modes are predicted (see Table 6):

Table 6: Summary of Test Beam Design

Predicted Failure Beam Material Failure Mode Load,

Bending failure B1 and B2 Ti-6Al-4V 111 kips leading to excessive deflection Bending failure B3 Ti-6Al-4V 113 kips leading to excessive deflection

Shear failure by B4 and B5 CP titanium 36 kips web buckling

Shear failure by B6 CP titanium 38 kips web buckling

CHAPTER VI

FABRICATION OF TEST BEAMS

The US Army‟s division at Picatinny Arsenal (NJ) developed a Pulsed Gas Metal

Arc Welding process (referred to henceforth as GMAW-P), which involved a careful modification of the existing practices so as to be applicable to titanium and its alloys.

The linear weld speeds can be up to ten times faster than the corresponding speeds of tungsten inert gas (TIG) or gas tungsten arc welding (GTAW) processes. Also, the number of passes can be reduced by a factor of three. The new process developed by the

US Army division at Picatinny Arsenal (NJ) uses 100% helium shielding gas that facilitates good penetration capability and a double pulse template [39]. This welding method, which is a semi automatic pulse GMAW welding method, was used in flat position for this project. No post weld heat treatment was done for the welds. As previously mentioned, welding of titanium is standardized in a recently released welding specification put forth by the American Welding Society (AWS) [40].

The details of the fabrication of the six test beams are presented in this chapter.

Welded built-up beam concept is shown in Figure 3 of Chapter 1. The test beam was fabricated by welding two flange plates with the web plate as shown in Figure 22. All of the required parts for the six test beams were precision cut using water-jet cutting done

85 by a commercial agency (M&J Machine Inc.) in Akron, OH at their own facility. The beams were welded by technicians of the US Army facility in Picatinny Arsenal (NJ) using the method developed by them (GMAW-P). Special fixtures were fabricated to hold and clamp the parts together for the purpose of welding. Two of the beams were welded for demonstration at the Lockheed Martin Facility based in Akron (OH). The other beams were welded at the US Army facility at Picatinny Arsenal (NJ).

6.1 Preparation of Parts for the Test Beams

Grooves of suitable widths and 1/16 inch (0.0625 inch) depth were machined along the weld lines of the parts that were to receive the edges of the companion or mating part (see Figure 22 and Figure 23). These grooves were required to facilitate conformance with the welding procedure developed by Picatinny Arsenal. The edge of the mating part was precision machined to have a straight edge that is square to the groove. The precision machining ensured that there is a tight and snug fit of the mating part within the groove and there is no exposure of the underside or the backside of the groove to the ambient atmosphere. The back edge of the part sitting in the groove is not exposed to the ambient atmosphere while the welding was being done. The parts after the required edge preparation and grooving are shown in Figure 23.

Figure 22: Three Plate Assembly for a Typical Built-up Section

Figure 23: Test Beam Elements after Edge Preparation and Grooving

6.2 Machining of Parts for the Test Beams

M&J Machine Inc. used two CNC machines, one for larger parts and one for small parts. These two CNC machines are shown in Figures 24 and 25. Carbide end mill

⅛ inch and ¼ inch diameter bits were used to prepare the edges (see Figure 26).

Figure 24: CNC Machine for Machining Large Parts

Figure 25: CNC Machine for Machining Small Parts

Figure 26: Carbide End Mill Bits

6.3 Fixture for Welding the Test Beams

Initial fit up and tack welding was done using C-clamps and simple clamping tools as seen in Figure 27. For final welding, a fixture as seen in Figure 28, was used.

The fixture was fabricated by Picatinny Arsenal to hold the test beam parts together during welding (Figure 28).

Figure 27: General View of Fixturing for Tack Welding of Test Beams

6.4 Welding of Test Beams

All of the welds made for the test beams were fillet welds. The matching titanium

(or its alloy) filler metal wire diameter was 0.045 inch. The electrical characteristic of the GMAW-P process was current DC-pulse. The electrode work angle was either vertical or at 10 degrees push. All of the welds were made in a single pass. No inter-pass cleaning was necessary because the welds were made in a single pass. The torch gas used for primary welding was 100% helium at a flow rate of 50 cubic foot per hour. The speed of wire feed was 375 inches per minute at a voltage of 32.9 volts. The speed of welding was 9.5 inches per minute. The initiation or start temperature was 72o F (room temperature: 25oC) while the finish or ending temperature was about 365oF (185oC). The

US Army welding technicians certified that the welding parameters did conform to the requirements specified in the standard AWS D1.9/D1.9M: 2007 [2]. Argon was used as the backing gas for beams B1 (Ti-6Al-4V), B3 (Ti-6Al-4V), B5 (Commercially pure titanium) and B6 (Commercially pure titanium), while no backing gas was used for beams B2 (Ti-6Al-4V) and B4 (Commercially pure titanium) as one of the test variables.

No grooves were provided for beams B3 and B6. All welds are fillet welds. The details of the weld parameters and variables are summarized in Table 7 and Table 8.

Figure 28: General View of Fixture for Welding Test Beams

Figure 29: Close-up View of the Fixture

Table 7: Details of Welds Made for Different Test Beams (Data Provided by Picatinny Arsenal)

Heat and Base Filler Weld Joint GMAW Electrical Welded at Beam Lot Technique Welding Gases Metal Metal Position Characteristics (Location) Number

Primary Weld Torch Gas – 100% He, flow Ti- 6A4V rate 50 cfh, gas cup Lockheed B1 6Al- H9473 ELI size: bore 0.625 Martin 4V Backing Gas – 100% Ar Primary Weld Torch Ti- Gas – 100% He, flow 6A4V Lockheed B2 6Al- H9473 rate 50 cfh, gas cup

ELI Martin 4V size: bore 0.625 Backing Gas – None Primary Weld Torch

92 Stringer, Gas – 100% He, flow Ti- electrode work 6A4V Horizontal- Current DCEP – rate 50 cfh, gas cup Picatinny B3 6Al- H9473 angle – 10 ELI Flat Pulse size: bore 0.625 Arsenal 4V degrees push Backing Gas – 100% Single Pass Ar Primary Weld Torch Gas – 100% He, flow Picatinny B4 CP Ti CP Ti HC-14069 rate 50 cfh, gas cup Arsenal size: bore 0.625 Backing Gas – None Primary Weld Torch Picatinny B5 CP Ti CP Ti HC-14069 Gas – 100% He, flow Arsenal rate 50 cfh, gas cup size: bore 0.625 Picatinny B6 CP Ti CP Ti HC-14069 Backing Gas – 100% Arsenal Ar

Table 8: Procedure Qualification Record (Data Provided by Picatinny Arsenal)

Weld Filler Pass Wire Stringer Metal Voltage Time & Temperature Beam Date Welder Process Speed or Notes Diameter (Volts) Travel Start – End (ipm) Weave (inch) Speed (ipm) B1 & Ti-6Al-4V 22 Sec. 2/19/09 Indano 0.045 375 32.9 Stringer 72 365 B2 100% He 9.5” Ti-6Al-4V 22 Sec. No B3 2/26/09 Sanchez 0.045 375 32.9 Stringer 68 430 100% He 9.5” Grooves CP 100% 22 Sec. B4 2/28/09 Sanchez 0.045 375 32.9 Stringer 76 365 He 9.5”

CP 100% 22 Sec. B5 2/26/09 Sanchez 0.045 375 32.9 Stringer 65 385 He 9.5” CP 100% 22 Sec. No

93 B6 2/27/09 Sanchez 0.045 375 32.9 Stringer 65 340 He 9.5” Grooves

6.5 Test Beams

A typical tack welded built-up test beam is shown in Figure 31. The six finally welded built-up titanium test beams were shipped by Picatinny Arsenal to the University of Akron. Five of the six fully welded built-up test beams are shown in Figure 32(b).

The six beams fabricated in this project were used for the experimental evaluation of the structural performance of titanium built-up beams as described in chapters 7 and 8.

Figure 30: A Typical Tack Welded Titanium Test Beam

Figure 31(a): Typical Test Beam Fit

Figure 31(b): Fully Welded Titanium Test Beams

6.6 Summary

The details of the fabrication of six welded built-up test beams are presented in this chapter. The welding procedure that was developed at Picatinny Arsenal was used to weld the built-up test beams. The welds made by the method were visually sound and conformed to the titanium welding standard AWS D1.9/D1.9M [40]. Two beams were fabricated without the backing gas, and two beams were fabricated with no grooves machined in the parts.

CHAPTER VII

STATIC BEND TESTS OF TITANIUM ALLOY BEAMS

Two beams (B1 and B4) were tested to study the flexural performance of built-up welded titanium beams bent in single curvature under static loading. Beam B1 was made from Ti-6Al-4V material and beam B4 was made from commercially pure titanium (Gr.

2) material. The span of the two test beams was 24 inches. Another beam (B5) was made from commercially pure titanium (Gr. 2) and was tested under fatigue loading. The beam was able to withstand one million cycles as designed (details of the fatigue test for beam B5 are given in Chapter 8). The fatigue test was stopped after one million cycles because of load run out. This beam (B5) was tested under static loading after the fatigue test, i.e., after the beam was subjected to one million cycles of fatigue loading. Details of the static load test for B5 are also presented in this chapter. The test results correspond to the static load test that was performed after the beam was subjected to fatigue loads.

7.1 Test Set-Up

The typical test set-up for static bend tests of the beams that was used for this project is shown in Figure 33. The test beams were loaded using an INSTRON 5300 machine with a maximum loading capacity of 225 Kips (1000 KN). The beams were loaded using

96 a four-point loading arrangement over a simple span of 24 inches (610 mm). The total length of each specimen was 27 inches. Test beams were supported at the two member ends on two rollers that allowed the beams to behave as simply supported. These supports allow for free rotation at the ends of the beam while permitting free sliding of the beam at the supports. Half inch thick bearing plates with a typical width of 2 inches were provided over the roller supports at the two ends as seen in Figures 35 and 36.

The compression flange of each test beam was restrained from any lateral displacement at the supports. The restraint was provided with a fixture that was specifically designed and fabricated for the static tests of this thesis. Two fixtures were provided at the two ends of the test beam as seen in Figure 34. This figure shows a front view of the fixtures at the two ends. A side view of the fixture at one of the ends

(supports) is shown in Figure 35. The lateral displacement of the compression flange was prevented by the two threaded rods that were provided in each fixture. Two threaded rods were also attached to the vertical members of the fixture. A small square plate having a suitable nut welded to it is attached to the end of the threaded rod so as to adjust the extension of the threaded rod. Perfect lateral support was possible in both lateral directions once the square plates touched both side faces of the compression flange at each end. A steel plate was welded on to the bottom of each fixture so as to clamp the fixture to the reaction plate of the INSTRON testing machine. With this lateral restraint arrangement, the unbraced length of the test beam for the purpose of lateral torsional buckling calculations is taken as 24 in.

The loading fixture consisted of a spreader beam that made it possible to apply the load at two loading points that were separated by a distance of 4 inches (adjustable)

97 symmetrically, i.e., at 2 inches (50 mm) on either side of the mid-span of the test beam.

Two 0.25 inch thick plates with a width of 2 inches were provided under the two loading points so as to spread the load over a larger beam (web) length in order to prevent local element buckling due to concentrated nature of the loads. From the design calculations, the maximum unbraced length for the full development of plastic behavior (Lp) for the test beams is greater than 24 inches. Therefore, lateral restraints were not provided at the loading points.

Figure 32: Test set-up for Static Bend Test of Beams

Figure 33: Close-up View of the beam test set-up

7.2 Instrumentation

The development of strains over the entire duration of the static loading was recorded using strain gages located at seven key locations. A Digital Image Correlation

(DIC) system (ARAMIS) was used to capture the strain fields of each test beam during the entire range of static loading. The mid-span deflections were recorded using a digital dial gage. The failure modes were captured in the form of digital images in the DIC system and by digital cameras, while the test data were programmed to be collected by:

(i) The control unit of the INSTRON test machine, and

(ii) An independent stand-alone Data Acquisition System (DAS).

Figure 34: Side View of Lateral Support

Typical strain gage layout for each test beam (B1 and B4) is shown in Figure 37. Strain gages were carefully attached at the midspan on top and bottom flanges (one on each side) on the outer surface and inner surface of the flanges. Additionally, two strain gages were attached in a 45 degree pattern on the web at quarter span location on each side of the loading point (Figure 38).

Figure 35: Loading Fixture

100

Figure 36: Strain Gage Layout

Figure 37: Strain Gage Fixing and Strain Gages attached to Web

101

7.3 Test Procedure

A preload of 0.5 kips (2.25 kN) was initially applied to ensure firm contact between the beam and the supports.

(a) A loading rate of 1000 pounds per minute (i.e., 4.45 kN per minute) was used for loading the beam (B4) to failure for commercially pure titanium (Gr. 2) and to find the residual strength of beam B5.

(b) The loading rate was tripled for the Ti-6Al-4V beam because of its higher load carrying capacity coupled with the need to test the beam in a shorter time span (rate of loading affects the test results).

The images were captured on the DIC system at the same rate as the deflection readings and frequency of the data acquisition system which in turn was synchronized with manual data collection. This was done in order to maintain a consistent data acquisition rate by the three data collection systems.

7.4 Test Results

The two test beams (B1 and B4) failed at a static load greater than the predicted value obtained using the design methodologies developed in this study. The commercially pure titanium (Grade 2) beam (B4) failed at a load of 42 kips. The residual static strength (i.e., the strength determined from static bend test after two million cycles of fatigue loading) of Beam B5 at failure was determined to be 46 kips. The failure load predicted for this test beam using the proposed design methodology was 36 kips for

102 beams B4 and B5 (see Chapter 5). The failure for both beams occurred by web shear buckling followed by excessive deflection of the beam. This failure mode was predicted using the design methodology that is presented and discussed in Chapter 5.

7.4.1 Beam B4 – Commercially Pure Gr. 2 Titanium

The failure mode of beam B4 is shown in Figure 39. The failure mode captured by the DIC system as is shown in Figure 40.

Figure 38: Failure Mode of Commercially Pure Gr. 2 Titanium Beam (B4) by Web Shear Buckling

103

Figure 39: Failure Mode of Commercially Pure Gr. 2 Titanium Beam (B4) by Web Shear Buckling as Captured in DIC ARAMIS System

A close up view of the failure mode of beam B4 is shown in Figure 41. The beam failure was initiated by web shear buckling, followed by excessive deflection. The web plate seen in Figure 41 is extensively buckled as predicted by the theory detailed in Chapter 5.

From physical inspection, the welds between the web and the flanges along with the connecting stiffeners were found to be intact and appear not to have failed. There were no visible cracks. The beam maintained its structural integrity during the entire range of loading.

104

Figure 40: Final Failure Mode of Commercially Pure Gr. 2 Titanium Beam (B4) Note Complete Web Shear Buckling on One Half of the Beam

7.4.2 Beam B5 – Commercially Pure Gr. 2 Titanium (After Fatigue Test)

Beam B5, that was loaded under static loading after it was tested in cyclic loading for one million cycles, failed in a manner similar to the failure mode of beam B4. The failure was initiated by web shear buckling followed by excessive deflection as seen in

Figure 42. Strain gages were not attached to this test beam for the static test. However, the deflections were recorded over the entire range of static loading.

105

Figure 41: Failure by Web Shear Buckling of Beam B5

106

Web shear buckling of beam B5 is clearly seen in Figure 42. The picture in Figure 42 shows the view from the front (DIC side), while the bottom picture shows the view from the back side. The two pictures show that, for this beam, web buckling occurred on both sides of the loading points. The bottom picture shows that while web buckling of the left side shear panel buckled out of plane of the picture toward the viewer, and the right side panel buckled away from the viewer. Once again, the welds were intact and performed well over the entire range of loading without any visible signs of distress at the ultimate failure load of the beam.

7.4.3 Beam B1 – Ti-6Al-4V Titanium Alloy

Beam B1, which is a Ti-6Al-4V titanium alloy beam, failed at a load of 131 kips.

The predicted failure load for this beam was 111 kips (see Chapter 5). Failure of the beam occurred by excessive deflection followed by buckling of the compression flange between the two loading points. The failure mode of the beam is as shown in Figure 43.

The failure mode that was captured by the DIC system is shown in Figure 44. There was evidence of complete plasticization of the beam length between the two loading points.

The straightening and stretching of the bottom flange as seen in Figure 44 is an evidence of tensile yielding of the bottom flange, while the top compression flange completely yielded and buckled to a multiple wave form as seen in Figures 45 and 46. The proposed design method predicted the failure mode to be plasticization of both the compression and tension flanges. Therefore, the failure mode was as expected.

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There was no visible distress or cracking of welds of the test beam, and the welds were intact over the entire range of static loading. There was permanent deformation of the beam because of excessive stressing of the compression and tension flanges.

Figure 42: Failure Mode of Beam B1 (Ti-6Al-4V) by Excessive Deflection

Figure 43: Failure of Beam B1 (Ti-6Al-4V) as Captured in DIC System

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Figure 44: Failed Beam B1 (Ti-6Al-4V) after Unloading and Removal from the Test Set-up

Figure 45: Compression Flange (Top Flange) Local Buckling of Beam B1 (Ti-6Al-4V)

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7.5 The Load versus Deflection Curves

Two deflections curves were obtained from the tests on each test beam: one from the digital dial gage and the other from readings of the test machine [INSTRON]. The load versus deflection curves for beam B1 are shown in Figure 47. The shape of the load versus deflection curves is quite similar to the stress versus strain curves obtained for the material using small round tensile specimens. Initial part of the load-deflection curve is linear up to about 90 kip load after which the curve bends significantly to indicate the onset of yielding in the material.

Load Vs Deflection 140000

120000

100000 Instron 80000 Dial Gage

60000 Elastic Load, LbsLoad,

40000 Ti-6Al-4V Beam B1 20000

0 0 0.2 0.4 0.6 0.8 1 1.2 Deflection, in

Figure 46: Load-Deflection Curve of Beam B1 (Ti-6Al-4V)

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The load versus deflection curve also demonstrates the ductile nature of the beam under static loading. The shape of the curves can be classified as being that of a classic ductile beam that has significant reserve strength and deflection capability to provide the required warning prior to catastrophic failure. Figure 47 also shows the deflection curve predicted using the classic elastic beam bending theory. This figure shows that there is a perfect match between the predicted deflection and the deflections measured during the test before the beam reached its elastic limit.

The load versus deflection curves of beams B4 and B5 (tested after run out during the fatigue test) are shown in Figures 48 and 49. These deflection curves demonstrate a distinct softening of the beam upon reaching a load of about 25 kips for beam B4 and about 37 kips for beam B5. This softening can be rationalized from a shear buckling point of view. The softening of the beam occurred when the web reached the corresponding limit for elastic shear buckling load, while the beam carried a load beyond the elastic shear buckling limit into the post-buckling gain in strength [43] due to

“Tension-Field Action”. This is a classic welded beam behavior for metallic structures.

The figure also shows the deflection curve predicted using the classic elastic beam bending theory. The elastic deflection method was found to under-estimate the deflection of the titanium beams. The beams deflected more than what was predicted using classic elastic beam bending theory. At a level of service limit load, which is normally about

50% of the failure load, the actual deflections of the beam were found to be about 50% greater than the predicted values. However, additioinal investigation is required to explain this difference.

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Load Vs Deflection 45000

40000

35000 Instron 30000 Dial Gage 25000

20000 Elastic Load, LbsLoad, 15000

10000 CP Ti Beam B4 5000

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Deflection, in

Figure 47: Load-Deflection Curve of Beam B4 (Commercially Pure Gr. 2 Titanium)

Load Vs Deflection 50000

45000 Elastic

40000 Instron

35000

30000 Dial Gage 25000

20000 Load, Lbs Load, 15000

10000 CP Ti Beam B5 5000

0 0 0.2 0.4 0.6 0.8 1 Deflection, in

Figure 48: Load-Deflection Curve of Beam B5 (Commercially Pure Gr. 2 Titanium) after Fatigue Test

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7.6 The Load versus Strain Relation

The load-strain data collected from the data acquisition system were plotted and the relationships are shown in Figures 50 to 54 for beam B4 (commercially pure Gr. 2 titanium beam). Figures 50, 51 and 52 show strain curves on the flanges at the mid-span location. Figures 53 and 54 show the corresponding curves for one web of the beam.

These figures also show the theoretical strain curves that were derived from the analysis.

The theoretical strains and those recorded during the static test of the beam accord well for this beam for flange strains up until the beam reaches its elastic limit. The curves beyond is load corresponding to elastic web shear buckling (approximately 25 to 30 kips) deviate from the strain values obtained from the static test.

Load Vs Strain 70000

60000

Theoretical Strain 50000

40000

Strain gage 1 30000 Load, Lbs Load,

Strain gage 2 20000

10000 CP Ti Beam B4 Strain Gage 1&2 0 -0.004 -0.0035 -0.003 -0.0025 -0.002 -0.0015 -0.001 -0.0005 0 0.0005 Strain, in

Figure 49: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Top Flange Outside Strains

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Load Vs Strain 70000

60000

Theoretical Strain 50000

40000

Strain gage 3 30000 Load, Lbs Load,

20000

10000 CP Ti Beam B4 Strain Gage 3 0 -0.0035 -0.003 -0.0025 -0.002 -0.0015 -0.001 -0.0005 0 0.0005 Strain, in

Figure 50: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Top Flange Inside Strains

Load Vs Strain 70000

60000

50000 Theoretical Strain

40000

30000 Strain gage 5 Load, Lbs Load, Strain gage 4

20000

10000 CP Ti Beam B4 Strain Gage 4&5 0 0 0.001 0.002 0.003 0.004 0.005 0.006 Strain, in

Figure 51: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Bottom Flange Outside Strains

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Load Vs Strain 35000

30000 Theoretical Strain 25000 Strain gage 6

20000

15000 Load, LbsLoad,

10000

5000 CP Ti Beam B4 Strain Gage 6 0 -0.018 -0.016 -0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 Strain, in

Figure 52: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Web Strains (45 Degrees)

Load Vs Strain 35000

30000 Theoretical Strain

25000 Strain gage 7

20000

15000 Load, Lbs Load,

10000

5000 CP Ti Beam B4 Strain Gage 7 0 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 Strain, in

Figure 53: Load-Strain Curves for Beam B4 (Commercially Pure Gr. 2 Titanium) Web Strains (135 Degrees)

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Similarly, Figures 55, 56 and 57 show strain curves on the flanges at the mid-span location. Figures 58 and 59 show the corresponding curves for one web of the beam.

These figures also show the theoretical strain curves that were derived from the analysis.

The theoretical strains and those recorded during the static test of the beam accord fairly closely for this beam for the flange strains. In Figure 57, strain gage 4 showed erratic readings and therefore, the readings are ignored.

In general, the strains obtained from the test results match reasonably well for the two test beams.

Load Vs Strain 100000

90000

80000 Strain Gage 2 70000 Theoritical Strain 60000 Strain Gage 1 50000

Load, Lbs Load, 40000

30000

20000 Ti-6Al-4V Beam B1 Strain Gage 1 & 2 10000

0 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 Strain, in

Figure 54: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Top Flange Outside Strains

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Load Vs Strain 100000

90000

80000

70000

60000 Strain Gage 3 50000 Theoritical Strain

Laod, Lbs Laod, 40000

30000

20000 Ti-6Al-4V Beam B1 Strain Gage 3 10000

0 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 Strain, in

Figure 55: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Top Flange Inside Strains

Load Vs Strain 100000

90000

80000 Strain gage 4 70000

60000 Strain gage 5 Theoritical 50000 Strain

Laod, LbsLaod, 40000

30000

20000 Ti-6Al-4V Beam B1 Strain Gage 4 & 5 10000

0 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 Strain, in

Figure 56: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Bottom Flange Outside Strains

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Laod Vs Strain 100000

90000

Theoretical Strain 80000

70000

60000 Strain gage 6 50000

Load, Lbs Load, 40000

30000

20000 Ti-6Al-4V Beam B1 Strain Gage 6 10000

0 -0.0035 -0.003 -0.0025 -0.002 -0.0015 -0.001 -0.0005 0 Strain, in

Figure 57: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Web Strains (45 Degrees)

Load Vs Strain 100000

90000

80000

70000 Theoretical Strain 60000

50000 Strain gage 7

Load, Lbs Load, 40000

30000

20000 Ti-6Al-4V Beam B1 Strain Gage 7 10000

0 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 Strain, in

Figure 58: Load-Strain Curves for Beam B1 (Ti-6Al-4V) Web Strains (135 Degrees)

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7.7 Summary

Both the commercially pure (Grade 2) and Ti-6Al-4V alloy test beams failed in modes that were predicted by using the methodologies developed in this study. However, the test beams demonstrated significant reserve strength following initial yielding. The deflection curves along with the predicted deflection curves are presented in this chapter.

These curves and a comparison of load versus strain relationships obtained from tests with those predicted using theoretical methods demonstrate a reasonably close match between the theoretical predictions and the experimental test results until the elastic limit of the material.

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CHAPTER VIII

FATIGUE TESTS OF TITANIUM ALLOY BEAMS

The primary objective of the fatigue tests conducted on the titanium alloy beams is to investigate the fatigue performance of welded built-up titanium beams under cyclic loading. The dimensional and fabrication details of welded built-up titanium beams made from commercially pure titanium and Ti-6Al-4V alloy are presented in earlier chapters. Stiffeners were welded at the supports as well as the central loading points of the beams to prevent any web local failures. Beams B2 and B3 were made from Ti-6Al-

4V while beams B5 and B6 were made from commercially pure Gr. 2 titanium. These four beams were tested under fatigue loading. The details of the fatigue tests are given in this chapter.

8.1 Test Setup and Instrumentation

The four welded built-up test beams were all identical in length (total length of 27 inches) with 24 inches span between the simple supports at the two ends. The two central loading points are 4 inches apart. The test beams were loaded in fatigue using an MTS loading frame with a maximum capacity of 50 kips and a stroke of 10 inches. The standard four-point bending test setup was used for the fatigue tests. The details of the

120 test setup are shown in Figure 60. The reaction beam fixture used in these tests was a commercially available fixture for conducting standard four point bend tests and fatigue tests. The specimens were supported on two rollers that allowed the beam ends to behave in a simply supported condition. Loading was applied through a loading fixture that was attached to the load cell of the MTS test frame at the top. The loading fixture (spreader beam) was specifically fabricated for this project. The two central loading points of the spreader beam were 4 inches apart to match the two stiffener locations (Figure 61). No steel bearing plates were provided under the loading points because the loose plates and parts in the test setup can move and become unstable during fatigue loading. No strain gages were attached to the test specimen for the purpose of recording strains. The mid- span deflection was constantly measured over the entire fatigue test using an LVDT

(Linear Variable Differential Transducer) that sent the electronic data to the MTS controller all through the fatigue loading. The load data and the central deflection data were collected by the MTS controller. A web camera was installed to monitor the fatigue test of the last Ti-6Al-4V beam (B3).

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Figure 59: Test Setup for Fatigue Tests

Figure 60: Test Setup for Fatigue Tests

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8.2 Test Procedure

The theoretical failure load of the beams was calculated using the design equations presented in Chapter 5. These predicted loads were used for determining the range of loading of the test beams under fatigue loading conditions. The failure loads for beams B5 and B6 (Commercially Pure Gr. 2 titanium) were predicted to be 36 kips and

38 kips respectively. Failure loads of 111 kips and 113 kips were predicted for beams B5 and B6 (Ti-6AL-4V). A minimum load of 0.5 kip was initially applied to each test beam for fatigue tests in order to ensure firm contact between the beam and the loading points or the supports. Load was applied in a sinusoidal wave form at a constant frequency of

5Hz.

The maximum and minimum load values were calculated such that they fall within 22 and 45% of the maximum predicted flexural failure load of the corresponding test beam. The stress ratio (R), which is the ratio of the maximum load to the minimum load for fatigue tests, was fixed to be 0.1. A summary of the maximum load and minimum load for each test beam are shown in Table 9. The predicted failure load for each fatigue test beam is also listed in the table along with the stress ratio (Pmax/Pu) for the purpose of ready reference. Due the limited number of fatigue test specimens available for this project, the tests were commenced at a higher stress ratio than would normally have been done had there been many samples available for the purpose of testing.

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Table 9: Maximum and minimum loads applied to the test specimens for fatigue tests

Predicted Failure Load (P) Pmax/Pu Load Cycles (Nf) Load (kips) Pu Max.(kips) Min.(kips) (%) CP Gr. 2 Ti Beam B5 Stage 1 20 2.0 55.5 35,364 Stage 2 8 0.8 22.2 1,000,000 36 1,000,000 Stage 3 17 1.7 44.7 (Did Not Fail) CP Gr. 2 Ti Beam B6 Stage 1 17 1.7 44.7 1,000,000 38 30,000 Stage 2 25 2.5 65.8 (Failed) Ti-6Al-4V Beam B2 25,248 Stage 1 111 25 2.5 22.5 (Failed) Ti-6Al-4V Beam B3 30,286 Stage 1 113 25 2.5 22.5 (Failed)

The test beams were periodically inspected during the fatigue tests to make sure that there is no visual cracking or damage to the beam under the load cycles. Particular attention was paid to the welds, fixtures, and loading hardware. The number of cycles, actual load levels, and deflections recorded by the MTS controller were monitored to see if there is a progressive reduction in the loads or an increase in deflection.

8.3 Stress Ratios and Loads for Fatigue Tests

Beams B5 and B6 were tested first and beams B2 and B3 were tested later in the test program.

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8.3.1 Beam B5 (CP Gr. 2 Titanium)

The very first beam that was tested to study fatigue behavior of titanium beams in this project was beam B5 which is made from commercially pure Gr. 2 titanium. It was a challenge to determine the stress ratio for the test beam because of the limited number of test specimens available for this thesis. Therefore, fatigue testing was initiated at a very high stress ratio of about 55% with the maximum load of 20 kips and a minimum load of

2.0 kips. However, the test beam deflected rigorously under such high stress ratio.

Therefore, the test was paused after the beam was loaded to just over 35 thousand load cycles, and the stress ratio was reduced to 22.2% with maximum load of 8 kips and minimum load of 0.8 kips. The fatigue test ran smoothly after the reduction in the stress ratio to 22.2%. The test was paused when the total number of cycles reached one million.

The stress ratio was increased to 44.7% in order to potentially initiate failure. However, the beam was able to withstand another million cycles. The fatigue test was classified to be a run out test because it did not fail even after 2 million load cycles that were applied during the test. There were no visible signs of distress both in the beam and in the welds.

Typical variation of load cycles with time for the test on beam B5 is plotted for

Stage 3, and is shown in Figure 62. The corresponding variation of deflection with time is as shown in Figure 63. Upon completion of the fatigue test, beam B5 was loaded in a static test setup (see Chapter 7) and deformed to failure under a static load. The test results corresponding to the static load test, which is a residual strength test after run out in the fatigue load test, are detailed in Chapter 7.

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0 -2000

-4000

-6000

-8000

-10000

LOAD (lbs.) LOAD -12000

-14000

-16000

-18000 21 22 23 24 25

TIME (sec.) Figure 61: Typical Load-Time History for Beam B5 – CP Gr. 2 Titanium (Stage 3)

-0.04

-0.06

-0.08

-0.10

DEFLECTION (in.)

-0.12

21 22 23 24 25 TIME (sec.) Figure 62: Typical Deflection-Time History for Beam B5 – CP Gr. 2 Titanium (Stage 3)

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8.3.2 Beam B6 (CP Gr. 2) Titanium

The fatigue test for beam B6 was started with a high stress ratio of about 44.7% with the maximum load of 17 kips and a minimum load of 1.7 kips. After approximately

320,000 cycles at this stress ratio, the test was paused due to failure of the left support

(breaking of the fastener bolt). The test was restarted after replacing the broken fastener with a high strength fastener. The fatigue test ran smoothly following this initial glitch at this stress ratio to complete one million load cycles. There were no visual signs of distress or cracks in the welds. Furthermore, there was no abnormal increase in the deflection at this stage. With an intention of causing failure in this fatigue test, the stress ratio was then increased to 65.8% which was intentionally selected to be high so as to initiate failure with the objective of understanding the fatigue failure mode. The beam deflections were understandably very large, and the beam shook rigorously to accommodate the large central deflection at 5 hertz (cycles per second) load cycle. The beam eventually failed close to 30,000 cycles. The beam failed by the initiation of a crack at the bottom of the beam and broke into two pieces except for a small part that was intact in the compression flange to hold the two halves together. The failure occurred quickly, so it was not possible to capture the actual failure mode accurately. Typical variation of the load cycles with time is shown for beam B6 for stage 2 in Figure 64. The corresponding deflection variation with time is shown in Figure 65.

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8.3.3 Beams B2 and B3 (Ti-6AL-4V)

For the Ti-6Al-4V test beams B2 and B3, the stress range selected was 22.5% with the maximum load of 25 kips and minimum load of 2.5 kips. Typical load cycles and deflections over a short time period are shown for the two beams in Figures 66 to 69.

Both the beams failed in fatigue with fatigue life of 30,286 cycles for beam B2 and

25,248 cycles for beam B3. Crack initiation is believed to have occurred at the welds of the bottom flange. The failure was catastrophic with both beams failing by complete tearing of the beam into two parts. The failure mode of beam B2 is as shown in Figures

70 and 71.

-5000

-10000

-15000

LOAD (lb) LOAD

-20000

-25000 30 31 32 33 34 35 TIME(Sec)

Figure 63: Typical Load-Time History for Beam B6 – CP Gr. 2 Titanium (Stage 2)

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-0.06

-0.08

-0.10

-0.12

DELECTION (in) DELECTION -0.14

-0.16

30 31 32 33 34 35 TIME (Sec)

Figure 64: Typical Deflection-Time History for Beam B6 – CP Gr. 2 Titanium (Stage 2)

-5000

-10000

-15000

LOAD ( lbs.) -20000

-25000

-30000 30 31 32 33 34 35

TIME (sec.)

Figure 65: Typical Load-Time History for Beam B2 – Ti-6Al-4V

129

-0.04

-0.06

-0.08

-0.10

-0.12

DEFLECTION (in.) -0.14

-0.16

30 31 32 33 34 35 TIME (sec.)

Figure 66: Typical Deflection-Time History for Beam B2 – Ti-6Al-4V

-5000

-10000

-15000

LOAD ( lbs.) -20000

-25000

-30000 30 31 32 33 34 35

TIME (Sec.)

Figure 67: Typical Load-Time History for Beam B3 – Ti-6Al-4V

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-0.04

-0.06

-0.08

-0.10

-0.12

-0.14

DEFLECTION (in.) DEFLECTION -0.16

-0.18

30 31 32 33 34 35

TIME (Sec.)

Figure 68: Typical Deflection-Time History for Beam B3 – Ti-6Al-4V

The overall failure mode of beam B2 is as shown in Figure 70. An enlarged close up view of the failure of the beam is as shown in Figure 71. As shown in Figure 72, cracking at the bottom flange (presumably at the welds) may have triggered the failure.

The number of load cycles that the beam was able to withstand was very small (25,248).

131

Figure 69: Overall Failure Model of Beam B2 (Ti-6Al-4V)

132

Figure 70: Failure Model of Beam B2 (Ti-6Al-4V)

Figure 71: Failure Initiation at the Bottom Flange of Beam B2 (Ti-6Al-4V)

133

Similarly, the overall failure mode of beam B3 is shown in Figure 73. An enlarged close up view of the failure of the beam is shown in Figure 74. Cracking at the bottom flange

(presumably at the welds) may have triggered the failure. The number of load cycles that the beam could withstand was very small (30,286).

Figure 72: Overall Failure Model of Beam B3 (Ti-6Al-4V)

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Figure 73: Failure Mode of Beam B3 (Ti-6Al-4V)

8.4 Summary

Fatigue tests described in this chapter reveal that welded built-up beams made from commercially pure (Gr. 2) titanium have better fatigue life than those made from Ti-

6Al-4V. For example, the commercially pure titanium beams B5 was able to withstand one million cycles with a stress ratio of 22.2%, and 44.7% for nextmillion cycles.

However, Ti-6AL-4V beams B2 and B3 failed catastrophically at stress ratio of 22.5% for a very low number of load cycles (nearly 25 to 30 thousand).

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CHAPTER IX

ANALYSIS OF TEST RESULTS

The pertinent discussion of test results was done in Chapter 3 for material characterization and the related tests. The results of microstructure characterization, mechanical testing, and hardness testing were presented in detail and discussed in the chapter for CP Ti (Gr. 2) and for Ti-6Al-4V alloy.

The results of the static tests of welded built-up test beams are described in detail in Chapter 7. The results of the static tests were also analyzed and theoretical predictions of the test beam performance were presented in the chapter. Similarly, the results of fatigue tests are outlined and discussed in Chapter 8 along with the relevant analysis of the test results. However, the important findings from the three referred chapters are summarized in this chapter.

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9.1 Tensile Deformation, Fracture Behavior, Influence of Material Composition on

Microstructural Development, and Hardness

A study of the tensile deformation, fracture behavior, influence of material composition on microstructural development and hardness of Ti-6Al-4V and commercially pure titanium (Grade 2) both in the annealed condition provided the key findings that are listed in chapter 10 on conclusions.

9.2 Static Bend Tests of Welded Built-Up Titanium Beams

A summary of the failure loads that were determined from tests and the corresponding predicted loads is provided in Table 10. The failure loads obtained for the three beams are greater than the predicted failure loads. The actual strength from the tests are greater than the predicted strength by 16 to 28% demonstrating that there will be significant reserve strength available in the test beams when the beams are designed in conformance with the methodologies presented in this thesis. The predicted and actual failure modes match well. However, excessive deflections at failure may limit the usable strength to something closer to the predicted theoretical loads in order to limit the deflections.

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Table 10: Summary of Failure Loads and Predicted Strengths

Predicted Failure Failure Mode Beam Material Load, Difference Both Predicted and Actual Predicted Actual 131 kips +18.0% Bending failure leading to B1 Ti-6Al-4V 111 kips excessive deflection 42 kips +16.7 Shear failure by web B4 CP Ti (Gr. 2) 36 kips buckling 46 kips +27.8% Shear failure by web B5 CP Ti (Gr. 2) 36 kips buckling

The load versus deflection curves presented in Chapter 7 demonstrate that the predicted deflection curve for Ti-6Al-4V beam (B1) matched very closely with the deflection curves obtained from the test. Beams B4 and B5 demonstrate a distinct softening of the beam upon reaching a load that corresponds to elastic shear buckling load. The elastic deflections determined for the two beams underestimated the deflections when compared with deflections recorded from the static bend tests.

The load versus strain curves that were determined from the tests for beam B1 (Ti-

6Al-4V) and B4 (CP Ti - Gr. 2) matched very well with those determined by elastic beam bending theory for the initial part of the loading regime. The difference between the theoretical strain values and the strain values obtained from tests increased as the load exceeded the yield limit of the corresponding material. The strains obtained from the tests for web panels deviated from the theoretical values much more than the longitudinal strains that were obtained for the top and bottom flanges.

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9.3 Fatigue Tests of Welded Built-Up Titanium Beams

The results of fatigue tests are analyzed and presented in Chapter 8. The discussion is not repeated in this section.

9.4 Summary

The test results and the analysis of the test results that were developed in the project are described in three previous chapters. The relevant chapter may be referred to for complete details of the analysis of the test results.

139

CHAPTER X

CONCLUSIONS

The following primary conclusions can be derived from the research work carried out in this report.

10.1 Tensile Deformation, Fracture Behavior, Influence of Material Composition on

Microstructural Development and Hardness

(i) The as-received commercially pure (Grade 2) in the annealed condition essentially

revealed the primary alpha (α) grains intermingled with small pockets of the beta (β)

grains. High magnification observation revealed clearly the alpha (α) phase lamellae

located well within the beta (β) grain.

140

(ii) The Ti-6Al-4V alloy exhibited a duplex microstructure consisting of the near

equiaxed alpha (α) and the transformed beta (β) phases. The primary near

equiaxed shaped alpha (α) grains was well distributed in a lamellar matrix with

transformed beta.

(iii) The Ti-6Al-4V alloy has an elastic modulus of 125 GPa, while the Commercially

pure (CP: Grade 2) titanium has an average elastic modulus of 115 GPa, both in the

longitudinal orientation of the as-provided annealed plates.

(iv) The yield strength and tensile strength of the Ti-6Al-4V alloy are marginally lower

in the longitudinal orientation than the transverse orientation. The ultimate tensile

strength is only marginally higher than the yield strength indicating the tendency for

strain hardening beyond yield to be low.

(v) The yield strength and ultimate tensile strength of CP (Grade 2) is noticeably higher

in the longitudinal orientation than in the transverse orientation. In both

orientations, the tensile strength is higher than the yield strength indicating the