A Dissertation. entitled. Deformation History and Load Sequence Effects on Cumulative Fatigue Damage. and Life Predictions.

A Dissertation entitled Deformation History and Load Sequence Effects on Cumulative Fatigue Damage and Life Predictions By Julie Colin Submitted as partial fulfillment of the requirements for the Doctor of Philosophy in Engineering Dr. Ali Fatemi, Advisor College of Graduate Studies The University of Toledo December 2009

The University of Toledo College of Engineering I HEREBY RECOMMEND THAT THE DISSERTATION PREPARED UNDER MY SUPERVISION BY Julie Colin ENTITLED Deformation History and Load Sequence Effects on Cumulative Fatigue Damage and Life Predictions BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN ENGINEERING Recommendation concurred by Dissertation Advisor: Dr. Ali Fatemi Dr. Mohamed Samir Hefzy Committee Dr. Yong Gan On Final Examination Dr. Efstratios Nikolaidis Dr. Douglas Nims Dean, College of Engineering

An Abstract of Deformation History and Load Sequence Effects on Cumulative Fatigue Damage and Life Predictions Julie Colin Submitted as partial fulfillment of the requirements for the Doctor of Philosophy Degree The University of Toledo December 2009 Fatigue loading seldom involves constant amplitude loading. This is especially true in the cooling systems of nuclear power plants, typically made of stainless steel, where thermal fluctuations and water turbulent flow create variable amplitude loads, with presence of mean stresses and overloads. These complex loading sequences lead to the formation of networks of microcracks (crazing) that can propagate. As stainless steel is a material with strong deformation history effects and phase transformation resulting from plastic straining, such load sequence and variable amplitude loading effects are significant to its fatigue behavior and life predictions. The goal of this study was to investigate the effects of cyclic deformation on fatigue behavior of stainless steel 304L as a deformation history sensitive material and determine how to quantify and accumulate fatigue damage to enable life predictions under variable amplitude loading conditions for such materials. A comprehensive experimental program including testing under fully-reversed, as well as mean stress iii

and/or mean strain conditions, with initial or periodic overloads, along with step testing and random loading histories was conducted on two grades of stainless steel 304L, under both strain-controlled and load-controlled conditions. To facilitate comparisons with a material without deformation history effects, similar tests were also carried out on aluminum 7075-T6. Experimental results are discussed, including peculiarities observed with stainless steel behavior, such as a phenomenon, referred to as secondary hardening characterized by a continuous increase in the stress response in a strain-controlled test and often leading to runout fatigue life. Possible mechanisms for secondary hardening observed in some tests are also discussed. The behavior of aluminum is shown not to be affected by preloading, whereas the behavior of stainless steel is greatly influenced by prior loading. Mean stress relaxation in strain control and ratcheting in load control and their influence on fatigue life are discussed. Some unusual mean strain test results are presented for stainless steel 304L, where in spite of mean stress relaxation fatigue lives were significantly longer than fully-reversed tests. Prestraining indicated no effect on either deformation or fatigue behavior of aluminum, while it induced considerable hardening in stainless steel 304L and led to different results on fatigue life, depending on the test control mode. In step tests for stainless steel 304L, strong hardening induced by the first step of a high-low sequence significantly affects the fatigue behavior, depending on the test control mode used. For periodic overload tests of stainless steel 340L, hardening due to the overloads was progressive throughout life and more significant than in high-low step tests. For aluminum, no effect on deformation behavior was observed due to periodic iv

overloads. However, the direction of the overloads was found to affect fatigue life, as tensile overloads led to longer lives, while compressive overloads led to shorter lives. Deformation and fatigue behaviors under random loading conditions are also presented and discussed for the two materials. The applicability of a common cumulative damage rule, the linear damage rule, is assessed for the two types of material, and for various loading conditions. While the linear damage rule associated with a strain-life or stress-life curve is shown to be fairly accurate for life predictions for aluminum, it is shown to poorly represent the behavior of stainless steel, especially in prestrained and high-low step tests, in load control. In order to account for prior deformation effects and achieve accurate fatigue life predictions for stainless steel, parameters including both stress and strain terms are required. The Smith- Watson-Topper and Fatemi-Socie approaches, as such parameters, are shown to correlate most test data fairly accurately. For damage accumulation under variable amplitude loading, the linear damage rule associated with strain-life or stress-life curves can lead to inaccurate fatigue life predictions, especially for materials presenting strong deformation memory effect, such as stainless steel 304L. The inadequacy of this method is typically attributed to the linear damage rule itself. On the contrary, this study demonstrates that damage accumulation using the linear damage rule can be accurate, provided that the linear damage rule is used in conjunction with parameters including both stress and strain terms. By including both loading history and response of the material in damage quantification, shortcomings of the commonly used linear damage rule approach can be circumvented in an effective manner. v

In addition, cracking behavior was also analyzed under various loading conditions. Results on microcrack initiation and propagation are presented in relation to deformation and fatigue behaviors of the materials. Microcracks were observed to form during the first few percent of life, indicating that most of the fatigue life of smooth specimens is spent in microcrack formation and growth. Analyses of fractured specimens showed that microcrack formation and growth is dependent on the loading history, and less important in aluminum than stainless steel 304L, due to the higher toughness of this latter material. vi

Acknowledgments First and foremost, I would like to thank my advisor Dr. Ali Fatemi, for his guidance and support over the past three years. I would like to thank Dr. Yong Gan, Dr. Mohamed Samir Hefzy, Dr. Efstratios Nikolaidis, Dr. Douglas Nims for serving on my Ph.D. committee. Their time and advice are greatly appreciated. I would also like to acknowledge Dr. Said Taheri, Dr. Jean-Philippe Sermage, and Jean-Christophe Le Roux for providing me data and for their feedback and advice. Electricité de France is greatly acknowledged for financial support. I would like to extend my sincere gratitude to Dr. Atousa Plaseied, Nisha Cyril, and Jonathan Williams, for helping me learn to use the material testing machines and procedures. I would also like to thank my colleagues in the fatigue and fracture laboratory for their help and friendship. The timely service of Mr. John Jaegly, Mr. Tim Grivanos, and Mr. Randall Reihing from the machine shop of the MIME Department is greatly appreciated. I would like to acknowledge Dr. Joseph Lawrence for training me on the Atomic Force Microscope, and Dr. Cora Lind for allowing me to use her laboratory and equipment. Finally, I would like to thank my parents, family and friends for their support. vii

Table of Contents page An Abstract of... iii Acknowledgments... vii Table of Contents... viii List of Tables... xi List of Figures... xiii List of Nomenclature... xxii List of Abbreviations... xxiv 1. Introduction... 1 1.1 Background and Significance... 2 1.2 Objective and Outline... 3 2. Literature Review... 8 2.1 Introduction... 8 2.2 Cumulative Damage... 9 2.2.1 Rainflow cycle counting method... 10 2.2.2 Linear Damage Rule (LDR)... 11 2.2.3 Other cumulative damage models... 13 2.2.4 Crack initiation versus crack growth in damage accumulation... 16 2.3 Deformation-Fatigue Relationship... 19 2.3.1 Mechanisms involved in deformation and fatigue of stainless steel... 19 2.3.2 Deformation and ductility... 24 2.4 Loading Parameters Influencing Deformation and Fatigue Life Behaviors... 25 2.4.1 Service loading... 25 2.4.2 Overloads and load sequence effects... 26 2.4.3 Mean stress effects... 28 2.5 Summary... 30 3. Experimental Program... 35 3.1 Experimental Plan... 35 3.2 Materials and Specimens... 35 3.3 Equipments... 37 viii

3.3.1 Test machines and instruments... 37 3.3.2 Alignment... 38 3.4 Tests Procedures and Data Acquisition... 38 3.4.1 Monotonic tensile tests... 38 3.4.2 Constant amplitude fully-reversed fatigue tests... 39 3.4.3 Mean strain and mean stress tests... 40 3.4.4 Initial overstrain tests... 41 3.4.5 Step tests... 41 3.4.6 Periodic overload tests... 42 3.4.7 Random loading tests... 43 4. Deformation Behavior and Load Sequence Effects... 57 4.1 Monotonic Deformation Behavior... 58 4.2 Cyclic Deformation Behavior... 60 4.3 Effect of Loading Sequence or History on Cyclic Deformation... 62 4.4 Conclusions... 64 5. Constant Amplitude Behavior... 79 5.1 Introduction... 79 5.2 Constant Amplitude Fully-Reversed Fatigue Test Results and Effect of Control Mode... 80 5.3 Mean Strain and Mean Stress Effects... 85 5.4 Prestraining Effects... 89 5.5 Secondary Hardening in Stainless Steel 304L... 92 5.6 Fatigue Life Correlations and Predictions for Constant Amplitude Tests... 98 5.7 Conclusions... 100 6. Variable Amplitude Loading... 134 6.1 Introduction... 134 6.2 Step Load Tests... 136 6.3 Periodic Overload Tests... 141 6.4 Random Loading... 145 6.5 Fatigue Life Correlations and Predictions for Variable Amplitude Tests... 149 6.6 Conclusions... 150 ix

7. Cracking Behavior and Damage Evolution... 193 7.1 Introduction... 193 7.2 Crack Analysis... 194 7.2.1 Procedure of crack analysis... 194 7.2.2 Crack type definitions... 195 7.3 Cracking Behavior under Constant Amplitude Loading... 197 7.3.1 Constant amplitude fully-reversed behavior... 197 7.3.2 Mean strain and mean stress effects... 198 7.4 Effect of Prestraining on Cracking Behavior... 200 7.4.1 Cracks due to prestraining... 200 7.4.2 Crack evolution... 201 7.5 Loading Sequence Effects on Cracking Behavior... 204 7.6 Conclusions... 205 8. Conclusions and Recommendations... 222 8.1 Literature Review... 223 8.2 Load Sequence Effects on Deformation Behavior... 225 8.3 Constant Amplitude Behavior... 226 8.4 Variable Amplitude Loading... 228 8.5 Cracking Behavior and Damage Evolution... 231 8.6 Possible Future Research... 232 References... 234 x

List of Tables Table 3.1 Composition of the two grades of SS304L used in this study. 46 Table 3.2 Table 4.1 Table 5.1 Table 5.2 Result of the Rainflow cycle counting applied to the random loading history with amplitudes of +/- 100 presented in Figure 3.12(b). Summary of the mechanical tensile properties for SS304L CLI, SS304L THY and Al 7075-T6. Summary of constant amplitude fatigue test results for SS304L CLI. Summary of constant amplitude fatigue test results for SS304L THY. 46 66 104 105 Table 5.3 Summary of constant amplitude fatigue test results for Al 7075- T6. 106 Table 6.1 Summary of step tests results for SS304L CLI. 153 Table 6.2 Summary of step tests results for SS304L THY. 154 Table 6.3 Summary of step tests results for Al 7075-T6. 155 Table 6.4 Summary of POL tests for SS304L and Al 7075-T6. 156 Table 6.5 Comparison of H-L step tests and periodic overload tests for SS304L CLI. 157 Table 6.6 Summary of random loading test results for SS304L. 158 Table 6.7 Summary of random loading test results for Al 7075-T6. 159 Table 6.8 Table 6.9 Table 6.10 Fatigue limits for the different approaches and materials used for fatigue life predictions. Summary of fatigue life predictions under variable amplitude loading for SS304L. Summary of fatigue life predictions under variable amplitude loading for Al 7075-T6. 160 161 162 Table 7.1 Summary of crack analysis for SS304L CLI. 208 xi

Table 7.2 Summary of crack analysis results for SS304L THY. 210 Table 7.3 Summary of crack analysis results for Al 7075-T6. 211 Table 7.4 Variations in diameter due to polishing in prestrained, then polished specimens for SS304L CLI. 212 xii

List of Figures Figure 1.1 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 3.1 Crack network configuration in depth (T max = 320 C, ΔT = 150 C, N = 300,000 cycles) in stainless steel 304L [6]. Schematic of damage curve concept of summing cumulative damage in complex loading [18]. Optical micrograph showing slip bands in a fractured specimen of SUS304-HP stainless steel tested at ε a = 0.4% [41]. Optical micrographs in a fractured specimen of SUS304-HP stainless steel tested at ε a = 0.9% showing a) slip band features, b) morphologies of martensite [41]. Optical micrographs in a fractured specimen of SUS304-HP stainless steel tested at ε a = 2.0% showing: a) and b) slip band features, and c) different morphologies of martensite [41]. FATHER testing structure in some T-junctions of piping systems made of stainless steel 304L, and computed instantaneous nondimensional temperature field (time=10s) under representative loading. The test simulates how the hot fluid from the horizontal pipe does not instantaneously mix with the cold fluid from the vertical pipe [55]. Loading sequence made of 1000 instants obtained from Finite Element results of the FATHER structure in Figure 2.5 [55]. Microstructure of (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 7 32 33 33 33 34 34 47 Figure 3.2 Specimen geometry and dimensions (dimensions in mm). 48 Figure 3.3 Strain history used in prestrained tests and some H-L step tests or SS304L. 49 Figure 3.4 Hysteresis loops corresponding to the strain history in Figure 3.3. The second strain level is conducted in the presence of small mean strain (transition through zero load). 49 Figure 3.5 Stress-strain paths of the cycles subsequent to prestraining, or higher level in H-L step tests for Al 7075-T6 (paths A and B have mean strain, paths C and D have mean stress). 50 xiii

Figure 3.6 Loading history for step tests with (a) L-H, and (b) H-L sequence. 51 Figure 3.7 Figure 3.8 Figure 3.9 Loading histories for periodic overload tests for Al 7075-T6 with (a) fully tensile POL, and (b) fully compressive POL. Load histories for periodic overload tests for SS304L with (a) tension-compression POL, and (b) compression-tension POL. Representation of the Racetrack algorithm for loading spectrum simplification. 52 53 54 Figure 3.10 Part of the mockup loading history obtained from EDF. 54 Figure 3.11 Figure 3.12 Figure 3.13 Figure 4.1 Result of the racetrack algorithm conducted on the spectrum presented in Figure 3.10. Randomly generated spectrum. (a) Original spectrum, and (b) simplified spectrum. Rainflow cycle counting of the spectrum presented in Figure 3.12. (a) Reordered spectrum, and (b) results of Rainflow cycle count in terms of reversals. True stress versus true plastic strain for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 55 55 56 67 Figure 4.2 Monotonic tension experimental stress-strain curves and superimposed Ramberg-Osgood fits for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 68 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Comparison of the monotonic tension experimental stress-strain curves between SS304L CLI and THY grades. Stress amplitude versus calculated plastic strain amplitude data and fits for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075- T6. Stress amplitude versus strain amplitude for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Stress response in fully-reversed constant amplitude straincontrolled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 69 70 71 72 xiv

Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Strain response in fully-reversed constant amplitude loadcontrolled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Hysteresis loops for fully-reversed constant amplitude straincontrolled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Superimposed monotonic tension and cyclic curves for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Comparisons between cyclic stress-strain curves for SS304L CLI and THY grades. Strain history for the incremental step test on SS304L (CLI and THY). Stress response for incremental step tests for SS304L (a) CLI, and (b) THY. Superimposed stress response for incremental step tests in strain control for (a) SS304L CLI, SS304L THY, and (c) Al 7075-T6. Stress amplitude versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Calculated plastic strain amplitude versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Total, elastic, and plastic strain amplitude versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075- T6. SWT parameter versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. FS parameter versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Comparison between SS304L CLI and THY grades. (a) Strainlife curves, (b) stress-life curves, (c) SWT-life curves, and (d) FSlife curves. Strain-life curves including elastic, plastic and total strain amplitudes for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 73 74 75 76 76 77 78 107 108 109 110 111 112 113 xv

Figure 5.8 Figure 5.9 Figure 5.10 Figure 5.11 Figure 5.12 Figure 5.13 Figure 5.14 Hysteresis loops in a fully-reversed constant amplitude loadcontrolled test at 412 MPa stress amplitude for SS304L CLI. Strain response in fully-reversed constant amplitude loadcontrolled tests for SS304L CLI, (a) at 412 MPa stress amplitude, (b) at 243 MPa stress amplitude, and (c) at 210 MPa stress amplitude. Strain histories for equivalent strain-controlled tests are also plotted for comparison. Strain response in fully-reversed constant amplitude loadcontrolled tests for SS304L THY, (a) at 300 MPa stress amplitude, and (b) at 274 MPa stress amplitude. Strain histories for the equivalent strain-controlled tests are also plotted for comparison. Representation of the different R ratios used in mean strain and mean stress tests for SS304L. Stress amplitude response in mean strain, strain-controlled tests for SS304L CLI in (a) linear scale, and (b) log scale. Mean stress response in mean strain, strain-controlled tests for SS304L CLI in (a) linear scale, and (b) log scale. Stress amplitude response in mean strain, strain-controlled tests at ε a = 0.3% for SS304L THY in (a) linear scale, and (b) log scale. 114 115 116 117 118 119 120 Figure 5.15 Mean stress response in mean strain, strain-controlled tests at ε a = 0.3% for SS304L THY in (a) linear scale, and (b) log scale. 121 Figure 5.16 Figure 5.17 Figure 5.18 Figure 5.19 Figure 5.20 Mean strain and strain amplitude in mean stress load-controlled tests for SS304L CLI at 215 MPa stress amplitude in (a) linear scale, and (b) log scale. Strain-life curves including all constant amplitude data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Stress-life curves including all constant amplitude data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Stress response in tests presenting secondary hardening for (a) SS304L CLI, and (b) SS304L THY. Observation of secondary hardening in stress amplitude response for SS304L in constant amplitude fully-reversed conditions. Both failed and runout tests are represented. 122 123 124 125 126 xvi

Figure 5.21 Figure 5.22 Figure 5.23 Figure 5.24 Figure 5.25 Figure 5.26 Figure 5.27 Figure 6.1 Figure 6.2 Determination of a threshold in cumulative plastic strain in tests presenting secondary hardening for (a) SS304L CLI, and (b) SS304L THY. Cumulative plastic strain in tests conducted at strain amplitude levels where secondary hardening was observed for (a) SS304L CLI, and (b) SS304L THY. Distributions of Vickers hardness measurements across the gage section and the grip section of a SS304L CLI specimen tested at fully-reversed (CA, FR) 0.2% constant strain amplitude, and a SS304L THY specimen tested at fully-reversed 0.25% constant strain amplitude. Both specimens presented secondary hardening (SH). Results obtained from measurements in the gage section of a SS304L CLI specimen tested at fully-reversed 0.2% constant strain amplitude that did not present secondary hardening are also shown. SWT curves including all constant amplitude fatigue data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. FS curves including all constant amplitude fatigue test data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Observed versus predicted life for all constant amplitude fatigue tests of the all three materials using strain-life or stress-life approach. Observed versus predicted life for all constant amplitude tests and all three materials using (a) SWT-life curve, and (b) FS-life curve. Stress responses from strain-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Fully-reversed (FR) constant amplitude (CA) response is also shown as reference for comparison with the second step response. Strain responses in load-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Fully-reversed (FR) constant amplitude (CA) response is also shown for comparison with the second step response. 127 128 129 130 131 132 133 163 164 xvii

Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.10 Figure 6.11 Figure 6.12 Mean stress responses from strain-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Fully-reversed (FR) constant amplitude (CA) response is also represented for comparison with the second step response. Mean strain responses in load-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Fully-reversed (FR) constant amplitude (CA) response is also shown as reference for comparison with the second step response. Cycle ratio sums in step tests calculated with the LDR and strainlife or stress life curves for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Cycle ratios in step tests with strain-life or stress-life curves for (a) SS304L CLI, (b) SS304LTHY, and (c) Al 7075-T6. The line in each figure represents the LDR. Cracks observed in the gage section of failed specimens in step tests. (a) L-H (0.4%-1% strain amplitude) step test of Al 7075-T6. (b) H-L (1%-0.4% strain amplitude) step test of Al 7075-T6. (c) L-H (0.25%-1% strain amplitude) step test of SS304L CLI. (d) H- L (1%-0.25% strain amplitude) step test of SS304L CLI. The direction of loading is indicated by the double-headed arrow. Cycle ratio sums in step tests calculated with LDR and SWT curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Cycle ratios in step tests with SWT curve for (a) SS304L CLI, (b) SS304LTHY, and (c) Al 7075-T6. The line in each figure represents the LDR. Cycle ratio sums in step tests calculated with LDR and FS curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Cycle ratios in step tests with FS curve for (a) SS304L CLI, (b) SS304LTHY, and (c) Al 7075-T6. The line in each figure represents the LDR. Predicted versus remaining life in step tests, using LDR and strain-life or stress-life curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 165 166 167 168 169 170 171 172 173 174 xviii

Figure 6.13 Figure 6.14 Figure 6.15 Figure 6.16 Figure 6.17 Figure 6.18 Figure 6.19 Figure 6.20 Figure 6.21 Figure 6.22 Figure 6.23 Predicted versus remaining life in step tests for SS304L CLI using (a) LDR and SWT curve, and (b) LDR and FS curve. Predicted versus remaining life in step tests for SS304L THY using (a) LDR and SWT curve, and (b) LDR and FS curve. Predicted versus remaining life in step tests for Al 7075-T6 using (a) LDR and SWT curve, and (b) LDR and FS curve. Stress amplitude response in strain-controlled POL tests for (a) SS304L CLI, and (b) SS304L THY. Mean stress relaxation in strain-controlled POL tests for (a) SS304L CLI, and (b) SS304L THY. Strain response in load-controlled POL tests for SS304L CLI. (a) Strain amplitude response. (b) Mean strain response. Predicted versus observed number of blocks to failure for POL and random loading tests using LDR and strain-life or stress-life curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Predicted versus observed number of blocks to failure for POL and random loading tests of SS304L CLI using (a) LDR and SWT-life curve, and (b) LDR and FS-life curve. Predicted versus observed number of blocks to failure for random loading tests of SS304L THY using (a) LDR and SWT-life curve, and (b) LDR and FS-life curve. Predicted versus observed number of blocks to failure for POL and random loading tests of Al 7075-T6 using (a) LDR and SWTlife curve, and (b) LDR and FS-life curve. Random loading test deformation response for SS304L CLI. (a) Stress response in a strain-controlled test at 1% maximum strain amplitude. (b) Strain response in a load-controlled test at 245 MPa maximum stress amplitude. (c) Midlife hysteresis loops in a strain-controlled test at 1% maximum strain amplitude. (d) Midlife hysteresis loops in a load-controlled test at 245 MPa maximum stress amplitude. 176 177 178 179 180 181 182 184 184 186 187 xix

Figure 6.24 Figure 6.25 Figure 6.26 Figure 6.27 Figure 6.28 Random loading test deformation response for SS304L THY. (a) Stress response in a strain-controlled test at 1% maximum strain amplitude. (b) Strain response in a load-controlled test at 280 MPa maximum stress amplitude. (c) Midlife hysteresis loops in a strain-controlled test at 1% maximum strain amplitude. (d) Midlife hysteresis loops in a load-controlled test at 280 MPa maximum stress amplitude. Random loading test deformation response for Al 7075-T6. (a) Stress response in a strain-controlled test at 1% maximum strain amplitude. (b) Strain response in a load-controlled test at 345 MPa maximum stress amplitude. (c) Midlife hysteresis loops in a strain-controlled test at 1% maximum strain amplitude. (d) Midlife hysteresis loops in a load-controlled test at 345 MPa maximum stress amplitude. Maximum stress response in strain-controlled random loading (a) for virgin and prestrained duplicate tests at 0.3% maximum strain amplitude for SS340L CLI, and (b) for virgin and prestrained tests at 0.3% maximum strain amplitude for SS304L THY. Damage ratio sums calculated with LDR and strain-life, SWT and FS curves in random loading strain-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) and Al 7075-T6. Damage ratio sums calculated with LDR and stress-life, SWT and FS curves in random loading load-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. 188 189 190 191 192 Figure 7.1 Reference area for crack analysis. 213 Figure 7.2 Bending resulting from uneven loading conditions due to the presence of a macrocrack. 213 Figure 7.3 Crack reference types for SS304L. 214 Figure 7.4 Crack reference types for Al 7075-T6. 215 Figure 7.5 Specimen surface after prestraining (10 cycles at 2% strain amplitude) shown on left, and after prestraining and then polishing shown on right. 216 xx

Figure 7.6 Figure 7.7 Crack evolution in a prestrained (10 cycles at 2% strain amplitude) then polished SS304L CLI specimen cycled in load control at 412 MPa, with N f 1470 cycles. The last two photos were taken in different sections of the specimens at failure. Evolution of cracks marked 1 and 2 in the first picture was followed throughout life. Displacement amplitude and crack length versus normalized life for a prestrained (10 cycles at 2% strain amplitude) and then polished SS304L CLI specimen in load control with 412 MPa stress amplitude. Crack growth is represented for the two cracks indicated in Figure 7.6. 217 218 Figure 7.8 Evolution of microcracks on the surface of a prestrained (10 cycles at 2% strain amplitude) SS304L CLI specimen cycled at 412 MPa in load control, with N f 2080 cycles. Polishing was conducted after prestraining, and successively every 200 cycles. The photos were taken before polishing. The last photo was taken at failure. 219 Figure 7.9 Figure 7.10 Stress response for virgin, prestrained (10 cycles at 2% strain amplitude) and then polished specimens of SS304L CLI cycled in strain control at 0.25% strain amplitude. Cracks observed in the gage section of failed SS304L CLI specimens in strain-controlled step tests for (a) a L-H (0.25%-1% strain amplitudes) test, and (b) a H-L (1%-0.25% strain amplitudes) test. 220 221 Figure 7.11 Cracks observed in the gage section of failed Al 7075-T6 specimens in strain-controlled step tests for (a) a L-H (0.4%-1% strain amplitudes) test, and (b) a H-L (1%-0.4% strain amplitudes) test. 221 xxi

List of Nomenclature a crack length a t A 0 A f b c C D D min e transitional crack length original cross section area cross section area at fracture fatigue strength exponent fatigue ductility exponent material parameter damage ratio minimum specimen diameter engineering strain E, E' monotonic, midlife cycle modulus of elasticity % EL percent elongation k material constant K monotonic strength coefficient K' cyclic strength coefficient n number of cycles applied, monotonic strain hardening exponent n' cyclic strain hardening exponent n i N N f 2N f P f R number of cycles at stress amplitude σ i number of cycles number of cycles to failure number of reversals to failure load at fracture radius of curvature of neck % RA percent reduction in area R ε R σ S S y S y ' S u strain ratio stress ratio engineering stress monotonic yield strength cyclic yield strength ultimate tensile strength xxii

β Δε Δε e Δε p Δγ max /2 Δσ ε ε a ε e ε f ε f ' ε m ε max ε min ε p ν e ν p σ σ a σ f σ f ' σ i σ m σ max σ min σ n, max σ n, a σ n, m ø material constant true strain range elastic strain range plastic strain range maximum shear strain amplitude true stress range true strain strain amplitude true elastic strain true fracture ductility fatigue ductility coefficient true mean strain true maximum strain true minimum strain true plastic strain elastic Poisson ratio plastic Poisson ratio true stress true stress amplitude true fracture strength fatigue strength coefficient stress amplitude level for n i cycles true mean stress true maximum stress true minimum stress maximum normal stress alternating normal stress mean normal stress specimen diameter xxiii

List of Abbreviations bcc CA CLI DLDR EDF fcc FR FS HCF hcp HV H-L IOS LC LCF LDR L-H NF OL PS PSB POL SC SEM SFE S-N SS SWT TEM THY V εc body-centered cubic constant amplitude Creuset-Loire Industries double linear damage rule électricité de France face-centered cubic fully-reversed Fatemi-Socie parameter high cycle fatigue hexagonal-closed packed Vickers hardness high-low initial overstrain load-controlled low cycle fatigue linear damage rule low-high no failure overload prestrain persistent slip bands periodic overload small cycles (as opposed to OL in POL tests) scanning electron microscopy stacking fault energy stress-life stainless steel Smith-Watson-Topper parameter transmission electronic microscopy Thyssen virgin material strain-controlled xxiv

Chapter One Introduction From human bodies to concrete buildings, materials are subjected to cyclic loading. Consequently, fatigue failure is one of the most common types of failure and it must be taken into consideration in design of many structures and components. Fatigue properties can be determined through basic fatigue testing, and models can be used to approximate the behavior of the material under the condition of use. Rules are usually conservative, in order to increase factors of safety. This can be non-economical and high safety factors cannot be used in certain applications. For instance, an airplane would never take off the ground if high factors of safety were used in its design. Furthermore, the majority of components are not subjected to constant amplitude loading. Most loading histories are complex, and can involve variable amplitude loading. An option to evaluate the behavior of a component or structure under such conditions consists of testing under actual conditions. Although this remains the most reliable means to obtain the response of a component or structure under complex loading, testing can be very costly and time consuming. In addition, optimization by testing is usually not a viable solution, as any modification of component geometry, material or loading history has to be followed by a new set of testing. The size and cost of some structure also render testing at all steps of the design conception impossible. In contrast, a model can be computed as many times as required, making the optimization process more readily achievable. Testing can then be 1

2 limited to the final component or structure as a verification method, rather than a design and development method. In order to optimize the replacement of parts of (or whole) components and structures subjected to variable amplitude loading, accurate life prediction models under these types of loading are required. Constitutive models are also important, as will be presented in Chapter 2. However, fatigue life predictions cannot be made from deformation behavior alone. A reliable damage quantification parameter and a cumulative damage rule, along with constant amplitude material fatigue behavior are needed for life predictions. 1.1 Background and Significance Stainless steel 304 is used in many applications, from aeronautical components and structures [1] to pressure vessels [2], and nuclear power plants [3]. In this latter application, it is a constituent of the cooling system, referred to as Residual Heat Removal System (RHRS). Due to water turbulent flow and thermal fluctuations, the type of loading encountered is often variable amplitude loading, with overstresses followed by lower amplitude loading. Even though the highest temperatures are not extreme (as compared to the melting temperature or processing temperatures of the stainless steel), thermal fluctuations can result in microcracks [4, 5]. These microcracks develop into shallow crack networks, as shown in Figure 1.1 [6] and can propagate until leakage occurs [3]. This phenomenon is known as crazing. As thermo-mechanical fatigue and mechanical fatigue are closely related [5], only mechanical fatigue was studied here, as it is more readily implemented.

3 There is a strong need for an accurate and reliable damage accumulation model in order to evaluate this phenomenon. To develop this model, the deformation history effect on subsequent loading and fatigue behaviors in presence or absence of mean stress must be considered on different materials. Overloads and load sequence interactions should also be analyzed. One type of material, such as aluminum alloys, may exhibit little or no load history effect, whereas the behavior of another one, such as austenitic stainless steel, may significantly depend on its loading history. Results will permit to determine whether deformation history effect and fatigue behaviors can be related and determine the required characteristics of a reliable life prediction model. 1.2 Objective and Outline Chapter 2 discusses the implication of load sequencing and interaction effects on many components and structures. Particularly, the literature review focuses on variable amplitude loading and deformation history effect in service loading of the cooling systems of nuclear power plants. For some components of these systems, the formation of crack networks has been observed in the mixing zones, where the thermo-mechanical loading due to temperature gradients is especially large. In addition, the importance of damage accumulation rules is presented, focusing on previous works conducted on stainless steel. Some insights of the mechanisms occurring during deformation and fatigue of this material are also given. Different parameters influencing fatigue life are introduced, including mean stress and prestraining. The importance of the relations that can exist between deformation and fatigue behaviors are discussed as well. The overall goals of this project were to investigate the deformation history effect of two types of materials, and to evaluate the influence of prestraining, mean stress and

4 variable amplitude loading on deformation and cumulative fatigue damage behavior. With respect to deformation history effect, different types of materials can be defined. This includes materials with very little or no deformation history effect such as aluminum 7075-T6, materials with relatively small deformation history effect such as medium carbon steels, and materials with strong deformation history effect such as austenitic stainless steels. In order to determine the required characteristics of a reliable life prediction model under complex loading, the deformation history effect on subsequent loading and fatigue behavior must be considered. Deformation or load history effect of a material on subsequent cyclic loading depends on the degree of cyclic hardening of the material. This in turn depends on how easy the dislocations can cross slip. The easier the cross slip, the less dependence of the deformation behavior on loading history. For fcc metals, the ease of cross slip depends on the stacking fault energy (SFE) of the material. In fcc metals with low SFE such as austenitic stainless steels planar slip occurs readily and the deformation behavior greatly depends on the loading history. In contrast, fcc metals with high SFE, such as aluminum alloys, are more easily able to cross slip during cyclic loading, and their deformation behavior is relatively independent of prior loading history. Because aluminum 7075-T6 (Al 7075-T6) and stainless steel 304L (SS304L) present extreme cases with respect to deformation history dependence, these two materials were chosen to investigate the influence of the deformation behavior on fatigue life and assess the applicability of appropriate fatigue life prediction parameters under variable amplitude loading conditions. As the composition of the stainless steel 304L used in RHRS can vary, two grades of SS304L, obtained from Creusot Loire Industrie

5 (CLI) and Thyssen (THY) were used in the experimental program. This also allowed to study variations in deformation and fatigue behaviors between grades, and to relate differences to the composition of the materials. Experimental program and testing procedures are presented in Chapter 3. In Chapter 4, differences between the two materials, in terms of deformation history sensitivity are assessed. Aluminum 7075-T6 presents a cyclic curve with very little softening or hardening. It is expected to have fairly linear damage accumulation behavior with respect to variable amplitude loading, i.e. the linear damage rule (LDR) can be applied to predict its fatigue life. Also, prestraining and overloading are not expected to have significant effect on its deformation or fatigue behavior. In contrast, stainless steel 304L presents a cyclic curve with significant hardening and its deformation behavior is shown to be significantly altered by prior loading. This raises the question whether these differences in deformation behavior can be related to and influence fatigue behavior. Experimental results under constant amplitude loading, including mean strain or stress and prestraining effects under different control modes are discussed in Chapter 5. Secondary hardening characterized by a strong cyclic hardening associated with continued cycling in high cycle fatigue (HCF) and an extension in fatigue life observed for SS304L is also presented in Chapter 5. Influence of loading sequence in step tests, periodic overload tests, and under random loading conditions are presented in Chapter 6. The applicability of the commonly used linear damage rule is assessed for both materials and the influence of deformation history effect on fatigue behavior is evaluated. For damage accumulation under variable amplitude loading, the LDR associated with

6 strain-life (ε-n) or stress-life (S-N) curves can lead to inaccurate fatigue life predictions, especially for materials presenting strong deformation memory effect, such as SS304L. The inadequacy of this method is typically attributed to the LDR itself. On the contrary, this study demonstrates that damage accumulation using the LDR can be accurate, provided that the LDR is used in conjunction with parameters including both stress and strain terms. By including both loading history and response of the material in damage quantification, shortcomings of the commonly used linear damage rule approach can be circumvented in an effective manner. Parameters including both stress and strain terms, such as the Smith-Watson-Topper and Fatemi-Socie parameters, are shown to correlate all fatigue test data fairly accurately. Analysis of cracking behavior under various loading conditions and results on microcrack initiation and propagation are presented in Chapter 7, in relation to deformation and fatigue behaviors of the materials. Finally, main results and conclusions are gathered in Chapter 8.

Figure 1.1 Crack network configuration in depth (T max = 320 C, ΔT = 150 C, N = 300,000 cycles) in stainless steel 304L [6]. 7

Chapter Two Literature Review 2.1 Introduction Most components are subjected to cyclic loading. The loading is often variable amplitude with multiple overloads and with the presence of mean stress. Machining and treatments, such as shot-peening and welding, can also induce prehardening and residual stresses. To accurately predict fatigue life under these conditions, it is important to first understand the deformation behavior of material and its prior loading history effect. Different models have been proposed to represent the effect of variable amplitude loading on deformation behavior, and rules have been developed for damage accumulation under this type of loading. In addition, to understand the mechanisms of the damage occurring in materials, microstructure analysis can be used, since some materials such as stainless steel undergo considerable structural alterations under cyclic loading [7, 8]. Fatigue life can also greatly be affected by environment. It is decreased in corrosive environment, or water. In particular, the behavior of stainless steel is altered by moisture [2] as the strain-life curve is significantly lowered in water. However, thermal conditions and corrosive environments will not be considered here. This literature review will be more focused on stainless steel than on aluminum, as the deformation behavior of stainless steel is more easily altered by overloading and it is the main material under investigation here. 8

9 2.2 Cumulative Damage The term cumulative damage refers to the fatigue effects of loading events other than constant amplitude cycles [9]. Cumulative damage does not refer to fatigue properties only. Significant damage can be caused by events that do not consume a considerable amount of fatigue life by themselves. For instance, overloads can induce hardening and exhaust the ductility of the material. Although, they do not represent significant damage by themselves, their presence greatly affects the subsequent deformation and fatigue behaviors of the material. Therefore, their effects must be taken into account to achieve accurate fatigue life predictions. In fatigue, damage is most commonly defined as a fraction of life or cycle ratio (n/n f ) that is taken away. It is important to note that the same damage fraction at some point of the history can induce different results than it would at another time of the loading history [10, 11]. For instance, a block of low amplitude loading will have barely any effect if no crack is present in a structure, as it will not cause crack initiation. In contrast, the same block applied after a higher level amplitude block may cause growth of a crack that has already formed and could lead to fracture. This was confirmed for stainless steel 304L in a study of damage accumulation tests by Lehéricy and Mendez [12]. Therefore, in considering cumulative damage it is also important to evaluate load sequence effects. Quantification of fatigue damage can be done by several means: metallurgical, physical and mechanical [13]. The metallurgical method involves the observation of the number of dislocations and slip bands that represent the physical aspect of the damage. The mechanical approach studies the influence of the damage on mechanical parameters such as strain, stress, stiffness or hardness. This process can also be related to fracture

10 mechanics if crack nucleation and growth are considered separately. The physical approach includes magnetic, optical acoustic, and X-ray diffraction analyses to measure density, electrical, magnetic, and thermal properties of the material [13]. All these means can be combined to evaluate damage occurring in the material under cyclic loading. Some properties can even be measured during loading to follow the evolution of the material behavior and evaluate the damage in real time. Magnetization can, for example, be used to evaluate martensitic formation, and assess the relationship between phase transformation, hardening behavior, and damage accumulation of stainless steel under cyclic loading [14], as is explained in Section 2.3.1. Although physical and metallurgical means can be used, the most readily available parameters during fatigue testing are mechanical. Thus, load drop due to stiffness loss because of cracking, or measure of the change in elastic modulus [11] is commonly used. Evaluation of the damage is certainly essential in order to predict fatigue lives. However, damage caused must be related to the applied loading in order to develop any model. 2.2.1 Rainflow cycle counting method An important aspect of the loading history is the number of applied cycles. It is necessary to use a standardized and reproducible cycle counting method to evaluate the number of load cycles applied to a specimen or component in order to accurately account for damage and predict its behavior. ASTM standard E1049 [15] defines proper methods to be used for cycle counting in fatigue analysis for variable amplitude loading. When the loading varies, it is sometimes difficult to evaluate the exact number of cycles applied to the component. Also, a given level of stress or strain amplitude can lead

11 to fracture when comprised in a certain type of loading sequence, and be hardly damageable when included in another type of loading sequence. Therefore, the cycle counting method used should also take into account low amplitude cycle in certain type of loading sequence. First proposed by Matsuishi and Endo [16], the Rainflow Cycle Counting Method, which is the most commonly used cycle counting method, is based on the decomposition of the loading sequence into peaks and valleys. The number of cycles, the amplitude and the mean of the applied strain or stress can be computed, and damages from the loading sequence can be accounted for. As this process can become very fastidious for a large number of cycles, computer programs can be used. Other cycle counting methods also exist and most of them can be integrated to software to facilitate the process. They will not be detailed here, with an exception for the racetrack algorithm that will be briefly mentioned and explained in Chapter 3. The reader can refer to [9] for further information on cycle counting methods. 2.2.2 Linear Damage Rule (LDR) One of the first and still most widely used cumulative damage theories is the Palmgren-Miner Linear Damage Rule (referred to as LDR or Miner s rule) [9]. It is presented by the following equation: i n N i f i D (2.1) where D is the damage, n i the number of cycles applied to the specimen or component at a certain amplitude, and N fi the expected life at this amplitude. Failure is expected to occur when the sum of the ratios is equal to unity. The Linear Damage Rule does not take into account any sequence or load history effect, and it considers damage accumulation to

12 follow a linear path. In addition, it does not distinguish between crack initiation and growth phases. This may be a problem when different load sequences are applied. In step tests, for instance, whether the sequence is low-high (L-H) or high-low (H-L) may change the outcome of the test, and usually the latter case leads to shorter lives [10, 11, 13, 17]. As it will be presented in Section 2.2.4, microcracks can initiate in smooth specimens subjected to cyclic loading. For H-L step tests, microcracks that have formed during the higher level can grow during the lower level. In contrast, for L-H sequences microcracks initiation is limited during the first step. Thus, the number of cracks and their length may be different depending on the sequence of loading. Although the LDR presents some shortcomings, it is still widely used because of its simplicity and ease of implementation. In addition, none of the many nonlinear damage rules proposed over the last several decades have proved to be robust and applicable to a wide range of loading conditions and/or materials [17]. Moreover, the application of LDR does not require any parameters, which makes this rule practical. To account for the shortcomings of the LDR, some researchers have tried to modify it, while keeping its simplicity. A modified version of the linear damage rule, known as the double linear damage rule, has been proposed by Manson and Halford to take into account different phases of damage development. These two phases can be crack initiation and growth phases, or they can represent different levels of loading [18]. This method is equivalent to using a bilinear fit on the damage curves. Damage curves are usually power laws of the form: N f α n D (2.2)

13 where α is a function of N f [10]. For complex loading, computation of the cumulative damage through damage curves can be inaccurate, due to the miscounting of cycle ratio in the transition from one curve to the other, as shown in Figure 2.1 [18]. Therefore, Manson and Halford developed a double linear damage rule (DLDR) by analytically replacing damage interaction by two straight lines. The knee point coordinates are represented by: n N 1 1 knee A N N 1 2 β (2.3) n N 2 2 knee B N N 1 2 β (2.4) Details on how to obtain the different parameters A, B and β, and determine the kneepoint can be found in [18]. Manson and Halford proposed the DLDR to account for loading sequence effects. After applying it to four different types of alloys, they concluded that the DLDR will give more accurate and conservative life prediction than the LDR. There exists a great number of damage rules [13, 17], some very simple and some very complex. As any rule has its own shortcomings, and some rules are developed and intended for particular materials and/or loading conditions, the LDR along with Rainflow cycle counting method are still universally and most commonly used. 2.2.3 Other cumulative damage models A large number of cumulative damage models have been proposed since the development of the LDR. Different approaches have been used, such as damage lines [10, 11]. This literature review does not intend to give an exhaustive list of cumulative

14 damage models that exist. For a detailed review of cumulative damage models, the reader can refer to [17]. Several researchers used lines of damage to predict fatigue lives. One of the first work was done by Richart and Newmark [10], who used an S-N approach, and introduced the idea of lines of equal damage, after French [19] who talked about probable damage lines. However, Richart and Newmark related the damage to cycle ratio and stress level, and implemented a graphical method for life predictions. Although results were promising for two-stress level tests, this method can be difficult and tedious to apply to multi-stress level tests. Later, Brook and Parry [11] tried to predict the remaining life of stainless steel (Rex 535 that would now be close to SS316) after a given number of cycles and compared it with the actual remaining life using damage lines. They generated reference damage curves, using the changes of apparent dynamic modulus and damping energy (work) over the life of the material. Using these reference curves to estimate remaining lives, Brook and Parry then generated lines of equal damage from testing at different stress levels. The lines of equal damage, represented as stress amplitude versus remaining life could finally be used for fatigue life prediction in multi-stress step tests. Brook and Parry suggested that failure would occur when a given energy has been accumulated in the material. They also stated that because the lines of equal damage are independent of the loading sequence, they permitted to predict remaining lives or lives at multi-stress levels more accurately than the LDR. Although their prediction was fairly close to experimental lives observed in multi-stress level tests, this method is very costly. A great number of tests had to be conducted to develop the lines of equal damage, and those lines

15 were specific to given stress levels (they must be extrapolated for other levels) and materials. In addition, Brook and Parry concluded that experimental lives for this material presented so much scatter that it was safer to monitor the extent of damage of each specimen in order to very accurately predict failure. Also, as Richart and Newmark had done, they used a stress-life approach. As the behavior of stainless steel with respect to overloads is quite different in strain or load-controlled conditions [20], a stress-life approach, or a strain-life approach alone might not be accurate enough to estimate the damage accumulation for this type of material. Overloads induce hardening in materials such as stainless steel 304L. Under strain-controlled conditions, the stress amplitude is increased by the overload, its value after the overload being greater than it was before. In contrast, under load-controlled conditions, the strain amplitude response is lowered by the presence of an overload. Since load sequence effects can significantly affect fatigue damage accumulation in a deformation history sensitive material, a damage quantification parameter which includes both stress and strain terms can be used. In this way, both the applied load and materials response influence damage. Such parameter is the Smith-Watson-Topper (SWT) parameter [21]. This parameter takes into account both stress and strain amplitudes, and also accounts for mean stress effects. Therefore, it can estimate damage more accurately for materials with strong deformation history dependence, such as stainless steel 304L. Another parameter, which uses both stress and strain terms, and can also account for mean stress effect, is the Fatemi-Socie (FS) critical plane parameter for multiaxial fatigue [22]. Although the data presented in this study are for uniaxial loading, this parameter

16 was used for comparison with the SWT parameter. Both parameters are presented in Chapter 5. Similarly, Jono stated that due to load sequence effects, fatigue life predictions based on the stress-life curve can be difficult [23]. Therefore, using the LDR expressed in terms of plastic strain range-pair for five types of materials under random loading, he obtained relatively accurate fatigue life predictions. Plasticity is a crucial aspect of fatigue damage [24] and accumulated plastic strain is an important factor to be considered in damage accumulation modeling. When using both stress and strain terms, the plasticity behavior of the material is indirectly taken into account. 2.2.4 Crack initiation versus crack growth in damage accumulation For fatigue testing of smooth specimens under fully-reversed constant amplitude loading, crack initiation is usually used as a failure criterion, where the presence of a crack is associated with a load drop in strain control, or a change in the specimen stiffness [25]. Here, crack initiation life refers to the life associated with crack nucleation and microcrack growth on the order of one millimeter. For this type of testing, crack initiation usually constitutes the main part of fatigue life. For ductile materials, such as stainless steel 304L, the fatigue strength is unaffected when the length of the crack remains below the grain size [12]. Although fatigue life is often reduced to crack initiation in smooth specimens, very small cracks (below the grain size) can be present before any alterations in the overall mechanical properties (such as change in stiffness or load drop) are detectable. Golos and Ellyin [26] observed that in H-L step tests of ASTM A-516 carbon steel, when a significant portion of life is spent at higher amplitude, cracks initiate and sufficiently grow to permit continuous crack growth at lower strain

17 amplitude. They also noted that for high strain amplitude of the first step only a small portion of life can be attributed to crack initiation. Murakami and Miller investigated the relationship between microcracks and fatigue damage, for a medium carbon steel in low cycle fatigue (LCF) [27]. Using loss of fracture ductility as a mean to evaluate damage, they concluded that it is directly related to the presence of small surface cracks in LCF. They also stated that the LCF process in plain specimens was nearly entirely dominated by the growth of a single dominant crack that initiated during the first few stress cycles. They postulated that prior fatigue history has little or no effect on fatigue damage or subsequent microcrack growth, once the cracks have reached a certain length (of 400 μm for the medium carbon steel). Murakami and Miller attribute the cause of the loss of fracture ductility during LCF to the presence of small surface cracks of a critical length, which was found to be 0.4 mm for 70/30 brass. Pompetzki et al. showed that crack closure and fatigue damage following overloads for small cracks in smooth specimens is similar to the behavior of crack growth rates under similar conditions for long cracks in large specimens [28]. They also postulated that crack growth retardation can occur in smooth specimens, due to periodic overloads, when they are applied sporadically [28]. Vormwald and Seeger [29] investigated crack closure under variable amplitude loading for smooth specimens. They concluded that large cycles in variable amplitude loading were followed by an instantaneous drop in opening stress and strain of small surface cracks, and that a great number of small cycles was necessary to increase crack opening strains and stresses. Although crack initiation and growth phenomena vary

18 depending on the material, the growth of small cracks is generally involved under variable amplitude loading, even in smooth specimens. Therefore, growth of microcracks can represent a considerable part of the fatigue life under variable amplitude loading. Some models have been proposed that consider crack growth under variable amplitude loading [23, 30, 31]. For instance, the LDR can be modified to be used for crack growth under variable amplitude loading. However, linear rules are not recommended when crack closure can occur [32]. Obrtlik et al. studied the evolution of crack in stainless steel 316L notched specimens [30]. They showed that crack propagation rate can be separated into two phases. In the first phase the crack propagates at a constant rate, whereas in the second phase, the crack propagation rate increases linearly with increasing crack length. Orbtlik and co-workers determined that separation between the two phases occurs at the transitional crack length, a t, that is dependent on the plastic strain amplitude. Other researchers have confirmed that the kinetics of crack growth in LCF domain is controlled by plastic strain amplitude and crack length, a, for stainless steel 304L as well [12]: d a d N C Δε p 2 β a (2.5) Lehericy and Mendez [12] also showed that preliminary damage (caused by precycling) will greatly affect fatigue strength and endurance limit at HCF, if the maximum surface crack length extends over several grains. Otherwise, effects of precycling on subsequent fatigue strength are limited. In austenitic stainless steels, crack growth can also be affected by microstructural alterations. Khan and Ahmed [33] studied crack growth of single-edge notched stainless

19 steel specimens under variable amplitude loading and concluded that two mechanisms may occur. The first one is beneficial and due to martensitic transformation (described in Section 2.3.1) that induces an increase in the specific volume and creates compressive residual stresses at the tip of the crack, hence limiting crack growth. The other phenomenon is the reduction in ductility due to the hardening produced by martensitic transformation that is detrimental since it allows faster crack propagation. The relative contribution of these two phenomena is dependent on the strain amplitude applied [33]. 2.3 Deformation-Fatigue Relationship 2.3.1 Mechanisms involved in deformation and fatigue of stainless steel Under cyclic loading, materials usually exhibit cyclic softening or hardening [9]. Additional softening or hardening may occur during multi-stress level tests, due to rearrangement and modification of the behavior of slip bands involved in fatigue damage mechanisms. Planar slip face-centered cubic metals, such as austenitic stainless steel, and body-centered cubic alloys present a deformation behavior that highly depends on the loading history, whereas the behavior of wavy slip face-centered cubic metals, such as aluminum, is very little altered by previous loading [13]. In austenitic stainless steel, the γ austenite matrix is face-centered cubic (fcc). As the stacking fault energy (SFE) is low, planar slip occurs readily and the deformation behavior of stainless steel greatly depends on the loading history. Some austenitic stainless steels are also metastable at room temperature [34]. Phase transformation in austenitic stainless steel can lead to the formation of α, and ε martensite that have a body-centered cubic, and a hexagonal-closed packed structure

20 (hcp), respectively [34]. Mangonon and Thomas showed that the martensitic transformation follows the sequence γ ε α, where the ε hcp phase is thermodynamically stable with respect to the two other phases [35]. Mangonon and Thomas also observed that the intersections of ε bands serve as a nucleation site for the formation of the α phase. Plasticity and deformation behavior of stainless steel have been studied extensively over the past decades. One of the main characteristics of stainless steel is its strong hardening behavior under cyclic loading. Hardening under monotonic or cyclic loading in austenitic stainless steel has been related to stress or strain-induced austenite to martensite phase transformation. Angel [36] stated that the martensitic transformation does not imply diffusion of atoms, since the compositions of the two phases are the same. He postulated that the transformation occurs by a process of nucleation and growth. As it had been suggested by previous researchers, Angel confirmed that nuclei are already present in the system since screw dislocations act as nuclei, and that the energy that must be released for the phase transformation to happen constitutes the main controlling factor. Shrinivas et al. later confirmed that in stress-induced transformation, it is the increase in energy that permits the transformation [37]. Angel demonstrated that two processes, martensite formation and slip process, are coexisting when stainless steel is subjected to stresses. Depending on the importance of the resistance to slip, the martensite transformation will occur, more or less easily. For instance, at higher temperatures, martensite formation occurs to a lesser extent and the slip process occurs more readily. Angel concluded that formation of martensite is a function of stress, plastic strain and deformation energy [36]. However, Maxwell and coauthors later suggested that, in

21 austenitic 18/8 (304) stainless steels, lathlike strain-induced martensite forms due to plastic deformation, and that it differs from the stress-induced plate martensite that forms in Fe-Ni-C alloys [38]. Shrinivas and co-workers mentioned that transformation from austenite to martensite can also happen because of heat treatment, forming body-centered tetragonal martensite. The martensitic transformation leading to the formation of bcc or hcp martensites is, however, directly related to plastic deformation [37]. Hardening related to austenite to martensite phase transformation is especially important at LCF, where plastic deformation is significant [39, 40]. While stress-induced transformation is energy related, the mechanisms involved in strain-induced transformation are more complex, and can be strain-rate dependent under certain conditions [2]. Baudry and Pineau demonstrated that martensitic transformation occurs at a greater extent at higher strain amplitude [39]. Martensitic formation could also be a function of time/cycle during which a certain amount of plastic strain is applied. To take into account this parameter, Baudry and Pineau suggested the use of the cumulative strain (NΔε p ). The dislocation structure in stainless steel is also dependent on the level of strain amplitude [39, 41]. Ye and co-workers [41] studied the evolution of the microstructure of stainless steel 304 under increasing strain amplitude, and observed that: 1) at low strain amplitude, dislocation arrays are mainly planar and slip planes are mostly limited to a single grain, 2) at intermediate strain amplitude, cells start to develop as a result of interactions between dislocations of different slip systems, and 3) at high strain amplitude, cellular structure is fully developed. Associated to the development of cells, and similar to the mechanisms occurring under monotonic tension loading, at high plastic

22 strain amplitude, the density of shear bands is continuously increased under cyclic loading, and both tensile and compressive parts of the loading contribute to this phenomenon [39]. In contrast, at lower strain amplitude, Baudry and Pineau observed that the density of shear bands and thus the number of nucleation sites is more limited and martensitic transformation occurs to a lesser extent before failure. They also showed that the transition between the two states depends on the stability of the material [39]. Ye and co-workers [41], using their experimental results on stainless steel SUS304-HP, stated that two mechanisms are in concurrence under cyclic loading. These are softening because of the microstructure rearrangements (formation of cells and subgrains) and hardening due to martensitic formation. They suggested that at low strain amplitude, the first mechanism is prevalent, whereas at high strain amplitude, martensitic formation, thus hardening is more important, as can be seen from Figures 2.2 to 2.4. In these photos, significant differences in microstructure can be observed, related to the level of strain amplitude applied. Martensite is not significantly present for a test conducted at 0.4% strain amplitude (S y = 275 MPa for this material), however, the density of martensite phase increases with increasing strain amplitude [41]. This is in agreement with Baudry and Pineau [39], who observed the existence of a critical plastic strain necessary to induce martensite formation. Study of the magnetization of stainless steel under cyclic loading by Takahashi et al. confirmed that martensitic formation occurs only after a critical stress/strain value has been reached [14]. Takahashi and co-workers concluded that increasing plastic strain amplitude induces a multiplication of the number of dislocations, leading to a greater number of slip systems and the apparition of glide planes and band structure of

23 dislocations. The presence of many shear bands makes the development of numerous martensite nucleation sites readily possible. The number of shear bands also increases with increasing number of cycles. Therefore, at low strain amplitude, martensite transformation could occur after a considerable number of cycles, and could possibly explain the secondary hardening sometimes observed at HCF in stainless steel 304L [42]. This phenomenon is discussed in further details in Chapter 5. Some differences can exist between different types of stainless steel. Lebedev and Kosarchuk stated that martensitic transformation is dependent on stainless steel composition, stacking fault energy and temperature [34]. The chemical elements influencing this transformation the most are nickel, chromium, and carbon, and the stability of the austenite with respect to martensitic transformation can be evaluated using the nickel equivalence [34]: Ni eq = %Ni + 0.65%Cr + 0.98%Mo + 1.05%Mn + 0.35%Si + 12.6%C (2.6) The lower the nickel equivalence, the more metastable the alloy. Nickel is usually used to improve the stability of the γ austenite because it stabilizes the fcc structure at room temperature [43]. In addition to temperature and composition of the alloy, other factors can influence the austenite to martensite phase transformation. For instance, during working, precipitation of chromium carbide decreases the amount of carbon and chromium in the solid solution, leading to a less stable austenite phase [40]. Laser-shock peening and deep rolling by inducing dislocation rearrangements can also influence martensitic transformation [44]. Thus, in addition to residual mean stresses, these processes can

produce a modification of the microstructure on surface, and affect fatigue life more significantly than intended to. 24 2.3.2 Deformation and ductility Under variable amplitude loading, overloads can alter the deformation behavior of materials, especially for materials with strong deformation history dependence. For instance, and as it is explained in the next section, prestraining or overloading can induce hardening in stainless steel. This hardening decreases the ductility of the material and can significantly alter fatigue life [45]. Although prestraining itself also produces damage, the subsequent reduced ductility is an important factor to consider. Another deformation-related process that can affect fatigue life is ratcheting. It occurs when the plastic deformation upon loading is not followed by an equal amount of yielding upon unloading. It can be detrimental to fatigue life as it can facilitate buckling in the compressive strain directions, or exhaustion of the ductility in the tensile strain direction [46]. Ratcheting, or cyclic creep, usually occurs under load-controlled conditions in presence of mean stress and was observed for stainless steel at room temperature [47] and at 288 C [48]. Kang et al. [49] studied ratcheting of stainless steel 304 under load-controlled and strain-controlled conditions, at different mean stress levels, and observed that, under load control, the amount of ratcheting increases with increasing mean stress. They also mentioned that the effects of the amplitude of stress on ratcheting are relatively more important than the effects of mean stress in load control [49]. Therefore, maximum stress can be considered in order to evaluate ratcheting behavior, as it will be presented in Chapter 5. For mean strain tests in strain control, Kang and co-

25 workers noted that the stress amplitude response is affected by the increase in mean strain, whereas the cyclic hardening/softening of the specimen is not altered. Due to complex alteration occurring in stainless steel under monotonic or cyclic loading, constitutive models exist to predict the deformation behavior of the material. For instance, Chaboche et al. [50] introduced a new internal variable to be included in constitutive equations, to overcome the shortcomings of classical plasticity formulations that only allowed cyclic hardening description through the cumulated plastic strain. The cumulated plastic strain in classical plasticity formulations could not account for the effects of previous plastic strain amplitude and strain history effect [50]. Using the new internal variable, they modeled the strain history effect on cyclic hardening of stainless steel 316 fairly accurately. More recently, Chaboche and Nouailhas proposed a unified constitutive model for cyclic viscoplasticity specific to stainless steels [51]. This latter model was used by Haddar and Fissolo [3] when they proposed a model that takes into account elasto-plastic (with Chaboche s model) and crack propagation behaviors, crack shielding and thermal gradient (loading) to model crazing in cooling systems of nuclear power plants. Crazing is a fatigue and fracture mechanics related phenomenon with unusual crack growth patterns, with plasticity being an important part of the process. 2.4 Loading Parameters Influencing Deformation and Fatigue Life Behaviors 2.4.1 Service loading Service loading of stainless steels 304 and 316, often used in pressure vessels applications, usually implies thermal loading. Thermal fatigue causes the formation of

26 crack networks that can develop until leakage occurs [3, 52]. Focus on crack networks propagation in piping systems made of stainless steel can also be found in [53] and [54]. Haddar and Fissolo [3] simulated the service loading of stainless steel 304L by analysis of a parallelepipedic specimen continuously heated and subjected to cyclic thermal shocks. This reflects the type of service loading found in the cooling system of nuclear power plants, specifically in the hot and cold water mixing zones. Thermal cycles encountered at the T-junction of RHRS are presented in Figure 2.5 [55]. Haddar and Fissolo [3] observed initiation of cracks and formation of crack networks due to temperature gradients occurring across the wall thickness. These temperature gradients constitute the source of thermo-mechanical fatigue as they induce significant stress variations in the material. Similar analysis was also performed by Maillot et al. [52]. From damage analysis of mockup structures of similar components, times to crack initiation under complex thermal, mechanical, and thermo-mechanical conditions were computed. They used finite element analysis, a constitutive plasticity model, and a two scale damage model proposed by Desmorat et al. [55] in their analysis. The service loading spectrum in this latter study contains frequent overloads with presence of mean stress and is presented in Figure 2.6 [55]. These events can have a substantial influence on the deformation and fatigue behaviors of a material. As a result of complex loading, cracking has been observed near the weld tips in addition to far from the welds [52, 56] in RHRS. 2.4.2 Overloads and load sequence effects One of the aspects of variable amplitude loading is the presence of overloads. In design, their effect must be taken into account from both deformation and fatigue points

27 of view. One of the types of overloads encountered is preloading. For austenitic stainless steels 316 and 304, preloading leads to hardening of the material. Lieurade and coworkers studied the effect of step tests on fully-annealed and prehardened stainless steel 316L [57]. They observed a strong deformation history effect in both cases that induces modification of the stress amplitude response. This effect was more significant when the difference between the two levels of strain amplitude was greater and the number of cycles applied at the highest level was larger. Through microstructural observations, the authors concluded that structural changes can occur quickly and the material will retain the structure induced by the highest amplitude level. For a H-L step test, microstructural alterations occur very slowly at the lower level, and the microstructure formed at higher level does not disappear readily. Lieurade and co-workers also observed these effects for constant amplitude tests on prehardened specimens [57]. Effect of precycling on crack growth was investigated by Lehéricy and Mendez [12] for stainless steel 304. They concluded that fatigue strength and endurance limit at the lower loading amplitude level are affected only if cracks have propagated over more than a single grain during precycling. For aluminum alloys 2024-T4 and 7075-T6, Topper et al. [58] observed that load sequence effect was small when the amplitudes of the steps were relatively close to each other. Stronger sequence effect was believed to occur for metals with a distinct yield point. Cold-working, shot-peening, or prehardening are sometimes used to create beneficial residual stresses on the surface of the material [5, 9, 45]. However, this also creates significant strain-hardening that can be detrimental to fatigue life for austenitic stainless steels [5]. Raman and Padmanabhan studied the effect of different levels of

28 cold-working on stainless steel 304LN, and showed that depending on the level of loads applied to the cold worked material, and on the nature of the preloading itself, the treatment can be beneficial or detrimental [45]. The effect of cold working on fatigue life in strain-controlled tests depends on whether HCF or LCF is considered. In LCF, the effect can be related to the decrease in the ductility of the material. Therefore, Raman and Padmanabhan concluded that cold-working can have a detrimental effect in LCF. At low strain amplitude, however, the effect is reversed. The strength of the material is increased and cold-working becomes beneficial in HCF [45]. In load control, overloads, compressive or tensile, often shorten crack initiation life for a smooth component. After testing smooth aluminum 2024-T351 specimens under periodic overloads and underloads, Pompetzki et al. concluded that both tensile and compressive overloads were followed by a period of accelerated damage in load control. Because of periodic overloads and underloads, smaller cycles below the fatigue limit can significantly contribute to damage [28]. As explained in Section 2.2.4, microcracks can be present at the surface of smooth specimens. Therefore, crack retardation can also occur in smooth specimens in load control, due to periodic overloads, when they are applied sporadically [28]. Jurcevic et al. [59] also investigated the effect of periodic overloads in damage accumulation of smooth specimens of aluminum 2024-T351 in load control and observed that fully-reversed periodic overloads have more effects on damage accumulation than single periodic tensile or compressive overloads. 2.4.3 Mean stress effects In complex loading histories, a major factor to take into account is the presence of mean stress. Mean stress, defined as the mean value of the maximum and minimum

29 stresses, can also have significant effects on both deformation and fatigue behaviors. A common effect of mean stress on deformation behavior in load control is known as ratcheting, which is defined as progressive plastic strain accumulation due to unsymmetrical load cycling. The amount of ratcheting is related to the level of mean stress, as well as the level of stress amplitude, as described in Section 2.3.2. It is well known that compressive mean stress is beneficial to fatigue life, whereas tensile mean stress is detrimental to fatigue life [9]. DuQuesnay et al. [60] studied the effect of mean stress on fatigue behavior of 2024-T351 aluminum alloy and suggested that mean stress effects are mainly related to crack closure, and that both minimum and maximum stresses must be taken into account. They showed that an effective stress range, defined as the range between maximum and opening stress, to correct for crack closure effects can be used for accurate life predictions under mean stress conditions. Another process that can occur in strain-controlled mean stress tests is mean stress relaxation. The mechanisms of mean stress relaxation slightly differ depending on whether a material cyclically hardens or softens. For both cyclically softening and cyclically hardening materials these mechanisms are related to variation in flow stress [46]. Mean stress relaxation is common, and it has been observed in stainless steel 304L, where the phenomenon is rather important [61]. Compressive mean stresses are recognized to have beneficial effect on fatigue life, whereas tensile mean stresses are detrimental. Therefore, the entire loading history must be considered to be able to evaluate deformation and fatigue behaviors. To account for mean stress effects, one of the most commonly used models is the modified Goodman equation, in a stress-life approach [9]. A common mean stress correction model for

strain-life approach is the Smith-Watson-Topper (SWT) parameter [21], which is discussed in Section 5.2. 30 2.5 Summary Service load histories of many components and structures are often composed of overloads, mean stress and variable amplitude loading. When designing components and structures, it is necessary to compute damage accumulation to evaluate the fatigue life under complex loading conditions. For this, a number of rules, model and parameters have been developed, to predict deformation behavior and to accurately account for fatigue damage. One of the most commonly used damage accumulation rules is the Linear Damage Rule. Its application does not necessitate determination of any parameters, its computation is fairly simple, and it often provides reliable results. For complex load histories and for materials with strong deformation history effects such as stainless steels, the LDR might be associated with parameters including both loading history and response of the material for accurate fatigue life predictions. Stainless steel 304L is used in many applications, including the cooling system of nuclear power plants, where the loading is also complex, consisting of multiple overloads and in the presence of mean stress. Stainless steel is known to have a strong cyclic hardening behavior and is recognized to harden after overloading or preloading. Hardening in stainless steel has been associated to strain and/or stress induced martensitic transformation. This process is related to the number of slip and shear band systems and induces considerable alteration of the microstructure of stainless steel. These microstructural modifications are reflected in the dramatic change in deformation behavior encountered under variable amplitude cycling. As deformation and fatigue

31 behavior are strongly related for stainless steel, both must be investigated to compute damage under cyclic loading. Effects of mean stress, overloads, and loading sequence were studied by previous researchers, and many parameters have been used to evaluate damage induced by these different events. Deformation and fatigue behaviors have been evaluated and different reasons have been proposed to explain the phenomena occurring under complex loading. This study intended to assess the applicability of the LDR and its accuracy under such loading effects for two types of materials, presenting extreme behaviors with respect to deformation history sensitivity.

32 Figure 2.1 Schematic of damage curve concept of summing cumulative damage in complex loading [18].

33 Figure 2.2 Optical micrograph showing slip bands in a fractured specimen of SUS304-HP stainless steel tested at ε a = 0.4% [41]. Figure 2.3 Optical micrographs in a fractured specimen of SUS304-HP stainless steel tested at ε a = 0.9% showing a) slip band features, b) morphologies of martensite [41]. Figure 2.4 Optical micrographs in a fractured specimen of SUS304-HP stainless steel tested at ε a = 2.0% showing: a) and b) slip band features, and c) different morphologies of martensite [41].

34 Figure 2.5 FATHER testing structure in some T-junctions of piping systems made of stainless steel 304L, and computed instantaneous non-dimensional temperature field (time=10s) under representative loading. The test simulates how the hot fluid from the horizontal pipe does not instantaneously mix with the cold fluid from the vertical pipe [55]. Figure 2.6 Loading sequence made of 1000 instants obtained from Finite Element results of the FATHER structure in Figure 2.5 [55].

Chapter Three Experimental Program 3.1 Experimental Plan As presented in Chapter 1, two grades of stainless steel 304L and aluminum 7075- T6 were chosen as materials to evaluate the influence of deformation history effect on damage accumulation. The deformation history effect of the materials was first assessed by means of incremental step tests to establish the differences between materials and grades. The mechanical tensile and baseline fatigue curves and properties were then generated, so that the strain-life, stress-life, SWT-life and FS-life curves could be produced for future fatigue life predictions under more complex loadings. Influence of different parameters, including mean stress or mean strain and prestraining were considered separately and the ability of the four aforementioned approaches to correlate data under these different conditions was evaluated. The capability of the LDR to represent damage accumulation under variable amplitude loading was then assessed in step load tests, periodic overload tests, and random loading tests. The experimental program is presented in this chapter. 3.2 Materials and Specimens Aluminum 7075-T6 and two grades of stainless steel 304L were used in this study. The two grades of stainless steel 304L from Creusot Loire Industrie (CLI) and Thyssen (THY) were obtained from EDF (Renardières). Their chemical compositions are 35

36 presented in Table 3.1, where it can be noticed that both SS304L grades present low carbon content (hence the designation L). Microstructure photos are shown in Figure 3.1 for all three materials. All materials were progressively polished to a 0.05 µm surface finish. Etching was then realized using an etching agent consisting of 10 ml nitric acid, 10 ml acetic acid, 15 ml hydrochloric acid and 2 drops of glycerol. For SS304L, the average grain size averaged between about 50 μm to 100 μm. The stainless steel specimens were machined from 3 cm thick plates in the rolling direction, while aluminum specimens were machined from 19 mm diameter round bars in the longitudinal direction. Cylindrical solid specimens were machined following ASTM E606 [25] suggested configuration, except for a large secondary radius introduced in the gage section rather than a uniform diameter gage section. This secondary radius slightly reduces the diameter in the middle of the gage section, resulting in slightly higher stress at this location, compensating for the slightly higher stress at the intersection of the gage section and the shoulder. Specimen geometry and dimensions are presented in Figure 3.2. Slightly smaller specimens, with gage section diameter of 4.2 mm were used for most aluminum tests. The smaller diameter allowed a 10 kn machine to be used for these tests, while a 50 kn machine was used for larger diameter specimens. No geometry effect was observed by comparison of data obtained with the two types of specimens. All specimens were machined in the Mechanical, Industrial, and Manufacturing Engineering Machine Shop at the University of Toledo. To eliminate polishing marks, a commercial round-specimen polishing machine was used to polish the gage section of the specimens. Three different grits of aluminum oxide lapping film were used to reach a

37 surface finish of 0.2 μm. Polishing marks coincided with the longitudinal axis of the specimens. The polished surfaces were carefully examined to ensure complete removal of machining marks within the test section prior to testing. ASTM E606 [25] recommends the use of tape or epoxy to protect the specimen surface from the knife-edges of the extensometer. M-coat D was found to be the best alternative, and was used as protection in all tests. Four to five layers of coating were applied, with a drying time of 15 minutes at room temperature between layers, and a final curing time of one hour at 65 C. 3.3 Equipments 3.3.1 Test machines and instruments Instron 8801 closed-loop servo-hydraulic axial load frames in conjunction with Instron Fast-Track digital controllers were used for conducting the tests. Two machines were used with load cell capacities of 10 kn and 50 kn. Hydraulically operated wedge grips with semi-circular cavities for the 10 kn machine and hydraulically operated grips using universal tapered collets for the 50 kn were employed to secure the end of the specimen in series with the load cell. ASTM class B1 extensometers with 6 mm gage length (capable of measuring strain up to 10% and down to -5%) and with 7.62 mm gage length (capable of measuring of +/- 15% strain) were used to measure and control the strain. Calibration was checked regularly throughout the testing program, with a calibration device containing a micrometer barrel in divisions of 0.00254 mm. Both extensometer readings were in accordance with ASTM E83 standard [62].

38 3.3.2 Alignment Great care was taken to align the load train, including load cell, grips, specimen, and actuator. Misalignment can result from both tilt and offset between the central lines and the load train components and can induce bending of the specimen during loading. Bending was minimized so that the maximum bending strains were below the maximum allowed ASTM Standard E606 [25] value of 5% of the minimum axial strain range imposed during the test program. To verify the alignment, ASTM standard E1012 [63], type A, method 1 was followed. Two arrays of four strain gages were attached to the upper and lower ends of a 12.7 mm diameter straight bar with uniform section. Within each array, gages were equally spaced around the circumference of the bar. Alignment was checked regularly and remained within the allowable ASTM limits for the duration of the testing program. 3.4 Tests Procedures and Data Acquisition 3.4.1 Monotonic tensile tests Tensile tests were conducted on all three materials to obtain tensile properties following ASTM E8M [64], using the Instron Bluehill software. In strain control, strain rate of 4.2x10-5 s -1 was used up to 1% strain, then 8.3x10-5 s -1 up to 12% strain. Although the point of ultimate tensile strength was not reached for SS304L, the extensometer was removed to avoid any damage (due to upper limit of 15% strain) and the test was continued in displacement control until fracture. After fracture and careful reassembly of the two broken parts, gage lengths after fracture and neck radii were measured using an optical comparator with 10X magnification and divisions of 0.0254 mm. Final diameters

were measured with Vernier caliper with divisions of 0.0254 mm. The same instruments were used to measure specimen dimensions prior to testing. 39 3.4.2 Constant amplitude fully-reversed fatigue tests Fatigue properties were obtained from strain-controlled, fully-reversed constant amplitude fatigue tests, conducted with Instron LCF and SAX softwares. Triangular waveform was used and frequencies were adapted so that strain rate was nearly the same in all tests. For some long life tests of Al 7075-T6, the strain control mode was switched to load control, when the behavior was fully elastic (below 0.5% strain amplitude). The test frequency was increased (up to 60 Hz), to reduce the testing time. This could be done because under elastic loading no heat is generated and the cycling frequency does not affect the outcome of the test. For SS304L, cyclic frequencies varied between 0.2 and 7 Hz in strain-controlled tests. Preliminary tests were conducted to ensure that effects of frequency or strain rate with respect to fatigue life, stress response, and temperature were negligible for the range of frequencies used in this study. Tests between 0.1% and 0.2% strain amplitude were performed at cyclic frequencies ranging between 1 Hz and 15 Hz. Temperature increased linearly with increasing frequency and strain amplitude, but remained below 20 C increase, and stress response and fatigue life were not affected by test frequency. Failure was defined as 25% load drop in strain-controlled tests and 25% displacement increase for load-controlled tests, compared to values from midlife, or fracture, whichever occurred first. Fatigue data were recorded at 2 n cycles or more frequently, when needed. The load or displacement change used for failure definition

40 corresponded to the presence of multiple macrocracks for stainless steel and at least one macrocrack for aluminum. Typical macrocrack lengths were several millimeters. All fatigue tests were duplicated, except for some of the runout tests. Runout tests are tests that were stopped before failure occurred, after at least 10 6 cycles. An arrow is used in figures where these data are presented to indicate that failure did not occur. For the SS304L CLI grade, previous data obtained from EDF (referred to as MMC in plots) were used to generate the fits, as they matched the data obtained in this study very well. For SS304L THY and aluminum, fits were generated from data obtained in this study only. 3.4.3 Mean strain and mean stress tests Mean strain tests were conducted in strain control and mean stress tests in load control for SS304L. Because of significant level of mean strain in these tests, the strain amplitude in strain control, or load amplitude in load control for the higher mean level were reached gradually over up to ten cycles. Tests were started in tension when tensile mean strain or tensile mean stress was present, and in compression for tests with compressive mean strain or compressive mean stress. For aluminum, all mean strain and mean stress tests were conducted at 0.5% strain amplitude. As the behavior is fully elastic at this level, both test control modes are equivalent and load control was used, to allow better control of the mean stress. Tests were conducted with Instron Waverunner and SAX softwares, with triangular waveform and using frequencies similar to the ones used in fully-reversed constant amplitude fatigue tests. More details about each specific test are presented in Chapter 5, where the results are discussed. To fully represent the behavior of the

materials and because of the presence of significant mean strain, true stress and true strain rather than engineering values were used in all tests. 41 3.4.4 Initial overstrain tests Initial overstrain or prestrained tests were conducted for all materials. Prestraining was conducted at 2% total strain amplitude for 10 cycles for SS304L and 1.4% total strain amplitude for 10 cycles for aluminum. To avoid large mean stress during the subsequent cycles in either strain control or load control, the strain amplitude was gradually decreased for SS304L, as shown in Figure 3.3 for strain history and Figure 3.4 for the corresponding hysteresis loops. This procedure has been previously used and was described in [65]. For aluminum, using this method was not necessary since the subsequent cycles were conducted in load control due to elastic behavior, and mean stress could be easily avoided, when desired. For this material, prestrained tests were conducted with the smallest cycles at different locations of the hysteresis loops of the prestraining level, in the presence of mean stress or mean strain, as indicated in Figure 3.5. Instron SAX and Waverunner softwares were used to conduct these tests, with triangular waveforms and frequencies used were similar to the ones used in fully-reversed constant amplitude fatigue tests. Results for prestrained tests are discussed in Chapter 5. 3.4.5 Step tests H-L and L-H step tests at different levels and different cycle ratios were conducted for both materials, in either strain or load control. The strain or load history for these tests are represented in Figures 3.6(a), and 3.6(b), for L-H, and H-L sequences, respectively. For the H-L sequence in strain control, different procedures were used to

42 switch from the higher level to the lower level, to control the amount of mean stress resulting from the higher level, due to residual plastic strain. For SS304L, one test procedure involved the presence of mean stress at the lower strain amplitude level. Another procedure used consisted of gradually decreasing the higher strain amplitude to zero, before switching to the lower strain amplitude level, similar to prestrained tests as shown in Figures 3.3 and 3.4. The latter procedure produced negligible mean stress for this material. However, since this procedure was not used in all tests, mean stress was present in some SS304L CLI tests. For aluminum, H-L step tests were conducted in different conditions, with the smallest cycles at different locations of the hysteresis loops of the higher level, similar to prestrained tests, as shown in Figure 3.5. Due to fully elastic behavior at the lower level, this level was carried out in load control so mean stress could be easily controlled. Step tests are described in further details in Chapter 6. Instron SAX, and Waverunner softwares were used to conduct these tests, with triangular waveforms and frequencies at each level similar to the ones used in fully-reversed constant amplitude fatigue tests at the same level. 3.4.6 Periodic overload tests Periodic overload tests for Al 7075-T6 were conducted with smaller cycles at 0.5% strain amplitude, and periodic overloads at 1.4% strain amplitude were applied about every 10% of the expected fatigue life based on LDR. This resulted in a load block composition of one overload cycle every one thousand small cycles. The frequency was adapted so that a constant strain rate could be maintained throughout the test. Tests were carried out in load control, while ensuring desired levels of strain were reached. This

43 method permits to avoid mean stress during smaller cycles. However, mean stress was present during the overloads, as either fully compressive or fully tensile overloads were applied. Loading histories for these tests are presented in Figures 3.7(a), and 3.7(b), for fully tensile, and fully compressive overloads, respectively. For SS304L CLI, fully-reversed overloads in between fully-reversed small cycles were applied. Duplicate tests were conducted, one with overloads starting in tension, the other one with overloads starting in compression, as shown in Figures 3.8(a), and 3.8(b), respectively. For SS304L CLI, periodic overloads consisted in one fully-reversed cycle at 1% strain amplitude, with the lower level at 0.25% or 0.4% strain amplitude for tests in strain control. Different overload to smaller cycle ratios were used to allow comparison with the results of strain-controlled H-L step tests. For load-controlled tests, periodic overloads consisted of one fully-reversed cycle at 375 MPa stress amplitude in between fully-reversed smaller cycles, with the smaller cycle amplitude at 240 MPa. For SS304L THY, only one periodic overload test was conducted, in strain control, with one fully-reversed overload at 0.4% strain amplitude every 5000 fullyreversed cycles at 0.25% strain amplitude. The purpose of this test was to investigate the effect of periodic overloads on the deformation and fatigue behavior of the material at runout level. Instron Waverunner software was used to conduct periodic overload tests. Further details and results of periodic overload tests are presented in Chapter 6. 3.4.7 Random loading tests The actual loading occurring in the cooling system of nuclear power plants has been simulated by Desmorat and co-workers, as was presented in Figure 2.6 [55]. A mockup load history obtained similarly and provided by EDF was considered as random

44 loading spectrum. However, for the purpose of this project, the loading history had to be applicable at different amplitudes to get fatigue lives at several levels. The mockup history was simplified using a racetrack algorithm represented in Figure 3.9. This procedure was named after an analogy with a racetrack car since it follows the loading history within two bands (threshold). Data points that do not represent any change in direction are eliminated [9]. The original and resulting histories are presented in Figures 3.10 and 3.11, respectively. To evaluate the accuracy of a life prediction parameter for random loading, a good damage distribution is required. As can be seen from Figure 3.11, this was not achieved by simplifying the mockup load history. Because of its considerable length, simplification to shorten the load history led to an almost fully-reversed spectrum, which was not desirable. Therefore, a random loading history was generated. Random numbers between 1 and -1 were generated, leading to the load spectrum shown in Figure 3.12(a). This history was then slightly simplified, to eliminate intermediate points between each reversal segment, leading to the load history shown in Figure 3.12(b). The Rainflow cycle counting method, which algorithm is given in ASTM Standard E1049 [15], was employed on the reordered spectrum presented in Figure 3.13(a). No filtering process was used and all reversals were accounted for. The resulting reversals and damage distribution are presented in Figure 3.13(b), and Table 3.2, respectively. In this table, the mean and amplitude values were calculated using maximum and minimum values of +/-100. The relative percent of damage is also indicated. The history was amplified to reach the desired maximum and minimum strain or stress values in the block. It should be noted that tests conducted in strain control and

45 load control are not comparable, due to plastic deformation. Instron SAX software was used to conduct random loading tests. Further details for random loading tests are given in Chapter 6.

46 Table 3.1 Composition of the two grades of SS304L used in this study. 304L CLI 304L THY C (%) 0.029 0.023 Mn (%) 1.86 1.13 Si (%) 0.37 0.49 S (%) 0.004 0.004 P (%) 0.029 0.024 Ni (%) 10 10.1 Cr (%) 18 18.5 Mo (%) 0.04 0.09 Cu (%) 0.02 0.1 N 2 (%) 0.056 0.028 Fe balance balance Table 3.2 Result of the Rainflow cycle counting applied to the random loading history with amplitudes of +/- 100 presented in Figure 3.12(b). cycle max min range mean % Damage 2-3-2' 16-78 94-31 2.39 4-5-4' 53-79 132-13 6.62 7-8-7' 6-91 97-43 2.61 9-10-9' 56-91 147-18 9.20 11-12-11' 45-89 134-22 6.96 14-15-14' 67 6 60 36 0.51 13-16-13' 75-91 165-8 13.04 18-19-18' 62-50 112 6 4.10 22-23-22' 7-53 60-23 0.51 6-17-6' 93-96 189-2 19.52 20-24-20' 48-95 143-23 8.44 25-26-25' 33-41 74-4 1.14 27-28-27' 21-40 61-10 0.55 29-30-29' 17-64 82-23 1.53 1-31-1' 100-99 199 0 22.71 32-33-32' 100 53 46 76 0.17 100.00

47 100 µm (a) 100 µm (b) 100 µm (c) Figure 3.1 Microstructure of (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

48 Figure 3.2 Specimen geometry and dimensions (dimensions in mm).

Stress (MPa) Strain 49 PS at 2% Time Figure 3.3 Strain history used in prestrained tests and some H-L step tests or SS304L. 600 PS @ 2% transition (zero load) lower level 0-600 -2.5% 0.0% 2.5% Strain Figure 3.4 Hysteresis loops corresponding to the strain history in Figure 3.3. The second strain level is conducted in the presence of small mean strain (transition through zero load).

Stress (MPa) 50 Pre-straining mean strain (A, B) mean stress (C, D) D A C B Strain ` Figure 3.5 Stress-strain paths of the cycles subsequent to prestraining, or higher level in H-L step tests for Al 7075-T6 (paths A and B have mean strain, paths C and D have mean stress).

Strain or Load Strain or Load 51 n 2 n 1 Time (a) n 1 n 2 Time (b) Figure 3.6 Loading history for step tests with (a) L-H, and (b) H-L sequence.

Strain Strain 52 2.0% 0.0% Time -2.0% 2.0% (a) 0.0% Time Figure 3.7-2.0% (b) Loading histories for periodic overload tests for Al 7075-T6 with (a) fully tensile POL, and (b) fully compressive POL.

Strain or Load Strain or Load 53 One block Time One block (a) Time (b) Figure 3.8 Load histories for periodic overload tests for SS304L with (a) tensioncompression POL, and (b) compression-tension POL.

54 original loading history resulting history after racetrack count Figure 3.9 Representation of the Racetrack algorithm for loading spectrum simplification. Figure 3.10 Part of the mockup loading history obtained from EDF.

55 Figure 3.11 Result of the racetrack algorithm conducted on the spectrum presented in Figure 3.10. (a) (b) Figure 3.12 Randomly generated spectrum. (a) Original spectrum, and (b) simplified spectrum.

56 1 17 32 1 3 5 7 9 11 13 15 19 14 21 22 24 26 28 30 33 2 4 6 8 10 12 16 18 20 23 25 27 29 31 (a) 3 5 7 7' 9 13 15 9' 11 11' 14 14' 13' 19 22 22' 17 24 26 28 30 1 1 32 33 32' 2 2' 4 4' 8 10 12 16 18 18' 23 6 25 25' 2727' 29 6' 20 20' 29' 31 (b) Figure 3.13 Rainflow cycle counting of the spectrum presented in Figure 3.12. (a) Reordered spectrum, and (b) results of Rainflow cycle count in terms of reversals.

Chapter Four Deformation Behavior and Load Sequence Effects With respect to deformation history effect, different types of materials can be defined. This includes materials with very little or no deformation history effect such as aluminum, materials with relatively small deformation history effect such as medium carbon steels, and materials with strong deformation history effect such as austenitic stainless steels. In order to determine the required characteristics of a reliable life prediction model under complex loading, the deformation history effect on subsequent loading and fatigue behavior with or without mean stress or strain must be considered. Deformation or load history effect of a material on subsequent cyclic loading depends on the degree of cyclic hardening of the material. This in turn depends on how easy the dislocations can cross slip. The easier the cross slip, the less dependence of the deformation behavior on load history. For face-centered cubic (fcc) metals, the ease of cross slip depends on the stacking fault energy (SFE) of the material. In fcc metals with low SFE, such as austenitic stainless steels, planar slip occurs readily and the deformation behavior greatly depends on the loading history. In contrast, fcc metals with high SFE such as aluminum alloys are more easily able to cross slip during cyclic loading, and their deformation behavior is relatively independent of prior load history. Aluminum 7075-T6 and stainless steel 304L chosen in this investigation present extreme cases with respect to load sequence effects and, therefore, permit to assess the 57

58 applicability of appropriate fatigue life prediction parameters under prestrained and/or mean stress or strain conditions. In this chapter, monotonic and cyclic deformations including incremental step test results are presented and discussed to illustrate the deformation history effect on cyclic deformation behavior (i.e. stabilized cyclic stress-strain curve). Comparisons of deformation behaviors between materials and grades are also presented. 4.1 Monotonic Deformation Behavior True stress (σ) and true strain (ε) were calculated from engineering stress (S) and strain (e), using Equations (4.1) and (4.2) to obtain monotonic properties from the tensile tests, including modulus of elasticity (E), monotonic yield strength (S y ) obtained at 0.2% offset, ultimate tensile strength (S u ), percent elongation (%EL), and percent reduction in area (%RA). σ S(1 e) (4.1) ε ln(1 e) (4.2) The true fracture ductility (ε f ) was calculated from Equation (4.3), with A 0 and A f being the cross section area prior to testing and at fracture, respectively. A0 100 ε f ln ln (4.3) A 100 %RA f The true fracture strength (σ f ) was obtained using the Bridgman correction factor [66], based on Equation (4.4):

59 σ f 1 4 R D min P A f f ln 1 D 4R min (4.4) where P f is the load at fracture, R the radius of curvature of the neck, and D min the diameter of the fractured specimen in the thinnest part of the neck. Strength coefficient (K) and strain hardening exponent (n) were also obtained and are the intercept and the slope of the best line fit to true stress versus true plastic strain in log-log coordinates. The best fit line represented by Equation (4.5), fitted to data points between the yield point and the ultimate tensile strength (or the last value obtained in strain control prior to ultimate tensile strength). σ K ) ( ε n p (4.5) with σ ε p ε εe ε (4.6) E The stress-strain behavior can then be represented by the following Ramberg-Osgood type relationship: e p σ E σ K 1 n (4.7) Fits for all three materials are presented in Figure 4.1 and resulting Ramberg-Osgood curves superimposed on experimental monotonic curves are presented in Figure 4.2. Summary of the tensile properties for all three materials are presented in Table 4.1. The large values of percent reduction in area and true fracture strain for SS304L indicate the high ductility of the material. The two grades of SS304L present very similar

60 tensile properties. In Figure 4.3, monotonic stress-strain curves are superimposed for the two grades of SS304L and are shown to be nearly identical. 4.2 Cyclic Deformation Behavior The steady state hysteresis loops were used to determine the deformation properties of the materials. Cyclic strength coefficient (K') and cyclic strain hardening exponent (n') are the intercept and the slope of the best line fit to true stress amplitude (Δσ/2) versus true plastic strain amplitude (Δε p /2) data from midlife (i.e. stable) cycles in log-log scale: Δσ 2 K' Δ ε p 2 n' (4.8) where Δε p Δε Δσ 2 2 2E (4.9) and E is the modulus of elasticity obtained from the tensile tests. Fits for all three materials are presented in Figure 4.4. The cyclic stress-strain behavior can then be represented by the following Ramberg-Osgood type relationship: Δε 2 Δε 2 e Δε 2 p Δσ 2E Δσ 2K' 1 n' (4.10) These curves are presented in Figure 4.5 for all three materials. A clear distinction between the two materials is with regards to their response to cyclic loading. While Al 7075-T6 presents a stable response, SS304L exhibits significant transient behavior. As shown in Figure 4.6 which represents the stress response in strain control, and Figure 4.7 which presents total strain response in load control, significant

61 initial variations occurred in the response for SS304L. Although duplicate tests were conducted at each level, due to similarity of the results, test data from only one test are shown. For aluminum, steady state behavior was observed for all levels of strain or load amplitudes, as seen in Figures 4.6(c) and 4.7(c). It should be noted that the significant change in stress or strain amplitudes near fracture for some tests shown in Figures 4.6 and 4.7 is due to cracking, and not to a change in material response. In fully-reversed constant amplitude tests, the two grades of SS304L presented similar deformation behavior at high and intermediate strain amplitudes. In Figures 4.6(a) and 4.6(b), after initial variations, the stress response increased continuously with increasing cycles at high strain amplitudes of 2% and 1%, whereas the response was fairly steady at intermediate strain amplitudes (0.4% and 0.25% for SS304L CLI, and 0.6% 0.5% and 0.4% for THY). Figure 4.7 indicates similar behavior for tests conducted in load control, where hardening at higher amplitude is manifested by reduced strain amplitude with cycling. In strain-controlled tests, at lower strain amplitude levels (at and below 0.2% for SS304L CLI, and at and below 0.3% for SS304L THY), secondary hardening, characterized by a continuous increase in the stress response after initial softening, was observed in both materials. The phenomenon occurred to a greater extent and at higher strain amplitude in SS304L THY (ε a = 0.3%) than in SS304L CLI (ε a = 0.2%). The rate of hardening was also greater for SS304L THY than for SS304L CLI (characterized with a steeper slope). Secondary hardening is discussed in further details in Chapter 5. Figure 4.8 presents superimposed midlife hysteresis loops from one of the fullyreversed strain-controlled duplicate tests at each strain amplitude for stainless steel and

62 aluminum. Stainless steel 304L presented considerable amount of plastic deformation, even in HCF at total strain amplitude levels as low as 0.175% strain amplitude (Figure 4.8(a)), whereas Al 7075-T6 exhibits elastic behavior at and below 0.5% strain amplitude (Figure 4.8(c)). The monotonic yield strength of aluminum is 533 MPa (see Table 4.1), corresponding to 0.75% total strain. The 0.5% strain amplitude is well below the monotonic as well as the cyclic yield points. Superimposed cyclic and tensile stress-strain curves for all three materials are presented in Figure 4.9. As shown in Figure 4.9(a), SS304L CLI presents a bilinear behavior, with a transition around 0.3% strain amplitude. While the deformation curves under monotonic and cyclic loading are similar for Al 7075-T6, strong cyclic hardening is observed for SS304L. This hardening occurs after the inflection point in the cyclic stress-strain curve for SS304L CLI and becomes more significant at higher strain amplitudes (i.e. more than 100% hardening at 2% strain amplitude for SS304L CLI and about 125% hardening at 2% strain amplitude for SS304L THY). Although data from prestrained tests (PS) are also included in Figure 4.9, these data are discussed in the prestraining effects section in Chapter 5 (Section 5.4). As shown in Figure 4.10, where the cyclic stress-strain curves for the two grades of SS304L are superimposed, the cyclic deformation behaviors differ between the two grades, due in part to the bilinearity in the behavior of the SS304L CLI grade. The two curves intersect at about 1.5% strain amplitude. 4.3 Effect of Loading Sequence or History on Cyclic Deformation To demonstrate the difference in material response with respect to loading sequence, incremental step tests were conducted on the three materials. A single

63 specimen of each material was subjected to increasing and then decreasing strain amplitudes. Each strain level was maintained for a number of cycles large enough to obtain a fairly constant response (i.e. saturated response). The applied strain history for SS304L is presented in Figure 4.11. Only three strain levels were used for this material, as a relatively high number of cycles was required to obtain fairly steady (i.e. saturated) stress response (see Figure 4.12). For aluminum, four strain levels were used, with several increasing and decreasing sequences. As expected, the stress response for SS304L, as shown in Figure 4.12, is strongly affected by the prior higher strain amplitude cycles in the sequence. In contrast, for aluminum, the stress response was similar for identical total strain amplitude and the prior loading did not affect subsequent stress response of the material. This can be explained in terms of the difference in SFE for the two materials, discussed earlier. During cyclic loading, cross slip is difficult in stainless steel with low SFE making its deformation behavior dependent on the prior loading, while cross slip is easier in aluminum with high SFE making its deformation behavior independent of prior loading. Stable results from the incremental step tests of stainless steel and aluminum are presented in Figure 4.13. For aluminum (see Figure 4.13(c)), the stress response does not depend on previous loading, as it is stable and independent of the prior higher loads in the loading sequence. For SS304L (Figures 4.13(a) and 4.13(b)), however, the stress response is greatly affected by the prior higher loading. Aluminum is thus considered a material with little or no deformation history effect, whereas SS304L possesses a strong deformation history effect.

64 An incremental step test up to 1% strain amplitude was also carried out on a prestrained SS304L CLI specimen. Prestraining at 2% strain amplitude for 10 cycles induced strong hardening and the material had a different behavior as compared to the virgin material. The stress amplitude for the prestrained specimen was about 25% higher than for the virgin specimen, resulting in lower plastic strain amplitude at a given strain amplitude. Continuous softening was observed throughout the prestrained incremental step test, regardless of the loading sequence. In addition, while the unloading curve in the incremental step test for the virgin (V) specimen was above the loading curve (see Figure 4.13(a) where the results for the prestrained (PS) tests are superimposed), the loading and unloading curves were nearly identical for the prestrained specimen. This indicates that if the stress is saturated at a prior higher loading (i.e. 2% strain amplitude here), deformation behavior at subsequent loading-unloading to a lower level (i.e. 1% strain amplitude here) is independent of the load sequence (i.e. load history independent). 4.4 Conclusions 1) Stainless steel 304L and aluminum 7075-T6 represent extreme cases with respect to strain history dependence, and the deformation behavior with respect to loading history is related to their stacking fault energy. 2) Stainless steel 304L investigated in this study continuously hardens with increasing cycles in LCF as well as HCF, whereas for aluminum 7075-T6 steady state behavior was observed for the entire life regime. While the deformation curves under monotonic and cyclic loading are similar for the aluminum alloy, strong cyclic hardening was observed for stainless steel, which became more significant at higher strain amplitude.

65 3) While monotonic stress-strain curves are nearly identical for the two grades of SS304L, the cyclic deformation behaviors differ, due in part to the bilinearity in the behavior of the SS304L CLI grade. 4) Austenitic stainless steel presents a transient behavior in the stress response under strain control and in the strain response under load control, under fully-reversed constant amplitude cyclic loading. Also due to its low stacking fault energy, deformation behavior of this type of material is greatly dependent on prior loading history (strong deformation history effect), as shown by the incremental step tests for which the stress-strain loading and unloading paths do not coincide. 5) Aluminum possesses a higher SFE and thus has less sensitivity to overloading (i.e. little or no deformation history effect). Therefore, no effect of prestraining was observed for this material, while prestraining induced strong hardening in SS304L.

66 Table 4.1 Summary of the mechanical tensile properties for SS304L CLI, SS304L THY and Al 7075-T6. Monotonic Properties SS304L CLI SS304L THY Al 7075-T6 Modulus of elasticity, E (GPa) 196 193 70.6 Yield strength (0.2% offset), S y (MPa) 208 202 533 Ultimate tensile strength, S u (MPa) 585 608 578 Percent reduction in area, %RA 84 83 34 Strength coefficient, K (MPa) 680 804 704 Strain hardening exponent, n 0.214 0.255 0.05 True fracture strength, σ f (MPa)* 2051 1763 737 True fracture ductility, ε f (%) 186 178 41 Cyclic Properties SS304L CLI SS304L THY Al 7075-T6 Cyclic modulus of elasticity, E ' (GPa) 196 193 70.6 Fatigue strength coefficient, bilinear fit, σ f1 ' / σ f2 ' (MPa) 330 / 1,890 2,558 / 819 689 / 1,587 Fatigue strength exponent, bilinear fit, b 1 / b 2-0.037 / -0.204-0.239/ -0.104-0.032/ -0.145 Fatigue ductility coefficient, ε f ', bilinear fit, ε f1 ' / ε f2 ' 0.133 0.5218 / 0.0242 0.110 Fatigue ductility exponent, c, bilinear fit, c 1 / c 2-0.374-0.5566 / -0.2033-0.509 Cyclic strength coefficient, K', bilinear fit, K 1 ' / K 2 ' (MPa) 434 / 4742 2224 790 Cyclic strain hardening exponent n', bilinear fit, n 1 ' / n 2 ' 0.111/ 0.512 0.341 0.062 Cyclic yield strength, S y ' (MPa) 220 238 540 *using Bridgman correction factor for necking

67 (a) (b) (c) Figure 4.1 True stress versus true plastic strain for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

68 (a) (b) (c) Figure 4.2 Monotonic tension experimental stress-strain curves and superimposed Ramberg-Osgood fits for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress (MPa) 69 350 300 250 200 150 100 Monotonic curve (experimental) THY Monotonic curve (experimental) CLI 50 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Strain Figure 4.3 Comparison of the monotonic tension experimental stress-strain curves between SS304L CLI and THY grades.

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 70 1000 UT data MMC data 100 0.01% 0.10% 1.00% Plastic Strain Amplitude 10.00% 1000 (a) 100 0.10% 1.00% Plastic Strain Amplitude 10.00% 1000 (b) 100 0.10% 1.00% 10.00% Plastic Strain Amplitude (c) Figure 4.4 Stress amplitude versus calculated plastic strain amplitude data and fits for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 71 700 600 500 UT data MMC data 400 300 200 100 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Strain Amplitude 700 600 (a) 500 400 300 200 100 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Strain Amplitude 700 600 (b) 500 400 300 200 100 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Strain Amplitude (c) Figure 4.5 Stress amplitude versus strain amplitude for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 72 700 600 500 400 300 ε a 2% 1% 0.4% 0.25% 0.2% 0.175% 200 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N 700 600 500 400 300 (a) ε a 2% 1% 0.6% 0.5% 0.4% 0.3% 0.25% 200 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N 700 600 500 400 300 200 (b) 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Number of Cycles, N (c) ε a 2% 1.4% 1% 0.5% 0.4% 0.3% 0.23% Figure 4.6 Stress response in fully-reversed constant amplitude strain-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

73 (a) (b) (c) Figure 4.7 Strain response in fully-reversed constant amplitude load-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

True Stress (MPa) True Stress (MPa) True Stress (MPa) 74 700 0 ε a (starting on the outside) 2% 1% 0.40% 0.25% 0.20% 0.175% -700-2.5% 0.0% True Strain 2.5% (a) 700 0 ε a (starting on the outside) 2% 1% 0.6% 0.5% 0.4% 0.3% 0.25% -700-2.5% 0.0% True Strain 2.5% (b) 700 ε a (starting on the outside) 2% 1.4% 1% 0.50% 0-700 -2.5% 0.0% True Strain 2.5% (c) Figure 4.8 Hysteresis loops for fully-reversed constant amplitude strain-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

75 (a) (b) (c) Figure 4.9 Superimposed monotonic tension and cyclic curves for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress Amplitude (MPa) 76 700 600 500 400 300 200 Cyclic curve THY Cyclic curve CLI 100 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Strain Amplitude Figure 4.10 Comparisons between cyclic stress-strain curves for SS304L CLI and THY grades. Figure 4.11 Strain history for the incremental step test on SS304L (CLI and THY).

77 (a) (b) Figure 4.12 Stress response from incremental step tests for SS304L (a) CLI, and (b) THY.

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 78 550 500 450 400 350 300 250 200 150 100 50 0 700 600 500 400 300 V, up to 1% V, up to 2% PS, up to 1% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Strain Amplitude 550 500 450 400 350 300 increasing 250 decreasing 200 150 100 50 0 0.0% 0.5% 1.0% 1.5% Strain Amplitude 2.0% 2.5% 1, 3, 7 4, 6 (a) (b) 2 5 strain amplitude levels and sequence 200 100 0 0.0% 0.5% 1.0% Strain Amplitude 1.5% 2.0% (c) Figure 4.13 Superimposed stress response for incremental step tests in strain control for (a) SS304L CLI, SS304L THY, and (c) Al 7075-T6.

Chapter Five Constant Amplitude Behavior 5.1 Introduction As presented in Chapter 2, service loading is usually variable amplitude loading and involves the presence of mean stresses. Prehardening due to manufacturing process and treatments or due to preloading resulting from an initial load history can also exist. These parameters must be investigated separately in order to fully understand their relative influence on deformation and fatigue behavior of materials with strong deformation memory effect. This chapter discusses deformation history effect due to cyclic prestraining as well as mean stress and mean strain effects and their influence on fatigue life. Fullyreversed fatigue behaviors based on tests conducted under different control modes are presented. This is followed by discussions of deformation and fatigue behaviors in mean stress and mean strain tests, as well as on prestrained specimens. A discussion of the secondary hardening observed for SS304L is also presented. Finally, the Smith-Watson- Topper parameter [21] and Fatemi-Socie [22] parameters were employed to correlate the aforementioned test data. 79

80 5.2 Constant Amplitude Fully-Reversed Fatigue Test Results and Effect of Control Mode Constant amplitude fully-reversed fatigue tests were conducted on all three materials. Although only strain-controlled test results were used to generate baseline fatigue properties, load-controlled tests were also carried out to evaluate the effect of test control mode on fatigue and deformation behaviors. All test results are presented in Tables 5.1 to 5.3. Constant amplitude fully-reversed fatigue test data were used to generate the strain-life curves, represented by: Δε 2 Δε 2 e Δε 2 p σ f E ' (2 N f ) b ε f '(2N f ) c (5.1) where σ f ' is the fatigue strength coefficient, b is the fatigue strength exponent, ε f ' is the fatigue ductility coefficient, c the fatigue ductility exponent, E the modulus of elasticity, and 2N f is the number of reversals to failure. The elastic and plastic lines are represented by the following equations, where σ f ' and b are obtained from the best line fit of stress amplitude versus reversals to failure, and ε f ' and c are obtained from best line fit of plastic strain amplitude versus reversals to failure: Δσ 2 σ f '(2N f ) b (5.2) Δε 2 p ε f '(2N f ) c (5.3) Values of σ f ', ε f ', b and c were obtained by performing least squares fits, following ASTM standards E739 [67] concerning the dependent and independent variables. The fits were obtained from fully-reversed constant amplitude strain-controlled fatigue tests excluding

81 the runout data, and are presented in Figure 5.1 for the elastic line fits and Figure 5.2 for the plastic line fits. Runout tests are tests that were stopped before failure occurred, after at least 10 6 cycles for SS304L, and at least 10 7 cycles for Al 7075-T6. Bilinear fit has previously been found to better represent S-N data for aluminum alloys [68], and appeared to better represent stainless steel S-N data as well [42]. As shown in Figure 5.1, bilinear elastic lines were obtained for all three materials. The bilinearity occurs around 225 MPa stress amplitude and 2x10 4 reversals to failure for SS304L CLI, 330 MPa and 5000 reversals for SS304L THY, and 525 MPa and 2000 reversals for Al 7075-T6. For both grades of SS304L, data for tests where secondary hardening was observed were not used to generate the elastic line, due to significantly different behavior of the material during these tests. For the plastic line, Al 7075-T6 and SS304L CLI presented linear behavior, while SS304L THY data were better represented with a bilinear fit (see Figure 5.2). Bilinearity for this later material occurs at 0.6% total strain amplitude (0.45% plastic strain amplitude) and 5000 reversals to failure. In Equation (5.3), Δε p /2 is the calculated plastic strain amplitude, and values of Δε p /2 > 0.230% were used to obtain the fit for Al 7075- T6, and values of Δε p /2 > 0.15% were used for SS304L (CLI and THY) to obtain the fits. Mechanical properties for all three materials are presented in Table 4.1, and resulting strain-life curves are shown in Figure 5.3. Figure 5.3 represents the elastic, plastic and total strain-life curves for the three materials. For SS304L, runout tests data points are away from the curve due to secondary hardening, as it will later be discussed. Runout data are shown to the right of the vertical

82 line with an arrow in Figure 5.3. The total strain-life curves were obtained from addition of elastic and plastic strain lines. For use in fatigue life predictions, the Smith-Watson-Topper parameter [21] versus life curves represented by Equation (5.4) shown in Figure 5.4 and Fatemi-Socie parameter [22] versus life curves represented by Equation (5.5) and shown in Figure 5.5 were also generated. σ ) ε b b c ae ( σ f ') 2(2N f ) 2 max σ f ' ε f ' E(2N f (5.4) where and σ max σ a σm Δγ max 2 (1 σ k S n,max y ) (1 σ f ' νe ) (2N E f ) b (1 ν p ) ε f '(2N f ) c 1 σ f ' k (2N 2S y f ) b where Δ max γ 2 (1 Δεe νe) 2 (1 Δε νp) 2 p (1 σa νe) E (1 Δε νp) 2 p and σa σm σ n,max σn,a σn,m (5.5) 2 2 As was presented in Chapter 4, SS304L does not present a steady stress response in strain control (or strain response in load control), particularly during the first 20% of the life. For most materials, the midlife stress values in strain-controlled tests, or midlife strain values in load-controlled tests are typically used as stable response. To evaluate the effect of transient response, a linear cumulative procedure was used, and the average of stress value in each strain-controlled test was obtained from: n1σ1 n2σ2... nnσn σ (5.6) N f where σ i is the stress amplitude level which is nearly steady for n i cycles, and

83 n N (5.7) f n i i 1 The average stresses calculated from Equation (5.6) and midlife values were compared and no significant difference was observed. The same procedure was repeated for the strain response in load-controlled tests, and similar values to midlife values were obtained. Thus, midlife values can be used as adequate representation of the stable response of SS304L. Figure 5.6 represents the fully-reversed behavior for SS304L CLI and SS304L THY using strain-life, stress-life, SWT-life and FS-life curves. The two strain-life curves (Figure 5.6(a)) are fairly close to each other in LCF and intermediate fatigue lives, where similar behaviors were observed. In HCF, however, at equivalent strain amplitude the SS304L THY grade presented longer fatigue lives than the SS304L CLI grade. The runout level for SS304L THY was found to be higher than that for SS304L CLI (0.25% versus 0.2%). Likewise, the stress-life curves are relatively close in LCF, where similar behaviors were observed. At fatigue lives between 10 4 reversals and 10 6 reversals, at equivalent stress amplitude, SS304L THY presented longer fatigue lives than the SS304L CLI grade. Consequently, SWT-life and FS-life curves are also close to each other in LCF and somewhat differ in HCF. As seen in Figure 5.7 for all three materials, load-controlled test data are close to the curves based on strain-controlled data, showing little effect of the test control mode on fatigue life. Load (stress) levels used were those obtained from the midlife response in strain-controlled tests. For SS304L, although large mean strains (up to about 5%) were observed due to some ratcheting in fully-reversed load-controlled tests at the highest stress level, fatigue lives were not significantly affected and were only slightly shorter

84 than the corresponding lives in strain-controlled tests. An example of such ratcheting is shown in Figure 5.8 for a load-controlled test at 412 MPa for SS304L CLI. Most of the ratcheting occurred during the first few cycles, and the mean strain kept increasing slowly with every subsequent cycles. It should be noted that the higher stress amplitude of 433 MPa in load-controlled tests compared to the stress amplitude of 412 MPa and 403 MPa in the corresponding strain-controlled tests at 1% total strain amplitude in Table 5.1 is due to the difference between engineering and true values arising from the large mean strain. Strain responses for load-controlled tests at different levels are presented in Figures 5.9, and 5.10 for SS304L CLI, and SS304L THY, respectively. The strain levels of the corresponding strain-controlled tests are also represented for comparisons. For load-controlled tests the strain amplitude levels progressively reach the corresponding level in strain-controlled tests. An exception is for the SS304L THY test at 274 MPa, or 0.3% strain amplitude for the corresponding strain-controlled test. In load control, the strain amplitude level was slightly higher than 0.3%. Although stress levels were the same in the duplicate tests, differences in strain amplitude levels were observed, during the first part of life (see Figure 5.10). Nonetheless, strain response levels became identical after about 10% of fatigue life. Fully-reversed constant amplitude strain-controlled test results for SS304L CLI and SS304L THY were obtained from EDF and analyzed [42]. The fits so-obtained could be used for SS304L CLI as they fairly represent data obtained independently in this study. However, new fits had to be generated for SS304L THY due to significant differences between the two sets of data, mostly in HCF. EDF data for SS304L CLI are

marked as MMC in Figures 5.1 to 5.5 but were omitted in other figures presented in this chapter. 85 5.3 Mean Strain and Mean Stress Effects Mean strain tests in strain control and mean stress tests in load control were conducted for SS304L. R ratios and midlife mean stress values in load control and midlife mean strain values in strain control are listed in Tables 5.1, and 5.2, for SS304L CLI, and SS304L THY, respectively. For SS304L CLI, in strain control R ε ratios of 2,, 0, -1, and 0.75 were used, whereas R σ ratios of -0.67 and -0.55 corresponding to tensile mean stress levels of 40 and 60 MPa, respectively, were used in load control. These R ratios are represented in Figure 5.11. For SS304L THY, only a limited number of straincontrolled tests at R ε ratios of, 0, -1, and 0.75 were conducted to confirm the trend in behavior observed in SS304L CLI. For aluminum, preliminary prestrained tests with mean strain had shown no effects of mean strain, therefore, only mean stress tests in load control with tensile or compressive mean stress of about 200 MPa were conducted. To apply this mean stress, the R σ ratios were between -0.25 and -0.27 (with a nominal value of -0.25) for 200 MPa tensile mean stress, and between -3.19 and -3.67 (with a nominal value of -3.4) for 200 MPa compressive mean stress, as listed in Table 5.3. Deformation responses for mean strain and mean stress tests for SS304L are presented in Figures 5.12 to 5.16. In strain control, because of the considerable amount of plasticity, the mean stress relaxed to very low values during the first few percent of the fatigue life, as can be seen in Figures 5.13 and 5.15 for SS304L CLI and SS304L THY, respectively. Mean stresses were less than 10% of the stress amplitude at midlife for SS304L CLI, and less than 5% of the stress amplitude at midlife for SS304L THY, and

86 less than 20 MPa for both SS304L grades. As expected, the amount of relaxation was proportional to the amount of plastic deformation, and it took a larger number of cycles for mean stress to relax at lower strain amplitude levels. In load-controlled tests for SS304L CLI with different R σ ratios, mean strain increased throughout the tests, as can be seen from Figure 5.16. Some ratcheting occurred, but tests were only conducted for maximum stresses low enough so that ratcheting was not too large. The amount of ratcheting increased with increasing mean stress value, as expected [49]. Comparison of the hysteresis loops in load control for fully-reversed and mean stress conditions showed that considerable hardening is induced by the higher maximum stress with commensurate reduced ductility. As shown in Figure 5.16 for SS304L CLI, the total strain amplitudes for mean stress tests, for both R σ ratios, are about 30% smaller than those observed in the corresponding fully-reversed tests. For mean stress tests for aluminum, no ratcheting was observed, due to elastic behavior in these tests. However, some differences were observed, as at equivalent 0.5% strain amplitude the stress amplitude was about 10% higher for tensile mean stress tests than for compressive mean stress tests. As presented in Figure 5.12 and Table 5.1 for SS304L CLI, stress amplitudes at midlife for stainless steel tests with large tensile mean strain (R ε = 0.75), are about 8% higher than for the equivalent fully-reversed tests (R ε = -1), due to hardening of the material resulting from large maximum strain (ε max = 3.2%). The fatigue behavior in terms of both strain-life and stress-life curves is shown in Figures 5.17 and 5.18, where the curves represent the fully-reversed data. This hardening led to a reduction in fatigue life. At 0.25% strain amplitude, the reduction in life is 35% (i.e., average of fatigue lives

87 at R ε = 0.75 listed in Table 5.1 as 120,022 and 119,450 is 35% less than the average of fatigue lives at R ε = -1 listed as 189,960 and 188,780 cycles). At 0.4% strain amplitude the reduction in fatigue life is less significant (18% reduction). The effects of both tensile and compressive mean strain on deformation behavior and fatigue life for other R ε ratio tests (R ε = 0 and R ε = ) conducted at 0.4% strain amplitude were also small (35% and 20% reduction in average fatigue life for R ε = 0 and R ε =, compared with R ε = -1, respectively). For SS304L THY, mean strain tests were only conducted at the strain amplitude level of 0.3%. Shorter lives, by a factor of more than 3 and 7 at R ε = 0 and R ε = 0.75, respectively, were obtained in presence of tensile mean strain. Therefore, significant difference between SS304L CLI and THY were observed with regards to tensile mean strain on fatigue life, as the SS304L THY grade was more sensitive to tensile mean strain. For SS304L CLI, at 0.25% strain amplitude, all negative mean strain tests (R ε = 2 and R ε = ) were runout tests and secondary hardening was observed (Figure 5.12), hence significantly higher stress amplitude at midlife. Although the midlife mean stress levels were at or near zero for these tests, the effect of negative mean strain on fatigue life was very significant, with more than a factor of 10 increase in fatigue lives (as compared to fully-reversed loading at the same strain amplitude), as can be seen in Figure 5.17(a). This is contrary to common expectation that mean strain has an effect on fatigue life only if it induces a non-relaxing mean stress. Similar test conducted on SS304L THY at 0.3% total strain amplitude and with R ε = presented the same behavior. Stress responses for this test and the fully reversed test (R ε = -1) at 0.3% strain amplitude for the SS304L THY grade are presented in Figure 5.15, which shows mean stress relaxation. In Figure 5.14,

88 significant increase in fatigue life for the test conducted with R ε = (as compared to the fully-reversed test at identical strain amplitude level) can be observed. The significant increase in fatigue life is also notable in Figure 5.17(b) and Table 5.2 for this material. To attempt to explain this surprising behavior, stress amplitude, maximum stress, and minimum stress responses for fully-reversed tests along with all mean strain tests for SS304L in strain control were compared (at 0.25% and 0.3% strain amplitude for SS304L CLI and SS304L THY, respectively). However, no correlation could be made between the level of stress and the observed fatigue lives, as stress responses were nearly identical for the different R ε ratios, while fatigue lives drastically differed. In load-controlled tests of SS304L CLI with tensile mean stress, fatigue lives were similar to fully-reversed tests, as presented in Figures 5.17(a) and 5.18(a). This is in spite of relatively large midlife tensile mean stresses of 41 MPa with R σ = -0.67 and 62 MPa with R σ = -0.55. Reduction of fatigue life due to tensile mean stress would normally be expected. This can be explained by the beneficial effect of strain hardening due to high maximum strain in these load-controlled tests resulting in reduced strain amplitude, as previously discussed. This beneficial effect due to reduced strain amplitude is thought to nullify the detrimental effect of tensile mean stress. For aluminum, load-controlled tests were conducted at equivalent total strain amplitude of 0.5%. However, due to elastic behavior at this level, no difference is expected between load-controlled and strain-controlled tests. The results are presented in Figures 5.17(c) and 5.18(c), where the curves represent the fully reversed behavior. Tensile mean stress of 200 MPa with R σ -0.25 resulted in shorter fatigue life by a factor of about three, and compressive mean stress of -200 MPa with R σ -3.4 resulted in

89 longer life, by a factor of about five, as can be observed in Table 5.3 and Figures 5.17(c) and 5.18(c). A mean stress parameter is, therefore, needed for life predictions under mean stress conditions. The Smith-Watson-Topper parameter was used to correlate the data and these results will be presented and discussed in Section 5.6. 5.4 Prestraining Effects For stainless steel the influence of prestraining was investigated by prestraining specimens in strain control at fully-reversed 2% strain amplitude for 10 cycles, and then fatigue testing under either load control or strain control. To avoid a large mean stress resulting from prestraining, the strain amplitude was gradually reduced after prestraining [65], as was explained in Chapter 3 (see Figure 3.3). For aluminum prestraining consisted in 10 fully-reversed cycles at 1.4% strain amplitude. Tests were conducted under four different conditions with the smaller cycles at four locations of the prestrain cycle hysteresis loop, as described in Chapter 3 (see Figure 3.5). Based on the linear damage rule, prestraining cycles consumed only about 3% of life for SS304L and 6% of life for Al 7075-T6. Stress amplitudes at the 10 th cycle of prestraining were 501, 501, and 562 MPa for SS304L CLI, SS304L THY, and aluminum, respectively. Results for prestrained tests listed in Tables 5.1 to 5.3 are from midlife constant amplitude cycles following prestraining. Midlife stress amplitudes from fully reversed tests on prestrained specimens are presented in Figure 4.9, superimposed with the monotonic and cyclic stress-strain curves. Considerable hardening is induced in SS304L CLI (about 35%), as prestrained test data are well above the cyclic stress-strain curve. For SS304L THY, due to secondary hardening for virgin material, when taking midlife values, only about 10% of hardening

90 is observed at 0.3% strain amplitude for the prestrained material. For both SS304L CLI and SS304L THY grades, prestraining led to failure of the specimen for tests conducted at the virgin material runout level (0.2% and 0.25% strain amplitude for SS304L CLI and SS304L THY, respectively) and no secondary hardening was observed. A runout specimen for the prestrained SS304L CLI material was obtained at the lower level of 0.175% strain amplitude and no significant secondary hardening was observed in this test either. Comparison of the stress responses obtained for SS304L CLI from prestrained tests and from mean strain tests with R ε = 0.75, where the maximum strain was greater than 3% shows more hardening due to prestraining (see Table 5.1). Thus, the hardening in prestrained tests mostly results from cycling at high strain amplitude, rather than from high maximum strain. In contrast, the effect of prestraining on the deformation behavior of aluminum does not exist, since the prestrained data are similar to those for the virgin material (see Figure 4.9(c)). Prestraining neither affected the deformation nor the fatigue behavior of aluminum. Figures 5.17(c) and 5.18(c) show prestrained and virgin material fullyreversed (R = -1) data overlap on both strain-life and stress-life curves. Mean stress tests conducted on prestrained specimens for aluminum (i.e. tests with stress-strain paths C and D in Figure 3.5) showed no effect of prestraining with respect to deformation or fatigue behaviors either, as data points for mean stress tests for virgin and prestrained specimens also overlap in Figures 5.17(c) and 5.18(c). The effects of prestraining for SS304L were dependent on the test control modes, however. Prestraining followed by strain-controlled tests led to about the same lives as

91 those for the virgin material for the SS304L CLI grade. This is in spite of the stress amplitudes for prestrained tests being about 30% higher than the corresponding virgin material tests, due to the initial hardening (see Table 5.1). For tests at 0.175% strain amplitude, hardening slope in stress amplitude response versus cycles was steeper for the virgin material, as compared to the prestrained material (which was nearly flat), as can be seen from Figure 5.19(a). This is consistent with the fact that secondary hardening was observed to be related to plastic strain amplitude. The prestrained material exhibited lower ductility and consequently slower hardening than the virgin material. In strain-controlled tests, prestraining was found to have more effect on the fatigue behavior of SS304L THY than SS304L CLI. At 0.25% strain amplitude, prestraining led to 30% increase in stress response in SS304L CLI. At identical strain amplitude of 0.25%, for SS304L THY, the virgin material presented secondary hardening, leading to a stress response at midlife greater than the one for the equivalent prestrained test. When comparing stress responses at a given number of cycles, however, prestraining in SS304L THY led to a level of hardening similar to the one observed in SS304L CLI (about 40%). Reduction in fatigue lives by a factor of more than five were observed due to prestraining in SS304L THY, whereas fatigue lives for prestrained and virgin SS304L CLI materials were very similar. Therefore, the behavior of SS304L THY grade is more sensitive to prestraining than the behavior of the SS304L CLI grade. In load-controlled tests, however, SS304L THY and SS304L CLI presented similar behaviors, as considerable increase in fatigue lives were observed due to prestraining. For load-controlled tests of SS304L, prestrained specimens had strain amplitudes which were smaller than those for the virgin specimens at identical stress

92 levels (see Table 5.1 for SS304L CLI and Table 5.2 for SS304L THY). In LCF, under load control, fatigue life of prestrained SS304L CLI specimens was slightly longer than the virgin material (LCF tests were conducted on SS304L CLI only). In HCF, prestrained materials exhibited much longer life than virgin materials, resulting in runout tests. Similar behavior was observed for SS304L CLI and SS304L THY in HCF, since prestraining resulted in a reduction of strain amplitude of about 53% on average, leading to runout tests for both materials at the lower stress levels. When considering strain-life or stress-life approach, prestraining appears to have little effect from strain-life point of view (Figures 5.17(a) and 5.17(b)), while it has significant beneficial effect based on the stress-life curve (Figure 5.18(a) and 5.18(b)) where prestrained data are well above the curve. Therefore, using a damage parameter that considers both stress and strain is a more appropriate approach for fatigue life prediction and correlation of load-controlled and strain-controlled prestrained fatigue data. Such data correlations are presented and discussed in Section 5.6. 5.5 Secondary Hardening in Stainless Steel 304L Under certain conditions, SS304L exhibited secondary hardening. In such cases, after an initial hardening, softening was observed, followed by a second period of hardening that continued throughout the tests. Stress amplitude responses of tests with secondary hardening are presented in Figure 5.19(a) for SS304L CLI. This figure includes fully-reversed runout tests at 0.2% and 0.175% strain amplitudes as well as tests under negative mean strain conditions (R ε = 2 and R ε = ). The amount of hardening appears to be related to the strain amplitude level, as more hardening and greater hardening rates are observed at higher strain amplitude levels.

93 In Figure 5.19(b) for SS304L THY, secondary hardening is more significant, as up to 100% hardening was observed for the test at 0.3% strain amplitude with R ε =. As also seen in this plot, saturation can occur in the hardening process, since the stress amplitude response reaches a near plateau. Stress responses for all tests presenting secondary hardening under fully-reversed constant amplitude loading conditions are presented in Figure 5.20, including results for both SS304L grades. Comparisons between the two SS304L grades show that secondary hardening occurs at higher strain amplitude level, to a greater extent, and with higher hardening rates (steeper slopes) for SS304L THY than it does for SS304L CLI. In addition to the considerable secondary hardening, significant increases in fatigue lives were obtained, as specimens were cycled up to several million cycles without failure (i.e. runout test data in Figures 5.17(a) and 5.17(b), and 5.18(a) and 5.18(b)). One exception was for SS304L THY for the fully-reversed constant amplitude tests at 0.3% strain amplitude, where secondary hardening started before failure occurred. All secondary hardening tests were conducted with strain amplitudes at or below 0.25% for SS304L CLI. These are located near the transition in the cyclic stress-strain curve shown in Figure 4.9(a). A similar change in behavior was observed by Kaleta and Zietek at strain amplitude of 0.38% for SS304L [69], where superimposing hysteresis loops indicated an inflection point at this strain amplitude. For SS304L THY, all secondary hardening tests occurred at or below 0.3% total strain amplitude, although no drastic change in the stress-strain curve was observed at this point. However, for both SS304L CLI and SS304L THY, secondary hardening tests occurred at runout levels, or at values close to the runout level.

94 As mentioned earlier, hardening (not specifically secondary hardening) in austenitic stainless steels has been found to be linked to martensitic transformation at high strain amplitudes [34, 36, 39, 40], and can be strain-induced or stress-induced [36]. The amount of transformation, and thus the hardening, is proportional to the amount of plastic strain. Kaleta and Zietek determined the cyclic plastic strain amplitude threshold to be at 0.6% for AISI 304L stainless steel [69]. They proposed to consider this threshold as an additional material constant that can be included in plasticity models to evaluate the deformation behavior. Krupp et al. estimated a lower plastic strain amplitude value of 0.3% for AISI 301, 304 and 304L austenitic stainless steels [70]. Some researchers have postulated the importance of cumulative plastic strain in martensitic transformation [39]. A cumulative plastic strain amplitude threshold can be defined that depends on different factors, including the composition of the austenitic stainless steel [39]. Nickel, chromium, and most particularly carbon are known to stabilize the austenite phase [34, 69]. In the present study, cumulative plastic strain (N f Δε p /2) was computed for all tests for SS304L and plotted versus number of cycles to failure (Figure 5.21). From these plots, thresholds were identified (at 210 and 60 for SS304L CLI, and SS304L THY, respectively), above which secondary hardening was most likely to occur. For SS304L CLI, comparison of tests at similar total strain amplitudes showed that for specimens that failed, cumulative plastic strain never crossed the threshold, whereas secondary hardening started around this threshold for runout tests (Figure 5.22(a)). For SS304L THY (Figure 5.22(b)), secondary hardening was not always associated with runout fatigue lives. Nonetheless, for all tests presenting secondary hardening, the cumulative plastic strain exceeded the threshold for this SS304L grade as

95 well. While this threshold value can be used to predict when secondary hardening may start, it does not predict if or explain why it occurs. It is only an indication of the phenomenon, as attested by the prestrained test for SS304L CLI at 0.175% total strain amplitude, for which the cumulative plastic strain crossed the threshold, but only presented negligible secondary hardening (2%). Martensitic transformation might not entirely explain secondary hardening and other microstructure alterations could also co-occur in the material [8]. According to Gerland et al., a structure named corduroy structure (because it appears as alternated dark and light bands) can progressively form in the material, and occurs to larger extent when the material is subjected to many cycles at low strain amplitudes. The extent of this microstructure alteration has been shown to be related to the amount of secondary hardening [8]. During martensitic transformation, two types of martensite can form, the α phase (bcc) and the ε phase (hcp) [69, 71]. The α phase is ferro-magnetic and can be easily detected. In this investigation, qualitative magnetic measurements were made on different tested specimens using a commercial magnetometer. Strong magnetization was observed for specimens cycled at high strain amplitudes, and for specimens that exhibited secondary hardening. Accurate quantitative measurements can be made using more sensitive techniques, such as the vibrating sample magnetometer technique used by means of a super conducting quantum interface device (SQUID) described in [72]. A comparison between strain-controlled tests conducted on virgin and prestrained (10 cycles at 2% total strain amplitude) specimens at 0.175% strain amplitude for SS304L CLI can help to further understanding of this phenomenon. For the virgin

96 material, no significant amount of martensite was present before testing (i.e. no ferromagnetic properties). After cycling for 4x10 6 cycles, the specimen exhibited secondary hardening and magnetic properties, indicating formation of α martensite phase. For the prestrained specimen, cyclic loading at high strain amplitude induced martensitic transformation as verified by ferro-magnetic properties prior to the start of the fatigue test at 0.175% strain amplitude. Although the specimen survived more than 3x10 6 cycles and did not fail, under this total strain amplitude no significant secondary hardening was observed (see Figure 5.19). In an attempt to further characterized secondary hardening, micro-hardness (Vickers hardness) was measured across the grip sections and across the gage sections of a SS304L THY specimen and a SS304L CLI specimen. Both tests were conducted in strain control under constant amplitude fully-reversed conditions, presented secondary hardening, and were runout tests. The SS304L THY specimen was cycled at 0.25% strain amplitude, and the SS304L CLI specimen was tested at 0.2% strain amplitude. For comparison, measurements were also conducted across the gage section of a SS304L CLI specimen tested at 0.2% strain amplitude under the same conditions, but that did not present secondary hardening, and failed. The distributions for micro-hardness measurements are shown in Figure 5.23. The differences in mean hardness between gage section and grip section of the same specimen can be explained by the differences in stresses observed in the two parts of the specimen, arising from much larger diameter in the grip section, as compared to the gage section. Shift of mean hardness observed in the two SS304L CLI specimens tested under the same conditions, can be attributed to differences in stress levels as well, since secondary hardening resulted in higher stress

97 level for the runout specimen. Although the shift in mean hardness can be attributed to differences in hardening arising from different stress levels, the deviation in hardness measurements is the most significant feature in this comparison. For both SS304L CLI and THY secondary hardening specimens, the scatter in hardness observed for the gage section, and characterized by a broader distribution of hardness values, can only be attributed to heterogeneity in the material. Since the grip section, in both cases, was more homogeneous, as indicated by a narrow distribution of hardness values for this section, heterogeneity of the gage section is most likely due to scattered martensitic transformation within this region, as this is a local phenomenon. The higher Vickers hardness values most probably correspond to regions where phase transformation occurred. The results obtained in the gage section of the specimen that did not present secondary hardening are in accordance with this explanation, as the distribution of hardness values for this specimen is narrow as well. The effect of secondary hardening on the stiffness of SS304L was also studied, by evaluating changes in elastic modulus, measured from experimental hysteresis loops. However, due to the absence of a clear trend in stiffness behavior, no conclusion could be made based on changes in stiffness. As discussed earlier, martensitic transformation might not entirely explain secondary hardening and other microstructure alteration(s) could also co-occur in the material. Prestraining can induce sufficient initial hardening to prevent or hinder additional alteration(s) of the microstructure by cycling at lower strain amplitude.

5.6 Fatigue Life Correlations and Predictions for Constant Amplitude Tests As mentioned previously, because of the strong deformation history effect of SS304L, both strain and stress should be taken into account for accurate fatigue life prediction. To accomplish this, the Smith-Watson-Topper (SWT) (Equation 5.4) [21] and Fatemi-Socie (FS) parameters (Equation 5.5) [22] were used. These parameters include both strain and stress terms and can also take into account mean stress effects. Figure 5.24 shows all the constant amplitude fatigue data for SS304L and Al 7075-T6 correlated with the SWT parameter. No significant difference is observed between strain-life (Figure 5.17(c)), stress-life (Figure 5.18(c)), SWT (Figure 5.24(c)) and FS (Figure 5.25(c)) data correlations for aluminum. This is expected since prestraining did not affect the response of this material. In contrast, the SWT parameter correlates prestrained stainless steel data much better than strain-life curve (Figures 5.17(a) and 5.17(b)) or stress-life curve (Figures 5.18(a) and 5.18(b)). The prestrained data in strain-controlled HCF tests for SS304L CLI are not well correlated with the SWT parameter (Figure 5.24(a)) due to the high maximum stress in these tests, resulting from the material hardening that did not produce shorter lives. However, the FS parameter represents these data somewhat better, as seen in Figure 5.25(a). For SS304L CLI, it appears that SWT parameter slightly better represents mean strain data, whereas FS parameter fits prestrained data more accurately. For SS304L THY not as many tests were conducted, and the two parameters provide fairly equivalent results (Figures 5.24 (b) and 5.25(b)). 98

99 With respect to constant amplitude fatigue life behavior, comparisons of the strain-life, stress-life, SWT-life and FS-life curves for SS304L THY and SS304L CLI yield the same observations. The two SS304L grades presented very similar behavior in LCF, while SS304L THY presented slightly longer fatigue lives at intermediate and long lives. The SS304L THY grade seems to be more sensitive to mean strain and prestraining effects. Secondary hardening was also more significant in this material. One explanation might be the slightly lower carbon content in SS304L THY rendering this material slightly more likely to experience martensitic transformation. A good indicator of the relative stability of the austenite phase is the nickel equivalent, the lower it is, the more metastable the austenite. Using Equation 2.6 for nickel equivalence, Ni eq was found to be 24.2% and 23.8% for SS304L CLI and SS304L THY, respectively, indicating very small difference between the two grades of SS304L. For Al 7075-T6, the compressive mean stress data with or without prestraining are not well correlated with the SWT parameter, as can be seen from Figure 5.24(c). Although compressive mean stress data are better represented, tensile mean stress is not fully taken into account by the FS parameter either (Figure 5.25(c)). As different materials can have different mean stress sensitivities in fatigue behavior, an alternate form of the SWT parameter in the left side of Equation 5.4 may be used, where the maximum stress term can be raised to an exponent, or the mean stress term can be multiplied by a coefficient. The value of the exponent or coefficient can then be found from some experimental mean stress data fits [73]. However, while this approach can potentially account for mean stress sensitivities of different materials and improve life predictions, such improvements would be at the expense of requiring

100 additional material properties, necessitating collection of some mean stress test data for life predictions. Experimental versus predicted lives for all three materials based on the strain-life or stress-life, SWT, and FS approaches are presented in Figures 5.26 and 5.27. The dashed lines represent scatter bands of factors of two and five. The great majority of data are well predicted with the SWT or the FS parameter. For all three approaches, runout test data for SS304L are not well taken into account, because of the secondary hardening occurring at the runout level. 5.7 Conclusions 1) Load-controlled test data were similar to strain-controlled test data for the two types of materials, showing little effect of the test control mode on fully-reversed deformation and fatigue behaviors. In spite of large mean strain of about 5% due to ratcheting in some SS304L CLI fully-reversed load-controlled tests, fatigue lives were only slightly shorter than the corresponding lives in strain control. Therefore, strain-life, stress-life, SWT-life, and FS-life curves, although obtained by fitting strain-controlled data, represent load-controlled data very well. 2) In strain-controlled mean strain tests of SS304L, due to considerable amount of plasticity, the mean stress relaxed to less than 20 MPa during the first few percent of the fatigue life. In load-controlled mean stress tests conducted only for SS304L CLI, considerable ratcheting was observed, leading to hardening and about 30% reduction in strain amplitude. 3) The effect of mean stress in either strain-controlled or load-controlled tests of SS304L was small in most cases. This was due to mean stress relaxation in strain

101 control, and beneficial effect of hardening due to ratcheting nullifying detrimental effect of tensile mean stress in load control. The only exception was for straincontrolled tests with compressive mean strain at 0.25% strain amplitude for SS304L CLI and at 0.3% strain amplitude for SS304L THY, where secondary hardening was observed. For these tests, in spite of mean stress relaxation to near zero and contrary to expectations, fatigue lives were at least nine times longer than those in fully-reversed tests. Tensile mean strain was found to have relatively more effects on the behavior of SS304L THY than on the behavior of SS304L CLI, since shorter lives were observed in the presence of tensile mean strain for this material. Tensile mean strain was found to have little effect on the fatigue behavior for SS304L CLI. For aluminum, mean stresses had the expected effects, as tensile mean stress was detrimental, and compressive mean stress was beneficial to fatigue life. 4) Prestraining induced considerable hardening in SS304L. The hardening mostly results from prior cycling at high strain amplitude, rather than from prior high maximum strain. Prestraining appeared to have more effect on the deformation behavior of SS304L THY than CLI, in strain control. Reduction in fatigue lives by a factor of more than five were observed in SS304L THY, whereas fatigue lives for prestrained and virgin SS304L CLI materials were very similar in straincontrolled tests. In load-controlled tests, however, SS304L THY and SS304L CLI presented similar behaviors, as considerable increase in fatigue lives were observed due to prestraining. Hardening in load-controlled tests induced

102 significant reduction in strain amplitude response. Prestraining neither affected the deformation nor the fatigue behavior of Al 7075-T6. 5) All SS304L tests exhibiting secondary hardening had total strain amplitudes at or below 0.25% for SS304L CLI and at or below 0.3% for SS304L THY. Although for SS304L CLI all tests exhibiting secondary hardening presented runout fatigue life, some SS304L THY specimens failed after presenting secondary hardening. However, for SS304L THY, greater hardening rates were observed than for SS304 CLI. 6) Strong ferro-magnetic properties, typically associated with martensitic transformation and commonly believed to result from accumulation of plastic strain, were observed for specimens with or without secondary hardening. Vickers micro-hardness measurements revealed strong heterogeneity of the material in sections that presented secondary hardening for both SS304L CLI and THY. This heterogeneity can most likely be attributed to martensitic transformation. However, secondary hardening may be due to the formation of alternate structure(s) rather than or in addition to martensitic phase transformation. 7) With respect to constant amplitude fatigue behavior, the two SS304L grades presented very similar behaviors in LCF, while SS304L THY presented slightly longer fatigue lives at intermediate and long lives. The SS304L THY grade was found to be more sensitive to mean strain and prestraining effects. 8) A fatigue life parameter with both stress and strain terms is necessary to correlate stainless steel data due to the strong deformation history sensitivity of this material. The use of a mean stress parameter was also necessary to correlate mean

103 stress data for aluminum and stainless steel. The SWT and FS parameters were shown to correlate most of the fatigue data reasonably well for both grades of stainless steel and aluminum.

104 Table 5.1 Summary of constant amplitude fatigue test results for SS304L CLI. Specimen ID Control Mode R ø (mm) ε a (%) ε m (%) (Δε p /2) calculated (%) σ a (MPa) σ m (MPa) SWT (MPa) Fully-Reversed Tests UTCLI34 strain -1 5.11 2.00-0.02 1.67 592-1 1,522 6.89 630 UTCLI35 strain -1 5.09 2.00-0.02 1.68 626-5 1,560 7.09 504 UTCLI2 strain -1 5.12 1.00 0.00 0.79 412 1 898 2.82 2,350 UTCLI38 strain -1 5.16 1.00-0.01 0.79 403 0 890 2.79 2,190 UTCLI1 strain -1 5.08 0.390-0.01 0.26 252 0 439 0.88 30,680 UTCLI5 strain -1 5.16 0.400 0.00 0.28 243 3 439 0.90 23,142 UTCLI4 strain -1 5.16 0.246 0.00 0.14 208 7 322 0.52 189,960 UTCLI10 strain -1 5.14 0.250 0.00 0.14 212 7 328 0.53 188,780 UTCLI11 strain -1 5.11 0.200 0.00 0.10 200 8 286 0.41 416,826 UTCLI12 strain -1 5.07 0.200 0.00 0.09 215 3 292 0.42 >3,400,000 UTCLI37 strain -1 5.12 0.200 0.00 0.10 200 17 291 0.42 359,676 UTCLI19 strain -1 5.12 0.200 0.00 0.09 217-3 289 0.41 >3,908,057 UTCLI85 strain -1 5.14 0.175 0.00 0.07 211-7 264 0.35 >8,087,768 UTCLI39 load -1 5.13 0.969 5.41 0.75 433 6 913 2.82 1,780 UTCLI40 load -1 5.13 1.017 4.89 0.80 433 5 934 2.96 1,756 UTCLI22 load -1 5.06 0.395-0.24 0.27 242 1 434 0.88 39,990 UTCLI17 load -1 5.08 0.347-0.96 0.22 241 1 405 0.77 31,912 UTCLI18 load -1 5.08 0.249-0.43 0.14 209 1 320 0.52 306,982 UTCLI27 load -1 5.14 0.253-0.07 0.15 210 1 323 0.53 213,552 Mean Strain and Mean Stress UTCLI49 strain 2 5.16 0.255-0.75 0.14 229-7 332 0.53 >2,332,640 UTCLI25 strain 5.08 0.402-0.40 0.28 249 3 446 0.91 18,686 UTCLI32 strain 5.13 0.402-0.40 0.28 245 1 440 0.90 24,500 UTCLI29 strain 5.11 0.251-0.25 0.11 286-5 372 0.57 >7,817,714 UTCLI20 strain 0 5.08 0.398 0.40 0.27 254 9 452 0.91 16,856 UTCLI28 strain 0 5.08 0.398 0.40 0.27 253 7 450 0.91 18,184 UTCLI21 strain 0 5.08 0.250 0.25 0.14 215 18 338 0.54 99,804 UTCLI23 strain 0 5.11 0.248 0.25 0.14 213 14 332 0.53 86,106 UTCLI50 strain 0.75 5.16 0.389 2.76 0.25 265 6 454 0.90 21,768 UTCLI51 strain 0.75 5.12 0.390 2.76 0.25 270 5 458 0.91 22,434 UTCLI48 strain 0.75 5.13 0.245 1.74 0.13 225 15 339 0.53 120,622 UTCLI52 strain 0.75 5.16 0.246 1.74 0.13 225 15 340 0.53 119,450 UTCLI53 load -0.67 5.13 0.187 1.58 0.08 214 42 306 0.41 215,022 UTCLI59 load -0.67 5.17 0.191 1.56 0.08 213 41 308 0.42 115,634 UTCLI54 load -0.55 5.16 0.173 2.61 0.06 216 62 307 0.39 263,184 UTCLI60 load -0.55 5.16 0.170 2.39 0.06 215 62 304 0.38 255,824 Prestrained Tests* UTCLI66 strain -1 5.11 0.400-0.05 0.24 316 1 498 0.98 20,264 UTCLI70 strain -1 5.16 0.401-0.30 0.24 315 4 501 0.98 23,530 UTCLI64 strain -1 5.14 0.249-0.05 0.11 283 1 373 0.57 224,058 UTCLI68 strain -1 5.16 0.251-0.30 0.11 282 28 390 0.59 122,372 UTCLI83 strain -1 5.13 0.200-0.05 0.06 268 11 331 0.44 608,920 UTCLI84 strain -1 5.16 0.175-0.05 0.04 268-10 298 0.37 >6,288,160 UTCLI73 load -1 5.16 NA NA NA 409 0 NA NA 2,560 UTCLI74 load -1 5.13 0.945 0.72 0.73 415 4 881 2.68 2,192 UTCLI41 load -1 5.12 0.143-0.44 0.02 242 0 260 0.30 >2,270,350 UTCLI71 load -1 5.16 0.120-0.42 0.01 209 0 222 0.23 >1,082,282 *Prestraining was conducted at 2% strain amplitude for 10 cycles. FS (%) 2N f

105 Table 5.2 Summary of constant amplitude fatigue test results for SS304L THY. Specimen ID Control mode R ø (mm) ε a (%) ε m (%) (Δε p /2) calculated (%) σ a (MPa) σ m (MPa) SWT (MPa) Fully-Reversed Tests UTTHY4 strain -1 5.16 2.00-0.02 1.70 571 1.0 1,485 7.10 442 UTTHY5 strain -1 5.14 2.00-0.02 1.70 603 0.3 1,527 7.33 468 UTTHY2 strain -1 5.13 1.00 0.00 0.79 417 1.3 900 2.97 1,950 UTTHY3 strain -1 5.14 1.00-0.01 0.78 417 0.4 898 2.96 2,308 UTTHY11 strain -1 5.11 0.600 0.00 0.42 339 0.7 627 1.59 5,478 UTTHY12 strain -1 5.11 0.600 0.00 0.44 317 0.8 607 1.55 5,140 UTTHY22 strain -1 5.16 0.500 0.00 0.34 304 0.9 542 1.26 21,886 UTTHY9 strain -1 5.14 0.400 0.00 0.26 271 0.9 458 0.96 43,414 UTTHY24 strain -1 5.14 0.400 0.00 0.26 271 5.6 462 0.96 34,590 UTTHY7 strain -1 5.14 0.300 0.00 0.15 287-2.3 406 0.72 1,057,360 UTTHY10 strain -1 5.13 0.300 0.00 0.17 261-0.4 389 0.70 625,746 UTTHY6 strain -1 5.16 0.250 0.00 0.09 316-4.6 388 0.61 >4,043,156 UTTHY35 load -1 5.17 0.455 0.09 0.30 300 1.5 515 1.14 26,250 UTTHY30 load -1 5.16 0.431 0.21 0.28 301 1.3 501 1.08 37,252 UTTHY8 load -1 5.16 0.407 0.11 0.27 274 1.2 465 0.98 46,882 UTTHY31 load -1 5.14 0.410 0.10 0.27 275 0.9 467 0.99 40,400 Mean Strain Tests UTTHY13 strain 5.12 0.301-0.30 0.06 475-14.8 517 0.86 >8,354,260 UTTHY14 strain 0 5.14 0.299 0.30 0.18 234 2.0 369 0.67 177,882 UTTHY17 strain 0 5.11 0.299 0.30 0.18 239 1.5 373 0.68 256,188 UTTHY15 strain 0.75 5.14 0.294 2.08 0.16 257 6.4 387 0.68 107,410 UTTHY16 strain 0.75 5.13 0.294 2.08 0.16 255 7.6 386 0.68 113,610 *Prestrained Tests UTTHY19 strain -1 5.12 0.300-0.06 0.14 301 0.3 418 0.73 157,792 UTTHY20 strain -1 5.16 0.300-0.06 0.15 299 0.4 416 0.73 139,132 UTTHY41 strain -1 5.16 0.250-0.04 0.10 285 14.7 380 0.60 289,914 UTTHY42 strain -1 5.17 0.250-0.04 0.10 286-2.6 370 0.59 416,224 UTTHY18 load -1 5.13 0.186-0.04 0.04 276 0.4 315 0.42 >6,323,860 *Prestraining was conducted at 2% strain amplitude for 10 cycles. FS (%) 2N f

106 Table 5.3 Summary of constant amplitude fatigue test results for Al 7075-T6. Specimen ID Control mode R ø (mm) ε a (%) ε m (%) Δε p /2 calculated (%) σ a (MPa) σ m (MPa) SWT (MPa) Fully-Reversed Tests A41 strain -1 4.22 1.99-0.03 1.14 601-6 915 4.42 76 A54 strain -1 4.14 1.39-0.02 0.57 572-11 742 2.95 366 A53 strain -1 4.14 1.40-0.02 0.57 570-11 743 2.94 332 A78 strain -1 4.24 1.00 0.00 0.15 548-5 619 1.90 834 A81 strain -1 4.20 1.00-0.01 0.19 548-7 618 1.98 758 A28 strain -1 4.19 0.500 0.00 0.00 361 33 373 0.93 25,108 A17 strain -1 5.00 0.500 0.00 0.00 355-3 352 0.89 32,368 A11 strain -1 5.08 0.400 0.00 0.00 288 8 289 0.69 154,602 A30 strain -1 4.22 0.400 0.00 0.00 287 15 292 0.69 103,786 A82 load -1 4.24 0.940 0.40 0.17 547 5 605 1.94 592 A83 load -1 4.23 1.00 0.54 0.22 550 5 626 2.08 464 A42 load -1 4.17 0.300 0.00 0.00 207 0 209 0.47 1,415,406 A31 load -1 4.23 0.300 0.00 0.00 207 0 209 0.47 1,097,500 A38 load -1 4.23 0.230 0.00 0.00 159 0 161 0.34 3,495,724 A25 load -1 4.19 0.230 0.00 0.00 159 0 161 0.34 >24,946,798 Mean Strain and Mean Stress Tests A72 load -3.19 4.23 0.497-0.87 0.00 367-192 248 0.80 112,404 A73 load -3.53 4.23 0.497-0.91 0.00 367-205 238 0.80 153,932 A71 load -0.25 4.23 0.500 1.89 0.00 335 199 464 0.95 7,364 A70 load -0.25 4.24 0.500 1.09 0.00 332 200 433 0.94 10,724 *Prestrained Tests Without Mean Stress A58 load -1 4.17 0.508 0.47 0.00 352-4 353 0.88 21,602 A61 load -1 4.12 0.508 0.44 0.00 358 0 358 0.90 23,256 A59 load -1 4.14 0.496-0.46 0.00 355 0 353 0.89 19,958 A62 load -1 4.17 0.503-0.48 0.00 352 1 354 0.88 22,450 *Prestrained Tests With Mean Stress A68 load -0.26 4.24 0.497 0.64 0.000 338 198 433 0.96 9,690 A51 load -0.27 4.18 0.498 0.61 0.00 337 195 433 0.95 8,768 A67 load -3.67 4.20 0.499-0.85 0.00 365-209 235 0.79 104,014 A48 load -3.38 4.19 0.503-0.86 0.00 366-199 243 0.80 92,150 *Prestraining was conducted at 2% strain amplitude for 10 cycles. Although load control was used, it is equivalent to strain control due to elastic behavior. FS (%) 2N f

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 107 1000 UT data MMC data 100 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f 1000 (a) 100 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 1000 (b) 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Reversals to Failure, 2N f 1E+7 1E+8 (c) Figure 5.1 Stress amplitude versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Plastic Strain Amplitude Plastic Strain Amplitude Plastic Strain Amplitude 108 10.00% 1.00% 0.10% UT data MMC data 0.01% 1E+2 1E+3 1E+4 1E+5 1E+6 Reversals to Failure, 2N f 1E+7 (a) 10.00% 1.00% 0.10% 0.01% 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f (b) 10.00% 1.00% 0.10% 0.01% 1E+1 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f (c) Figure 5.2 Calculated plastic strain amplitude versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Strain Amplitude Strain Amplitude Strain Amplitude 109 10.00% 1.00% total elastic plastic total UT elastic UT plastic UT total MMC elastic MMC plastic MMC runout 0.10% 0.01% 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f (a) 10.00% 1.00% runout 0.10% 0.01% 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 10.00% fit total fit elastic fit plastic data total data elastic data plastic (b) data total data elastic data plastic total fit elastic fit plastic fit 1.00% runout 0.10% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Reversals to Failure, 2N f 1E+7 1E+8 (c) Figure 5.3 Total, elastic, and plastic strain amplitude versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

SWT (MPa) SWT (MPa) SWT (MPa) 110 10000 MMC data UT data 1000 runout 100 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f (a) 10000 1000 runout 100 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 (b) 10000 R -1-0.25-3.4 LC LC εc PS PS PS 1000 runout 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Reversals to Failure, 2N f (c) Figure 5.4 SWT parameter versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

FS FS FS 111 10.0% 1.0% runout UT data MMC data 0.1% 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 (a) 10.0% 1.0% runout 0.1% 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f (b) 10.0% R -1-0.25-3.4 LC LC εc PS PS PS 1.0% runout 0.1% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Reversals to Failure, 2N f 1E+7 1E+8 (c) Figure 5.5 FS parameter versus reversals to failure for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

112 (a) (b) (c) (d) Figure 5.6 Comparison between SS304L CLI and THY grades. (a) Strain-life curves, (b) stress-life curves, (c) SWT-life curves, and (d) FS-life curves.

Strain Amplitude Strain Amplitude Strain Amplitude 113 10.00% 1.00% εc LC Total Elastic Plastic runout 0.10% 0.01% 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 (a) 10.0% Total εc LC Elastic 1.0% Plastic runout 0.1% 0.0% 1E+2 1E+3 1E+4 1E+5 1E+6 Reversals to Failure, 2N f 1E+7 (b) 10.0% εc LC Total Elastic Plastic 1.0% 0.1% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Reversals to Failure, 2N f (c) Figure 5.7 Strain-life curves including elastic, plastic and total strain amplitudes for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress (MPa) 114 500 first cycle 84th cycle 0-500 -1.0% 0.0% 1.0% 2.0% 3.0% 4.0% 5.0% Strain Figure 5.8 Hysteresis loops in a fully-reversed constant amplitude load-controlled test at 412 MPa stress amplitude for SS304L CLI.

115 (a) (b) (c) Figure 5.9 Strain response in fully-reversed constant amplitude load-controlled tests for SS304L CLI, (a) at 412 MPa stress amplitude, (b) at 243 MPa stress amplitude, and (c) at 210 MPa stress amplitude. Strain histories for equivalent strain-controlled tests are also plotted for comparison.

116 (a) (b) Figure 5.10 Strain response in fully-reversed constant amplitude load-controlled tests for SS304L THY, (a) at 300 MPa stress amplitude, and (b) at 274 MPa stress amplitude. Strain histories for the equivalent strain-controlled tests are also plotted for comparison.

117 Figure 5.11 Representation of the different R ratios used in mean strain and mean stress tests for SS304L.

Stress Amplitude (MPa) Stress Amplitude (MPa) 118 400 ε a R ε = 2-1 0 0.75 0.25% 0.4% 300 200 100 400 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Cycle Ratio, N/N f (a) ε a R ε = 2-1 0 0.75 0.25% 0.4% 300 200 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N (b) Figure 5.12 Stress amplitude response in mean strain, strain-controlled tests for SS304L CLI in (a) linear scale, and (b) log scale.

Mean Stress (MPa) Mean Stress (MPa) 119 60 40 ε a R ε = 2-1 0 0.75 0.25% 0.4% 20 0-20 -40 60 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Cycle Ratio, N/N f (a) ε a R ε = 2-1 0 0.75 0.25% 0.4% 20 0-20 -40 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N (b) Figure 5.13 Mean stress response in mean strain, strain-controlled tests for SS304L CLI in (a) linear scale, and (b) log scale.

Stress Amplitude (MPa) Stress Amplitude (MPa) 120 600 500 ε a R ε = -1 0 0.75 0.3% 400 300 200 100 600 500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Cycle Ratio, N/N f (a) ε a R ε = -1 0 0.75 0.3% 400 300 200 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N (b) Figure 5.14 Stress amplitude response in mean strain, strain-controlled tests at ε a = 0.3% for SS304L THY in (a) linear scale, and (b) log scale.

Mean Stress (MPa) Mean Stress (MPa) 121 50 40 30 20 10 0-10 -20-30 -40-50 50 40 30 20 10 0-10 -20-30 -40-50 0.3% ε a R ε = -1 0 0.75 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Cycle Ratio, N/N f (a) ε a R ε = -1 0 0.75 0.3% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N (b) Figure 5.15 Mean stress response in mean strain, strain-controlled tests at ε a = 0.3% for SS304L THY in (a) linear scale, and (b) log scale.

Mean Strain Mean Strain Strain Amplitude Strain Amplitude 122 4.0% 3.5% 3.0% R σ -1-0.67-0.55 ε m ε a σ a = 215 MPa 0.4% 0.3% 2.5% 2.0% 0.2% 1.5% 1.0% 0.1% 0.5% 0.0% 0.0E+0 4.0% 3.5% 3.0% 2.5% Number of Cycles, N (a) R σ -1-0.67-0.55 σ a = 215 MPa ε m ε a 0.0% 1.2E+5 0.4% 0.3% 2.0% 0.2% 1.5% 1.0% 0.1% 0.5% 0.0% 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Number of Cycles, N (b) 0.0% Figure 5.16 Mean strain and strain amplitude in mean stress load-controlled tests for SS304L CLI at 215 MPa stress amplitude in (a) linear scale, and (b) log scale.

Strain Amplitude Strain Amplitude Strain Amplitude 123 10.0% 1.0% ε a = 0.25% or 0.4% in mean strain tests (εc) σ a = 215 MPa in mean stress tests (LC) R ε (εc) 2-1 0 0.75-1 (PS) R σ (LC) -1-0.67-0.55-1 (PS) runout 0.1% 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 (a) 10.0% R ε (εc) R σ (LC) -1 0 0.75-1 (PS) -1-1 (PS) 1.0% runout ε a = 0.3% in mean strain tests (εc) 0.1% 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f (b) 10.0% R -1-0.25-3.4 LC LC PS PS PS εc 1.0% ε a = 0.5% in all mean stress tests 0.1% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Reversals to Failure, 2N f (c) Figure 5.17 Strain-life curves including all constant amplitude data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 124 1000 R ε (εc) 2-1 0 0.75-1 (PS) R σ (LC) -1-0.67-0.55-1 (PS) runout ε a = 0.25% or 0.4% in mean strain tests (εc) σ a = 215 MPa in mean stress tests (LC) 100 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 (a) 1000 R ε (εc) -1 0 0.75-1 R σ (LC) -1-1 (PS) runout ε a = 0.3% in mean strain tests (εc) 100 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 (b) 1000 R -1-0.25-3.4 LC LC εc PS PS PS ε a = 0.5% in all mean stress tests 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Reversals to Failure, 2N f (c) Figure 5.18 Stress-life curves including all constant amplitude data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Stress Amplitude (MPa) Stress Amplitude (MPa) 125 350 340 330 320 310 300 290 280 270 260 250 240 230 220 210 200 190 49 ε a = 0.25 0.25% R2 R ε = 2 29 ε a = 0.25 0.25% Rinf R ε = 12 ε a = 0.20.2% R ε = -1 37 ε a = 0.20.2% R ε = -1 85 ε a = 0.175% R ε = -1 84 PS, 0.175ps ε a = 0.175% R ε = -1 0E+0 1E+6 2E+6 3E+6 4E+6 Number of Cycles, N (a) 500 450 400 350 300 250 UTTHY13 ε a = 0.3% (0.3%) R ε = Rin UTTHY7 ε a = 0.3% (0.3%) R ε = -1 Rε = -1 UTTHY10 ε a = 0.3% (0.3%) R ε = -1Rε = -1 THY6 ε a = 0.25% (0.25%) R ε Rε = -1 = -1 200 0E+0 1E+6 2E+6 3E+6 4E+6 5E+6 Number of Cycles, N (b) Figure 5.19 Stress response in tests presenting secondary hardening for (a) SS304L CLI, and (b) SS304L THY.

Stress Amplitude (MPa) 126 400 350 UTTHY7 (0.3%) UTTHY10 (0.3%) UTTHY6 (0.25%) UTCLI12 (0.2%) UTCLI37 (0.2%) UTCLI19 (0.2%) UTCLI11 (0.2%) UTCLI85 (0.175%) 300 250 200 150 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Number of Cycles, N Figure 5.20 Observation of secondary hardening in stress amplitude response for SS304L in constant amplitude fully-reversed conditions. Both failed and runout tests are represented.

127 (a) (b) Figure 5.21 Determination of a threshold in cumulative plastic strain in tests presenting secondary hardening for (a) SS304L CLI, and (b) SS304L THY.

128 (a) (b) Figure 5.22 Cumulative plastic strain in tests conducted at strain amplitude levels where secondary hardening was observed for (a) SS304L CLI, and (b) SS304L THY.

129 Figure 5.23 Distributions of Vickers hardness measurements across the gage section and the grip section of a SS304L CLI specimen tested at fully-reversed (CA, FR) 0.2% constant strain amplitude, and a SS304L THY specimen tested at fully-reversed 0.25% constant strain amplitude. Both specimens presented secondary hardening (SH). Results obtained from measurements in the gage section of a SS304L CLI specimen tested at fully-reversed 0.2% constant strain amplitude that did not present secondary hardening are also shown.

SWT (MPa) SWT (MPa) SWT (MPa) 130 10000 1000 R ε (εc) 2-1 0 0.75-1(PS) R σ (LC) -1-0.67-0.55-1 (PS) runout 100 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 10000 1000 (a) R ε (εc) -1 0 0.75-1 (PS) R σ (LC) -1-1 (PS) runout 100 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 10000 (b) R -1-0.25-3.4 LC LC εc PS PS PS 1000 100 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Reversals to Failure, 2N f (c) Figure 5.24 SWT curves including all constant amplitude fatigue data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

FS FS FS 131 10.0% 1.0% R ε (εc) R σ (LC) runout 2-1 0 0.75-1 (PS) -1-0.67-0.55-1 (PS) 0.1% 1E+2 1E+3 1E+4 1E+5 Reversals to Failure, 2N f 1E+6 1E+7 10.0% (a) 1.0% R ε (εc) R σ (LC) -1-1 0 0.75-1 (PS) -1 (PS) runout 0.1% 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Reversals to Failure, 2N f 10.0% (b) R -1-0.25-3.4 LC LC εc PS PS PS 1.0% 0.1% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Reversals to Failure, 2N f 1E+7 1E+8 (c) Figure 5.25 FS curves including all constant amplitude fatigue test data for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

132 1E+7 1E+6 Observed Life, 2N f 1E+5 1E+4 SS304L CLI THY Al 7075-T6 1E+3 R = -1 R -1 PS εc LC εc LC εc LC 1E+2 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Predicted Life, 2N f Figure 5.26 Observed versus predicted life for all constant amplitude fatigue tests of the all three materials using strain-life or stress-life approach.

133 1E+7 1E+6 Observed Life, 2N f 1E+5 1E+4 1E+3 1E+2 R = -1 R -1 PS SS304L Al 7075-T6 CLI THY εc LC εc LC εc LC 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Predicted Life, 2N f (a) 1E+7 Observed Life, 2N f 1E+6 1E+5 1E+4 1E+3 1E+2 R = -1 R -1 PS 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 Predicted Life, 2N f (b) SS304L CLI THY Al 7075-T6 εc LC εc LC εc LC Figure 5.27 Observed versus predicted life for all constant amplitude tests and all three materials using (a) SWT-life curve, and (b) FS-life curve.

Chapter Six Variable Amplitude Loading 6.1 Introduction As presented in Chapter 2, one of the aspects of variable amplitude loading is the presence of overloads. In design, their effect must be taken into account from a deformation and fatigue point of view. Load sequence effects must be considered, as the same loading applied at some point in the loading history would not have the same effect later in the loading history [10, 11]. Load sequence effects can also be altered due to the presence of microcracks in smooth specimens, which can exist from the early stage of fatigue life. These effects are investigated in this chapter, and study of the microcracks is related in Chapter 7. To evaluate fatigue life under variable amplitude loading, quantification of damage is necessary. In this study, cycle ratio (n/n f ) was used to represent damage ratio, as it can easily be computed and it is, therefore, the most commonly used method. A major requirement for a good life prediction parameter is to accurately relate the damage caused by the applied loading. For this purpose, different cycle counting methods have been developed [15] for fatigue life analysis. The Rainflow cycle counting method [16], based on the decomposition of the loading history into peaks and valleys, is the most common and was used in this study. 134

135 To compute damage, different damage accumulation rules can be used. Many rules and models for damage accumulation are available [17]. The most commonly used, partly because of its simplicity and ease of implementation, is the Palmgren-Miner Linear Damage Rule (LDR). This rule considers damage, quantified as damage fraction or cycle ratio, to accumulate in a linear fashion. However, it does not account for any load sequence or load interaction effects. In addition, it does not distinguish between crack initiation and crack growth phases. Due to these shortcomings, the LDR in conjunction with commonly used stress-life or strain-life curve can lead to inaccurate fatigue life predictions under variable amplitude loading. Although the inaccuracies are typically attributed to the LDR itself, it is shown in this chapter that the shortcomings of the commonly used approach can be circumvented by the use of parameters including both strain and stress terms. In this way, both the applied load and material response influence damage. Such parameters include the Smith- Watson-Topper [21] and Fatemi-Socie [22] parameters. In addition, these parameters can account for mean stress effects. Therefore, they are expected to estimate damage more accurately than a conventional strain-life or stress-life approach for materials with strong deformation history dependence, such as SS304L. This chapter discusses cyclic deformation and fatigue behaviors of SS304L (CLI and THY) and Al 7075-T6 under variable amplitude loading using strain-controlled as well as load-controlled tests. Load sequence effects were investigated in step tests with high-low (H-L) and low-high (L-H) sequences. Effects of periodic overloads were also analyzed, and random loading tests were conducted using the loading history presented in

136 Chapter 3 (Figure 3.12). To correlate a broad range of fatigue life data for a material with strong deformation history effect, such as stainless steel, it is shown that the Smith- Watson-Topper and Fatemi-Socie parameters correlate the data under different control modes and loading conditions reasonably well. 6.2 Step Load Tests H-L and L-H step tests at different levels and with different damage ratios were conducted for all materials, in either strain control or load control. For the H-L sequence in strain control, different procedures were used to switch from the higher to the lower level, to control the amount of mean stress resulting from the higher level, due to residual plastic strain, as discussed in Chapter 3. For SS304L, one test procedure involved the presence of mean stress at the lower strain amplitude level. Another procedure used consisted of gradually decreasing the higher strain amplitude to zero, before switching to the lower strain amplitude level [65] (similar to prestrained tests, Figures 3.3 and 3.4). The latter procedure produced negligible mean stress for this material. For Al 7075-T6, H-L step tests were conducted in different conditions, with the smallest cycles at different locations of the hysteresis loops of the highest level, as shown in Figure 3.5. Due to fully elastic behavior at the lower level, this level was conducted in load control so mean stress could be easily controlled. Experimental test conditions and results for the step tests of all three materials are gathered in Tables 6.1 to 6.3. Tests are grouped by loading sequence used and test control mode. Stress or strain values listed represent the stabilized response, and damage ratios were calculated using the LDR, with different approaches, as specified.

137 No change in deformation behavior due to load sequence effect was noticed for Al 7075-T6 in strain-controlled or load-controlled tests, for either H-L or L-H sequence, as expected (see Figures 6.1(c) and 6.2(c)). In contrast, significant hardening was observed for SS304L at the lower level in H-L step tests, as shown in Figures 6.1(a) and 6.1(b) for stress response in strain control and in Figures 6.2(a) and 6.2(b) for strain response in load control. For comparison purposes, constant amplitude fully-reversed responses are also presented in these figures. In strain-controlled tests, hardening was characterized by an increase of the stress response of up to 40% for SS304L CLI, as compared to midlife stress amplitude for fullyreversed constant amplitude test at equivalent strain amplitude (see Figure 6.1(a)). In load control, hardening led to a reduction of up to 60% in strain amplitude of the second level for SS304L CLI (see Figure 6.2(a)). The amount of hardening increased with more difference between the two levels and increasing the number of cycles applied at the higher level. For SS304L THY, in load-controlled H-L step tests, hardening led to a 50% reduction in the second step strain amplitude (see Figure 6.2(b)). In strain-controlled H-L step tests, however, the differences at midlife between second level stress amplitude and constant amplitude test at the same level were less drastic, since significant secondary hardening occurred in the fully-reversed constant amplitude test at 0.3% (see Figure 6.1(b) and Table 6.2). Nonetheless, hardening due to high level of strain was still significant for SS304L THY, in the first few percent of fatigue life at lower level, as

138 shown in Figure 6.1(b). Continuous softening occurred during the second step of the H-L step test. Figures 6.3 and 6.4 present mean stress responses in strain-controlled, and mean strain responses in load-controlled H-L step tests for SS304L CLI and SS304L THY. In strain-controlled tests for SS304L THY, the level of mean stress remained low all throughout the second step, due to gradual reduction of the strain amplitude in the transition from the higher strain level to the lower strain level, as shown in Figure 6.3(b). For SS304L CLI, however, the procedure of gradually reducing the strain amplitude was not used for all tests, and mean stress was present in some cases (see Figure 6.3(a) and Table 6.1). In load-controlled tests, due to high maximum stress, some ratcheting was observed in the first step of H-L step tests for both grades of SS304L (see Figure 6.4). Nonetheless, during the second step, mean strain levels presented a steady behavior, similar to the fully-reversed constant amplitude tests at equivalent load level, responses of which are also represented in Figure 6.4 for comparison. With regard to fatigue life, load sequence effect was observed for both Al 7075- T6 and SS304L. Cycle ratios were calculated with the LDR based on strain-life curve for strain-controlled tests and stress-life curve for load-controlled tests. Cycle ratio sums were found to be smaller for H-L sequence than for L-H sequences, in strain control, as can be seen in Figures 6.5 and 6.6 and Tables 6.1 to 6.3. For a H-L sequence, microcracks can initiate during the higher level and grow during the second step, as the stress or strain amplitude may be higher than the crack opening stress. In contrast, for a

139 L-H sequence, the stress or strain amplitude during the first step may be low enough that crack initiation is very limited. Therefore, the fatigue life at the higher level is only slightly affected, if at all, by the first step, leading to higher calculated cycle ratios. Microcracks mentioned here are small cracks and do not affect the overall mechanical behavior of the material. They are discussed in further details in Chapter 7. Figure 6.7 presents pictures of such cracks observed in the gage section, above the fracture cracks, in H-L and L-H step tests for SS304L CLI and Al 7075-T6. Cracks appear longer and deeper in the H-L sequence than for the L-H sequence. This indicates that cracks most likely initiated during the higher level in H-L sequences and grew at the lower level. For SS304L CLI, in H-L step tests, at equivalent damage for the first step (D = 0.1), shorter lives were obtained in strain-controlled tests as compared to load-controlled tests, and when the high level was conducted at higher strain amplitude (1% versus 0.5% strain amplitude), as can be seen in Table 6.1 and Figures 6.5(a) and 6.6(a). Comparison of H-L step tests conducted with the higher strain amplitude level at 1% with those at 0.5% strain amplitude showed greater cycle ratios in the latter case, based on LDR and the strain-life curve. One explanation of this observation is more hardening, and therefore higher resulting stress induced by the high step, when the high step is at higher strain amplitude. Another explanation is that cycling at 1% strain amplitude produces more crack nucleation sites than at 0.5% strain amplitude, and leads to shorter life in the second step. For SS304L THY, tests were only conducted with a higher level of 1% strain amplitude (Table 6.2 and Figures 6.5(b) and 6.6(b)).

140 Although similar trends in hardening behavior were observed in strain control and load control, the test control mode had a strong influence on the outcome of the step tests, regarding fatigue lives, for SS304L. In strain-controlled H-L step tests, hardening induced by the higher level led to smaller cycle ratios (i.e. shorter lives) due to higher stress amplitudes at the second strain level. Similar to prestraining, high level of loading was found to be more damaging for the SS304L THY grade than for the SS304L CLI grade (comparison between H-L step tests at equivalent cycle ratio of 0.1 in the first step can be made in Tables 6.1 and 6.2). In load-controlled tests, however, the hardening induced by the first load level resulted in smaller strain amplitude at the second load level leading to larger cycle ratios, as seen in Figures 6.5(a) and 6.6(a). Cycle ratios referred to here were calculated using the common approach of utilizing LDR with a strain-life curve in strain control, or with a stress-life curve in load control. This type of damage accumulation calculation leads to erroneous conclusions, as H-L sequence fatigue life is overpredicted in strain control (non conservative life predictions), while it is severely underpredicted in load control (overly conservative life predictions). As stated previously, to circumvent this shortcoming, parameters including both stress and strain such as Smith-Watson-Topper [21] (Equation 5.4) or Fatemi-Socie [22] (Equation 5.5) parameters can be used for damage accumulation calculations. The LDR was used with these parameters on experimental data obtained for H-L and L-H sequences with results presented in Figures 6.8 to 6.11 for the three materials. For SS304L CLI (Figures 6.8(a) to 6.11(a)) and SS304L THY (Figures 6.8(b) to 6.11(b)) significant improvement is observed using the SWT or the FS parameter, especially for

141 H-L step tests in load control. For Al 7075-T6 (Figures 6.8(c) to 6.11(c)) all three approaches (i.e. strain-life or stress-life, SWT, and FS) led to similar results, as expected. The SWT and FS parameters also account for the mean stress present in some tests, as previously discussed. Fatigue life predictions for the second step of the step tests were performed based on LDR in conjunction with strain-life or stress-life, SWT, or FS curves, using: n N 1 f1 n N 2 f2 1 (6.1) Predicted versus observed remaining lives (i.e. n 2 ) are presented in Figures 6.12 to 6.15 for strain-life or stress-life curves, SWT curve, and FS curve for all three materials. The dashed lines represent scatter bands of a factor of two and five. No significant difference was observed for Al 7075-T6 between strain-life or stress-life and SWT or FS curves. However, significant improvement is obtained using the SWT or FS parameter for SS304L CLI and SS304L THY, especially for H-L step tests. As also seen in Tables 6.1 and 6.2 and Figures 6.5, 6.8 and 6.10, damage ratios for these tests are close to unity using the SWT or FS parameters. Neither the strain-life nor the stress-life approach account for the hardening due to the higher level in H-L step tests. 6.3 Periodic Overload Tests Periodic overload test procedures used were discussed in Chapter 3. For Al 7075- T6, POL tests were conducted with smaller cycles at 0.5% strain amplitude and periodic overloads at 1.4% strain amplitude were applied about every 10% of the expected fatigue life based on the LDR. This resulted in a load block composition of one overload every

142 one thousand small cycles, as shown in Table 6.4. Tests were carried out in load control, while measuring strain and ensuring desired levels of strain were reached. This method avoided mean stress during smaller cycles. However, mean stress was present during the overloads, as either fully compressive or fully tensile overloads were applied (see Figure 3.7). For SS304L CLI, fully-reversed periodic overloads in between fully-reversed small cycles were applied. Duplicate tests were conducted, one with overloads starting in tension, the other one with overloads starting in compression (Figure 3.8). Both methods led to similar fatigue lives. One purpose of the periodic overload tests was to compare the results with H-L step tests. Therefore, similar levels of stress, strain and damage ratios per block were applied. Periodic overloads were conducted at 1% total strain amplitude in strain control, and 370 MPa in load control, while the lower levels were carried out at 0.4% or 0.25% fully-reversed strain amplitude in strain control, and at 240 MPa stress amplitude in load control. For the lower level of 0.25% strain amplitude, different overload to smaller cycle ratios were used, as indicated in the block composition column in Table 6.4. For SS304L THY, only one test was conducted, with overloads at 0.4% strain amplitude every 5000 cycles at 0.25% strain amplitude. This test was meant to investigate the effect of periodic overload on secondary hardening behavior. In contrast to Al 7075-T6, where neither prestraining nor periodic overloads affected the deformation behavior, progressive hardening was observed as a consequence of overloading for SS304L. In strain control, the stress response slowly relaxed in

143 between overloads, as shown in Figure 6.16 for one test of each grade, where stress responses for overloads and several small cycles at different instants in the block are represented. The larger stress amplitudes for the small cycles in Figure 6.16 correspond to cycles located right after the overload cycle, while the lower response amplitudes for the small cycles correspond to cycles near the end of a block. Stress response for the fully-reversed constant amplitude strain-controlled fatigue test is also presented for comparison. For SS304L, for H-L strain-controlled step tests, the material was softening all throughout the second step, whereas progressive hardening was observed in periodic overload tests with slight softening in between subsequent overloads. The frequent application of periodic overloads prevents any significant softening, resulting in more hardening than in the corresponding H-L step tests. In SS304L THY, secondary hardening was observed in the periodic overload test. Therefore, the hardening induced by the periodic overloads was limited, due to the level of the overloads (0.4 % strain amplitude, versus 1% for SS304L CLI), and the stress response was nearly identical to the fully-reversed constant amplitude test (see Figure 6.16(b)). Therefore, periodic overloads at relatively low strain amplitude do not prevent secondary hardening from occurring, and in this case, did not induce failure of the specimen (runout). As seen in Figure 6.17, mean stress levels remained low in all periodic overload tests in strain control, although the strain amplitude was gradually reduced after the overloads only in the SS304L THY test. Mean stress data are represented in the same fashion as the stress amplitude data in Figure 6.16.

144 In load-controlled POL tests, which were only conducted for SS304L CLI, hardening was characterized by lower strain amplitude as compared to the strain amplitude in fully-reversed constant amplitude test at equivalent stress amplitude level, as shown in Figure 6.18. Only one cycle for the smaller cycles is represented in this figure, since very small variations within a load block were observed. Steady behavior was obtained fairly rapidly. Comparison of periodic overload and H-L step tests at identical strain or stress amplitudes is shown in Table 6.5. In strain control, more hardening results from periodic overloading than from H-L step tests at the same equivalent overload level. This is manifested by higher stress amplitude at the lower strain level in POL tests, as compared to H-L step tests. More fatigue damage was caused by periodic overloads than by the high level in H-L step tests for equivalent cycle ratios (see Table 6.5). This is consistent with the hardening behavior, as higher levels of stress amplitude were observed in periodic overload tests, at identical strain amplitude to that in H-L step tests. With regard to fatigue lives, results are presented in Figures 6.19 to 6.22. For Al 7075-T6, tests conducted with tensile overloads led to slightly longer fatigue lives (about 20%) as compared to tests with compressive overloads. Prestraining which was applied for 10 cycles at 1.4% strain amplitude in these tests can complete the microcrack nucleation process. Propagation of microcracks can then represent the major part of the subsequent fatigue life [28, 74]. Under periodic overloads, tensile overloads induce beneficial residual compressive stress at the tip of cracks, increasing the threshold stress intensity during subsequent cycles. In contrast, compressive overloads tend to aid

145 microcrack opening and facilitate crack growth, reducing fatigue lives. For fatigue life prediction, use of the LDR associated with strain-life, stress-life, SWT or FS curves led to similar and relatively accurate predictions for aluminum (see Table 6.4 and Figures 6.19(c) and 6.22). For SS304L CLI, similar to step tests, the presence of hardening led to inaccurate life prediction using the LDR in conjunction with strain-life or stress-life curves. Shorter lives than predicted are obtained in strain control because of high stress levels, while conservative predictions are obtained in load control due to lower strain amplitudes (see Table 6.4 and Figure 6.19(a)). The SWT and FS parameter approaches led to more accurate predictions, as shown in Figure 6.20. For SS304L THY, only one test was conducted and was a runout. Due to the use of considerably longer blocks, resulting in a small total number of blocks, this test is not represented in Figures 6.19(b) and 6.21. 6.4 Random Loading For random loading tests, the procedure to obtain the loading history was presented in Chapter 3, with the resulting spectrum in Figure 3.12, and the Rainflow cycle count in Table 3.2. Random loading tests were conducted on virgin as well as prestrained specimens, and in both strain control and load control for all three materials. It should be noted that tests conducted in strain control and load control are not comparable, due to plastic deformation. Random loading test results are presented in Table 6.6 for SS304L and Table 6.7 for Al 7075-T6. Stress response for a strain-controlled random loading test and strain response for a load-controlled random loading test as well as the corresponding midlife hysteresis

146 loops are presented in Figures 6.23, 6.24, and 6.25 for SS304L CLI, SS304L THY, and Al 7075-T6, respectively. Hysteresis loops of SS304L appear very different depending on the test control mode, as seen by comparing Figure 6.23(c) with Figure 6.23(d) and Figure 6.24(c) with Figure 6.24(d). While the stress response was nearly fully-reversed in strain control for SS304L (see Figures 6.23(a) and 6.24(a)), some mean strain was present in load-controlled tests (see Figures 6.23(b) and 6.24(b)). Much lower strain amplitudes were observed in load-controlled tests of SS304L, as compared to the strain-controlled tests, leading to much longer lives in load control. For prestrained tests in strain control, different behaviors were observed for SS304L CLI and SS304L THY. For SS304L CLI, although higher stress response (about 30% as compared to virgin material) was observed, fatigue lives were very similar to the virgin material at the same strain amplitude level (see Table 6.6). For SS304L THY, however, hardening of only about 12% was observed with a reduction in fatigue life of about 75% (see Table 6.6). Figure 6.26 represents the maximum stress response in prestrained strain-controlled tests at 0.3% maximum strain for SS304L CLI and SS304L THY. The stress response for the virgin materials tested under the same conditions is also represented for comparison. For SS304L CLI a steady stress response was observed for both virgin and prestrained materials (see Figure 6.26(a)). For SS304L THY, due to higher strain amplitude runout level for this grade, secondary hardening associated with runout fatigue life was observed in the random loading test at 0.3% maximum strain for the virgin material. For the prestrained SS304L THY specimens tested under the same conditions, failure occurred and no secondary hardening was observed (see Figure

147 6.26(b)). This is in accordance with results obtained in prestrained constant amplitude tests, where prestraining was found to hinder secondary hardening for SS304L CLI at 0.175% strain amplitude. The behavior of the SS304L THY grade also appears to be more sensitive to prestraining, as reduction in fatigue life is more significant for this material. In prestrained load-controlled tests, hardening led to a reduction in strain amplitude of about 65% for SS304L CLI and about 50% for SS304L THY as compared to the virgin specimen tests. This led to an increase in fatigue life by a factor of more than nine for both SS304L CLI and SS304L THY grades, as most cycles in the loading history became non-damaging. For Al 7075-T6, the behavior being fully elastic at 0.5% maximum strain amplitude, only load-controlled tests were conducted at this level, since both control modes are equivalent. In strain-controlled tests at 1% maximum strain amplitude, the stress response presented very low mean stress for this material as well (see Figures 6.25(a) and 6.25(c)). Prestraining did not have any influence on the response of Al 7075- T6, as both strain levels and fatigue lives were identical as those obtained for the virgin material (see Table 6.7). Damage accumulation was computed using linear damage rule combined with strain-life or stress-life, SWT, and FS curves. In damage accumulation calculations, cycles below the fatigue limit, defined at 2x10 6 reversals (i.e. a horizontal line at 2N f > 2x10 6 reversals) for SS304L were accounted as non-damaging (D = 0). For aluminum, a

148 similar procedure was used with the fatigue limit corresponding to 2x10 8 reversals. Fatigue limit values for each criterion used for each material are presented in Table 6.8. Life predictions are presented in Tables 6.6 and 6.7 and in Figures 6.27 and 6.28 for damage ratios. For SS304L, similar to constant amplitude tests, prestraining effects were dependent on the test control mode, leading to longer fatigue life in load control. For strain-controlled random loading tests, more effects of prestraining were observed for SS304L THY than for SS304L CLI. Shorter fatigue lives were observed for prestrained SS304L THY, as compared to the virgin material. No significant effect of prestraining was observed for strain-controlled random loading tests for SS3044L CLI. As expected, life predictions obtained with the LDR used in conjunction with strain-life or stress-life curves were accurate for Al 7075-T6, but inaccurate for SS304L. Predicted versus observed lives in terms of number of blocks to failure were presented in Figures 6.19 to 6.22. The main difference was observed for prestrained SS304L CLI and SS304L THY, as tests in load control were runout. Differences in fatigue life predictions between the different approaches for random loading tests of SS304L are not as significant as for the step tests. Nonetheless, the SWT or FS parameters improve the predictions as compared to a more common strain-life or stresslife approach, especially for load-controlled tests. This is due to strong deformation history effect in SS304L, where including both stress and strain terms in the calculations leads to more accurate results. However, a random load history with higher overloads in a block and with longer blocks is expected to produce more differences in life predictions among the approaches. For Al 7075-T6, all approaches produced similar predictions.

149 6.5 Fatigue Life Correlations and Predictions for Variable Amplitude Tests Tables 6.9 and 6.10 for SS304L and Al 7075-T6, respectively, summarize all life predictions under variable amplitude loading, where the predicted to experimental life ratios based on either strain-life or stress-life curve and based on SWT and FS curves are listed. Better predictions result in N pred /N exp ratios closer to one in these tables. For step tests, the SWT or FS parameters in conjunction with LDR represent stainless steel data better than strain-life or stress-life approach, but predictions are similar for aluminum. For all three materials, in strain control, remaining cycle ratio in step tests based on LDR is generally over-predicted (i.e. non-conservative) in H-L tests. Very conservative predictions are obtained for H-L tests for SS304L THY and SS304L CLI in load control. For aluminum and SS304L CLI, remaining cycle ratio in L-H step test is generally underpredicted (i.e. conservative) in either strain control or load control. For periodic overload and random loading tests, LDR based on all parameters results in similar predictions for aluminum, while LDR based on the SWT or FS parameters significantly improves predictions for stainless steel. Similar to prestrained constant amplitude tests, prestraining followed by random loading was found to be more damaging for SS304L THY than for SS304L CLI. Although similar results were obtained using SWT or FS parameters, overall the SWT parameter resulted in slightly more conservative predictions.

150 6.6 Conclusions 1) In step tests, no change in deformation behavior was observed for Al 7075-T6 in either strain-controlled or load-controlled tests, and for either H-L or L-H sequence. In contrast, significant hardening was observed for SS304L CLI, at the low level, in H-L step tests. The level of hardening increased with more difference between the two levels and with increasing the number of cycles applied at the higher level. For SS304L THY, because of secondary hardening present in the fully-reversed constant amplitude test, differences in stress responses were not as drastic as for SS304L CLI. 2) In step tests, H-L sequence led to smaller damage sum (shorter life) than L-H sequences for both aluminum and stainless steel in strain control. Observation of longer and deeper microcracks within the gage section of the failed specimens in H-L tests compared to L-H tests indicates that small cracks can develop during the high level of H-L step tests, and grow at low level. 3) Due to significant hardening resulting from the high level in H-L step tests for SS304L, test control mode had a strong influence on fatigue life. Load-controlled tests presented much longer lives than strain-controlled tests, due to lower strain amplitude at the low level for both SS304L CLI and THY. However, in strain control, hardening due to high loading level in H-L step tests was more damaging for SS304L THY than for CLI. 4) Comparison of H-L step tests and periodic overload tests for SS304L CLI indicates that frequent application of periodic overloads induces more overall

151 hardening, as it limits any significant softening of the material. Periodic overloads induced relatively more damage than the high level of H-L step tests in strain control. 5) For SS304L THY, periodic overloads at relatively low strain amplitude did not prevent secondary hardening from occurring and did not induce failure of the specimen (runout test). 6) No influence of the test control mode or prestraining was observed in random loading tests for Al 7075-T6. In contrast, for SS304L, prestraining in such tests led to higher stress response in strain control, without any significant influence on fatigue life for SS304L CLI. However, prestraining was found to induce significant damage for SS304L THY, in accordance with results obtained for prestrained constant amplitude tests. In load-controlled random loading tests, prestraining led to about an order of magnitude longer fatigue lives for both materials. 7) Due to significant hardening and strong deformation history effects of a material such as SS304L, the conventional strain-life or stress-life curves in conjunction with the LDR can result in inaccurate life predictions under variable amplitude loading, especially for H-L step and periodic overload tests. Using this approach, remaining cycle ratios in step tests are generally under-predicted (i.e. conservative) in L-H step tests, but over-predicted (i.e. non conservative) in H-L step tests. Very conservative predictions were also obtained for load-controlled H-L step tests for stainless steel but not for aluminum, based on the LDR and

152 strain-life or stress-life curve. The use of a fatigue damage quantifying parameter involving both stress and strain, such as the SWT or FS parameters, leads to significantly better life predictions and can better reconcile differences between test results in different test control modes.

153 Table 6.1 Summary of step tests results for SS304L CLI. Specimen ID Control Mode ø (mm) ε a1 / ε a2 (%) / (%) ε m1 / ε m1 (%) / (%) (Δε p /2) 1 / (Δε p /2) 2 calculated n 1 / n 2 σ a1 / σ a2 (MPa) / (MPa) σ m1 / σ m2 (MPa) / (MPa D 1 / D 2 (ε-n or S-N) ΣD (ε-n or S-N) ΣD (SWT-N) (%) / (%) High-Low Step Tests UTCLI13 strain 5.08 1.00/0.250-0.01/0.00 0.80/0.10 580/11,672 401/286 0.5/7.9 0.51/0.12 0.63 0.95 0.77 UTCLI14 strain 5.08 1.00/0.250-0.01/0.00 0.79/0.10 580/4,786 404/298 1.1/22.0 0.51/0.05 0.56 0.73 0.63 UTCLI15 strain 5.13 1.01/0.249-0.01/0.00 0.81/0.12 117/32,046 385/256 0.9/33.1 0.10/0.34 0.44 1.10 0.6 UTCLI16 strain 5.12 1.00/0.251-0.01/-0.97 0.80/0.12 117/36,793 384/248 0.8/26.2 0.10/0.39 0.49 1.05 0.63 UTCLI26 strain 5.00 0.497/0.250 0.00/0.00 0.36/0.14 670/42,954 278/213 0.1/12.5 0.09/0.46 0.55 0.67 0.58 UTCLI61 strain 5.16 0.499/0.250 0.00/-0.02 0.36/0.11 670/75,769 280/215-0.9/-0.5 0.10/0.80 0.90 0.96 0.90 UTCLI62 load 5.13 0.398/0.227 0.11/0.10 0.26/0.12 670/106,903 262/210 1.1/0.3 0.10/0.82 0.92 0.83 0.79 UTCLI63 load 5.13 0.434/0.250 0.09/0.07 0.27/0.14 670/116,968 262/210 1.1/0.6 0.10/0.90 1.00 1.30 1.28 UTCLI42 load 5.16 1.03/0.157 4.75/4.57 0.81/0.03 235/366,166 432/255 4.8/0.5 0.27/20.4 20.67 1.67 0.78 UTCLI43 load 5.16 1.06/0.158 3.85/3.80 0.84/0.03 235/397,489 429/253 4.5/0.4 0.27/22.1 22.37 1.79 0.86 UTCLI36 load 5.11 1.06/0.123 4.46/4.62 0.84/0.01 235/>409,928 431/220 4.7/0.2 0.27/>3.1 > 3.37 > 0.52 > 0.39 Low-High Step Tests UTCLI33 strain 5.13 0.250/1.00 0.00/0.00 0.14/0.80 47,000/784 210/397-0.5/-3.2 0.5/0.69 1.19 1.3 1.3 UTCLI44 load 5.14 0.390/1.03-0.04/5.62 0.27/0.81 2,700/837 243/436 0.9/4.4 0.15/0.95 1.10 1.29 1.19 UTCLI45 load 5.16 0.376/1.03-0.16/5.26 0.25/0.81 2,700/799 242/435 0.9/4.5 0.15/0.9 1.05 1.22 1.12 ΣD (FS-N)

154 Table 6.2 Summary of step tests results for SS304L THY. Specimen ID Control Mode ø (mm) ε a1 / ε a2 (%) ε m1 / ε m1 (%) / (%) (Δε p /2) 1 / (Δε p /2) 2 calculated n 1 / n 2 σ a1 / σ a2 (MPa) / (MPa) σ m1 / σ m2 (MPa) / (MPa) D 1 / D 2 (ε-n or S-N) ΣD (ε-n or S-N) ΣD (SWT-N) (%) / (%) High-Low Step Tests UTTHY23 strain 5.12 1.00/0.300-0.01/0.00 0.80/0.16 107/57,306 389/265 0.5/0.5 0.10/0.14 0.24 0.86 0.70 UTTHY25 strain 5.16 1.00/0.300-0.01/0.00 0.80/0.16 107/66,606 388/262 0.9/1.2 0.10/0.16 0.26 0.96 0.79 UTTHY26 strain 5.14 1.00/0.300-0.01/0.00 0.80/0.15 530/34,597 415/290 0.8/2.0 0.50/0.08 0.58 1.19 1.00 UTTHY28 strain 5.14 1.00/0.300 0.00/0.00 0.80/0.15 530/31,332 416/289 0.4/1.1 0.50/0.07 0.57 1.12 0.96 UTTHY32 load 5.17 1.03/0.229 1.78/1.28 0.81/0.09 212/215,932 424/278 4.3/0.6 0.20/9.90 10.10 1.49 0.82 UTTHY33 load 5.14 1.08/0.228 2.59/2.05 0.85/0.08 212/227,745 428/280 4.7/0.6 0.20/10.44 10.64 1.60 0.87 ΣD (FS-N)

155 Table 6.3 Summary of step tests results for Al 7075-T6. Specimen ID Control Mode ø (mm) ε a1 / ε a2 (%) /(%) ε m1 / ε m1 (%) / (%) (Δε p /2) 1 / (Δε p /2) 2 calculated n 1 / n 2 σ a1 / σ a2 (MPa) / (MPa) σ m1 / σ m2 (MPa) / (MPa) D 1 / D 2 (ε-n or S-N) ΣD (ε-n or S-N) ΣD (SWT-N) (%) / (%) High-Low Step Tests Without Mean Stress A46 strain 4.20 1.40/0.502 0.00/0.50 0.59/0.00 87/3,280 565/351-13/0 0.50/0.23 0.73 0.79 0.81 A47 strain 4.19 1.42/0.499 0.01/0.50 0.61/0.00 87/4,743 573/350-14/0 0.50/0.33 0.83 0.92 0.92 A97 strain 4.20 1.00/0.399-0.01/-0.49 0.23/0.00 80/31,400 543/283-4/1 0.20/0.49 0.69 0.45 0.59 A98 strain 4.23 1.00/0.392-0.01/-0.18 0.23/0.00 80/20,047 542/284-1/1 0.20/0.31 0.51 0.31 0.44 A99 strain 4.23 1.00/0.396-0.01/-0.05 0.22/0.00 158/16,705 549/285-6/1 0.40/025 0.65 0.38 0.58 A100 strain 4.20 1.00/0.395-0.005/-0.06 0.21/0.00 158/9,321 557/286-5/1 0.40/0.14 0.54 0.3 0.49 A85 load 4.24 1.20/0.513 0.48/1.45 0.42/0.00 63/6,141 546/357 6/0 0.24/0.43 0.67 0.68 0.66 A86 load 4.23 1.10/0.405 0.27/0.09 0.32/0.00 53/21,040 546/285 6/0 0.20/0.33 0.53 0.48 0.47 A87 load 4.22 1.12/0.402 0.26/0.13 0.34/0.00 53/23,054 546/283 6/0 0.20/0.36 0.56 0.5 0.49 A90 load 4.17 1.03/0.401 0.36/0.34 0.25/0.00 120/10,373 548/286 6/0 0.45/0.16 0.62 0.46 0.45 A91 load 4.23 1.11/0.402 0.57/0.74 0.34/0.00 120/8,679 549/285 6/0 0.45/0.13 0.59 0.57 0.55 High-Low Step Tests With Mean Stress A55 strain 4.06 1.41/0.493-0.01/0.86 0.59/0.00 87/1,647 574/334-19/217 0.50/0.36 0.86 0.99 0.79 A65 strain 4.24 1.40/0.502 0.00/0.64 0.59/0.00 87/1,079 566/340-19/205 0.50/0.24 0.74 0.84 0.73 A52 strain 4.13 1.39/0.499 0.00/-0.88 0.58/0.00 87/33,569 570/367-17/-225 0.50/0.50 1.00 0.69 1.61 A69 strain 4.20 1.39/0.499 0.00/-0.85 0.57/0.00 87/33,495 579/372-18/-220 0.50/0.50 1.00 0.74 1.75 Low-High Step Tests A44 strain 4.19 0.503/1.40-0.09/0.01 0.00/0.59 7,000/96 366/570 0/-18 0.49/0.55 1.04 1.14 1.2 A45 strain 4.15 0.499/1.41-0.04/0.01 0.00/0.60 7,000/169 358/570 0/-17 0.49/0.97 1.46 1.63 1.7 A64 strain 4.23 0.498/1.40-0.02/0.01 0.00/0.61 3,952/156 351/562 0/-16 0.28/0.89 1.17 1.28 1.37 A66 strain 4.22 0.499/1.41 0.01/0.00 0.00/0.60 3,952/161 365/572 0/-18 0.28/0.92 1.20 1.41 1.5 A103 strain 4.22 0.390/1.00-0.11/-0.01 0.00/0.21 25,400/298 286/557 1/-7 0.39/0.75 1.14 0.64 1.03 A104 strain 4.19 0.388/1.00-0.12/-0.00 0.00/0.10 25,000/261 288/567 1/-8 0.39/0.66 1.04 0.61 0.97 A96 strain 4.22 0.394/1.00-0.02/-0.01 0.00/0.25 12,900/392 282/529 1/-6 0.20/0.98 1.18 0.55 1 A88 load 4.23 0.392/1.00-0.11/0.42 0.00/0.22 12,000/196 285/548 1/6 0.19/0.74 0.93 0.48 0.62 A89 load 4.24 0.398/1.11-0.03/0.60 0.00/0.32 12,000/131 286/548 1/6 0.19/0.50 0.69 0.62 0.63 A92 load 4.23 0.399/1.10-0.13/0.78 0.00/0.32 32,000/151 284/550 1/6 0.50/0.57 1.07 0.96 0.95 A93 load 4.24 NA/NA NA/NA NA/NA 32,000/115 286/545 0/0 0.50/0.44 0.94 NA NA ΣD (FS-N)

156 Table 6.4 Summary of POL tests for SS304L and Al 7075-T6. Specimen ID Test Control Mode ø (mm) ε aol / ε asc (%) / (%) ε mol / ε msc (%) / (%) (Δε p /2) OL / (Δε p /2) SC calculated (%) / (%) σ aol / σ asc (MPa) / (MPa) σ mol / σ msc (MPa) / (MPa) n OL / n SC Observed Number of Blocks to Failure Predicted Number of Blocks to Failure (ε-n or S-N) Predicted Number of Blocks to Failure (SWT-N) Predicted Number of Blocks to Failure (FS-N) Stainless Steel 304L CLI UTCLI76 strain 5.13 0.988/0.398 0.00/0.00 0.81/0.24 343/309-2/5 1/48 111 228 155 179 UTCLI81 strain 5.16 0.987/0.380-0.01/0.00 0.82/0.25 333/300 3/-3 1/48 138 228 171 190 UTCLI65 strain 5.16 0.986/0.398 0.00/0.00 0.81/0.24 337/305-3/5 1/48 117 228 159 182 UTCLI67 strain 5.16 0.987/0.250 0.00/0.00 0.81/0.11 347/271-2/20 1/334 84 230 82 160 UTCLI77 strain 5.16 0.989/0.250 0.01/0.00 0.82/0.12 336/262 3/-16 1/751 48 114 65 96 UTCLI78 load 5.16 NA/NA NA/NA NA/NA 375/242 0.4/0.3 1/55 705 NA NA NA UTCLI82 load 5.16 0.872/0.163-1.83/-1.40 0.68/0.04 370/239-0.5/0.4 1/55 756 239 1,169 1,264 Stainless Steel 304L THY UTTHY40 strain 5.17 0.394/0.250 0.00/0.00 0.23/0.11 321/272-2/-2 1/5,000 > 216 91 28 50 Aluminum 7075-T6 A57 strain* 4.12 0.360/0.495-0.99/-0.58-0.02/0.00 265/357-283/0 1/1,000 9.7 23.3 16.0 15.8 A49 strain* 4.20 0.378/0.499-0.99/-0.54-0.01/0.00 247/357-288/0 1/1,000 10.0 23.3 15.5 15.8 A60 strain* 4.15 0.418/0.496 0.82/0.44 0.03/0.00 276/349 258/0 1/1,000 13.0 23.3 17.0 18.2 A50 strain* 4.14 0.439/0.501 0.88/0.46 0.03/0.00 291/359 273/0 1/1,000 12.0 23.3 14.9 15.2 *10 cycles of prestraining were applied at 1.4% strain amplitude.

157 Table 6.5 Comparison of H-L step tests and periodic overload tests for SS304L CLI. Test Type Control Mode Stress or Strain Histories Stress or Strain Amplitude Responses Mean Stress ΣD (ε-n or S-N) ΣD (SWT-N) H-L step strain 1% / 0.25% 385 MPa /256 MPa 1 MPa /33MPa 0.44 1.10 0.60 H-L step strain 1% / 0.25% 384 MPa / 248 MPa 1 MPa / 26 MPa 0.49 1.05 0.63 ΣD (FS-N) POL strain 1% / 0.25% 347 MPa / 270 MPa 2 MPa / 20 MPa 0.36 0.99 0.53 POL strain 1% / 0.25% 336 MPa / 262 MPa 3 MPa / -16 MPa 0.42 0.69 0.50 H-L step load 412 MPa / 242 MPa 1.03% / 0.157% 5 MPa / 1 MPa 20.7 1.67 0.78 H-L step load 412 MPa / 242 MPa 1.06% / 0.158% 5 MPa / 0 MPa 22.4 1.79 0.86 POL load 412 MPa / 243 MPa 0.872% / 0.163% -1 MPa / 0 MPa 3.17 0.64 0.60 POL load 412 MPa / 243 MPa NA/NA 0 MPa / 0 MPa 2.96 NA NA

158 Table 6.6 Specimen ID Summary of random loading test results for SS304L. Test Control Mode ø (mm) ε max (%) ε min (%) σ max (MPa) σ min (MPa) Experimental Number of Blocks to Failure Predicted Number of Blocks to Failure (ε-n or S-N) Predicted Number of Blocks to Failure (SWT-N) Predicted Number of Blocks to Failure (FS-N) Virgin Stainless Steel 304L CLI UTCLI87 strain 5.13 0.996-0.997 378-371 211 266 227 250 UTCLI88 strain 5.14 1.00-1.00 384-379 196 264 220 245 UTCLI91 strain 5.12 0.499-0.495 261-256 1,601 2,311 2,211 2,317 UTCLI86 strain 5.16 0.499-0.494 263-258 1,740 2,320 2,064 2,313 UTCLI69 strain 5.13 0.297-0.293 226-225 14,463 19,723 19,985 19,942 UTCLI97 strain 5.18 0.295-0.295 221-223 15,566 19,863 21,346 20,447 UTCLI92 load 5.16 0.701-0.112 246-241 11,096 6,232 10,746 10,251 UTCLI80 load 5.16 0.640-0.201 247-242 10,884 6,112 9,381 8,988 Prestrained* Stainless Steel 304L CLI UTCLI89 strain 5.17 0.497-0.492 336-326 1,428 2,489 1,287 1,953 UTCLI94 strain 5.17 0.498-0.494 331-322 1,626 2,484 1,399 1,972 UTCLI58 strain 5.16 0.291-0.291 294-286 15,107 21,407 9,355 16,848 UTCLI93 strain 5.17 0.289-0.290 312-293 11,675 22,095 7,672 15,984 UTCLI90 load 5.14 0.079-0.204 241-240 >98,559 6,956 542,500 1,000,000 Virgin Stainless Steel 304L THY UTTHY27 strain 5.16 0.995-1.00 410-403 230 233 197 198 UTTHY21 strain 5.16 1.00-1.00 406-398 243 235 201 202 UTTHY34 strain 5.17 0.497-0.494 315-313 2,998 4,181 2,994 3,101 UTTHY36 strain 5.13 0.498-0.496 302-296 2,688 4,110 3,354 3,248 UTTHY46 strain 5.18 0.290-0.289 273-273 >103,242 145,254 32,677 77,100 UTTHY39 load 5.17 0.635-0.194 284-278 13,870 8,348 12,035 14,258 UTTHY37 load 5.16 0.409-0.393 278-273 14,892 10,264 17,692 17,707 Prestrained* Stainless Steel 304L THY UTTHY44 strain 5.16 0.287-0.286 307-297 26,550 155,233 31,477 61,864 UTTHY45 strain 5.17 0.288-0.287 308-296 21,144 152,711 30,923 61,279 UTTHY38 load 5.16-0.084-0.487 281-279 >100,000 8,126 177,756 767,000 *For prestrained tests, 10 cycles at 2% strain amplitude were applied.

159 Table 6.7 Summary of random loading test results for Al 7075-T6. Specimen ID Test Control Mode ø (mm) ε max (%) ε min (%) σ max (MPa) σ min (MPa) Experimental Number of Blocks to Failure Predicted Number of Blocks to Failure (ε-n or S-N) Predicted Number of Blocks to Failure (SWT-N) Predicted Number of Blocks to Failure (FS-N) Virgin Aluminum 7075-T6 A110 strain 4.19 0.986-0.984 541-558 184 173 191 188 A111 strain 4.19 0.987-0.983 536-555 198 172 197 182 A112 load 4.18 0.498-0.487 348-338 7,308 8,346 9,700 8,839 A107 load 4.18 0.483-0.492 349-340 7,218 9,521 10,237 9,963 Prestrained* Aluminum 7075-T6 A108 load 4.18 0.039-0.933 348-339 5,319 9,519 10,339 9,945 A109 load 4.18-0.055-1.05 347-338 5,539 8,458 9,779 8,941 *For prestrained tests, 10 cycles at 1.4% strain amplitude were applied.

160 Table 6.8 Fatigue limits for the different approaches and materials used for fatigue life predictions. Assumed life for fatigue limit Assumed σ a value for fatigue limit Assumed ε a value for fatigue limit Assumed SWT value for fatigue limit Assumed FS value for fatigue limit SS304L CLI SS304L THY Al 7075-T6 2x10 6 reversals 2x10 6 reversals 2x10 8 reversals 192 MPa 180 MPa 99 MPa 0.16% 0.22% 0.14% 243 MPa 277 MPa 99 MPa 0.31% 0.45% 0.20%

161 Table 6.9 Summary of fatigue life predictions under variable amplitude loading for SS304L. Test Loading Type Control Mode Stress or Strain Level Experimental Life (Cycles or Blocks) N pred /N exp (ε-n or S-N) N pred /N exp (SWT-N) N pred /N exp (FS-N) Stainless Steel 304L CLI H-L step strain 1%/0.25% 8,229 6.82 1.73 3.11 H-L step strain 1%/0.25% 34,420 2.48 0.92 1.65 H-L step strain 0.5%/0.25% 59,362 1.56 1.32 1.42 H-L step load 262 MPa/210 MPa 111,936 1.05 0.99 0.98 H-L step load 430 MPa/255 MPa 381,828 0.03 0.49 1.26 H-L step load 430 MPa/220 MPa >409,928 < 0.23 < 3.38 < 1.68 L-H step strain 0.25%/1% 784 0.73 0.63 0.60 L-H step load 243 MPa/435 MPa 818 0.92 0.76 0.81 POL strain 1%/0.4 122 1.88 1.33 1.51 POL strain 1%/0.25% 84 2.74 0.98 1.90 POL strain 1%/0.25% 48 2.38 1.35 2.00 POL load 375 MPa/242 MPa 731 0.32 1.55 1.67 RL strain 1% 204 1.30 1.10 1.22 RL strain 0.5% 1,671 1.39 1.28 1.39 RL strain 0.3% 15,065 1.32 1.37 1.34 RL load 246 MPa 10,990 0.56 0.92 0.87 RL strain* 0.5% 1,527 1.64 0.88 1.29 RL strain* 0.3% 13,391 1.65 0.64 1.24 RL load* 240 MPa >98,559 <0.07 <5.50 <10.15 Stainless Steel 304L THY H-L step strain 1%/0.3% 61,956 6.14 1.11 1.42 H-L step strain 1%/0.3% 32,965 6.43 0.74 1.05 H-L step load 425 MPa/280 MPa 221,839 0.08 0.58 1.27 RL strain 1% 237 0.99 0.84 0.85 RL strain 0.5% 2,843 1.46 1.12 1.12 RL strain 0.3% >103,242 <1.41 <0.32 <0.75 RL load 280 MPa 14,381 0.65 1.03 1.11 RL strain* 0.3% 23,847 6.53 1.32 2.61 RL load* 280 MPa >100,000 <0.08 <1.78 <7.67 *Prestrained for 10 cycles at 2% total strain amplitude.

162 Table 6.10 Summary of fatigue life predictions under variable amplitude loading for Al 7075-T6. Test Loading Type Control Mode Load Level Experimental Life (cycles or blocks) N pred /N exp (ε-n or S-N) N pred /N exp (SWT-N) N pred /N exp (FS-N) Aluminum 7075-T6 H-L step strain 1.4%/0.5% 4,012 1.85 1.71 1.76 H-L step strain 1%/0.4% 25,724 2.11 3.33 2.54 H-L step strain 1%/0.4% 13,013 3.26 5.93 3.88 H-L step load 546 MPa/357 MPa 6,141 1.78 1.78 1.95 H-L step load 546 MPa/285 MPa 22,047 2.35 2.67 2.76 H-L step load 548 MPa/286 MPa 9,526 3.73 4.79 4.83 H-L step strain 1.4%/0.5% 1,363 1.74 1.33 3.27 H-L step strain 1.4%/0.5% 33,532 1.00 3.81 0.34 L-H step strain 0.5%/1.4% 133 0.73 0.64 0.59 L-H step strain 0.5%/1.4% 159 0.80 0.69 0.63 L-H step strain 0.4%/1% 280 0.87 2.10 1.00 L-H step strain 0.4%/1% 392 0.81 2.09 1.00 L-H step load 285 MPa/548 MPa 164 1.37 2.22 1.82 L-H step load 284 MPa/550 MPa 151 0.88 1.09 1.09 POL load* -1.4%/0.5% 9.85 2.37 1.60 1.60 POL load* 1.4%/0.5% 12.5 1.87 1.27 1.33 RL strain 1% 191 0.90 1.02 0.97 RL load 0.5% 7,263 1.23 1.37 1.29 RL load* 0.5% 5,429 1.66 1.85 1.74 *Prestrained for 10 cycles at 1.4% strain amplitude.

Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) 163 450 400 350 300 250 200 150 450 400 350 H-L (1%-0.25%) εc H-L (1%-0.25%) εc H-L (0.5%-0.25%) εc CA FR (0.25%) εc 100 1E+1 1E+2 1E+3 1E+4 Number of Cycles, N 1E+5 (a) H-L (1%-0.3%) εc H-L (1%-0.3%) εc CA FR (0.3%) εc 300 250 200 150 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Number of Cycles, N 600 500 400 (b) H-L (1%-0.4%) εc H-L (1%-0.4%) εc CA FR (0.4%) εc 300 200 100 0 1E+1 1E+2 1E+3 1E+4 Number of Cycles, N (c) Figure 6.1 Stress responses from strain-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075- T6. Fully-reversed (FR) constant amplitude (CA) response is also shown as reference for comparison with the second step response.

Strain Amplitude Strain Amplitude Strain Amplitude 164 1.5% 1.0% H-L (412 MPa-243 MPa) LC H-L (412 MPa-210 MPa) LC H-L (262 MPa-210 MPa) LC CA FR (243 MPa) LC CA FR (210 MPa) LC 0.5% 0.0% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Number of Cycles, N 1.4% (a) 1.2% 1.0% CA FR (274 MPa) LC H-L (412-274 MPa) LC 0.8% 0.6% 0.4% 0.2% 0.0% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Number of Cycles, N 1.2% (b) H-L (547 MPa-286 MPa) LC H-L (547 MPa-286 MPa) LC 0.8% extensometer removed 0.4% 0.0% 1E+1 1E+2 1E+3 Number of Cycles, N 1E+4 (c) Figure 6.2 Strain responses in load-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Fully-reversed (FR) constant amplitude (CA) response is also shown for comparison with the second step response.

Mean Stress (MPa) Mean Stress (MPa) Mean Stress (MPa) 165 100 80 60 40 20 0-20 -40-60 -80-100 50 40 30 20 10 0-10 -20-30 -40-50 15 (a) (b) H-L (1%-0.25%) εc H-L (1%-0.25%) εc H-L (0.5%-0.25%) εc CA FR (0.25%) εc 1E+1 1E+2 1E+3 1E+4 1E+5 Number of Cycles, N H-L (1%-0.3%) εc H-L (1%-0.3%) εc CA FR (0.3%) εc 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Number of Cycles, N 10 5 H-L (1%-0.4%) εc H-L (1%-0.4%) εc CA FR (0.4%) εc 0-5 -10-15 1E+1 1E+2 1E+3 Number of Cycles, N 1E+4 (c) Figure 6.3 Mean stress responses from strain-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6. Fully-reversed (FR) constant amplitude (CA) response is also represented for comparison with the second step response.

Mean Strain Mean Strain Mean Strain 166 5.0% 4.0% 3.0% 2.0% H-L (412MPa-243 MPa) LC H-L (412 MPa-210 MPa) LC H-L (262 MPa-210 MPa) LC CA FR (243 MPa) LC CA FR (210 MPa) LC 1.0% 0.0% -1.0% 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Number of Cycles, N 3.0% (a) 2.0% 1.0% 0.0% -1.0% CA FR (274 MPa) LC H-L (412-274 MPa) LC -2.0% 1E+1 1E+2 1E+3 1E+4 Number of Cycles, N 1E+5 1E+6 1.2% (b) H-L (547 MPa-286 MPa) LC H-L (547 MPa-286 MPa) LC 0.8% extensometer removed 0.4% 0.0% 1E+1 1E+2 1E+3 Number of Cycles, N 1E+4 (c) Figure 6.4 Mean strain responses in load-controlled H-L step tests as a function of number of cycles for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075- T6. Fully-reversed (FR) constant amplitude (CA) response is also shown as reference for comparison with the second step response.

167 (a) (b) (c) Figure 6.5 Cycle ratio sums in step tests calculated with the LDR and strain-life or stress life curves for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075- T6.

168 (a) (b) (c) Figure 6.6 Cycle ratios in step tests with strain-life or stress-life curves for (a) SS304L CLI, (b) SS304LTHY, and (c) Al 7075-T6. The line in each figure represents the LDR.

169 100 µm 100 µm (a) (b) (c) 100 µm (d) 100 µm Figure 6.7 Cracks observed in the gage section of failed specimens in step tests. (a) L-H (0.4%-1% strain amplitude) step test of Al 7075-T6. (b) H-L (1%- 0.4% strain amplitude) step test of Al 7075-T6. (c) L-H (0.25%-1% strain amplitude) step test of SS304L CLI. (d) H-L (1%-0.25% strain amplitude) step test of SS304L CLI. The direction of loading is indicated by the double-headed arrow.

170 (a) (b) (c) Figure 6.8 Cycle ratio sums in step tests calculated with LDR and SWT curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

171 (a) (b) (c) Figure 6.9 Cycle ratios in step tests with SWT curve for (a) SS304L CLI, (b) SS304LTHY, and (c) Al 7075-T6. The line in each figure represents the LDR.

172 (a) (b) (c) Figure 6.10 Cycle ratio sums in step tests calculated with LDR and FS curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

173 (a) (b) (c) Figure 6.11 Cycle ratios in step tests with FS curve for (a) SS304L CLI, (b) SS304LTHY, and (c) Al 7075-T6. The line in each figure represents the LDR.

174 (a) (b)

175 (c) Figure 6.12 Predicted versus remaining life in step tests, using LDR and strain-life or stress-life curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075- T6.

176 (a) (b) Figure 6.13 Predicted versus remaining life in step tests for SS304L CLI using (a) LDR and SWT curve, and (b) LDR and FS curve.

177 (a) (b) Figure 6.14 Predicted versus remaining life in step tests for SS304L THY using (a) LDR and SWT curve, and (b) LDR and FS curve.

178 (a) (b) Figure 6.15 Predicted versus remaining life in step tests for Al 7075-T6 using (a) LDR and SWT curve, and (b) LDR and FS curve.

Stress Amplitude (MPa) Stress Amplitude (MPa) 179 400 350 POL (1%-0.25%) (εc) CA, FR (0.25%) (εc) OL 300 250 SC 200 150 0 10000 20000 30000 40000 Number of Cycles, N (a) 400 OL 350 300 SC 250 200 POL (0.4%-0.25%) (εc) CA FR (0.25%) (εc) 150 0.0E+0 5.0E+5 1.0E+6 1.5E+6 2.0E+6 Number of Cycles, N (b) Figure 6.16. Stress amplitude response in strain-controlled POL tests for (a) SS304L CLI, and (b) SS304L THY.

Mean Stress (MPa) Mean Stress (MPa) 180 10 5 0 OL -5 POL (1%-0.25%) (εc) CA FR (0.25%) (εc) -10-15 -20 5 0 0 10000 20000 30000 40000 Number of Cycles, N (a) POL (0.4%-0.25%) (εc) CA FR (0.25%) (εc) OL SC SC -5-10 0.0E+0 5.0E+5 1.0E+6 1.5E+6 2.0E+6 Number of Cycles, N (b) Figure 6.17 Mean stress relaxation in strain-controlled POL tests for (a) SS304L CLI, and (b) SS304L THY.

Mean Strain Strain Amplitude 181 1.0% POL (370 MPa-242 MPa) (LC) CA FR (242 MPa) (LC) OL 0.5% SC 0.0% 0.5% 0.0% 0 5000 10000 15000 20000 25000 Number of Cycles, N (a) POL (370 MPa-242 MPa) (LC) CA FR (242 MPa) (LC) -0.5% -1.0% -1.5% -2.0% 0 5000 10000 15000 20000 25000 Number of Cycles, N (b) SC OL Figure 6.18 Strain response in load-controlled POL tests for SS304L CLI. (a) Strain amplitude response. (b) Mean strain response.

Predicted Number of Blocks Predicted Number of Blocks 182 1E+6 1E+5 1E+4 POL, εc POL, LC Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, εc) Random Loading (PS, LC) 1E+3 1E+2 1E+1 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Observed Number of Blocks (a) 1E+6 Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, εc) 1E+5 Random Loading (PS, LC) 1E+4 1E+3 1E+2 1E+1 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Observed Number of Blocks (b)

Predicted Number of Blocks 183 1E+5 1E+4 POL (PS, εc) Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, LC) 1E+3 1E+2 1E+1 1E+0 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 Observed Number of Blocks (c) Figure 6.19 Predicted versus observed number of blocks to failure for POL and random loading tests using LDR and strain-life or stress-life curve for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Predicted Number of Blocks Predicted Number of Blocks 184 1E+6 1E+5 1E+4 POL, εc POL, LC Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, εc) Random Loading (PS, LC) 1E+3 1E+2 1E+1 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Observed Number of Blocks (a) 1E+6 POL, εc POL, LC Random Loading (V, εc) 1E+5 Random Loading (V, LC) Random Loading (PS, εc) Random Loading (PS, LC) 1E+4 1E+3 1E+2 1E+1 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Observed Number of Blocks (b) Figure 6.20 Predicted versus observed number of blocks to failure for POL and random loading tests of SS304L CLI using (a) LDR and SWT-life curve, and (b) LDR and FS-life curve.

Predicted Number of Blocks Predicted Number of Blocks 185 1E+6 1E+5 Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, εc) Random Loading (PS, LC) 1E+4 1E+3 1E+2 1E+1 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Observed Number of Blocks (a) 1E+6 Random Loading (V, εc) Random Loading (V, LC) 1E+5 Random Loading (PS, εc) Random Loading (PS, LC) 1E+4 1E+3 1E+2 1E+1 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 Observed Number of Blocks (b) Figure 6.21 Predicted versus observed number of blocks to failure for random loading tests of SS304L THY using (a) LDR and SWT-life curve, and (b) LDR and FS-life curve.

Predicted Number of Blocks Predicted Number of Blocks 186 1E+5 1E+4 POL, (PS, εc) Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, LC) 1E+3 1E+2 1E+1 1E+0 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 Observed Number of Blocks (a) 1E+5 1E+4 POL (PS, εc) Random Loading (V, εc) Random Loading (V, LC) Random Loading (PS, LC) 1E+3 1E+2 1E+1 1E+0 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 Observed Number of Blocks (b) Figure 6.22 Predicted versus observed number of blocks to failure for POL and random loading tests of Al 7075-T6 using (a) LDR and SWT-life curve, and (b) LDR and FS-life curve.

187 (a) (b) (c) (d) Figure 6.23 Random loading test deformation response for SS304L CLI. (a) Stress response in a strain-controlled test at 1% maximum strain amplitude. (b) Strain response in a load-controlled test at 245 MPa maximum stress amplitude. (c) Midlife hysteresis loops in a strain-controlled test at 1% maximum strain amplitude. (d) Midlife hysteresis loops in a load-controlled test at 245 MPa maximum stress amplitude.

188 (a) (b) (c) (d) Figure 6.24 Random loading test deformation response for SS304L THY. (a) Stress response in a strain-controlled test at 1% maximum strain amplitude. (b) Strain response in a load-controlled test at 280 MPa maximum stress amplitude. (c) Midlife hysteresis loops in a strain-controlled test at 1% maximum strain amplitude. (d) Midlife hysteresis loops in a load-controlled test at 280 MPa maximum stress amplitude.

189 (a) (b) (c) (d) Figure 6.25 Random loading test deformation response for Al 7075-T6. (a) Stress response in a strain-controlled test at 1% maximum strain amplitude. (b) Strain response in a load-controlled test at 345 MPa maximum stress amplitude. (c) Midlife hysteresis loops in a strain-controlled test at 1% maximum strain amplitude. (d) Midlife hysteresis loops in a load-controlled test at 345 MPa maximum stress amplitude.

Maximum Stress (MPa) Maximum Stress (MPa) 190 400 V RL 0.3% (εc) PS RL 0.3% (εc) V RL 0.3% (εc) PS RL 0.3% (εc) 300 200 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Number of Blocks (a) 450 PS RL 0.3% (εc) PS RL 0.3% (εc) 400 V RL 0.3% (εc) 350 300 250 200 0 20000 40000 60000 80000 100000 120000 Number of Blocks (b) Figure 6.26 Maximum stress response in strain-controlled random loading (a) for virgin and prestrained duplicate tests at 0.3% maximum strain amplitude for SS340L CLI, and (b) for virgin and prestrained tests at 0.3% maximum strain amplitude for SS304L THY.

191 (a) (b) (c) Figure 6.27 Damage ratio sums calculated with LDR and strain-life, SWT and FS curves in random loading strain-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) and Al 7075-T6.

192 (a) (b) (c) Figure 6.28 Damage ratio sums calculated with LDR and stress-life, SWT and FS curves in random loading load-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.

Chapter Seven Cracking Behavior and Damage Evolution 7.1 Introduction Crack networks have been observed in the cooling system of nuclear power plants, and their nucleation and growth are of concern in the safety of these structures. Because of the high toughness of SS304L, cracks can grow long before failure occurs in components made of such materials. These cracks are usually macrocracks (longer than 1 mm), and their study involves fracture mechanics. Crack nucleation and microcrack growth are typically considered in fatigue life of smooth specimens as macrocrack initiation (i.e. cracks on the size order of 1 mm). However, microcracks (smaller than 1 mm) can be present long before cracks become macrocracks and failure occurs. The presence and evolution of these microcracks is discussed in this chapter, for SS304L, and Al 7075-T6, under strain-controlled and loadcontrolled tests conditions. Effects of mean stress, prestraining, and variable amplitude loading are presented. 193

194 7.2 Crack Analysis 7.2.1 Procedure of crack analysis To ensure consistency of the results, analysis of the cracks was made in a systematic manner, using a Nikon optical microscope, equipped with a Nikon digital camera, and the same magnification was used throughout the analysis. A reference rectangular 10 mm x 0.9 mm area was marked on all specimens, as shown in Figure 7.1. For non broken specimens, this area corresponded to the gage section, including the main failure crack(s). For broken specimens, or unbroken specimens with large failure cracks, analysis was conducted in the same manner, above and below the main failure crack, starting from the edge of the crack. As stated in previous chapters, all failures and fractures occurred within the gage section. Following this procedure, results can be given as crack density, and are presented in Tables 7.1 to 7.3, where a crack density unit of number of cracks per 9 mm 2 was used. In these tables, the type of test conducted on each specimen is indicated. Specific details about loading conditions can be found in Chapters 3, 5, and 6. For photos presented in this chapter, only part of the reference area is shown, with the loading direction parallel to the vertical direction of the photo. Before fracture occurs, bending can result from uneven loading on opposite sides of a macrocrack, and can lead to significantly altered strain and stress conditions, as shown in Figure 7.2. Therefore, for broken specimens and those with macrocracks, analysis was made on the side of the fracture crack, where strain and stress conditions are relatively unaffected and the macrocrack shielding tends to preserve microcracking behavior of the specimen.

195 For unbroken specimen, the location of the reference area was randomly chosen. However, after cracks were accounted for in the designated area, it was ensured that similar cracking behavior was observed around the circumference of the specimens. Additional cracks found in this manner are marked with an asterisk in the tables. For most specimens, crack density analysis was realized after failure, and no microcracks smaller than 30 µm were accounted for. For three specimens, microcracks were monitored throughout the test. Tests were conducted in load control, and stopped every 200 cycles to photograph the surface of the specimen, in a predetermined marked area. For two tests, the specimen surface was polished every time the test was stopped, to remove any microcracks that had formed. In this latter case, referencing marks were drawn on the grips so that the specimen could be positioned in the loading grips in a consistent position and orientation. 7.2.2 Crack type definitions For each material, a variety of cracks were observed. To simplify the analysis, they were categorized depending on their length, relative intensity (i.e. depth), and whether crack coalescence occurred. For stainless steel, both grades (i.e. SS304L CLI and SS304L THY) presented similar cracking features. Therefore, identical crack type definitions were used for both SS304L grades (i.e. SS304L CLI and SS304L THY), as follows (presented in Figure 7.3): Type A: Shallow (hairline) microcracks, randomly oriented with length between 30 μm and 75 μm.

196 Type B: Shallow microcracks, perpendicular to the loading direction, with length between 75 μm and 600 μm. Type B : More intense microcracks than type B (appear darker and with some space between the two faces of the microcrack), perpendicular to the loading direction, with length between 75 μm and 600 μm. Type C: Shallow microcracks, perpendicular to the loading direction, with length of 900 μm or longer (covering the whole reference area and beyond). Type D: Coalescence of microcracks, perpendicular to the loading direction, typically longer than 900 μm. Type NC: Microcrack network, where microcracks are not easily distinguishable. For this type of feature, no crack density value is indicated in the tables. Type E: Very intense microcracks (large gap between the two edges of the microcrack), perpendicular to the loading directions, usually longer than 500 μm. Type F: Fracture cracks, indicated by a large gap between the two faces of the crack and considerable surface damage. For Al 7075-T6, microcracking features were different and the following definitions were used (presented in Figure 7.4): Type A: Shallow microcracks, about 100 μm to 300 μm long. Type A : Slightly more intense microcracks than type A, about 100 μm to 300 μm long. Type A : Intense microcracks (indicated by a gap between the two faces of a microcrack), about 100 μm to 300 μm long. Type B: Fairly shallow microcracks, about 300 μm to 600 μm long.

197 Type C: Shallow microcracks, about 600 μm to 900 μm long. Type C : More intense microcracks than type C (indicated by a gap between the two faces of a microcrack), about 600 μm to 900 μm long. Type D: Long cracks (usually coalescence of several cracks), with length of 900 μm or longer. Type E: Fracture cracks, characterized by the presence of a large gap between the two faces of the crack, at least 500 μm long. 7.3 Cracking Behavior under Constant Amplitude Loading 7.3.1 Constant amplitude fully-reversed behavior Because of the high toughness of SS304L, more microcracks were generally found in this material, as compared to aluminum. Microcrack coalescence was observed in both materials. This can be related to the type of crack growth known to occur in ductile behaving materials. With respect to loading amplitude, under fully-reversed constant amplitude loading, in specimens cycled at higher amplitude more microcracks were observed, and microcracks were usually more intense (deeper) at higher amplitude. Microcracks of type NC (i.e. microcrack network) were typical of high amplitude loading, in both strain and load control modes. An explanation of the presence of this type of cracking behavior is the higher amplitude of loading itself that permits more microcrack nucleation sites. For aluminum, observation was made difficult due to some oxidation on the specimen surface that could not be removed without affecting the surface cracks. However, differences were not as drastic as for SS304L between lower and higher

198 loading levels. Cycling at runout level under fully-reversed constant amplitude conditions did not generate any apparent microcracks, for either material, as expected. No significant influence of the test control mode was observed with regards to microcracking behavior, in fully-reversed constant amplitude tests, for both Al 7075-T6 and SS304L. This is consistent with the similarities in fatigue life observed under strain and load control modes, in constant amplitude fully-reversed tests. 7.3.2 Mean strain and mean stress effects For aluminum, due to fully elastic behavior at and below 0.5% strain amplitude, strain and load control mode are equivalent. For this material, only specimens tested in the presence of mean stress were studied, as no mean strain effects on fatigue life were observed. Comparison of specimens of constant amplitude tests conducted in the presence of tensile, and compressive mean stresses showed no microcracks in the latter case. This was associated with considerably longer fatigue lives, and can be explained by the crack closure phenomenon in the presence of compressive mean stress. As microcracks do not open during most part of the loading cycle, microcrack growth is very limited, leading to longer fatigue lives and no observable crack except for the failure one. In contrast, under tensile mean stress, microcracks are open for most part of the loading cycle and grow faster, resulting in shorter fatigue lives. In SS304L, mean strain tests were conducted in strain control. Mean stress levels were low during these tests, due to mean stress relaxation facilitated by considerable plastic deformation, and tensile mean strain did not have a significant effect on fatigue life. Surprisingly, however, compressive mean strain led to significantly longer lives, especially in HCF, as presented in Chapter 5. At 0.25% strain amplitude for SS304L CLI,

199 and 0.3% strain amplitude for SS304L THY, runout tests associated with secondary hardening were obtained in the presence of compressive mean strain. At equivalent number of applied cycles, the deformation behavior due to mean stress or mean strain was unaltered, as compared to fully-reversed constant amplitude tests at identical strain amplitude levels. Specimen that presented secondary hardening did not present any long or deep microcracks, and only microcracks of type A were observed. The presence of these cracks can be attributed to the great number of applied cycles in these tests, rather than to the presence of secondary hardening. For SS304L CLI (see Table 7.1), at intermediate strain amplitude of 0.4%, similar microcracking behavior was observed between tests with compressive and tensile mean strain. Numerous (60 microcracks for compressive and 40 microcracks for tensile mean strain tests) small, shallow microcracks and few (7 microcracks for compressive and 2 microcracks for tensile mean strain tests) deep and long microcracks were found after failure. At lower strain amplitude of 0.25%, tensile and compressive mean strain specimens presented similar densities of small shallow microcracks (about 20 microcracks). However, no long microcrack was observed on the surface of the secondary hardening runout specimen. Similar behavior was observed for SS304L THY. For this material, one of the secondary hardening tests was conducted up to more than 4x10 6 cycles, and presented an increase in stress response of up to 100%. However, secondary hardening did not lead to accelerated crack growth, as only microcracks of type A were observed (Table 7.2). The density of cracks in these unfailed specimens was related to the level of strain amplitude and the number of cycles applied. More microcracks were present at higher strain

200 amplitude level (for instance 22 at 0.25% strain amplitude versus zero at 0.175% strain amplitude for SS304 CLI) and at higher number of cycles. Nonetheless, this type of microcracks does not appear to have any influence on either deformation or fatigue behavior. 7.4 Effect of Prestraining on Cracking Behavior 7.4.1 Cracks due to prestraining Prestraining, which was applied for 10 cycles at 1.4 % and 2% strain amplitude for Al 7075-T6 and SS304L, respectively, can complete microcrack nucleation process in smooth specimens. Propagation of microcracks can then represent the major part of the subsequent fatigue life [28, 74]. This is in accordance with the observation of multiple microcracks in all prestrained SS304L specimens. More particularly, the surfaces of SS304L CLI specimens were examined immediately after prestraining and revealed the presence of multiple microcracks of type A. Examination of the surface of a specimen prestrained and then cycled at 0.175% strain amplitude until runout fatigue life revealed the presence of the same microcracks of type A and no other cracking features. The surface of this latter runout specimen and the surfaces of specimens examined immediately after prestraining showing nearly identical features suggests very little crack growth occurred in the specimen during cycling at 0.175% strain amplitude. This suggests that microcracks due to prestraining are not critical to fatigue life at very low subsequent loading levels (i.e. such as at 0.175% strain amplitude). At higher loading levels (i.e. such as 412 MPa stress amplitude) multiple longer microcracks of type B, D and E were observed at failure in a prestrained and then

201 polished specimen. This procedure is explained in Section 7.4.2. The density of these microcracks was higher than on the surface of the virgin material cycled at identical stressing level of 412 MPa stress amplitude (four times higher for microcracks of type B and 30 times higher for microcracks of type D). Since the fatigue life of the prestrained and then polished specimen was about 50% longer than for the virgin material, the higher densities of microcracks in this specimen might be related to the higher number of loading cycles applied, and cannot directly be attributed to prestraining. For SS304L, hardening remains a major result of prestraining, with significant effects on both subsequent deformation and fatigue behaviors. In aluminum microcracks were also observed in prestrained specimens. More microcracks were found in prestrained tests where tensile mean stress was present, similar to the virgin material. Microcracks due to prestraining did not significantly affect the fatigue behavior of this material either. 7.4.2 Crack evolution For five SS304L CLI specimens, the surface was polished after prestraining for 10 cycles at 2% strain amplitude, and re-examined to ensure that removal of the microcracks due to prestraining was complete, as presented in Figure 7.5. These specimens were then tested in three different fashions. Two duplicate tests were conducted in strain control at 0.25% fully-reversed constant strain amplitude. The three other specimens were tested in load control, at 412 MPa fully-reversed constant stress amplitude. For the three load-controlled tests, the tests were stopped every 200 cycles (corresponding to about 10% of expected life) to examine the surface. One specimen was

202 used to study microcrack evolution, and microcrack lengths of two microcracks were measured throughout the test. Surface photos and microcrack growth plot for this specimen are presented in Figures 7.6 and 7.7, respectively. The other two specimens were also examined every 200 cycles, then polished to remove any microcracks that had formed. Photos of the surface for one of these latter specimens are presented in Figure 7.8. Photos of the surface of the specimen before polishing are shown for each step. For the two successively polished specimens, polishing every 200 cycles resulted in a total reduction in diameter of about 0.11 mm for one specimen and 0.28 mm for the other. Details of the removed amount of material for each step are given in Table 7.4, in terms of reduction in diameter. More material was removed towards the end of the test, due to the formation of deeper microcracks. Diameters were measured prior and after polishing, and for load-controlled tests the applied load was adjusted appropriately. With respect to deformation behavior, removal of the microcracks after prestraining did not have any effect, as shown in Figure 7.9, where the stress response for virgin, prestrained, and prestrained then polished tests are presented. No alteration in the deformation behavior was observed due to polishing, as expected. Concerning fatigue life, polishing appeared to be beneficial, although the effects were somewhat less significant than expected. Polishing after prestraining resulted in 60% increase in fatigue life for the prestrained then polished specimen in strain control, and up to 120% increase in life for the specimens polished after prestraining and successively every 200 subsequent cycles in load control (Table 7.1). As seen in Figure 7.8, cracking features appear similar, especially from N = 960 to N = 1760, indicating

203 that not enough material was removed to fully eliminate the cracks. Therefore, crack growth was not prevented and polishing was only slightly beneficial to fatigue life. Figures 7.6 and 7.7 represent microcrack evolution for a prestrained then polished specimen test conducted at 412 MPa stress amplitude in load control. As seen in Figure 7.6, although microcracks started at an angle, they progressively became perpendicular to the loading direction. Microcrack growth of these microcracks was followed by microcracks coalescence, until they reached the size of a macrocrack (about 1 mm) which lead to failure of the specimen, with most of the microcrack growth occurring towards the end of the test. Microcrack lengths are plotted for two different microcracks, as a function of normalized life, with similar results in Figure 7.7. The deformation behavior of the material is also included, characterized by the displacement amplitude in this loadcontrolled test. The specimen presented steady state deformation behavior for most part of the test, after initial softening during the first 25% of life. In load-controlled tests, failure can be characterized by a sudden increase in displacement amplitude, due to the presence of macrocrack(s). This occurred during the last 5% of life, and was associated with considerable microcrack growth. The increase in microcrack growth rate cannot be attributed to hardening of the material, as displacement amplitude was fairly constant throughout the test. These results also confirm that failure in these smooth specimens is ultimately due to the presence of macrocrack(s) about 1 mm long. The presence of microcracks on the order of grain size at only 10% of life confirms the fact that fatigue life is dominated by microcrack growth in SS304L. This is in accordance with Murakami and Miller [27] who stated that in carbon steel S45C, LCF

204 process of plain specimens was nearly entirely dominated by a single crack that initiated in the first few stress cycles. For this material, they also observed that a grain-size crack can form after a negligibly small number of stress cycles. 7.5 Loading Sequence Effects on Cracking Behavior Loading sequence was present in all variable amplitude tests. In step tests, different microcracking behavior was observed between H-L and L-H sequences for both materials. Microcracks appear deeper for the H-L sequence than for the L-H sequence, as shown in Figure 7.10 for SS304L CLI. This indicates that microcracks most likely initiated during the high level in H-L sequence and then grew at the low level. The presence of longer and deeper microcracks of type E in H-L step tests in strain control, as compared to only microcracks of type A in the corresponding L-H test, confirms this hypothesis. Similar behavior was observed for aluminum, as presented in Figure 7.11. Prestraining always induced the development of many very shallow cracks (see Figure 7.5). As specimens were only analyzed after failure, the dominant microcracking behavior in prestrained specimens was, however, typical of the loading level, with many large, deep microcracks in specimens tested at high loading amplitude. Crack growth of microcracks formed due to prestraining was not a determining factor in fatigue life, as compared to the effect of hardening resulting from prestraining, as mentioned in Section 7.4.1. In H-L sequence step test, although the loading amplitude was lower (1% in H-L step tests versus 2% strain amplitude during prestraining), more cycles were applied. Therefore, some microcrack growth can occur during the first step of H-L step tests. This is confirmed by the presence of more microcracks of type E in H-L step test than in the corresponding prestrained test (3 microcracks versus 1 microcrack).

205 Comparison of microcracking behaviors between step tests and periodic overload tests for SS304L showed more deep microcracks of type B (3 microcracks in POL tests versus 1 microcrack in H-L step tests) due to periodic overloads. This is consistent with the fatigue life behavior, as greater damage (shorter fatigue lives) was observed due to periodic overloads than due to equivalent high level of H-L step tests. For Al 7075-T6, POL tests were conducted on prestrained specimens with fully tensile or fully compressive overloads. The latter specimens presented slightly shorter fatigue lives (20%) as compared to tests with fully tensile overloads. More microcracks of type A were observed in the test with tensile overloads than in the test with compressive overloads (9 microcracks versus 3 microcracks). However, a microcrack of type C was only found in the test with compressive overloads. The difference in fatigue lives being small, no definite conclusions can be made in this case. Specimens tested under random loading presented microcracking behavior similar to specimens tested under constant amplitude fully-reversed conditions, as the dominant microcracking behavior was representative of the higher level in the block. Considering results obtained in prestrained, step tests, and periodic overloads tests, this was to be expected. 7.6 Conclusions 1) High loading amplitudes always led to the formation of multiple coalescence of microcracks for SS304L, characterized as network (NC) type of microcracks. 2) In aluminum 7075-T6, mean stress was found to have the expected effects on microcracking behavior. Numerous microcracks were observed in the presence of tensile mean stress that prevents crack closure during most part of the loading

206 cycles. Compressive mean stress had the opposite effect, and no microcrack other than the failure crack was observed in this case. 3) In SS304L, compressive mean strain induced significantly longer lives associated with secondary hardening at low strain amplitude levels. However, this behavior could not be directly related to the presence or absence of microcracks. The number of microcracks seems to be dependent on the number of cycles applied, although no long or deep cracks were observed in any runout specimens, even for prestrained or periodic overload tests. 4) Prestraining led to the formation of multiple shallow microcracks in SS304L. Removal of these microcracks was beneficial to fatigue life. However, hardening due to prestraining appears to be a more important factor in the alteration of both deformation and fatigue behaviors than the presence of microcracks. 5) In aluminum 7075-T6, microcracking due to prestraining did not have any significant effect, although prestraining permits microcrack initiation. 6) Crack evolution was evaluated for a load-controlled specimen. It showed that most of the microcrack growth occurs in the last few percent of fatigue life, and that failure is ultimately due to the presence of macrocrack(s) of about 1 mm in length. 7) Removal of microcracks has a beneficial effect on fatigue lives. However, although examination of the surface of the specimen may indicate elimination of microcracks, this may not be the case. For complete microcracks removal, it is necessary to remove larger amounts of material to not only remove microcracks

207 visible by optical microscope, but also their established deformation and prior damage influence region. 8) Load sequence effect was observed in cracking behavior of both materials, especially in step tests. It was characterized by the growth of more microcracks in H-L as compared to L-H sequences. Variable amplitude specimens presented microcracking behavior characteristics of the higher level in the block.

208 Table 7.1 Summary of crack analysis for SS304L CLI. Specimen Control Strain or Stress 2N Test Type f, n 1 /n 2, or Density of Crack by Crack Type Comments ID Mode Level Blocks to Failure A B B' C D E NC F UTCLI2 CA FR strain 1% 2,350 30 20 0 35 0 3 yes UTCLI1 CA FR strain 0.40% 30,680 15 8 1 0 0 0 UTCLI11 CA FR strain 0.20% 416,826 20 0 0 0 0 0 UTCLI85 CA FR strain 0.175% >8,087,768 (NF) 0 0 0 0 0 0 SH UTCLI40 CA FR load 412 MPa 1,756 0 0 16 8 2 0 yes UTCLI22 CA FR load 243 MPa 39,990 0 0 0 0 0 0 yes UTCLI27 CA FR load 210 MPa 213,552 6 0 0 0 0 0 UTCLI51 Tensile mean strain strain 0.40% 22,434 40 0 4 0 0 2* UTCLI32 Compressive mean strain strain 0.40% 24,500 60 10 15 0 0 7* UTCLI48 Tensile mean strain strain 0.25% 120,622 25 0 0 0 0 1* UTCLI49 Compressive mean strain strain 0.25% > 2,332,640 (NF) 22 5* 0 0 0 0 SH UTCLI70 Prestrained (PS) strain 0.40% 23,530 85 0 4 0 0 0 UTCLI66 Prestrained (PS) strain 0.40% 20,264 73 2 0 0 0 2* UTCLI68 Prestrained (PS) strain 0.25% 122,372 90 1 0 0 0 2* UTCLI83 Prestrained (PS) strain 0.20% 608,920 80 0 4 0 0 0 UTCLI84 Prestrained (PS) strain 0.175% > 6,288,160 (NF) 70 0 0 0 0 0 UTCLI41 Prestrained (PS) load 243 MPa > 2,270,350 (NF) 70 0 0 0 0 0 UTCLI95 Prestrained (PS) strain 0.25% 228,764 0 0 0 0 0 2* UTCLI75 Prestrained (PS) strain 0.25% 324,210 0 0 0 0 0 1* UTCLI96 Prestrained (PS) load 412 MPa 2,948 0 0 55 0 60 20 yes 3* UTCLI72 Prestrained (PS) load 412 MPa 4,124 0 0 20 0 35 10 yes 2* UTCLI31 Prestrained (PS) load 412 MPa 4,164 0 10 0 0 2 0 yes 1+1* UTCLI33 Step (L-H) strain 0.25%/1% 47,000/784 60 0 0 0 0 0 yes UTCLI15 Step (H-L) strain 1%/0.25% 117/32,046 25 10 0 0 0 3* yes UTCLI26 Step (H-L) strain 0.5%/0.25% 670/42,954 44 0 1 0 0 2* UTCLI45 Step (L-H) load 243 MPa/412 MPa 2,700/799 0 0 0 0 0 30* yes UTCLI36 Step (H-L) load 412 MPa/210 MPa 235/>409,928 (NF) 0 0 0 0 0 0 yes UTCLI81 Periodic OL (POL) strain 1%/0.4% 138 65 0 3 0 0 11 yes

209 UTCLI65 Periodic OL (POL) strain 1%/0.4% 117 64 0 3 2 0 0 yes UTCLI77 Periodic OL (POL) strain 1%/0.25% (1/751) 48 0 0 0 0 0 0 yes UTCLI67 Periodic OL (POL) strain 1%/0.25% (1/334) 84 0 0 0 0 0 0 yes UTCLI78 Periodic OL (POL) load 412 MPa/243 MPa 705 0 0 0 0 0 11 yes UTCLI88 Random (RL) strain 1% 196 60 0 70 10 0 0 yes UTCLI86 Random (RL) strain 0.50% 1,740 30 1 0 1 0 2 UTCLI94 PS, Random (RL) strain 0.50% 1,626 60 0 0 2 1 1 UTCLI58 PS, Random (RL) strain 0.30% 15,107 75 0 0 0 1 0 UTCLI80 Random (RL) load 262 MPa 10,884 3 0 0 0 0 4* CA FR: Constant amplitude, fully-reversed. SH: Secondary hardening. * These cracks were found outside of the reference area. Specimens were polished after prestraining. Specimens were polished after prestraining, and every 200 subsequent cycles.

210 Table 7.2 Summary of crack analysis results for SS304L THY. Specimen ID Test Type Control Mode Strain or Stress Level 2N f, n 1 /n 2, or Blocks to Failure Density of Crack by Crack Type A B B' C D E NC F Comments UTTHY2 CA FR strain 1% 1,950 70 60 4 0 0 7* yes UTTHY11 CA FR strain 0.60% 5,478 50 10 0 4 1 5 UTTHY9 CA FR strain 0.40% 43,414 50 0 0 0 0 2* UTTHY7 CA FR strain 0.30% 1,057,360 20 0 0 0 0 0 UTTHY6 CA FR strain 0.25% >4,043,156 (NF) 0 0 0 0 0 0 SH UTTHY8 CA FR load 274 MPa 46,882 0 0 0 0 0 2 UTTHY30 CA FR load 300 MPa 37,252 60 1 0 0 0 0 UTTHY15 Tensile mean strain strain 0.30% 107,410 35 0 2 0 0 1 UTTHY13 Compressive mean strain strain 0.30% >8,354,260 (NF) 20 0 0 0 0 0 SH UTTHY41 Prestrained (PS) strain 0.25% 289,914 80 0 0 1 0 1 UTTHY18 Prestrained (PS) load 274 MPa >6,323,860 (NF) 75 0 0 0 0 0 SH UTTHY40 Periodic OL (POL) strain 0.4%/0.25% 216 0 0 0 0 0 0 UTTHY28 Step (H-L) strain 1%/0.3% 530/31,332 100 0 1 0 0 1 UTTHY32 Step (H-L) load 417 MPa/274MPa 212/215,932 100 0 0 0 0 1 yes UTTHY33 Step (H-L) load 417 MPa/274MPa 212/227,745 70 0 0 0 0 1 yes UTTHY36 Random (RL) strain 0.50% 2,688 20 2 0 0 0 1 UTTHY46 Random (RL) strain 0.30% >103,242 (NF) 0 0 0 0 0 0 SH UTTHY38 PS, Random (RL) load 300 MPa >100,000 (NF) 100 0 0 0 0 0 CA FR: Constant amplitude, fully-reversed. * These cracks were found outside of the reference area.

211 Table 7.3 Summary of crack analysis results for Al 7075-T6. Specimen ID Test Type Control Mode Strain or Stress Level 2N f, n 1 /n 2, or Blocks to Failure Density of Crack by Crack Type A A' A'' B C C' D E A41 CA FR strain 2% 76 not clear A54 CA FR strain 1.40% 366 0 0 4 0 0 0 0 0 A81 CA FR strain 1% 758 0 38 0 0 1 0 0 0 A102 CA FR load 0.40% 72,264 0 0 0 0 1+1* 0 0 0 A42 CA FR load 0.30% 1,415,406 0 0 0 0 0 0 1* 0 A38 CA FR load 0.23% 3,495,724 0 0 0 6 0 0 0 0 A25 CA FR load 0.23% >2,4946,798 (NF) 0 0 0 0 0 0 0 0 A48 Prestrained (PS), compressive mean stress strain 1.4%-0.5% 92,150 3 0 0 0 1 0 1* 0 A68 Prestrained (PS), tensile mean stress strain 1.4%-0.5% 9,690 0 0 12 0 0 0 0 0 A73 Compressive mean stress strain 0.50% 153,932 0 0 0 0 0 0 0 0 A70 Tensile mean stress strain 0.50% 10,724 0 0 9 0 0 0 0 0 A57 PS, Periodic compressive OL strain 1.4%-0.5% 9.7 0 0 3 0 1 0 0 0 A50 PS, Periodic tensile OL strain 1.4%-0.5% 12 0 24 9 0 0 5 0 0 A103 Step (L-H) strain 0.4%-1% 25,400/298 0 0 0 0 2* 1* 0 0 A99 Step (H-L) strain 1%-0.4% 158/16,705 6 0 4 0 0 0 0 0 A97 Step (H-L) strain 1%-0.4% 80/31,400 0 0 3 0 0 0 0 0 A87 Step (H-L) load 547 MPa-286 MPa 53/23,054 0 0 12 0 0 0 0 0 A107 Random (RL) strain 0.50% 7,218 0 0 3 0 0 0 0 0 A110 Random (RL) strain 1% 184 0 0 0 2 3 0 0 1* A109 PS, Random (RL) strain 0.50% 5,539 6 0 3 0 0 0 0 0 CA FR: Constant amplitude, fully-reversed. * Indicates that these cracks were found outside of the reference area.

212 Table 7.4 Variations in diameter due to polishing in prestrained, then polished specimens for SS304L CLI. UTCLI72 UTCLI31 Number of ø Number of ø cycles (N) (mm) cycles (N) (mm) 0 5.16 0 5.11 160 5.16 160 5.11 360 5.16 360 5.08 560 5.16 560 5.08 760 5.14 760 5.08 960 5.14 960 5.05 1160 5.13 1160 5.04 1360 5.11 1360 5.03 1560 5.10 1560 5.00 1760 5.05 1760 4.83 212

213 0.9 mm 10 mm Figure 7.1 Reference area for crack analysis. ε > ε a ε a Figure 7.2 Bending resulting from uneven loading conditions due to the presence of a macrocrack.

214 200 µm 200 µm 200 µm A B B 200 µm 200 µm 200 µm C D NC 200 µm 200 µm E F Figure 7.3 Crack reference types for SS304L.

215 200 μm 200 μm 200 μm A A A 200 μm 200 μm 200 μm B C C 200 μm D Figure 7.4 Crack reference types for Al 7075-T6.

216 200 µm 200 µm Figure 7.5 Specimen surface after prestraining (10 cycles at 2% strain amplitude) shown on left, and after prestraining and then polishing shown on right.

217 1 N = 160 N = 360 N = 560 2 200 µm 200 µm 200 µm N = 760 N = 960 N = 1160 200 µm 200 µm 200 µm N = N f N = N f 1470 200 µm 200 µm Figure 7.6 Crack evolution in a prestrained (10 cycles at 2% strain amplitude) then polished SS304L CLI specimen cycled in load control at 412 MPa, with N f 1470 cycles. The last two photos were taken in different sections of the specimens at failure. Evolution of cracks marked 1 and 2 in the first picture was followed throughout life.

218 Figure 7.7 Displacement amplitude and crack length versus normalized life for a prestrained (10 cycles at 2% strain amplitude) and then polished SS304L CLI specimen in load control with 412 MPa stress amplitude. Crack growth is represented for the two cracks indicated in Figure 7.6.

219 N = 160 N = 360 N = 560 200 µm 200 µm 200 µm N = 760 N = 960 N = 1160 200 µm 200 µm 200 µm N = 1360 200 µm N = 1560 200 µm 200 µm N = 1760 N = 1960 N = N f 200 µm 200 µm Figure 7.8 Evolution of microcracks on the surface of a prestrained (10 cycles at 2% strain amplitude) SS304L CLI specimen cycled at 412 MPa in load control, with N f 2080 cycles. Polishing was conducted after prestraining, and successively every 200 cycles. The photos were taken before polishing. The last photo was taken at failure.

220 Figure 7.9 Stress response for virgin, prestrained (10 cycles at 2% strain amplitude) and then polished specimens of SS304L CLI cycled in strain control at 0.25% strain amplitude.

221 100 µm 100 µm (a) (b) Figure 7.10 Cracks observed in the gage section of failed SS304L CLI specimens in strain-controlled step tests for (a) a L-H (0.25%-1% strain amplitudes) test, and (b) a H-L (1%-0.25% strain amplitudes) test. 100 µm 100 µm (a) (b) Figure 7.11 Cracks observed in the gage section of failed Al 7075-T6 specimens in strain-controlled step tests for (a) a L-H (0.4%-1% strain amplitudes) test, and (b) a H-L (1%-0.4% strain amplitudes) test.

Chapter Eight Conclusions and Recommendations The overall goal of this project was to investigate the deformation history effect on deformation and fatigue behaviors of two types of materials, and to evaluate the influence of prestraining, mean stress and variable amplitude loading on deformation and cumulative fatigue damage behavior. Because aluminum 7075-T6 (Al 7075-T6) and stainless steel 304L (SS304L) present extreme cases with respect to deformation history dependence, these two materials were chosen to investigate the influence of the deformation behavior on fatigue life and assess the applicability of appropriate fatigue life prediction parameters under variable amplitude loading conditions. After a literature review in Chapter 2, experimental program and testing procedures were presented in Chapter 3. In Chapter 4, differences between the two materials, in terms of deformation history sensitivity were assessed. Experimental results under constant amplitude loading, including mean strain or stress and prestraining effects under different test control modes were discussed in Chapter 5. Influence of loading sequence in step tests, periodic overload tests, and under random loading conditions were presented in Chapter 6. The applicability of the commonly used linear damage rule was assessed for both materials and the influence of deformation history effect on fatigue behavior was evaluated. For damage accumulation under variable amplitude loading, the 222

223 LDR associated with strain-life (ε-n) or stress-life (S-N) curves was shown to give inaccurate fatigue life predictions for SS304L that presents strong deformation memory effect. The inadequacy of this method is typically attributed to the LDR itself. On the contrary, this study demonstrates that damage accumulation using the LDR can be accurate, provided that the LDR is used in conjunction with parameters including both stress and strain terms. By including both loading history and response of the material, shortcomings of the common approach can be circumvented in an effective manner. Analysis of cracking behavior under various loading conditions and results on microcrack initiation and propagation were presented in Chapter 7, in relation to deformation and fatigue behaviors of the materials investigated. Conclusions for each chapter are presented in more details in Sections 8.1 to 8.5. Recommendations on future possible research on this topic are given in Section 8.6. 8.1 Literature Review Service load histories of many components and structures are often composed of overloads, mean stress and variable amplitude loading. When designing components and structures, it is necessary to compute damage accumulation to evaluate the fatigue life under complex loading conditions. For this, a number of rules, model and parameters have been developed, to predict deformation behavior and to accurately account for fatigue damage. 1) One of the most commonly used damage accumulation rules is the Linear Damage Rule. Its application does not necessitate determination of any parameters, its computation is fairly simple, and it often provides reliable results.

224 For complex load histories and for materials with strong deformation history effects such as stainless steels, the LDR might be associated with parameters including both loading history and response of the material for accurate fatigue life predictions. 2) Stainless steel 304L is used in many applications, including the cooling system of nuclear power plants, where the loading is also complex, consisting of multiple overloads and in the presence of mean stress. Stainless steel is known to have a strong cyclic hardening behavior and is recognized to harden after overloading or preloading. Hardening in stainless steel has been associated to strain and/or stress induced martensitic transformation. This process is related to the number of slip and shear band systems and induces considerable alteration of the microstructure of stainless steel. These microstructural modifications are reflected in the dramatic change in deformation behavior encountered under variable amplitude cycling. As deformation and fatigue behavior are strongly related for stainless steel, both must be investigated to compute damage under cyclic loading. 3) Effects of mean stress, overloads, and loading sequence were studied by previous researchers, and many parameters have been used to evaluate damage induced by these different events. Deformation and fatigue behaviors have been evaluated and different reasons have been proposed to explain the phenomena occurring under complex loading. This study intended to assess the applicability of the LDR and its accuracy under such loading effects for two types of materials, presenting extreme behaviors with respect to deformation history sensitivity.

225 8.2 Load Sequence Effects on Deformation Behavior 1) Stainless steel 304L and aluminum 7075-T6 represent extreme cases with respect to strain history dependence, and the deformation behavior with respect to loading history is related to their stacking fault energy. 2) Stainless steel 304L investigated in this study continuously hardens with increasing cycles in LCF as well as HCF, whereas for aluminum 7075-T6 steady state behavior was observed for the entire life regime. While the deformation curves under monotonic and cyclic loading are similar for the aluminum alloy, strong cyclic hardening was observed for stainless steel, which became more significant at higher strain amplitude. 3) While monotonic stress-strain curves are nearly identical for the two grades of SS304L, the cyclic deformation behaviors differ, due in part to the bilinearity in the behavior of the SS304L CLI grade. 4) Austenitic stainless steel presents a transient behavior in the stress response under strain control and in the strain response under load control, under fully-reversed constant amplitude cyclic loading. Also due to its low stacking fault energy, deformation behavior of this type of material is greatly dependent on prior loading history (strong deformation history effect), as shown by the incremental step tests for which the stress-strain loading and unloading paths do not coincide. 5) Aluminum possesses a higher SFE and thus has less sensitivity to overloading (i.e. little or no deformation history effect). Therefore, no effect of prestraining was observed for this material, while prestraining induced strong hardening in SS304L.

226 8.3 Constant Amplitude Behavior 1) Load-controlled test data were similar to strain-controlled test data for all three materials (Al 7075-T6 and two grades of SS304L), showing little effect of the test control mode on fully-reversed deformation and fatigue behaviors. In spite of large mean strain of about 5% due to ratcheting in some SS304L CLI fullyreversed load-controlled tests, fatigue lives were only slightly shorter than the corresponding lives in strain control. Therefore, strain-life, stress-life, SWT-life, and FS-life curves, although obtained by fitting strain-controlled data, represent load-controlled data very well. 2) In strain-controlled mean strain tests of SS304L, due to considerable amount of plasticity, the mean stress relaxed to less than 20 MPa during the first few percent of the fatigue life. In load-controlled mean stress tests conducted only for SS304L CLI, considerable ratcheting was observed, leading to hardening and about 30% reduction in strain amplitude. 3) The effect of mean stress in either strain-controlled or load-controlled tests of SS304L was small in most cases. This was due to mean stress relaxation in strain control, and beneficial effect of hardening due to ratcheting nullifying detrimental effect of tensile mean stress in load control. The only exception was for straincontrolled tests with compressive mean strain at 0.25% strain amplitude for SS304L CLI and at 0.3% strain amplitude for SS304L THY, where secondary hardening was observed. For these tests, in spite of mean stress relaxation to near zero and contrary to expectations, fatigue lives were at least nine times longer than those in fully-reversed tests. Tensile mean strain was found to have relatively

227 more effects on the behavior of SS304L THY than on the behavior of SS304L CLI, since shorter lives were observed in the presence of tensile mean strain for this material. Tensile mean strain was found to have little effect on the fatigue behavior for SS304L CLI. For aluminum, mean stresses had the expected effects, as tensile mean stress was detrimental, and compressive mean stress was beneficial to fatigue life. 4) Prestraining induced considerable hardening in SS304L. The hardening mostly results from prior cycling at high strain amplitude, rather than from prior high maximum strain. Prestraining appeared to have more effect on the deformation behavior of SS304L THY than CLI, in strain control. Reduction in fatigue lives by a factor of more than five were observed in SS304L THY, whereas fatigue lives for prestrained and virgin SS304L CLI materials were very similar in straincontrolled tests. In load-controlled tests, however, SS304L THY and SS304L CLI presented similar behaviors, as considerable increase in fatigue lives were observed due to prestraining. Hardening in load-controlled tests induced significant reduction in strain amplitude response. Prestraining neither affected the deformation nor the fatigue behavior of Al 7075-T6. 5) All SS304L tests exhibiting secondary hardening had total strain amplitudes at or below 0.25% for SS304L CLI and at or below 0.3% for SS304L THY. Although for SS304L CLI all tests exhibiting secondary hardening presented runout fatigue life, some SS304L THY specimens failed after presenting secondary hardening. However, for SS304L THY, greater hardening rates were observed than for SS304 CLI.

228 6) Strong ferro-magnetic properties, typically associated with martensitic transformation and commonly believed to result from accumulation of plastic strain, were observed for specimens with or without secondary hardening. Vickers micro-hardness measurements revealed strong heterogeneity of the material in sections that presented secondary hardening for both SS304L CLI and THY. This heterogeneity can most likely be attributed to martensitic transformation. However, secondary hardening may be due to the formation of alternate structure(s) rather than or in addition to martensitic phase transformation. 7) With respect to constant amplitude fatigue behavior, the two SS304L grades presented very similar behaviors in LCF, while SS304L THY presented slightly longer fatigue lives at intermediate and long lives. The SS304L THY grade was found to be more sensitive to mean strain and prestraining effects. 8) A fatigue life parameter with both stress and strain terms is necessary to correlate stainless steel data due to the strong deformation history sensitivity of this material. The use of a mean stress parameter was also necessary to correlate mean stress data for aluminum and stainless steel. The SWT and FS parameters were shown to correlate most of the fatigue data reasonably well for both grades of stainless steel and aluminum. 8.4 Variable Amplitude Loading 1) In step tests, no change in deformation behavior was observed for Al 7075-T6 in either strain-controlled or load-controlled tests, and for either H-L or L-H sequence. In contrast, significant hardening was observed for SS304L CLI, at the

229 low level, in H-L step tests. The level of hardening increased with more difference between the two levels and with increasing the number of cycles applied at the higher level. For SS304L THY, because of secondary hardening present in the fully-reversed constant amplitude test, differences in stress responses were not as drastic as for SS304L CLI. 2) In step tests, H-L sequence led to smaller damage sum (shorter life) than L-H sequences for both aluminum and stainless steel in strain control. Observation of longer and deeper microcracks within the gage section of the failed specimens in H-L tests compared to L-H tests indicates that small cracks can develop during the high level of H-L step tests, and grow at low level. 3) Due to significant hardening resulting from the high level in H-L step tests for SS304L, test control mode had a strong influence on fatigue life. Load-controlled tests presented much longer lives than strain-controlled tests, due to lower strain amplitude at the low level for both SS304L CLI and THY. However, in strain control, hardening due to high loading level in H-L step tests was more damaging for SS304L THY than for CLI. 4) Comparison of H-L step tests and periodic overload tests for SS304L CLI indicates that frequent application of periodic overloads induces more overall hardening, as it limits any significant softening of the material. Periodic overloads induced relatively more damage than the high level of H-L step tests in strain control.

230 5) For SS304L THY, periodic overloads at relatively low strain amplitude did not prevent secondary hardening from occurring and did not induce failure of the specimen (runout test). 6) No influence of the test control mode or prestraining was observed in random loading tests for Al 7075-T6. In contrast, for SS304L, prestraining in such tests led to higher stress response in strain control, without any significant influence on fatigue life for SS304L CLI. However, prestraining was found to induce significant damage for SS304L THY, in accordance with results obtained for prestrained constant amplitude tests. In load-controlled random loading tests, prestraining led to about an order of magnitude longer fatigue lives for both materials. 7) Due to significant hardening and strong deformation history effects of a material such as SS304L, the conventional strain-life or stress-life curves in conjunction with the LDR can result in inaccurate life predictions under variable amplitude loading, especially for H-L step and periodic overload tests. Using this approach, remaining cycle ratios in step tests are generally under-predicted (i.e. conservative) in L-H step tests, but over-predicted (i.e. non conservative) in H-L step tests. Very conservative predictions were also obtained for load-controlled H-L step tests for stainless steel but not for aluminum, based on the LDR and strain-life or stress-life curve. The use of a fatigue damage quantifying parameter involving both stress and strain, such as the SWT or FS parameters, leads to significantly better life predictions and can better reconcile differences between test results in different test control modes.

231 8.5 Cracking Behavior and Damage Evolution 1) High loading amplitudes always led to the formation of multiple coalescence of microcracks for SS304L, characterized as network (NC) type of microcracks. 2) In aluminum 7075-T6, mean stress was found to have the expected effects on microcracking behavior. Numerous microcracks were observed in the presence of tensile mean stress that prevents crack closure during most part of the loading cycles. Compressive mean stress had the opposite effect, and no microcrack other than the failure crack was observed in this case. 3) In SS304L, compressive mean strain induced significantly longer lives associated with secondary hardening at low strain amplitude levels. However, this behavior could not be directly related to the presence or absence of microcracks. The number of microcracks seems to be dependent on the number of cycles applied, although no long or deep cracks were observed in any runout specimens, even for prestrained or periodic overload tests. 4) Prestraining led to the formation of multiple shallow microcracks in SS304L. Removal of these microcracks was beneficial to fatigue life. However, hardening due to prestraining appears to be a more important factor in the alteration of both deformation and fatigue behaviors than the presence of microcracks. 5) In aluminum 7075-T6, microcracking due to prestraining did not have any significant effect, although prestraining permits microcrack initiation. 6) Crack evolution was evaluated for a load-controlled specimen. It showed that most of the microcrack growth occurs in the last few percent of fatigue life, and that failure is ultimately due to the presence of macrocrack(s) of about 1 mm.

232 7) Removal of microcracks has a beneficial effect on fatigue lives. However, although examination of the surface of the specimen may indicate elimination of microcracks, this may not be the case. For complete microcracks removal, it is necessary to remove larger amounts of material to not only remove microcracks visible by optical microscope, but also their established deformation and prior damage influence region. 8) Load sequence effect was observed in cracking behavior of both materials, especially in step tests. It was characterized by the growth of more microcracks in H-L as compared to L-H sequences. Variable amplitude specimens presented microcracking behavior characteristics of the higher level in the block. 8.6 Possible Future Research The experimental program included testing under various conditions, including prestraining, mean stress and mean strain, step tests, periodic overload tests, and random loading tests. SWT and FS parameters were shown to fairly correlate stainless steel and aluminum data for these conditions. As SWT or FS parameters include both loading history and response of the material, they led to fairly accurate life predictions for a material with strong deformation history sensitivity. However, in design, only the loading history is usually known, and the material response needs to be evaluated. This can be realized through testing (as was done in this study), or by using deformation models. For implementation of the SWT and FS parameters solely based on loading history, a constitutive plasticity model is required. The variety of experimental data presented in this study could be used as a mean to verify

233 the accuracy of a model, under various loading conditions and for different types of materials. Based on the work of Murakami and Miller [27] and the results presented in Chapter 7, microcrack growth represents a significant part of fatigue life of smooth specimens. Further study of microcrack initiation and growth, and in particular study of the propagation of cracks in HCF would be of great interest in the understanding of the formation and evolution of crack networks (crazing). Influence of polishing, or surface removal at different times in the fatigue process could help the understanding and prevention of crack network formation. Although this study could be conducted on any material, the high toughness of SS304L makes it a material of choice. The austenite to martensite transformation has been extensively studied in austenitic stainless steels. Evolution of magnetic properties [72] is one mean to quantify the amount of transformation and X-Ray diffraction can also be used [75]. However, the aspect of the transformation in HCF remains unclear and the phenomenon described as secondary hardening still needs to be explained. Analysis of microstructure alterations under TEM could give some insights in the mechanisms occurring in the material, and lead the way to accurately predict whether secondary hardening will occur. As this process can be beneficial to fatigue life, it would be of great interest to know how to trigger it.

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