Fatigue behavior in the presence of periodic overloads including the effects of mean stress and inclusions

Transcription

1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2011 Fatigue behavior in the presence of periodic overloads including the effects of mean stress and inclusions Justin Lindsey The University of Toledo Follow this and additional works at: Recommended Citation Lindsey, Justin, "Fatigue behavior in the presence of periodic overloads including the effects of mean stress and inclusions" (2011). Theses and Dissertations This Thesis is brought to you for free and open access by The University of Toledo Digital Repository. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of The University of Toledo Digital Repository. For more information, please see the repository's About page.

2 A Thesis entitled Fatigue Behavior in the Presence of Periodic Overloads Including the Effects of Mean Stress and Inclusions by Justin Lindsey Submitted to the Graduate Faculty in partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering Dr. Ali Fatemi, Committee Chair Dr. Mohamed Samir Hefzy, Committee Member Dr. Efstratios Nikolaidis, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo December 2011

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4 An Abstract of Abstract Fatigue Behavior in the Presence of Periodic Overloads Including the Effects of Mean Stress and Inclusions By Justin Lindsey Submitted to the Graduate Faculty in partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering The University of Toledo December 2011 Variable amplitude loading of components or structures can result in failures which occur much sooner than would be predicted by commonly used life prediction models, utilizing constant amplitude loading. The goal of this study was to investigate the effect of periodic overloads on fatigue behavior of smooth specimens made from five grades of steel and one grade of aluminum. This history included a periodic fullyreversed overload cycle followed by smaller cycles in the presence of a mean stress. Life predictions were performed for each test by implementing the Linear Damage Rule along with the strain-life equation or Smith-Watson-Topper (SWT) mean stress parameter. Life predictions were then compared to experimental results. Life predictions with the SWT parameter showed an increase in accuracy versus the strain-life method but there still remained predictions that were unaffected by the use of this parameter. Presence of periodic overloads in a load history resulted in increased damage for small cycles not only at strain levels above the fatigue limit, but also in damage for cycles below the fatigue limit. Additional tests were performed in order to identify the amount of damage resulting from individual aspects of the load history. These aspects included small cycles in the presence of mean stress without overloads, fully-reversed small cycles with iii

5 overloads, as well as variations in the number of small cycles per load block. Comparison of these different aspects showed that in some cases the application of mean stress in the periodic overload history resulted in little to no additional small cycle damage. Anisotropy resulting from sulfide inclusions was examined by applying the periodic overload history to three sets of steel 4140 containing three different levels of sulfur content (0.004%, 0.012%, and 0.077%). The specimens were machined so that the axis of the specimen was transverse to the rolling direction of the material. Results of the testing showed that, although the sulfur content has a drastic effect on fully-reversed constant amplitude fatigue lives, there is little noticeable different between the materials with different levels of sulfur in the presence of periodic overloads. iv

6 Acknowledgements First, I would like to thank Dr. Ali Fatemi for all of his time and effort. I would like to thank Dr. Mohamed Samir Hefzy and Dr. Efstratios Nikolaidis for serving on my thesis defense committee. I would also like to acknowledge Dr. Tom Oakwood from AISI and Dr. Tim Topper from the University of Waterloo for their feedback and advice. I would like to extend my gratitude to Dr. Julie Colin, Dr. Nima Shamsaei, and Sean McKelvey for helping me learn to use the material testing machines and procedures. Additionally, I extend gratitude to the MIME machine shop staff, Mr. John Jaegly, Mr. Time Grivanos, and Mr. Randall Reihing. The funding for this project was provided by AISI. David Anderson of AISI provided direction for specimen grinding. Materials and its chemical analysis were provided by Robert Cryderman of Gerdau-MacSteel. Specimen heat treatment and metallurgical analysis was provided by Peter Bauerle of Chrysler Group LLC. v

7 Contents Abstract... Acknowledgements... Contents... List of Tables... List of Figures... List of Abbreviations... List of Symbols... iii v vi viii x xiii xiv 1 Introduction Some Relevant Previous Studies Introduction Loading Parameters Influencing Fatigue Life Behavior Effect of Mean Stress on Fatigue Life Overload and Load Sequence Effects Cumulative Damage Rainflow Cycle Counting Method Linear Damage Rule (LDR) Effect of Anisotropy on Constant Amplitude Fatigue Life Summary Experimental Program and Results Material and Specimen Preparation vi

8 3.1.1 Materials Specimen Testing Equipment Experimental Procedures Monotonic Tension Tests Constant Amplitude Fully-Reversed Fatigue Tests Mean Strain and Mean Stress Tests Periodic Overload Tests Deformation Behavior Monotonic Deformation Behavior Transient and Steady-State Cyclic Deformation Behaviors Constant Amplitude Fully-Reversed Fatigue Test Results Constant Amplitude Mean Strain and Mean Stress Fatigue Test Results Periodic Overload Fatigue Tests and Results Analysis of Experimental Results Effect of Mean Stress on Fatigue Life Effect of Periodic Overloads on Fatigue Life Effect of Heat Treatment Variation on Fatigue Life Effect of Anisotropy on Fatigue Behavior Summary and Conclusions References vii

9 List of Tables 3.1 Composition of the five steel grades used in this study (courtesy of Gerdau-MacSteel) Summary of AISI Bar Fatigue Group experimental program as related to the data in this study Summary of the mechanical tensile properties for the materials used in this study. Properties for Steel 4140 were provided in [29] and for Al 7075-T6 in [7] Summary of constant amplitude fatigue test results for steel 8622 (Atm) and (Vac) Summary of constant amplitude fatigue test results for steel 8620 (30 HRC) and (36 HRC) Summary of constant amplitude fatigue test results for steel 4140 (ULS), (Lo S), and (Hi S) [29] Summary of constant amplitude fatigue test results for aluminum 7075-T6 [7] Summary of periodic overload fatigue test results for steel 8622 (Atm) and (Vac) Summary of periodic overload fatigue test results for steel 8620 (30 HRC) and (36 HRC) Summary of periodic overload fatigue test results for steel 4140 (ULS), (Lo S), and (Hi S) Summary of periodic overload fatigue test results for aluminum 7075-T Summary of constant amplitude mean stress test fatigue life predictions Summary of periodic overload fatigue life predictions for steel 8622 (Atm) and (Vac) viii

10 4.3 Summary of periodic overload fatigue life predictions for steel 8620 (30 HRC) and (36 HRC) Summary of periodic overload fatigue life predictions for steel 4140 (ULS), (Lo S), and (Hi S) Summary of periodic overload fatigue life predictions for aluminum T ix

11 List of Figures 2-1 Equivalent lives of fully-reversed cycles subjected to periodic compressive underloads for (a) 2024-T351 aluminum and (b) SAE 1045 steel [16] Variation of interactive damage per block (at 150 MPa) with number of small cycles between overloads for 2024-T351 aluminum [17] Variation of normalized interactive damage per block (at 150 MPa) with number of small cycles between overloads for 2024-T351 aluminum [17] Generalized variation in damage with stress and the number of small cycles following an underload or overload [18] Steady state crack opening stress for three stress ratios as a function of maximum stress for DP 590 steel [21] Microstructure of (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), (d) 8620 (36 HRC), (e) 4140 (ULS), (f) 4140 (Lo S), (g) 4140 (Hi S), and (h) Al 7075-T6 (courtesy of the Chrysler Materials Engineering Lab) Specimen geometry and dimensions for (a) 8622 (Atm), 8622 (Vac), 8620 (30 HRC), 8620 (36 HRC), Al 7075-T6, and (b) 4140 (ULS), 4140 (Lo S), 4140 (Hi S) Loading histories for periodic overload tests (a) with small cycle mean stress or strain, and (b) without small cycle mean stress or strain Stress response in fully-reversed constant amplitude strain-controlled tests for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) Superimposed experimental monotonic tension and calculated cyclic stress-strain curves for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) Superimposed calculated monotonic and calculated cyclic stress-strain curves for (a) 4140 (ULS), (b) 4140 (Lo S), (c) 4140 (Hi S), and (d) Al 7075-T6. These plots are reproduced from [7, 29] x

12 3-7 Stress amplitude versus reversals to failure for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) Stress amplitude versus reversals to failure for (a) 4140 (ULS), (b) 4140 (Lo S), (c) 4140 (Hi S), and (d) Al 7075-T Total, elastic, and plastic strain amplitude versus reversals to failure for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) Total, elastic, and plastic strain amplitude versus reversals to failure for (a) 4140 (ULS), (b) 4140 (Lo S), (c) 4140 (Hi S), and (d) Al 7075-T SWT parameter versus reversals to failure for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) SWT parameter versus reversals to failure for (a) 4140 (ULS), (b) 4140 (Lo S), (c) 4140 (Hi S), and (d) Al 7075-T A comparison of the fully-reversed constant amplitude data for the two 8622 steel grades superimposed based on the (a) strain-life curve and (b) SWT curve A comparison of the fully-reversed constant amplitude data for the two 8620 steel grades superimposed based on the (a) strain-life curve and (b) SWT curve A comparison of the fully-reversed constant amplitude data for the three 4140 steel grades superimposed based on the (a) strain-life curve and (b) SWT curve Strain-life curves including all constant amplitude data for (a) 8620 (30 HRC), (b) 8620 (36 HRC), and (c) Al 7075-T (a) Stress amplitude response and (b) mean stress response in mean strain, strain-controlled tests for steel 8620 (30 HRC) and (36 HRC) Periodic overload data superimposed with the constant amplitude strainlife curve for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) Periodic overload data superimposed with the constant amplitude strainlife curve for (a) 4140 (ULS), (b) 4140 (Lo S), (c) 4140 (Hi S), and (d) Al 7075-T Periodic overload data superimposed with the SWT curve for (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), and (d) 8620 (36 HRC) xi

13 3-21 Periodic overload data superimposed with the SWT curve for (a) 4140 (ULS), (b) 4140 (Lo S), (c) 4140 (Hi S), and (d) Al 7075-T A comparison of the periodic overload data for the two 8622 steel grades superimposed with the (a) strain-life curve and the (b) SWT curve A comparison of the periodic overload data for two 8620 steel grades superimposed with the (a) strain-life curve and the (b) SWT curve A comparison of the periodic overload data for three 4140 steel grades superimposed with the (a) strain-life curve and the (b) SWT curve Equivalent constant amplitude fully-reversed life of the mean stress tests conducted for (a) 8620 (30 HRC), (b) 8620 (36 HRC), and (c) Al 7075-T Predicted versus observed number of blocks to failure for all eight materials using the LDR and (a) strain-life curve, and (b) SWT-life curve The interactive damage per block of POL tests performed with varying number of small cycles per block for Al 7075-T A comparison of the experimental life to failure of specimens subjected to two different strain levels for steel 8620 and one strain level for Al T xii

14 List of Abbreviations CA FR HCF HB HRB HRC H-L LC LCF LDR L-H LYS OL POL POLw/MS POLwo/MS SC S-N SWT UYS YPE εc constant amplitude fully-reversed high cycle fatigue Brinell Rockwell B-scale hardness number Rockwell C-scale hardness number high-low load-controlled low cycle fatigue linear damage rule low-high lower yield strength overload periodic overload periodic overload test with small cycle mean stress periodic overload test without small cycle mean stress small cycles (as opposed to OL in POL tests) stress-life Smith-Watson-Topper parameter upper yield strength yield point elongation strain-controlled xiii

15 List of Symbols A 0 original cross section area A f cross section area at fracture b fatigue strength exponent B number of blocks in a periodic overload test B f number of blocks to failure in a periodic overload test c fatigue ductility exponent C material parameter D 0 initial diameter D f final diameter D damage ratio D min minimum specimen diameter e engineering strain E, E' monotonic, midlife cycle modulus of elasticity %EL percent elongation k material constant K monotonic strength coefficient K' cyclic strength coefficient L 0 initial gage length L f final gage length n number of cycles applied, monotonic strain hardening exponent n' cyclic strain hardening exponent n i number of cycles at stress amplitude σ i n sc number of small cycles in an overload block N number of cycles N * life for a given a for the m = 0 case N f number of cycles to failure 2N f number of reversals to failure N f,ol constant amplitude life to failure at the overload level N f,sc (eq) calculated equivalent life of the small cycles in an overload test P f load at fracture R radius of curvature of neck %RA percent reduction in area R ε strain ratio R σ stress ratio S engineering stress xiv

16 S y S y ' S u β Δε Δε e Δε p i eff Δσ ε ε a a,sc a,ol ε e ε f ε f' ε m m,sc m,ol ε max ε min ε p σ σ a a,sc a,ol ar σ f σ f' σ i σ m m,sc m,ol σ max σ min monotonic yield strength cyclic yield strength ultimate tensile strength material constant true strain range elastic strain range plastic strain range strain based damage parameter intrinsic strain range at which a crack does not propagate effective local strain range true stress range true strain strain amplitude small cycle strain amplitude overload cycle strain amplitude true elastic strain true fracture ductility fatigue ductility coefficient true mean strain small cycle mean strain overload cycle mean strain true maximum strain true minimum strain true plastic strain true stress true stress amplitude small cycle stress amplitude overload cycle stress amplitude equivalent completely reversed stress amplitude true fracture strength fatigue strength coefficient stress amplitude level for n i cycles true mean stress small cycle mean stress overload cycle mean stress true maximum stress true minimum stress xv

17 Chapter One 1 Introduction Many structures are subjected to varying types of cyclic loading. As a result, fatigue failure is one of the most common types of failure and must be taken into consideration in the 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. Fatigue models are usually conservative, in order to allow factors of safety and avoid fatigue failures. Additionally, the majority of components are not subjected to constant amplitude loading. Most loading histories are complex, and can involve variable amplitude loading. Evaluation of the behavior of a component or structure under such load histories can consist 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 structures 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 1

18 achievable. Testing can then be limited to the final component or structure as a verification method, rather than a design and development method. In order to replace the testing of components or structures subjected to variable amplitude loading, accurate life prediction models that take into account these types of loading are required. A reliable damage quantification parameter and a cumulative damage rule, along with constant amplitude material fatigue behavior are needed for life predictions. This study investigates the response of eight materials to the presence of periodic overloads. Two of the steel materials were of the same grade but with a different environmental pressure applied during heat treatment. One batch of specimens was heat treated in an atmospheric condition and the other batch was heat treated in the presence of a vacuum. Two additional steel materials were of the same grade but had different cooling rates applied after heat treatment. The different cooling rates resulted in a difference in hardness between the two sets of specimens. The three remaining steel materials were of the same grade but had different levels of sulfur content. The sulfur content levels were classified as ultra low (0.004%), low (0.012%), and high (0.077%). The steel materials which include a variation in the sulfur content were also specifically machined so that the sulfur inclusions in the material were transverse to the loading direction of the specimen. Lastly, specimens of an aluminum alloy were used in this study to provide a comparison to the trends seen for the steels. Tests were performed on smooth specimen by applying a load history considered to be a worst case scenario in terms of damage applied to the material. The resulting fatigue lives were then compared with the constant amplitude results for each material in order to identify any trends. Additionally, specimen batches that were of the same steel 2

19 grade were compared in order to observe the effect of the different heat treatment conditions and sulfur content levels in the presence of overloads. Specifically, for the material with sulfide inclusions, it was of interest to observe how the anisotropic behavior of the inclusions would affect the fatigue life in the presence of overloads. Additional tests were performed in order to investigate individual aspects of the periodic overload history applied in this study. The load history was made up of a loading block which was repeated until failure. The loading block contained a single overload followed by a certain number of small cycles. The small cycles were performed in the presence of a mean stress which was applied in order to maintain a constant maximum stress between the overload and small cycles. Therefore, in order to isolate the different effects, additional tests were performed on specimens with only a mean stress applied, with an overload applied but with no mean stress, and with the same periodic overload history including mean stress but with a variation in the number of small cycles per block. These aspects were isolated in an attempt to gain a better understanding of how damage results and accumulates throughout the overload testing. Life predictions were also performed for each test using commonly applied methods. The comparison of the predicted lives with the experimental results provided a general understanding of how these methods performed under the specific load history applied and allowed for conclusions to be drawn about any potential shortcomings of each method. Chapter two presents a review of some previous studies that are relevant to the current study. This includes effects of mean stress, overloads, load sequences, and material anisotropy, as well as methods for accounting for the accumulation of damage in 3

20 variable amplitude loading. Chapter three describes the experimental procedures used and results obtained. Specimen preparation, metallurgical analysis, testing equipment and procedures are all discussed. Chapter four provides a comparative analysis and discussion of results. Life predictions are performed for mean stress and periodic overload tests employing commonly used fatigue life prediction methods. The individual effects of mean stress and periodic overloads on small cycles are compared with the combined effect of mean stress with periodic overloads on small cycles. Trends in small cycle damage accumulation after overloads are identified and discussed. The effects of heat treatment procedures and anisotropic effects on fatigue life are also discussed. Chapter five summarizes the findings of this study. 4

21 Chapter Two 2 Some Relevant Previous Studies 2.1 Introduction Most components and structures are subjected to cyclic loading. Additionally, the loading may be variable in nature with occasional overloads and/or with cycles having mean stress. In order to be able to predict the life of components subjected to this loading it is important to understand how a material will react under each of these individual conditions. Anisotropy can also be introduced into a material by processing and manufacturing. Therefore, it is also important to understand the synergistic effects of the material characteristics and loading conditions. Models have been developed in order to quantify the effects of mean stress and variable amplitudes on a material. Cumulative damage rules have also been developed for damage accumulation under these loading conditions. This chapter presents some of the previous research regarding these aspects of fatigue. 5

22 2.2 Loading Parameters Influencing Fatigue Life Behavior Effect of Mean Stress on Fatigue Life Mean stress can have a significant impact on constant amplitude cycling of a material. Mean stress is defined as the mean value of the maximum and minimum of a stress cycle. Generally, it is understood that tensile mean stress is detrimental to fatigue life and compressive mean stress is beneficial to fatigue life. The hardness of a material can affect the degree to which the effects of mean stress are observed. In the case of higher hardness steels, mean stress can have a significant impact on the material with high tensile mean stresses causing a severe reduction in life [1]. At stress raisers, the local mean stress strongly influences the life to crack initiation [2]. A common practice in engineering design is to introduce compressive surface residual stresses, as these act as local compressive mean stresses, having the beneficial effect of retarding fatigue crack initiation and early growth [3]. Loading of a material beyond its yield strength can result in the relaxation of these residual stresses and the loss of the beneficial effects. Attempts have been made to model cyclic mean stress relaxation for steel based on the concept that the amount of relaxation that occurs is dependent on the plastic deformation involved [4]. The mean stress was expressed as a nonlinear function of cycle number, stress amplitude, the material s cyclic yield stress and strain, as well as its strain hardening exponent. It was also observed in [1] that relaxation which decreased the mean stress to a level below 10% of the stress amplitude at half life did not significantly alter fatigue lives. Mean stress testing of three aluminum alloys produced two observable regions of behavior in [2]. As expected, there were large amounts of relaxation at 6

23 relatively large strain amplitudes. But it was also found that a degree of relaxation can occur even where the plastic strains are very small. The modest stress changes that occurred in the latter situation were nevertheless sufficiently large to be significant from the viewpoint of obtaining accurate life predictions. DuQuesnay et al. [5] studied the effects of mean stress on SAE 1045 steel and 2024-T351 aluminum. The authors attempted to explain the effects of mean stress by relating the results of tests performed on smooth specimens to observations made during fatigue crack growth testing of long and short cracked specimens. They suggested that the damage caused to the material is mainly related to crack closure and is the result of the effective stress range. This effective stress range was defined as the difference between the maximum stress and the crack opening stress of a material. Using an effective stress range parameter, they were able to obtain a good correlation of test data and provide accurate prediction of life to failure. A number of different models have been developed for including mean stress effects in fatigue life calculations, such as those of Goodman, of Morrow, and of Smith- Watson-Topper. Dowling et al. [6] analyzed mean stress test data for a large number of different materials including steels, aluminum alloys, and one titanium alloy. The authors performed the analysis using the Goodman, Morrow, Smith-Watson-Topper (SWT) and Walker equations. Of interest to the current study was the application of the SWT and Walker equations. The forms of the equations used in their analysis were: 1 R ar max (2.1) 2 1 R ar max (2.2) 2 7

24 where Equation 2.1 is the stress-life version of the SWT relationship, and Equation 2.2 is the Walker relationship. ar is the equivalent fully-reversed stress amplitude, max is the maximum stress in a cycle, and R is the stress ratio for the loading cycle. For the Walker equation, is used as a fitting parameter. Dowling et al. [6] demonstrated the accuracy of some common mean stress parameters for use in stress-life fatigue life prediction. The authors state that the Goodman method employing the ultimate tensile strength is highly inaccurate and should not be used. Better results were observed on a high strength steel in [1], which demonstrated that life predictions using the Goodman and Morrow equations were all within a factor of three scatter bands. The SWT method is often concluded to be a good choice for general use due to its simplicity and level of correlation with test data. This is shown for the stress-life SWT parameter for a wide range of materials in [6] as well as in the strain-life version in [1, 7]. The Walker equation, which uses an additional fitting parameter was shown to provide the best accuracy and Dowling et al. recommend that this method be used in situations where the fitting parameter can be obtained from test data [6]. In their analysis, Dowling et al. [6] also identified a trend for both steels and aluminum alloys that describes how the fitting parameter of the Walker equation changes with the strength of the material. They identified that, for steels, the fitting parameter decreased with increasing strength. It was then postulated that this is indicating an increasing sensitivity to mean stress and also more brittle behavior that is increasingly dominated by the maximum stress, and less affected by the stress amplitude [6]. They 8

25 developed a relationship in order to estimate for steels. A linear curve fit to the data resulted in: ( u in MPa). (2.3) u The coefficient of determination, R 2, was stated to be 0.68 for the steels in their study. For aluminum, they observed that a value for of provided a good fit for higher strength aluminum and a value of 0.65 provided a good fit for lower strength aluminum. Additional research performed by Dowling [8] provided a similar analysis for various mean stress equations applied to strain-life conditions. He recommends a procedure in which the desired strain amplitude is used with the standard strain-life equation to calculate the life to failure if the tests were fully-reversed. The life to failure that was solved for in the previous step is then used with a mean stress parameter such as Equations 2.1 and 2.2 and a stress-life equation to solve for the life to failure in the presence of the mean stress. After repeating the same analysis as was completed for the stress-life equations in [6], Dowling concluded that a mean stress equation can be incorporated into the strainlife curve in a manner that is consistent with the stress-based use of the same equation [8]. He, however, suggested that doing this for the Smith-Watson-Topper equation provided a relationship that differs from the common usage of the parameter. This is a result of the difference in how the mean stress is handled in regards to the plastic strain term in the SWT equation. He states that because the mean stress effect is most important where the loading is mostly elastic, this difference by itself may not have a large effect on life estimates [8]. 9

26 In a paper used to identify the effectiveness of the SWT parameter, Smith et al [9] provided a discussion of how the different aspects of the SWT equation show the characteristics of the material that it is modeling. It is stated that only two power function curves on a life plot are needed to make up the equation. This is similar to the constant amplitude strain-life equation which is also comprised of two power function curves. For the strain-life equation, one curve represents the response behavior of a material to plastic strain and the other represents the behavior in response to the stress amplitude. For the SWT equation, one curve represents the behavior of the material for all values of R ratio; the other curve demonstrates the effect of plastic strain on life for a wide range of stress conditions [9] Overload and Load Sequence Effects From a practical point of view, it is important to understand how a material responds to overloads. The term overload denotes the application of a few very high loads or strain cycles amongst a majority of lower level cycles. Overload cycles can occur at anytime during life and may have mean stress. One of the ways that the effects of overloads are studied is with overload test patterns applied to smooth specimens. One of the types of overloads encountered is preloading. Pre-loading is when the overloads occur entirely at the beginning of a loading history which can result in a sequence effect on the subsequent cycles to failure. For aluminum alloys 2024-T4 and 7075-T6, Topper et al. [10] observed that load sequence effect was small when the amplitudes of the steps were relatively close to each other. Additionally, a stronger sequence effect was believed to occur for metals with a distinct yield point. Research 10

27 performed by Colin and Fatemi [11] confirmed that shorter lives would result from a H-L load sequence than from a L-H sequence for both stainless steel 304L and aluminum 7075-T6. They also noted longer and deeper micro-cracks within the gage section of the failed specimens in H-L tests compared to L-H tests. They explained that small cracks can develop during the high level of H-L step tests, and grow at the low level [11]. Additionally, the higher amplitude pre-cycles introduce deformation that can cause hardening in the material. This results in a difference of the deformation characteristic of the lower level cycles that follow the higher level pre-cycles, especially for materials with strong deformation history dependence such as stainless steels [12, 13]. The deformation memory effect can induce hardening in stainless steel which will decrease the ductility of the material and alter the fatigue life [12]. Although pre-cycles themselves also produce damage, the subsequent reduced ductility was an important factor to consider. Therefore, it was concluded that using a damage parameter that involves both stress and strain in conjunction with the LDR will result in more accurate life predictions than using the stress-life or strain-life curve for specimens subjected to loading patterns that include sequence effects [7]. While researchers have noted a shortening of fatigue life and a reduction in the fatigue limit due to the application of initial overloads, it has also been observed that this effect was magnified by the application of periodic overloads [14]. Further evidence of these effects was observed when researchers performed an investigation of history editing techniques [14]. This is the procedure by which a complicated load history is simplified by eliminating cycles that are thought to cause little to no damage to the material or component. Histories shortened in this manner were then applied to smooth specimens to 11

28 investigate the effect on fatigue life. Conle and Topper [14] found that when the changes in fatigue life were related to the magnitudes of the strain cycles removed, it was found that neither initially overstrained nor periodically overstrained constant amplitude fatigue life data could correctly predict the effect of small cycle omissions on fatigue life. They then used a procedure where a history editing technique was applied to remove strain levels below certain predefined thresholds. The edited histories were then applied to smooth specimens in order to investigate the reduction in total damage that would result from removing the strain levels from the original history. For the three different maximum strain levels applied to the service loading history used in their study, a range from 18 to 58 percent of the damage in the history came from strain levels that were initially predicted to cause no damage. Dowdell et al. [15] investigated the use of a modified life parameter for the prediction of fatigue life of SAE 1045 steel. By completing variable amplitude block loading tests on smooth specimens they produced a modified life curve. The modified life curve was then used to predict the life to failure of four random loading variable amplitude tests. The authors used the fracture mechanics concept of crack closure to explain the reduction in life due to the overloads. The compressive overload was thought to cause the material at the crack tip to flatten, lowering the stress at the crack tip and, therefore, increasing the effective stress [15]. The increase in the effective stress results in an increase in the crack growth rate and a decrease in the life at a certain load level. The effective stress at the crack tip is the difference between the stress necessary to just open the crack (i.e. threshold stress) and the applied stress. The threshold stress is the stress necessary to cause crack growth and it is usually expressed as the sum of a 12

29 materials intrinsic stress and crack opening stress. In the research by Dowdell et al., it was also noted that since the threshold lowering effect holds for a large, but limited number of subsequent cycles, the largest compressive peak stress will dominate that loading program if its frequency of application is sufficiently large. Use of this threshold lowering effect provided accurate results for life predictions of their random loading history tests performed. Instead of using step tests to obtain a modified life curve as in the research by Dowdell et al., DuQuesnay et al. [16] performed periodic compressive overload tests at specific load levels to obtain a similar curve. The authors then introduced the idea of an equivalent life to failure for the smaller fully-reversed cycles in each test. The equivalent life calculation uses the Linear Damage Rule (LDR) [3] to take into account the damage caused by the overloads during the repeated application of a loading block. The equivalent life to failure for the material was then plotted versus the stress amplitude of the smaller cycles in the loading history. The plotting of this data superimposed with the constant amplitude data for the same material identifies a trend where the data produced in the presence of periodic overloads deviates from constant amplitude stress-life curve. Figure 2-1 includes the equivalent life plots for 2024-T351 aluminum and SAE 1045 steel from [16]. This figure shows the maximum stress of the overload history versus the calculated equivalent life to failure. The periodic overload data are plotted using symbols which denote the number of small cycles per block. The effect of the overload can be seen in the difference between the constant amplitude (data with circular symbols) and periodic overload fatigue lives at the same maximum stress. It was identified that even after using this newly formed curve, these modified life curves would still over predict 13

30 fatigue lives for variable amplitude histories with large compressive overloads of the type used in their study. It was speculated that a decrease in the crack closure level following the compressive overloads may also be responsible for the increased rate of damage accumulation observed in smooth specimens. DuQuesnay et al. [16] were able to confirm that periodic compressive overloads can drastically reduce the fatigue threshold for smooth specimens. Additionally, they demonstrated that the interactive effect of the overload cycle on the smaller cycles can significantly increase the damage done by the smaller cycles, even if the overload cycle is applied once in thousands of smaller cycles. Jurcevic et al. [17] investigated the effects of overload cycles that go into compression then tension (C-T) before continuing on with the smaller cycles and overloads that go into tension then compression (T-C) before continuing on with the smaller cycles. These experiments were performed on smooth specimens made from 2024-T351 aluminum. They identified a trend showing that C-T overloads caused damage that was higher than that for T-C overloads. They also identified that in many cases the C-T overloads caused an increase in damage that was larger by a factor of approximately three over the T-C overloads. In contrast, Colin and Fatemi [11] performed similar testing for stainless steel 304L and concluded that there was little noted difference between T-C and C-T overloads for that material. Pompetzki et al. investigated the effects of compressive underloads and tensile overloads on smooth specimens of 2024-T351 aluminum [18] as well as on SAE 1045 steel [19]. The concept of interactive damage was used in order to compare the results. The interactive damage is based on the assumption that all variable amplitude testing should result in a damage summation equal to unity. Therefore, in a variable amplitude 14

31 test, the difference between the damage summation and unity is considered the damage that resulted from the interaction of the overload cycles on the smaller subsequent cycles. It is also assumed that overload cycles have a pronounced effect on the fatigue behavior of subsequent smaller cycles; however, the reverse does not apply [17]. Completion of their test plan produced data where tensile overloads were shown to result in shorter fatigue lives than when compressive underloads were applied. The only noted difference in this trend was for the case of tensile overloads applied infrequently to aluminum, which was stated to cause crack growth retardation and, therefore, conservative life predictions. It was noted that this transition to crack retardation occurred when there was over 1,000 small cycles in each block. Testing performed by Colin and Fatemi [11] on 7075-T6 aluminum specimens showed that the application of a tensile overload would result in an increase in fatigue life over the application of a compressive overload. The tensile overloads were applied infrequently with 1,000 small cycles per block and the loading history resulted in a 20% increase in fatigue life over the compressive overload history. The number of small cycles per block was of a similar quantity to that which was suggested to result in crack retardation. It was stated in [19], in reference to tensile overloads, that for long cracks, the acceleration period of damage is very short while the subsequent delay can either cause crack arrest or require a large number of cycles before the crack grows through the plastic zone created by the tensile overload. For short cracks in smooth specimens, the acceleration in crack growth is the most important consequence of tensile overload, while the delay is of secondary importance [19]. 15

32 Jurcevic et al. [17] also attempted to show that the amount of interactive damage of each smaller cycle in a loading block decays as a power function following the application of an overload cycle. There was then a summation method presented which required two constants, one describing the rate of decay of the damage after the overload and the other representing the damage resulting from the first smaller cycle after an overload. The initial damage constant could be found from running a periodic overload test with only one small cycle per block, then taking the resulting interactive damage to be the amount resulting from only the first small cycle. The rate of decay of the damage was found from comparing two or more tests with the same loading levels, but with variations in the frequency of application of the overload cycle. Figure 2-2 shows a plot of their results for the variation of interactive damage per block with variation in small cycles at an arbitrary stress amplitude of 150 MPa [17]. In this figure, a comparison is drawn between T-C and C-T overloads. It can then be seen that the damage appears to accumulate at a similar rate for each type of loading, but there is a difference in the magnitude of the damage. A secondary comparison was then performed by normalizing the interactive damage after an overload by using the damage of the initial cycle after the overload. Figure 2-3 displays the normalized T-C and C-T overload data compared with compressive and tensile overload data from previous studies. This investigation indicated that the rate of damage accumulation for different types of overloads was nearly the same. Differences resulting from the overload types were identified as the magnitude of the damage of the first cycle used to normalize the data as well as the number of the small cycles after a T-C or C-T overload where the damage of each cycles appeared to remain constant [17]. A high level of accuracy was achieved when the small cycle damage 16

33 summation method was used to predict the life to failure of specimen subjected to random loading histories. By analyzing data from aluminum 2024-T351, general trends were observed for variations in small cycle stress level, variations in the number of small cycles, and the loading direction of the overload cycle [18]. Figure 2-4 shows a three dimensional representation of how much damage is caused by each cycle after both compression and tension overloads. Distinctions are made between load histories where the small cycles are below or above the constant amplitude fatigue limit [18]. Below the fatigue limit, the limiting quantity of damage for the small cycles is zero. Above the fatigue limit, the limiting quantity of damage is the cycle s steady-state value. It is then above the fatigue limit where, depending on the type of overload, the damage of the small cycles can decrease to below the steady-state value, possibly with the result of an increase in life to failure of the specimen. Topper and Lam [20] devised a method to increase the accuracy of life predictions using smooth specimens subjected to variable amplitude loading patterns. They incorporated an equation to compute the crack opening stress level for a material, given as: S op 2 S max S max 1 S min S (2.4) y where S op is the crack opening stress, S max is the maximum stress applied, S y is the yield strength of the material, S min is the minimum stress applied, and and are material constants. This was in an attempt to estimate the effective strain range that a material would experience after an initial overload. The assumption used when analyzing the 17

34 variable amplitude service histories was that the crack opening stress level from the largest cycle in the history persists throughout the history after its initial application. The succeeding smaller cycle stresses in the history were then compared against the crack opening stress value of the initial overload cycle to identify an estimate of the magnitude of the smaller cycle stress which is fully effective. This fully effective stress or strain of each cycle is then compared with an experimentally determined effective curve. The effective curve results from applying a periodic overload pattern to smooth specimens. The periodic overload history applies a constant overload stress or strain level to small cycles that have the same applied maximum stress or strain level. The stress or strain amplitude of the small cycles is then varied for each test which is performed. The objective is to capture the effect of lowering the crack opening stress level of the smaller cycle below its minimum stress causing the smaller cycles to be fully effective. Recent work [21] employed Equation 2.4 to model measurements of the crack opening stress of steel DP 590. This analysis was performed at three different R ratios and the results are shown in Figure 2-5. This figure displays an important trend that helps to describe the interaction between an overload and proceeding small cycles. As the maximum stress of a fully reversed cycle increases from zero, a crack is predicted to open under increasing tensile loads. This is predicted to occur for increasing maximum stress until the maximum stress reaches a point where the crack opening stress will start to decrease. Eventually, the maximum stress reaches a point where the crack is predicted to be open under compressive loads. It is suggested in [20] that at high strain levels with large plastic strains, Equation 2.4 gives a crack opening stress that is too low. It is suggested by the authors that the crack opening stress level be taken as half the minimum 18

35 stress when Equation 2.4 gives a lower value than is observed. As was previously described, the crack opening stress of the overload persists for the succeeding small cycles in a load history until a sufficient amount of small cycles has been completed in order to recover the steady-state crack opening stress of the small cycles. For generating the effective curve described earlier, it would be important to make sure that the crack opening stress of the overload is below the minimum stress of the small cycles in order for it to be considered fully effective. 2.3 Cumulative Damage Cumulative fatigue damage modeling plays an important role in the life prediction of components and structures. One of the first and most simplistic concepts introduced was the Linear Damage Rule (LDR) which assumes that damage to the material accumulates in a linear fashion. Since the introduction of the LDR there have been many aspects of fatigue loading identified which result in the nonlinear accumulation of fatigue damage. For example, the concepts of crack nucleation and crack growth introduce different aspects into the damage accumulation process which appear to be nonlinear in nature. Also, the application of periodic overloads and pre-cycling to a specimen can often create situations where damage is not summed linearly. Many cumulative fatigue damage models have been suggested to help account for the nonlinearity of damage accumulation [22]. The LDR does not require any additional parameters and is commonly used for life prediction in variable amplitude loading situations. Therefore, this study focused on the application of the LDR. The linear damage rule is then used in conjunction with the Rainflow Cycle Counting Method to 19

36 provide fatigue life predictions. Both the linear damage rule and the Rainflow Cycle Counting Method are discussed in the following sections Rainflow Cycle Counting Method In order to be able to account for the damage that will result from a loading history, it is necessary to know the number of applied cycles. It is also important to be able to have a standard and reproducible method of accounting for the cycles in a loading history. ASTM standard E1049 [23] defines proper methods to be used for cycle counting in fatigue analysis for variable amplitude loading. The most commonly used cycle counting method is the Rainflow Cycle Counting Method which was first proposed by Matsuishi and Endo [24] as a method of 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 then the damage from the loading sequence can be accounted for. The reader can refer to [3] for additional information on cycle counting methods Linear Damage Rule (LDR) The Palmgren-Miner Linear Damage Rule (LDR) [3] is one of the most commonly used cumulative damage theories. The LDR is represented by the following equation: ni D (2.5) N i f i 20

37 where D is the damage, n i is the number of cycles applied to the specimen at a certain amplitude in a variable amplitude load history, and N fi is the expected life at this amplitude in constant amplitude loading. Failure is predicted to occur when the sum of the ratios is equal to unity. The LDR assumes that damage accumulates in a linear manner which has proven to be a non-conservative assumption due to some situations where damage accumulation has been shown to be nonlinear. One such situation is associated with the differentiation between crack initiation and crack growth. This can create a situation where the timing of the application of different amounts of damage can have a larger impact on the life of a component. This is highlighted in the testing of sequence effects where a number of higher level cycles will be applied before the testing of the specimen at a lower loading level. The application of those higher level cycles can cause the initiation of cracks that are then able to grow during the application of the lower loading level. The application of the higher level cycles before the smaller cycles increases the amount of damage associated with the small cycles which is disregarded by the LDR. Another occurrence of nonlinear damage accumulation is associated with the application of periodic overloads during a loading history. The application of the overload creates an interaction effect on the subsequent smaller cycles, as discussed in Section Pompetzki et al. [18] have shown the interactive damage on smaller cycles to vary as a summation of a power function and, as such, is not possible for the LDR to account for. It has been suggested that damage accumulates non-linearly at high and low stresses, but linearly at medium stresses [25]. This was investigated in [25] where 21

38 variable amplitude tests were performed on stainless steel specimens. It was found that the linear damage rule is applicable in some places and not at all in other places. It was also noted that the previous statement that the LDR was applicable only for medium stress amplitudes, is an oversimplification. Three examples were given of loading for stainless steel where, for each case, the LDR gave a different result. For one condition the LDR was applicable, for one it was highly non-conservative, and for one it was highly conservative. This research was summarized with the statement that if average specimens results are considered, there is a region within which damage accumulation is reasonably linear. Outside this region, damage accumulation becomes very non-linear [25]. The term, average specimen, in this case appears to reference a specimen that would perform with little scatter from the modeled fatigue behavior. Nonlinear cumulative fatigue damage rules have been proposed to remedy the deficiencies associated with the linear damage assumption. These theories account for the nonlinear nature of fatigue damage accumulation by using nonlinear relations [3]. In a review of common damage accumulation models [22] the two-stage linear damage approach was described to improve on the LDR shortcomings, while still retaining its simplicity. The Double Linear Damage Rule (DLDR) can consider cycle ratios for two separate stages in the fatigue damage process, such as damage due to crack initiation and due to crack propagation. Earlier work showed the potential for the DLDR as a method that would add accuracy to life predictions [26]. Later work continues to show that the DLDR can provide more accuracy while still not requiring additional parameters and only a small amount of addition work [27]. 22

39 Despite its shortcomings, additional support for the LDR can be found from the observation that many service histories are such that sequence effects either cancel each other or are entirely unpredictable. In those cases, nothing is gained by the addition of a more detailed damage accumulation analysis, and the simpler prediction methods should be used because they provide equally close predictions [3]. Therefore, the LDR continues to be used in many applications due to its simplicity and ease of use. Additionally, the LDR does not require any additional parameters to be found before it can be applied, which makes it more practical in a wider range of applications. 2.4 Effect of Anisotropy on Constant Amplitude Fatigue Life Inclusions are major contributors to fatigue and mechanical anisotropy in steels. It is not practically possible or commercially feasible to always avoid these defects. Metal working processes such as rolling and forging result in elongated inclusions. The properties of these steels are often different in the longitudinal and transverse directions as a result of anisotropy. Sulfur in steels is often in the form of sulfide inclusions like manganese sulfide (MnS) [28]. The presence of sulfur (S) improves the machinability of steel. However, sulfide inclusions are deformable and get elongated in the rolling direction, causing a considerable difference in the effective inclusion areas as seen from the longitudinal and transverse directions. This in turn changes the stress concentrations caused in the two directions and affects the properties in each direction differently. Furthermore, sulfides are often present in clusters. Poorly spaced inclusions favor crack propagation and the coalescing of small cracks originating at inclusions to form larger ones [29]. 23

40 For anisotropic metallic materials, a series of stages occurring in fatigue crack initiation at inclusions were identified in [30]. The initial stage was stated to be the debonding of the inclusion from the matrix. Lankford [31] found that this de-bonding took place by the first tensile loading even at a stress level close to the fatigue limit. Additional stages were identified as gradual growth of the de-bond seam, and eventual nucleation of micro-cracks as point surface defects within the matrix. Pessard et al. [32] identified two different types of fatigue behavior for anisotropic fatigue behavior of metallic materials. Specifically, two different fatigue initiation mechanisms were identified that depend on the ultimate tensile strength of the material. They noted that for materials with higher tensile strengths, the fatigue strength could be reduced by nearly 50% in the transverse loading direction. Ma et al. [33] state that there is still a lack of understanding the effects of inclusions on crack initiation and fatigue limit. The reason is that the effects of inclusions on the fatigue properties depend on several factors, such as chemical composition, size, distribution, shape, adhesion of inclusions to the matrix, and elastic constants of inclusions and matrix. Cyril et al. [28] performed experiments on specimens with three different sulfur levels (high: 0.077% S; low: 0.012% S and ultra low: 0.004% S), each at two hardness levels and in both the longitudinal and transverse rolling direction. At 40 HRC, there was about two orders of magnitude difference at 1% strain amplitude and about one order of magnitude difference at 0.325% strain amplitude between the high sulfur and the ultra low sulfur materials in the transverse direction. However, at 40 HRC there was not much difference between the low and the ultra low sulfur level materials at either the high or the low strain amplitude levels. Also, the fatigue life of the ultra low sulfur material in the 24

41 transverse direction was very close to the fatigue lives of the longitudinal specimens. It was explained that the maximum size of the inclusions in the transverse direction appeared to be the same for the ultra low and low S materials despite a more sparse inclusion distribution for the ultra low S material. The high sulfur and the low sulfur materials had the same fatigue limit at 40 HRC and at 50 HRC. This indicated that in the long life regime in the transverse direction, the sulfur level dominates more than the difference in hardness effect. However, in the transverse direction, the ultra low sulfur material at 50 HRC had a higher fatigue limit than the one at 40 HRC. It appears that when the sulfur level is reduced to that extent, the effect of the increased hardness begins to show for the transverse samples. At 40 HRC, in the transverse direction, the fatigue strength was 25% lower for the high sulfur material when compared to the ultra low sulfur material. The fatigue limit for the transverse samples of low and ultra low sulfur at 40 HRC were about 8% lower than the corresponding values in the longitudinal direction [28]. 2.5 Summary When designing components and structures, it is necessary to compute relatively accurate expected fatigue life for complex load histories. These load histories are often composed of variable amplitude loading including overloads and mean stresses. Therefore, it is necessary to be able to account for the damage resulting from these aspects of the load history. For this, a number of rules, models, and parameters have been developed to predict the deformation behavior and to account for fatigue damage. One of the most commonly used life prediction models is the SWT parameter, which 25

42 incorporates both the stress and strain response of a material. This allows the parameter to take into account prior loading as well as applied mean stress. In order to increase the accuracy of the life predictions in relation to variable amplitude loading, experiments can be conducted in order to obtain the effective strainlife curve. The effective curve helps to capture the interactive effects that a single periodic overload can have on smaller subsequent cycles. Although use of the effective curve can increase the accuracy of variable amplitude life predictions, there still remains aspects of variable amplitude loading that are not taken into account by using this method. One of the most commonly used damage accumulation models is the Linear Damage Rule. Its application does not necessitate the determination of any parameters, its computation is fairly simple, and it can provide reliable results in many situations. Shortcomings of the LDR have been identified which allow for engineers to evaluate when its use will be most applicable. Greater success with the LDR will come from its use with parameters that include both loading history and response of the material. The sulfur content of a material is often adjusted in order to increase its machinability. Certain manufacturing processes such as rolling can deform the sulfur inclusion in a material creating a state of anisotropy. For materials with large inclusion sizes, such as steels with high sulfur contents, there can be a large variation in the fatigue behavior depending on the loading direction. Models have been proposed in order to predict the response of a material to the presence of inclusions. Researches have had success in predicting the anisotropic behavior of metallic materials, but it has been identified that there still remains many challenges. A materials response to inclusions can 26

43 depend on chemical composition, size, distribution, shape, adhesion of inclusions to the matrix, and elastic constants of inclusions and matrix. 27

44 (a) (b) Figure 2-1: Equivalent lives of fully-reversed cycles subjected to periodic compressive underloads for (a) 2024-T351 aluminum and (b) SAE 1045 steel [16]. 28

45 Figure 2-2: Variation of interactive damage per block (at 150 MPa) with number of small cycles between overloads for 2024-T351 aluminum [17]. Figure 2-3: Variation of normalized interactive damage per block (at 150 MPa) with number of small cycles between overloads for 2024-T351 aluminum [17]. 29

46 Figure 2-4: Generalized variation in damage with stress and the number of small cycles following an underload or overload [18]. 30

47 Figure 2-5: Steady state crack opening stress for three stress ratios as a function of maximum stress for DP 590 steel [21]. 31

48 Chapter Three 3 Experimental Program and Results 3.1 Material and Specimen Preparation Materials Aluminum 7075-T6, two grades of steel 8622 with different heat treatment processes, three grades of steel 4140 with different sulfur contents, and two hardness levels of steel 8620 were use in this study. The steel materials were provided by AISI. For this study the materials were designated as 8622 (Atm), 8622 (Vac), 8620 (30 HRC), 8620 (36 HRC), 4140 (ULS), 4140 (Lo S), 4140 (Hi S), and Al 7075-T6. The test specimens for the two grades of steel 8622 were prepared from a steel 8822 grade with low side chemistry. The samples of steel 8622 (Atm) were quenched and tempered by austenitizing at 1700 F (927 C) prior to quenching in 150 F (66 C) oil and then tempering at 1050 F (566 C) to an aim hardness of HRC. The samples of steel 8622 (Vac) were quench and tempered by austenitizing at 1700 F (927 C) prior to gas quenching in Nitrogen at a vacuum pressure of 18 bar and then tempering at 350 F (177 C) to an aim hardness of HRC. 32

49 The test specimens for the two hardness levels of steel 8620 were heat treated using a procedure that would simulate a carburizing cycle. The samples for both hardness levels were heat treated by austenitizing at 1700 F (927 C) for three and a half hours before lowering the temperature to 1600 F (871 C) for forty minutes. Quenching was performed in 140 F (60 C) oil and then tempering at 350 F (177 C) to an aim hardness of 30 HRC for steel 8620 (30 HRC) and to an aim hardness of 36 HRC for steel 8620 (36 HRC). The variation in hardness between the two material conditions was the result of different material diameters during heat treatment. A larger diameter resulted in a slower cooling rate and a lower hardness of the final specimen. Three different grades of steel 4140 were produced with varying amounts of sulfur content. The three levels of sulfur content were 0.004%, 0.012%, and 0.077% which were considered ultra-low sulfur (ULS), low sulfur (Lo S), and high sulfur (Hi S). All three grades of 4140 steel were heat treated at Chrylser to a desired hardness of 40 HRC. The chemical compositions for the steels are presented in Table 3.1. For each material, a specimen was sectioned to obtain a general microstructure description. The samples were prepared with standard test procedures for sectioning, mounting, polishing, and etched with 3% Nital. The microphotographs of the microstructures of each material are shown in Figure Specimen In this study, identical round specimens were used for monotonic and fatigue tests. The specimen configuration and dimensions are shown in Figure 3-2. This 33

50 configuration deviates slightly from the specimen geometry recommended by ASTM Standard E606 [34]. The recommended specimens have uniform gage sections. The specimen geometry shown in Figure 3-2 differs by using a large secondary radius in the gage section to compensate for the slight stress concentration at the gage to grip section transition. Before heat treatment, specimen blanks for the two 8620 steel grades were machined from bars of SAE 8620 hot rolled steel. Each specimen blank was cut to a length of 5.5 inches and the diameter was reduced from the starting bar diameter of inches to 0.95 inches for the 8620 (30 HRC) and to 0.75 inches for the 8620 (36 HRC). For the three 4140 steel grades, 150 mm square cross-section continuous cast billets were forged into 65 mm square cross-section bars. From these bars, 65 mm wide slabs were cut lengthwise. Square cross-sectioned 16 mm x 16 mm x 65 mm transverse fatigue sample blanks were cut from the slabs. The rough (i.e. oversized dimensions) specimens were then machined from the sample blanks before heat treatment. After heat treatment the 4140 steel specimens were ground to the final dimensions. After machining, the specimens were then polished prior to testing. A commercial round-specimen polishing machine was used to polish the specimen gage section. Three different grits of aluminum oxide lapping film 30 μm, 12 μm, and 3 μm were used. Polishing marks coincided with the longitudinal direction of the specimen. The polished surfaces were carefully examined under magnification to ensure complete removal of machine marks within the test section. 34

51 3.2 Testing Equipment An INSTRON 8801 closed-loop servo-controlled hydraulic axial load frame in conjunction with a Fast-Track digital servo-controller was used to conduct the testing of the 8622 steel grades, 8620 steel grades, and Al 7075-T6. The load cell used had a capacity of 50 kn. An MTS closed-loop servo-controlled hydraulic axial load frame in conjunction with a Fast-Track digital servo-controller was used to conduct the testing of the 4140 steel grades. The load cell used had a capacity of 100 kn. Hydraulically operated grips using universal tapered collets for the 50 kn machine and hydraulically operated wedge grips with semi-circular cavities for the 100 kn machine were employed to secure the specimens' ends in series with the load cell. ASTM class B1 [35] extensometers were used to control total strain during testing. While working with the Instron axial load frame the extensometer had a gage length of 7.62 mm. and was capable of measuring strains up to 15%. While working with the MTS axial load frame the extensometer had a gage length of 6 mm. and was capable of measuring strains from -5% to 10%. The calibration of the extensometers was verified using a displacement apparatus containing a micrometer barrel in divisions of in. In order to protect the specimens' surface from the knife-edges of the extensometer, ASTM Standard E606 [34] recommends the use of transparent tape or epoxy to 'cushion' the attachment. While working with the 8622 steel grades, M-coat D was used as protection. 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. For the remaining specimens of this study it was found that application of transparent tape allowed for more consistency of the material thickness between the knife edge and 35

52 the specimen. Therefore, transparent tape was considered to be the best protection. The testing of the 8620 steel grades, 4140 steel grades, and Al 7075-T6 were performed using three layers of transparent tape. Significant effort was put forth to align the load train (load cell, grips, specimen, and actuator). Misalignment can result from both tilt and offset between the central lines of the load train components. In order to align the machine, a round strain-gage bar was used. The Strain-gage bar has two arrays of four strain gages per array with one array arranged at the upper and lower ends of the uniform gage section. This was done in accordance with ASTM Standard E1012 [36]. 3.3 Experimental Procedures Monotonic Tension Tests Monotonic tests in this study were performed using test methods specified by ASTM Standard E8 [37]. Two specimens were used to obtain the monotonic properties for each material condition. In order to protect the extensometer, strain control was used up to 10% strain, until the point of ultimate tensile strength had been crossed. After this point, displacement control was used until fracture. Instron Bluehill software was used for the monotonic tests. For the elastic and initial yield region (0% to 1% strain) a strain rate of mm/mm/min was chosen. This strain rate was about one half of the maximum allowable rate specified by ASTM Standard E8 for the initial yield region. After the strain reached 1% a strain rate of mm/mm/min was used up until the extensometer was removed. This strain rate was ten percent of the maximum allowable rate specified 36

53 by ASTM Standard E8 for the region after yielding. After the extensometer was removed, a displacement rate of 0.2 mm/min was used. After the tension tests were concluded, the broken specimens were carefully reassembled. The final gage lengths of the fractured specimens were measured with a Vernier caliper having divisions of in. Using an optical comparator with 10X magnification and divisions of in, the final diameter and neck radius were measured. It should be noted that prior to the test, the initial diameter was measured with this same instrument Constant Amplitude Fully-Reversed Fatigue Tests All constant amplitude fatigue tests in this study were performed according to ASTM Standard E606. It is recommended by this standard that at least ten specimens be used to generate the fatigue properties. For the eight materials in this study, the number of specimens tested varied from 13 to 20 and were tested at a minimum of six different strain amplitudes. Instron LCF and SAX software was used for performing straincontrolled tests. During each strain-controlled test, the total strain was recorded using the extensometer output. Specimen failure was defined as a 50% load drop in straincontrolled tests and a 30% displacement increase in load-controlled tests, compared to midlife, or fracture, whichever occurred first. Test data were automatically recorded at 2 n cycles or more frequently, if necessary, throughout each test. Strain control was used in all tests with plastic deformation. For one of the elastic tests, strain control was used initially to determine the stabilized load, then load control was used for the remainder of the test and for the rest of the elastic tests, load control was 37

54 used throughout. The reason for the change in control mode was due to the frequency limitation on the extensometer. For the strain-controlled tests of the eight materials in this study, the applied frequencies ranged from 0.2 Hz to 5 Hz in order to maintain a nearly constant strain rate. For the load-controlled tests, load waveforms with frequencies of up to 35 Hz were used in order to shorten the overall test duration. All tests were conducted using a triangular waveform except the tests run above 20 Hz, when a sinusoidal waveform was used Mean Strain and Mean Stress Tests A few mean strain tests were conducted in strain control for 8620 (30 HRC) and 8620 (36 HRC) steels. Tests were started in tension when tensile mean strain or tensile mean stress was present. For the steel materials, tests were performed with R = 0 and R = 0.3. For aluminum, mean strain and mean stress tests were conducted at 0.3% strain amplitude with R = As the behavior for the aluminum 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 SAX software, with triangular waveforms and using frequencies similar to the ones used in fully-reversed constant amplitude fatigue tests Periodic Overload Tests The overload tests were conducted to investigate the effects of periodic overloads on the fatigue life from the smaller subsequent cycles. For each material in this study, 5 to 12 specimens were tested at a minimum of four different strain amplitudes. The 38

55 periodic overload tests were performed with Instron Waverunner software. During each test, the total strain was recorded using the extensometer output. Test data were automatically recorded throughout each test. Two input signals were used in this study. The first input signal consisted of a periodic fully-reversed overload of the type shown in Figure 3-3(a). The load history in these tests consisted of repeated blocks made up of one fully-reversed overload cycle followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle. The second input signal consisted of a periodic fullyreversed overload of the type shown in Figure 3-3(b). The load history in these tests consisted of repeated blocks made up of one fully-reversed overload cycle followed by a group of smaller fully-reversed constant amplitude cycles. In both cases, the overload cycles were applied at frequent intervals to maintain a larger effective strain range resulting in the subsequent cycles being fully effective. With the overload histories utilized in this study, as the large cycles become more frequent, the fraction of the total damage done by them increases. The fully-reversed strain amplitude for the overload cycle corresponded to about 10 4 cycles to failure as recommended by Topper and Lam [20]. The number of small cycles per block, n sc, were adjusted so that they cause about 80% to 90% of the damage per block. Small cycle strain levels were selected near to or below the run out level of the constant amplitude tests. For steel materials the lowest small cycle strain amplitudes tested were between 23% and 42% of the respective runout strain amplitude in fullyreversed constant amplitude testing. For Al 7074-T6 the small cycle strain amplitude for 39

56 all tests was 0.3%. The number of small cycles per overload cycle ranged between 16 and 3076 for steels and 1 and 512 for Al 7074-T6. Periodic overload tests were performed in both strain control and load control. For load-controlled tests on materials with significant transient cyclic deformation response, one thousand pre-cycles at the overload strain level were used to help stabilize the material response. With the stress response of a material nearing cyclic stability, the remainder of the test can be performed in load-control with a constant or near constant strain level. Jurcevic et al. [17] have also shown that the presence of the pre-cycles help to initiate micro-cracks and reduce scatter in fatigue life. The initiation of micro-cracks during the pre-cycles is thought to not be important in variable amplitude tests where the high load levels rapidly initiate a micro-crack [18]. After completion of these initial cycles the second portion of the test was started using the previously mentioned periodic overload history of either Figure 3-3(a) or 3-3(b). For the load-controlled tests, calculations were performed based on the cyclic stress-strain curve in order to arrive at the steady state stress amplitudes for the desired strain amplitudes in the periodic overload history. The use of an extensometer in a strain-controlled test limits the frequencies that a test can be performed at. Therefore, the load-controlled periodic overload pattern allows for higher frequencies to be used. In the majority of load-controlled tests an extensometer was left on the specimen in order to capture the total strain data. The only tests that deviated from this procedure were the tests for aluminum where the material response was all elastic and it was shown that load-control was equivalent to strain-control. In this case, the Hooke s law was used to calculate the strain amplitude at the desire stress level. 40

57 3.4 Deformation Behavior Monotonic Deformation Behavior The properties determined from monotonic tests were the modulus of elasticity (E), yield strength (S y ), ultimate tensile strength (S u ), percent elongation (%EL), percent reduction in area (%RA), true fracture strength ( f ), true fracture ductility ( f ), strength coefficient (K), and strain hardening exponent (n). True stress ( ), true strain ( ), and true plastic strain ( p ) were calculated from engineering stress (S) and engineering strain (e), according to the following relationships which are based on a constant volume assumption: S 1 e (3.1) ln 1 e (3.2) p e (3.3) E The true stress ( ) versus true strain ( ) plot is often represented by the Ramberg- Osgood equation: 1 / n e p (3.4) E K The strength coefficient, K, and strain hardening exponent, n, are the intercept and slope of the best line fit to true stress ( ) versus true plastic strain ( p ) data in log-log scale: n p K (3.5) In accordance with ASTM Standard E739 [38], when performing the least squares fit, the true plastic strain ( p ) was the independent variable and the true stress ( ) was the 41

58 dependent variable. To generate the K and n values, the range of data used was chosen according to the definition of discontinuous yielding specified in ASTM Standard E646 [39]. Therefore, the valid data range occurred between the end of yield point extension and the strain at maximum load. The true fracture strength was corrected for necking according to the Bridgman correction factor [3]: Af f (3.6) 4R D f 1 ln 1 D f 4R where P f is load at fracture, R is the neck radius, and D f is the diameter at fracture. The true fracture ductility, f, was calculated from the relationship based on constant volume: Ao 1 f ln ln (3.7) Af 1 RA where A f is the cross-sectional area at fracture, A o is the original cross-sectional area, and RA is the reduction in area. A summary of the monotonic properties for the materials in this study is provided in Table 3.3. The monotonic stress-strain curves for the 8622 and 8620 steels are shown in Figure 3-5. Similar plots for the 4140 steel grades and Al 7075-T6 used in this study can be found in Figure 3-6. P f 42

59 3.4.2 Transient and Steady-State Cyclic Deformation Behaviors Transient cyclic response describes the process of cyclic-induced change in deformation resistance of a material. Data obtained from constant amplitude straincontrolled fatigue tests were used to determine this response. Plots of stress amplitude variation versus applied number of cycles can indicate the degree of transient cyclic softening/hardening. Also, these plots show when cyclic stabilization occurs. A composite plot of the transient cyclic response for the 8620 and 8622 steels studied are shown in Figure 3-4. Even though multiple tests were conducted at each strain amplitude, data from one test at each strain amplitude tested is shown in these plots. Similar plots for the 4140 steel grades and Al 7075-T6 used in this study can be found in [7, 29]. Another cyclic behavior of interest was the steady state or stable response. Data obtained from constant amplitude strain-controlled fatigue tests were also used to determine this response. The properties determined from the steady-state hysteresis loops were the cyclic modulus of elasticity (E'), cyclic strength coefficient (K'), cyclic strain hardening exponent (n'), and cyclic yield strength (S y '). Half-life (midlife) hysteresis loops and data were used to obtain the stable cyclic properties. Similar to monotonic behavior, the cyclic true stress-strain behavior can be characterized by the Ramberg-Osgood type equation: 2 e p 2 2 2E 2K 1 / n (3.8) It should be noted that in Equation 3.8 and the other equations that follow, E is the average modulus of elasticity that was calculated from the monotonic tests. 43

60 The cyclic strength coefficient, K', and cyclic strain hardening exponent, n', are the intercept and slope of the best line fit to true stress amplitude ( /2) versus true plastic strain amplitude ( p /2) data in log-log scale: p K 2 2 n (3.9) In accordance with ASTM Standard E739 [38], when performing the least squares fit, the true plastic strain amplitude ( p /2) was the independent variable and the stress amplitude ( /2) was the dependent variable. The true plastic strain amplitude was calculated by the following equation: 2 p 2 2E (3.10) Cyclic deformation properties including E', S y ', n', and K', that resulted from the analysis of deformation behaviors of the materials in this study, are listed in Table 3.3. The cyclic stress-strain curve reflects the resistance of a material to cyclic deformation and can be vastly different from the monotonic stress-strain curve. In Figure 3-5, superimposed plots of experimental monotonic curve and cyclic curves are shown for the 8620 and 8622 steels. In Figure 3-6, similar curves are shown for the 4140 steels and Al 7075-T6. As can be seen in these figures, the seven steel materials exhibit varying degrees of cyclic softening and the aluminum material showed a small amount of cyclic hardening. 44

61 3.5 Constant Amplitude Fully-Reversed Fatigue Test Results Constant amplitude strain-controlled fatigue tests were performed to determine the strain-life curve. The following equation relates the true strain amplitude to the fatigue life: e 2 2 p 2 E ' f b ' 2N 2N c f f f (3.11) where f ' is the fatigue strength coefficient, b is the fatigue strength exponent, f ' is the fatigue ductility coefficient, c is the fatigue ductility exponent, E is the monotonic modulus of elasticity, and 2N f is the number of reversals to failure. The fatigue strength coefficient, f ', and fatigue strength exponent, b, are the intercept and slope of the best line fit to true stress amplitude ( /2) versus reversals to failure (2N f ) data in log-log scale: 2 ' b f 2N f (3.12) In accordance with ASTM Standard E739 [38], when performing the least squares fit, the stress amplitude ( /2) was the independent variable and the reversals to failure (2N f ) was the dependent variable. These plots are shown in Figures 3-7 and 3-8 for all eight materials in this study. To generate the f ' and b values, all data, with the exception of the run-out tests, in the stress-life figure were used. Runout tests are tests that were stopped before failure occurred, after at least 10 6 cycles for the steel specimens and at least 10 7 for the aluminum specimens. A bilinear fit has previously been found to better represent S-N data for 7075-T6 [7]. As shown in Figure 3-10(d), a bilinear elastic line where the bilinearity occurs around 525 MPa and 2000 reversals was obtained for Al 7075-T6. 45

62 The fatigue ductility coefficient, f ', and fatigue ductility exponent, c, are the intercept and slope of the best line fit to calculated true plastic strain amplitude ( p /2) versus reversals to failure (2N f ) data in log-log scale: p 2 calculated ' f 2N c f (3.13) In accordance with ASTM Standard E739, when performing the least squares fit, the calculated true plastic strain amplitude ( p /2) was the independent variable and the reversals to failure (2N f ) were the dependent variable. The calculated true plastic strain amplitude was determined from Equation Figures 3-9 and 3-10 represent the elastic, plastic, and total strain-life curves for the eight materials and the corresponding superimposed fatigue data. A summary of the strain-life fatigue properties for the materials used in this study is provided in Table 3.3. Tables 3.4 to 3.7 provide the summary of the fatigue test results for each material. The constant amplitude fully-reversed data for Al 7075-T6 and the three steel 4140 conditions were generated in [7] and [29], respectively. A parameter often used in fatigue life prediction is the Smith-Watson-Topper (SWT) parameter [9], represented by: b b c max a [( f ') (2N f ) f ' f ' E(2N f ) ] (3.14) E where max a. A plot of the SWT parameter versus reversals to failure for each m material is shown in Figures 3-11 and These figures display the SWT parameter based on Equation 3.14 and superimposed fatigue data for each material. Comparison plots were assembled in order to compare the fatigue behavior of the similar materials. The comparisons were performed for the two 8622 steels, the two

63 steels, and the three 4140 steels. The comparisons include a combined strain-life plot and a combined SWT plot for each set of steels. The comparisons for the steels are represented by Figure 3-13 for steel 8622, Figure 3-14 for steel 8620, and Figure 3-15 for steel A discussion of the comparison results in the previously mentioned figures is provided in Section 4.3 for steels 8622 and 8620, and in Section 4.4 for steel Constant Amplitude Mean Strain and Mean Stress Fatigue Test Results Mean strain tests in strain control were performed for the 8620 (30 HRC) and 8620 (36 HRC) steel. Tests were performed with a tensile mean strain using R = 0 at a = 0.250% and R = 0.3 at a = 0.175%. For both materials the strain amplitude of 0.250% is just above the fully-reversed fatigue limit and the strain amplitude of 0.175% is below the fatigue limit. A summary of the test results can be found in Table 3.5. Figure 3-16 shows all of the constant amplitude data superimposed on a strain-life plot. Figure 3-11 shows the same data superimposed on a SWT plot. The tensile mean strain affected the material as expected, causing a decrease in life of about 28% for 8620 (30 HRC) and about 60% for 8620 (36 HRC) at R = 0 and a = 0.250%. A difference was noted between the two steels at the strain level below the fatigue limit where the 8620 (30 HRC) steel experienced failure but the 8620 (36 HRC) steel continued to exhibit no failure. Deformation responses for mean strain tests for 8620 (30 HRC) and 8620 (36 HRC) are presented in Figure The strain amplitudes in the mean strain tests of these steels were considered to be fully elastic. Little discernable softening of the materials was seen and a significant mean stress relaxation was observed. The lack of cyclic softening 47

64 is thought to be the result of the elastic strain amplitude applied. The amount of mean stress relaxation is thought to have resulted from the maximum stress in each test being beyond the cyclic yield strength of the material. For aluminum, load-controlled tests were conducted at equivalent total strain amplitudes of 0.5% and 0.3%. The R ratio tested for this study was R = Additional tests for the same material were performed in [7] at R = -3.4 and R = -0.25, and the data were included in this study. Due to the elastic behavior at this level, no difference was expected between the load-controlled and strain-controlled tests. The results are presented superimposed on a strain-life plot in Figure 3-16(c) and on a SWT plot in Figure 3-12(d). A summary of the test results can be found in Table 3.7. The tests resulted in a decrease of the fatigue life in the presence of a tensile mean stress and an increase of fatigue life in the presence of a compressive mean stress, as expected. Additional discussion of the mean stress and strain tests performed for this study is provided in Section Periodic Overload Fatigue Tests and Results Periodic overload fatigue tests were performed for all eight of the materials in this study. The periodic overload test results were plotted using the strain amplitude of the small cycles in the overload block and the calculated equivalent life to failure. The equivalent fatigue life for the smaller cycles was obtained using the linear damage rule: B N f n ol f, ol N B f n sc f, sc( eq) 1 (3.15) 48

65 where B f is the number of loading history blocks that were repeated before specimen failure, n ol is the number of overload cycles in a loading history block, N f,ol is the number of cycles to failure if only overloads were applied in a test, n sc is the number of smaller cycles in a loading history block, and N f,sc(eq) is the computed equivalent fatigue life for the smaller cycles. The calculation of the equivalent life to failure attempts to take into account damage of the overload cycle by assuming that overload damage can be fully accounted for through the calculation of its damage ratio. One of the objectives of the overload testing of the steel materials was to generate the effective strain-life curve as described in Chapter 2. This requires the application of a periodic overload pattern of the type showing in Figure 3-3(a) where the small cycles are subjected to a mean stress or strain (POL w/ms). Figures 3-18 and 3-19 show the results of this type of periodic overload history. The equivalent fatigue life data for the eight materials were superimposed on the constant amplitude strain-life plot. Tables 3.8 to 3.11 present a summary of the periodic overload test results for each of the eight materials. The periodic overload data shows a distinct deviation from the strain-life curve for all of the materials. A further analysis of the deviation of the periodic overload data is presented in Section 4.2. For all but one of the materials there were sufficient data to form an effective strain-life curve. For Al 7075-T6 the objective was not to generate the effective curve but to observe the effect of varying the number of small cycles per block, n sc. The effective strain-life curve is generated as a least squares fit to the equivalent fatigue life data resulting from the periodic overload tests, based on: eff * i (3.16) 49

66 where eff, is the effective local strain range, i is the intrinsic strain range at which a crack does not propagate, and * is a strain-based damage parameter. The strain range * is then the part of the strain range which causes fatigue crack growth and damage [20]. This parameter was shown in [20] to be related to fatigue life by a power law: N d f * A 2 (3.17) where A and d are material constants. In this study, it was assumed that eff is the strain range of the small cycles in the periodic overload history. Therefore, once a constant value of i was selected, * could be solved for by using Equation This calculation was repeated for each of the periodic overload tests used to create the effective curve for a material. A power law best fit trend line was then fit to the resulting * versus 2N f data which resulted in values for the constants A and d from Equation The value of i was then adjusted in order to arrive at the best fit to the overload data. A plot of the SWT parameter for both the constant amplitude and overload data provides another method of comparison between the two sets of data, where the mean stress present in the small cycles is assumed to be taken into account. The SWT plot for each material is shown in Figures 3-20 and Similar to the strain-life plots, the effective curve for the SWT plot was generated from the overload data for all but the Aluminum material used in this study. As with the constant amplitude strain-life curve and effective strain-life curve, the overload data and effective SWT-life curve diverged from the constant amplitude SWT-life curve. This indicates that, even when the effect of the mean stress in accounted for, there still remains an additional effect of the overloads on the small cycles. 50

67 Additional periodic overload testing was performed using the loading history shown in Figure 3-3(b). This was a periodic overload pattern where the loading for small cycles was fully reversed (POL wo/ms). Tests of this nature were performed for 8620 (30 HRC), 8620 (36 HRC), and Al 7075-T6. Results from the testing of this load history are shown superimposed with the strain-life curve in Figures 3-18 and 3-19 and with the SWT curve in Figures 3-20 and Application of the POL wo/ms load history to steel 8620 resulted in similar lives to failure as when the POL w/ms load history is applied. Al 7075-T6, however, showed a distinct difference between the results for the two load histories. An analysis of this occurrence is based on the research in [20]. In [20] it is assumed that behavior of a material in the presence of periodic overloads is similar to that of small crack growth in notched specimen. It is also assumed that damage to a material only occurs when a micro-crack is open. The stress or strain range in which the microcrack is open is referred to as the effective stress or strain range [20]. Additionally, it is shown in [17] that the crack opening stress of the overload persists for the following cycles until it recovers back to the steady-state condition of the small cycles. Applying this concept to the data in this study, for the 8620 steel material to have a similar life to failure for both the POL w/ms and POL wo/ms load histories, the effective stress range would need to be the same in both cases. This would occur when, for both load histories, the crack opening stress of the overload is below the minimum stress of the small cycles. The difference in life seen for Al 7075-T6 would result from a situation where the crack opening stress of the overload caused a difference between the effective stress ranges for the two load histories. For example, the crack opening stress could have been below the 51

68 minimum stress for the POL w/ms history but above the minimum stress when the mean stress was removed for the POL wo/ms history. Comparison plots were assembled in order to compare the periodic overload fatigue behavior of the similar materials. The comparisons were performed for the two 8622 steels, the two 8620 steels, and the three 4140 steels. The comparisons include a combined strain-life plot and a combined SWT plot for each set of steels. The comparisons for the steels are represented by Figure 3-22 for steel 8622, Figure 3-23 for steel 8620, and Figure 3-24 for steel A discussion of the comparison results in the previously mentioned figures is provided in Section 4.3 for steel 8622 and 8620, and in Section 4.4 for steel

69 Table 3.1: Composition of the five steel grades used in this study (courtesy of Gerdau-MacSteel) (ATM & VAC) 8620 (30 & 36 HRC) 4140 (ULS) 4140 (Lo S) 4140 (Hi S) Carbon, C (%) Manganese, Mn (%) Phosphorus, P (%) Sulfur, S (%) Silicon, Si (%) Chromium, Cr (%) Aluminum, Al (%) Nickel, Ni (%) Molybdenum, Mo (%) Copper, Cu (%) Tin, Sn (%) Vanadium, V (%) Niobium, Nb (%) Boron, B (%) Calcium, Ca (%) Titanium, Ti (%) Lead, Pb (%) Zirconium, Zr (%) Nitrogen, N2 (%)

70 Table 3.2: Summary of AISI Bar Fatigue Group experimental program as related to the data in this study. AISI Iteration Steel Grade Condition Desired Hardness 100/ (8822 Low Side) Quenched Core (Atm) HRC 102/ (8822 Low Side) Quenched Core (Vac 1700F) HRC ULS (Trans.) Quenched and Tempered 40 HRC Lo S (Trans.) Quenched and Tempered 40 HRC Hi S (Trans.) Quenched and Tempered 40 HRC 119/ Sim. Carb. Core Sec. Controlled HRC 120/ Sim. Carb. Core Sec. Controlled HRC 54

71 Table 3.3: Summary of the mechanical tensile properties for the materials used in this study. Properties for Steel 4140 were provided in [29] and for Al 7075-T6 in [7] T6 Hardness (ATM) (VAC) (30 HRC) (36 HRC) (ULS) (Lo S) (Hi S) Brinell (HB)(converted) Rockwell C-scale (HRC)(measured) Monotonic Properties Modulus of elasticity, E (GPa) Yield strength (0.2% offset), S y (MPa) Upper yield strength, UYS (MPa) Lower yield strength, LYS (MPa) Yield point elongation, YPE (%) Ultimate tensile strength, S u (MPa) Percent elongation, %EL Percent reduction in area, %RA Strength coefficient, K (MPa) 1, , , , Strain hardening exponent, n True fracture strength, σ f, (MPa) True fracture ductility, ε f (%) Cyclic Properties Cyclic modulus of elasticity, E' (GPa) Fatigue strength coefficient, σ f ' 1 (MPa) 1, , , , Fatigue strength coefficient, σ f ' 2 (MPa) , Fatigue strength exponent, b % Fatigue strength exponent, b Fatigue ductility coefficient, ε f ' Fatigue ductility exponent, c Cyclic strength coefficient, K' (MPa) 1, , , , Cyclic strain hardening exponent, n' Cyclic yield strength, S y ' (MPa)

72 Table 3.4: Summary of constant amplitude fatigue test results for steel 8622 (Atm) and (Vac). Test (Δε ε a ε p /2) Specimen m σ a σ m SWT control R calculated ID (%) (%) (MPa) (MPa) (MPa) mode (%) 2N f 8622 (Atm) strain strain strain strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , load , load , load ,763, load >10,000, load >10,000, (Vac) strain strain strain , strain , strain , strain , strain , load , load , load , load ,691, load >10,000, load >10,000,000 56

73 Table 3.5: Summary of constant amplitude fatigue test results for steel 8620 (30 HRC) and (36 HRC). Test (Δε ε a ε p /2) Specimen m σ a σ m SWT control R calculated ID (%) (%) (MPa) (MPa) (MPa) mode (%) 2N f 8620 (30 HRC) strain strain strain strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , load >10,000, load >10,000, load >10,000, strain , strain , (36 HRC) strain strain strain strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , strain , load ,843, load >10,000, load >10,000, strain >10,000, strain ,772 57

74 Table 3.6: Summary of constant amplitude fatigue test results for steel 4140 (ULS), (Lo S), and (Hi S) [29]. Test (Δε ε a ε p /2) Specimen m σ a σ m SWT control R calculated ID (%) (%) (MPa) (MPa) (MPa) mode (%) 2N f 4140 (ULS) 99-9 strain strain strain strain , strain , strain , strain , strain , strain , strain , strain , load , load , load , load , load ,011, load ,712, load >10,000, (Lo S) strain strain strain , strain , strain strain , strain , strain , strain , load , load , load , load , load , load , load ,808, load >10,000,000 58

75 4140 (Hi S) 81-9 strain strain strain strain strain strain strain , strain , strain , load , load , load , load , load , load , load >10,000, load >10,000, load ,978 59

76 Table 3.7: Summary of constant amplitude fatigue test results for aluminum 7075-T6 [7]. Specimen ID Test control mode R (Δε ε a ε p /2) m σ a σ m SWT calculated (%) (%) (MPa) (MPa) (MPa) (%) A41 strain A54 strain A53 strain A78 strain A81 strain A28 strain ,108 A17 strain ,368 A11 strain ,602 A30 strain ,786 A82 load A83 load A42 load ,415,406 A31 load ,097,500 A38 load ,495,724 A25 load ,946,798 A72 load ,404 A73 load ,932 A71 load ,364 A70 load ,724 A103 load ,788 A105 load ,858 2N f 60

77 Table 3.8: Summary of periodic overload fatigue test results for steel 8622 (Atm) and (Vac). 61 Spec. ID Test Control Mode ε a,sc (%) ε m,sc (%) (Δε p /2) sc (calculated) (%) σ a,sc (MPa) Load History Description σ m,sc (MPa) n sc ε a,ol (%) ε m,ol (%) (Δε p /2) ol (calculated) (%) POL w/ms Tests for 8622 (Atm) strain strain strain strain strain , strain strain strain , strain strain strain , strain ,525 POL w/ms Tests for 8622 (Vac) strain , strain , load , strain strain , strain load , strain , strain , strain , load ,725 σ a,ol (MPa) σ m,ol (MPa) n ol Exp. Life (Blks)

78 Table 3.9: Summary of periodic overload fatigue test results for steel 8620 (30 HRC) and (36 HRC). 62 Spec. ID Test Control Mode ε a,sc (%) ε m,sc (%) (Δε p /2) sc (calculated) (%) σ a,sc (MPa) Load History Description σ m,sc (MPa) n sc ε a,ol (%) ε m,ol (%) (Δε p /2) ol (calculated) (%) POL w/ms Tests for 8620 (30 HRC) strain , load load load load ,246 POL w/ms Tests for 8620 (36 HRC) load , load , load load load ,307 POL wo/ms Tests for 8620 (30 HRC) strain , load ,401 POL wo/ms Tests for 8620 (36 HRC) strain load ,131 σ a,ol (MPa) σ m,ol (MPa) n ol Exp. Life (Blks)

79 Table 3.10: Summary of periodic overload fatigue test results for steel 4140 (ULS), (Lo S), and (Hi S). Spec. ID Test Control Mode ε a,sc (%) ε m,sc (%) (Δε p /2) sc (%) σ a,sc (MPa) Load History Description σ m,sc (MPa) n sc ε a,ol (%) ε m,ol (%) (Δε p /2) ol (%) σ a,ol (MPa) σ m,ol (MPa) n ol Exp. Life (Blks) 63 POL w/ms Tests for 4140 (ULS) strain , strain , load load load load load , load ,158 POL w/ms Tests for 4140 (Lo S) load load load , load load load load load load , load ,695

80 64 POL w/ms Tests for 4140 (Hi S) load load load load load load load load load load load load

81 Table 3.11: Summary of periodic overload fatigue test results for aluminum 7075-T6. 65 Spec. ID Test Control Mode ε a,sc (%) ε m,sc (%) (Δε p /2) sc (calculated) (%) σ a,sc (MPa) Load History Description σ m,sc (MPa) n sc ε a,ol (%) ε m,ol (%) (Δε p /2) ol (calculated) (%) POL w/ms Tests A108 load A109 load A110 load A111 load A25 load ,905 POL wo/ms Tests A104 load ,352 A106 load ,874 A102 load ,918 A107 load ,222 A101 load ,846 σ a,ol (MPa) σ m,ol (MPa) n ol Exp. Life (Blks)

82 50 μm (a) (b) 40 μm 40 μm (c) (d) 66

83 (e) 20μm (f) 20μm (g) 20μm (h) Figure 3-1: Microstructure of (a) 8622 (Atm), (b) 8622 (Vac), (c) 8620 (30 HRC), (d) 8620 (36 HRC), (e) 4140 (ULS), (f) 4140 (Lo S), (g) 4140 (Hi S), and (h) Al 7075-T6 (courtesy of the Chrysler Materials Engineering Lab). 67