Axial and torsion fatigue of high hardness steels

Transcription

1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2011 Axial and torsion fatigue of high hardness steels Chad M. Poeppelman The University of Toledo Follow this and additional works at: Recommended Citation Poeppelman, Chad M., "Axial and torsion fatigue of high hardness steels" (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 Axial and Torsion Fatigue of High Hardness Steels by Chad M. Poeppelman Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering Dr. Ali Fatemi, Committee Chair Dr. Efstratios Nikolaidis, Committee Member Dr. Yong Gan, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo May 2011

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4 An Abstract of Axial and Torsion Fatigue of High Hardness Steels by Chad M. Poeppelman Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering The University of Toledo May 2011 Abstract The objectives of this study were to investigate the fatigue behavior of three high hardness steels, where each of the three steels had a hardness of 60 HRC (653 HB). Solid specimens of three different materials were tested under normal environmental laboratory conditions. Axial monotonic and fatigue properties were obtained through the use of a uniaxial testing machine. A large portion of the axial fatigue testing was performed under fully-reversed loading conditions, but a portion of the testing was conducted to evaluate the effects of introducing a mean stress. Fully-reversed pure torsion fatigue data were also generated using an axial-torsion test machine. The focus of the testing was directed toward longer life tests with several shorter life tests to obtain the stress-life curves in both the low and high cycle regimes. Significant scatter in the experimental data in some instances necessitated a statistical investigation. The fully-reversed axial testing produced both surface and subsurface specimen failures for all three steels, while the pure torsion testing resulted in surface failure on the maximum principal plane. The axial stress-life curves were predicted by using material hardness, and the predictions were found to be reasonable when compared with the experimental curves for iii

5 two of the three steels. With the maximum principal stress, maximum principal strain, von-mises, and Tresca criteria, the hardness predicted stress-life curves were converted into shear stress-life predictions. As a result, the maximum principal strain criterion was found to provide the best prediction. The same criteria were then used to correlate the axial and torsion fully-reversed data for each material, and the maximum principal strain criterion was found to provide the best predictions. The area parameter for the axial fatigue limit prediction provided estimated fatigue limits for subsurface inclusion failures. This parameter was found to predict fatigue limits that were lower than the experimental fatigue limit at 10 7 cycles. The modified Goodman parameter and Gerber parameter predictions were found to exceed the 900 MPa stress amplitude median life. The modified Goodman equation resulted in a better prediction than the Gerber parameter. For the particular R ratio of -0.5 tested, the SWT (Smith-Watson-Topper) parameter was found to produce similar results to the modified Goodman equation. iv

6 Acknowledgements I would like to thank my advisor, Dr. Ali Fatemi, for his guidance and instructional support during this endeavor. In addition, I would like to thank Dr. Nikolaidis and Dr. Gan for their support while serving on my master s thesis committee. Special thanks are also in order for the industries responsible for providing the steels to be tested and the funding to do so. John Jaegly and the MIME Machine Shop deserve my sincere gratitude for providing assistance with the machines and miscellaneous issues. Also, I want to thank my colleagues in the Fatigue and Fracture Research Laboratory for their guidance and support. Finally, I would like to acknowledge my parents, Mike and Kathy, and my two sisters Jill and Jessica for helping me to complete this degree. v

7 Contents Abstract Acknowledgements Contents List of Tables List of Figures List of Symbols iii v vi viii x xiv 1 Introduction 1 2 Literature Review Prediction of Axial Stress-life Curve from Material Hardness Correlation of Axial and Torsion Data and Prediction of Torsion Fatigue Prediction of Fatigue Limit from Inclusion Size Axial Mean Stress Effects Summary Experimental Program Specimen Geometries Testing Equipment Uniaxial Testing Machines Axial-Torsion Testing Machine Alignment Test Methods and Procedures Monotonic Axial Testing Constant Amplitude Fatigue Tests vi

8 3.3.2 Axial Fatigue Tests Torsion Fatigue Tests Experimental Results and Analysis Monotonic Tension Deformation Behavior Fully Reversed Constant Amplitude Fatigue Behavior Axial Fatigue Torsion Fatigue Failure Location and Mode Tensile Mean Stress Effects on Axial Fatigue Behavior Statistical Analysis Fractography Predictions and Discussion of Results Predictions of Axial Fatigue Behavior from Hardness Predictions of Torsional Fatigue Behavior from Hardness Predictions of Torsional Fatigue Behavior from Axial Data Prediction of Fatigue Limit by using Inclusion Size Mean Stress Effects and Life Predictions for Axial Loading Summary and Conclusions 105 References 108 vii

9 List of Tables 2.1 Inclusion shape, size, and locations, nominal fracture stress, and estimated fatigue limit for individual fracture origins with the area parameter for subsurface failures of high hardness bearing steels (Murakami, 2002) Size and location of inclusions at fatigue fracture origin and the predicted fatigue limits for quenched and tempered 0.46% carbon steel having a hardness of 650 HV (Murakami et al., 1998) Summary of monotonic tensile test results Summary of fully-reversed (R = -1) axial fatigue test results for the HSS1 material Summary of fully-reversed (R = -1) axial fatigue test results for the HSS2 material Summary of fully-reversed (R = -1) axial fatigue test results for the HSS3 material Summary of fully-reversed (R = -1) torsion fatigue test results for the HSS1 material Summary of fully-reversed (R = -1) torsion fatigue test results for the HSS2 material Summary of fully-reversed (R = -1) torsion fatigue test results for the HSS3 material Summary of fully-reversed axial and torsion (R = -1) fatigue properties Summary of axial mean stress (R = -0.5) fatigue test results for the HSS2 and HSS3 materials. 65 viii

10 4.10 Axial fatigue Anderson-Darling Statistic values for HSS1, HSS2, and HSS Torsion fatigue Anderson-Darling Statistic values for HSS1, HSS2, and HSS Projected axial fatigue lives of the HSS1, HSS2, and HSS3 steels at a given stress amplitude level for different probabilities of survival Projected torsion fatigue lives of the HSS1, HSS2, and HSS3 steels at a given stress amplitude level for different probabilities of survival Predicted fatigue limit with the area parameter for subsurface failures. 98 ix

11 List of Figures 2-1 Comparison of experimental axial curve to axial strain-life predictions by the Roessle-Fatemi hardness method for the SAE 9254 AL FG 58 HRC steel (McClaflin, 2001) Comparison of experimental and predicted uniaxial fatigue lives by the Roessle-Fatemi hardness method for eight steels (Kim et al., 2002) Axial tension-compression experimental data for an oil-tempered Si-Cr spring steel with a hardness of 598 HV (Akiniwa et al., 2008) Relationship between hardness and fatigue strength for steels (Murakami et al., 1989) Experimental and predicted shear stress amplitude versus fatigue life curves for a high strength quenched and tempered spring steel having a hardness of 58 HRC (McClaflin and Fatemi, 2004) Shear strain amplitude versus fatigue life from experiments and predictions using the Roessle-Fatemi hardness method for the SAE 9254 AL FG 58 HRC steel (McClaflin, 2001) Comparison of experimental and predicted shear fatigue lives by the Roessle- Fatemi hardness method and equivalent strain (i.e. von-mises) criterion for eight steels (Kim et al., 2002) Definition of area (Murakami and Endo, 1994) Distributions of size of non-metallic inclusions that acted as a fracture origin for high carbon chromium steel with a hardness of 760 HV (Nakajima et al., 2010) S-N curve [tension-compression, R = -1] for a quenched and tempered 0.46% carbon steel with a hardness of 650 HV (Murakami et al., 1998). 30 x

12 2-11 Ratio of experimental to predicted fatigue strength (a) without residual stress as a consideration, and (b) with residual stress as a consideration (Murakami et al., 1998) Stress amplitude versus cycles to failure of unnotched SAE 1045 HR steel with hardness variations for axial fatigue tests with R = 0.8 and R = 0.9 (Karadag and Stephens, 2003) Comparison of calculated life versus experimental life for 1045 HR steel at R = 0.8 and 0.9 when using three S-N mean stress models (Karadag and Stephens, 2003) S-N diagram with R = -1, R = 0, and R = 0.5 for carbon chromium bearing steel having a hardness range of 750 to 795 HV (Sakai et al., 2006) Maximum stress versus cycles to failure with R = -1, R = 0, and R = 0.5 for carbon chromium bearing steel having a hardness range of 750 to 795 HV (Sakai et al., 2006) Stress amplitude versus mean stress at 10 8 cycles with R = -1, R = 0, and R = 0.5 for carbon chromium bearing steel having a hardness range of 750 to 795 HV (Sakai et al., 2006) Strain amplitude versus reversals to failure for all strain ratios employed on SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991) Predicted versus experimental fatigue life when using the modified Goodman parameter for the SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatem, 1991) Predicted versus experimental fatigue life when using the Gerber parameter for the SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991) Mean stress data correlation with the linear and bilinear SWT mean stress parameter for the SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991) Axial specimen configuration and dimensions (mm) Torsion specimen configuration and dimensions (mm) Testing machines used (a) Instron 8801 axial, (b) MTS axial, and (c) Instron 8822 axial-torsion. 43 xi

13 4-1 Monotonic tensile stress-displacement curves showing ultimate tensile strength for (a) HSS1, and (b) HSS2 and HSS Fully-reversed (R = -1) axial fatigue stress-life plots with best fit lines for (a) HSS1, (b) HSS2, and (c) HSS Fully-reversed (R = -1) torsion fatigue stress-life plots with best fit lines for (a) HSS1, (b) HSS2, and (c) HSS Broken axial specimens (ordered by stress level and cycles to failure) for (a) HSS1, (b) HSS2, and (c) HSS Surface and subsurface axial test specimen pictures of HSS1 ordered by stress level and cycles to failure (left to right and top to bottom) Surface and subsurface axial test specimen pictures of HSS2 ordered by stress level and cycles to failure (left to right and top to bottom) Surface and subsurface axial test specimen pictures of HSS3 ordered by stress level and cycles to failure (left to right and top to bottom) Broken HSS1 torsion specimens arranged by cycles to failure for shear stress amplitude level of (a) 1100 MPa, (b) 1000 and 950 MPa, (c) 900 MPa, (d) 825 MPa, (e) 750 and 700 MPa, and (f) spiral break pattern Broken HSS2 torsion specimens arranged by cycles to failure for shear stress amplitude level of (a) 900 and 850 MPa, (b) 800 MPa, (c) 775 MPa, (d) 700 MPa, (e) 650 and 625 MPa, and (f) spiral break pattern Broken HSS3 torsion specimens arranged by cycles to failure for shear stress amplitude level of (a) 900 MPa, (b) 850 MPa, (c) 800 MPa, (d) 750 MPa, (e) 700 and 650 MPa, and (f) spiral break pattern HSS2 and HSS3 axial mean stress test specimens arranged by stress level and cycles to failure from left to right Axial mean stress (R = -0.5) test results with superimposed fully-reversed axial fatigue test results for HSS2 and HSS Lognormal probability of failure versus axial fatigue life for (a) 1300 MPa stress amplitude and HSS1, (b) 850 MPa stress amplitude and HSS2, and (c) 1000 MPa stress amplitude and HSS3. 80 xii

14 4-14 Lognormal probability of failure versus torsion fatigue life for (a) 1000 MPa stress amplitude and HSS1, (b) 775 MPa stress amplitude and HSS2, and (c) 800 MPa stress amplitude and HSS Stress amplitude versus cycles to failure at different probabilities of survival for the axial tested specimens of (a) HSS1, (b) HSS2, and (c) HSS Stress amplitude versus cycles to failure at different probabilities of survival for the torsion tested specimens of (a) HSS1, (b) HSS2, and (c) HSS SEM fractographs for axial loading of (a) HSS1A-14 specimen with surface failure, (b) HSS1A-03 specimen with subsurface failure, and (c) HSS1 axial subsurface failure specimen SEM fractographs for axial loading of (a) HSS1A-08 specimen with surface failure, and (b) HSS1A-07 specimen with subsurface failure SEM fractographs for axial loading of (a) HSS2A-15 specimen with subsurface failure, and (b) HSS3A-09 specimen with subsurface failure SEM fractograph of an axial premature failure specimen of HSS1 material showing (a) subsurface failure at low magnification, (b) subsurface failure at high magnification, and (c) small pore magnification Roessle-Fatemi hardness predictions for axial loading with experimental data for HSS1, HSS2, and HSS Shear stress-life predictions from the Roessle-Fatemi hardness method and failure criteria equations for (a) HSS1, (b) HSS2, and (c) HSS Experimental and predicted shear stress amplitude versus fatigue life curves for (a) HSS1, (b) HSS2, and (c) HSS Equivalent fully-reversed stress amplitude for mean stress data with modified Goodman and Gerber criteria Axial stress amplitude versus cycles to failure with modified Goodman and Gerber criteria predictions and comparisons with mean stress (R = -0.5) experimental results. 104 xiii

15 List of Symbols A... axial fatigue coefficeint at one cycle A final... final cross-sectional area at fracture A o... shear fatigue coefficeint at one cycle A original... original minimum cross-sectional area b... axial fatigue strength exponent b o... shear fatigue strength exponent c... axial fatigue ductility exponent D final... final specimen test diameter D original... original specimen test diameter E... modulus of elastcity HB... Brinell hardness number HRC... Rockwell C-scale hardness number HV... Vickers hardness number K t... stress concentration factor N f... cycles to failure 2N f... reversals to failure P... load P max... maximum load (in monotonic testing) R... stress ratio R a... surface roughness parameter R ε... strain ratio %RA... percent reduction in area S f... fatigue limit S u... ultimate tensile strength T... torque Α... exponent within the area parameter model Δσ/2... axial stress amplitude Δτ/2... shear stress amplitude ε a... strain amplitude ε f '... axial fatigue ductility coefficient σ a... alternating stress σ f... monotonic true fracture stress xiv

16 σ f '... axial fatigue strength coefficient σ m... mean stress σ max... maximum stress σ Nf... fully-reversed fatigue strength at N f cycles σ w... fatigue limit for area parameter model σ wo... fatigue strength (in Murakami hardness method) τ f '... shear fatigue strength coefficient xv

17 Chapter 1 1 Introduction The area of fatigue has been a primary focus in the design field for many years. Machines and structures ranging from the agricultural industry to the roads and bridges in our transportation sector are all subject to fatigue loading. For instance, the world of agriculture revolves around the working capabilities of a tractor. From the moving engine components to the output of the power-take-off (PTO), cyclic loading occurs. Research and development when correctly combined with laboratory testing can help to improve the capabilities, efficiency, and safety of many machines and devices used all over the world today. The stress-life (S-N) and strain-life (ε-n) approaches are commonly used today in industry when discussing the subject of fatigue. The stress-life approach, the method used in this investigation, requires the knowledge of material properties such as the fatigue strength coefficient and exponent to predict fatigue behavior. Properties of this nature are typically available for many axial loading cases. However, despite the fact that steels are used extensively in industry, properties of this nature are not generally available for torsional loading applications. From a graduate researcher s point of view, this is surprising since many components in applications undergo torsional and multiaxial (for 1

18 example, axial and torsion) loadings quite frequently. To add to the complexity of the problem, very limited data are available for more brittle high strength steels. In many applications, case hardening is often used to improve fatigue and wear resistance by creating compressive residual stresses and higher hardness at the surface such as for gear teeth, shafts, bearings, tools, and dies. The investigation described throughout this document considers both axial and torsional testing for three high strength steels and, therefore, representative of the surface material in case-hardened components as well. While the earlier section of this document describes the actual testing results found under different loading conditions, the latter portion considers several prediction methods and parameters. Time, cost, and efficiency usually dictate the amount and type of testing that is done. The field of fatigue would greatly benefit if an acceptable prediction method could reduce the time and costs associated with testing while providing reliable predictions. This work investigates the use of material hardness to predict axial fatigue properties required to obtain stress-life curves. The Roessle-Fatemi hardness method (2000) estimates the axial fatigue properties for steels from easily measured Brinell hardness and elastic modulus values. Such a method can quickly provide fatigue life estimates that otherwise would need to be generated by extensive fatigue testing. The maximum principal stress, maximum principal strain, von-mises, and Tresca criteria were used to extend the Roessle-Fatemi estimation one step further and enable the prediction of a shear stress-life curve based on hardness for the three steels investigated. The maximum principal stress, maximum principal strain, von-mises, and Tresca criteria were used to better understand the relationship between the axial and torsion 2

19 experimental data. A better understanding of the relationship between axial and torsion data for high hardness steels means that shear stress-life curves can be predicted for steels only having generated axial fatigue data. As a result, this investigation compares the axial and torsion stress-life curves for the three high hardness steels tested. Steels have many inherent defects such as inclusions which often control failure type and location. Murakami s method has shown that material inclusion size, as a function of projected area, and material hardness can be used to successfully predict fatigue limits. Equations are available for both surface and subsurface inclusions and can correct for residual stresses or mean stress when applicable. As such a method has great potential in applications, the ability of Murakami s method is investigated for the high hardness steels considered in this investigation. Often, machine components are subjected to loads that reflect nonzero mean stress conditions. Mean stress effect, is therefore, another aspect of fatigue behavior examined in this investigation. A limited number of specimens were subjected to cyclic loading with mean stress to gain a better understanding of mean stress and its effects with respect to high hardness steels. The modified Goodman, Gerber, and SWT (Smith- Watson-Topper) criteria were considered in an attempt to predict the mean stress behavior from the fully-reversed test results. In the context of this investigation, Chapter 2 reviews the literature regarding the above topics. Chapter 3 describes the experimental program while Chapter 4 presents the tensile and fatigue test results for the three steels. Chapter 4 also considers the data from a statistical standpoint. The latter portion of Chapter 4 also presents some SEM fractography obtained from the fully-reversed axial testing. Chapter 5 presents 3

20 discussion and analysis of the experimental results with respect to the prediction methods mentioned above. Finally, Chapter 6 summarizes the findings of this study before presenting the final conclusions. 4

21 Chapter 2 2 Literature Review Fatigue failure is an area of primary focus in engineering design. Components are axially loaded in many instances where mean stresses sometimes also exist. In addition, many other components undergo torsion loadings. High hardness steels are often used in applications where loadings of this type are found. This chapter reviews previous studies regarding medium to high hardness steels in five particular areas. The first area concerns predicting the axial stress-life curve from material hardness, while the second topic further extends the axial stress-life prediction to a shear stress-life prediction by using different failure criteria. Failure criteria can also be used to correlate axial and shear stress-life data. Fatigue limit predictions from inclusions are discussed as the fourth topic, while mean stress predictions are considered in a following discussion. The results found in the literature with regards to these topics can be related and compared to the experimental and predicted results obtained in the present study. 5

22 2.1 Prediction of Axial Stress-life Curve from Material Hardness The ability to quickly and accurately make predictions regarding the axial stresslife curve of a material has always been a topic of interest. Predictions that can be made without extensive experimental fatigue testing are beneficial since both time and costs associated with material fatigue testing can be significantly reduced. Significant effort has been directed toward obtaining a prediction method requiring only easily obtained material information. One such material property that can be easily measured is hardness since hardness testing provides a simple way to obtain such information. In a study conducted by Roessle and Fatemi (2000), it was determined that both the axial fatigue strength coefficient (σ f ') and axial fatigue ductility coefficient (ε f ') of steels could be correlated with the Brinell hardness of a material to obtain such predictions. The methods used to predict material lives are the stress-life (S-N) approach, often referenced as Basquin s equation, and the strain-life (ε-n) approach known as the Coffin-Manson relationship (Stephens et al., 2000). Basquin s equation is stated as: b / 2 f '(2N f ) (2.1) where Δσ/2 represents the axial stress amplitude. The reversals to failure is represented by 2N f while b represents the axial fatigue strength exponent. Both S-N and ε-n equations require knowing the fatigue strength coefficient and the fatigue strength exponent, while the strain-life equation also requires knowing the fatigue ductility coefficient and fatigue ductility exponent. The fatigue limit of steels has been estimated from ultimate strength in many cases. Also sometimes referred to as the endurance limit, the fatigue limit is defined as 6

23 the limiting value of the median fatigue strength as N f, cycles to failure, becomes very large (Stephens et al., 2000). This is the strength for which a knee exists where failure will not occur, regardless of the number of cycles or reversals completed. The approximation that is considered when analyzing steels is as follows: S S f f 0.5S u 700 MPa for for S S u u 1400 MPa 1400 MPa (2.2) where S f is the fatigue limit and S u is the ultimate tensile strength. Predictions based on Equation 2.2 have been found to be non-conservative for most steels (Roessle and Fatemi, 2000). The fatigue limit is considered constant at high ultimate tensile strength levels because inclusions play a significant role in high cycle fatigue (Stephens et al., 2000). The relations developed by Roessle and Fatemi (2000) are integrated into the strain-life approach. To develop the relations, monotonic and fatigue properties for 20 steels commonly used in the ground vehicle industry were obtained through straincontrolled fatigue testing. Data published for 49 other steels were also gathered to increase the pool of steels considered. In general, the 20 steels investigated by Roessle and Fatemi (2000) ranged in ultimate tensile strength from 582 MPa to 2360 MPa with a Brinell hardness range of 163 to 536 HB. For the other 49 gathered steels, the ultimate tensile strength varied from 345 MPa to 2585 MPa with a Brinell hardness ranging from 80 to 660 HB. After performing various best fits of the data for the many steels, the fatigue strength and fatigue ductility coefficient equations relating to material hardness were developed. The fatigue strength coefficient relation was determined to be (Roessle and Fatemi, 2000): 7

24 ' 4.25 ( HB) 225 (2.3) f where HB is the measured Brinell hardness and the fatigue strength coefficient is in MPa. The fatigue ductility coefficient relation was determined to be (Roessle and Fatemi, 2000): ( HB) 487 ( HB) f ' (2.4) E where the modulus of elasticity, E, is in MPa. The fatigue strength exponent, b, and fatigue ductility exponent, c, were determined to be and -0.56, respectively, after evaluating the overall ranges for the 69 materials. Roessle and Fatemi (2000) noted that the fatigue strength exponent was the same as the estimate provided by Muralidharan and Manson (1988) in their proposed Universal Slopes Method. The end result from extensive testing and analysis was the following correlation that involves only material hardness and modulus of elasticity (Roessle and Fatemi, 2000): ( HB) ( HB) 487( HB) (2N f ) (2N f ) a (2.5) E E where ε a is the strain amplitude. When compared against the existing experimental data, Roessle and Fatemi (2000) concluded that Equation (2.5) proved to provide accurate predictions for steels having measured Brinell hardness values greater than 150 but less than 700. The material hardness, which can be measured by way of a nondestructive test, and the modulus of elasticity are the only required information needed to effectively use the Roessle-Fatemi hardness equation. 8

25 McClaflin (2001) used the Roessle-Fatemi hardness equation to predict the axial response of a SAE 9254 AL FG quenched and tempered steel. The material of interest was a high strength steel having a Rockwell C hardness of 58 (584 HB). The predicted axial fatigue curve by Equation 2.5 and experimental axial curve are shown in Figure 2-1. The Roessle-Fatemi hardness equation produced a conservative prediction. The Roessle-Fatemi hardness equation was used in predicting uniaxial fatigue properties for determining the expected lives of eight different steels by Kim et al. (2002). Fully-reversed strain-controlled experimental data were used to verify the capability of the hardness equation where the eight tested materials had an ultimate tensile strength ranging from 508 MPa to 1100 MPa while ranging in hardness from 153 to 327 HB. As can be seen in Figure 2-2, 78% of the experimental life data differed by a factor of two from the predicted life values, while 95% of the data were within a factor of five. For midrange hardness values, the Roessle-Fatemi hardness equation was found to slightly over predict the fatigue life. There are other correlations involving axial fatigue strength and material hardness that have been proposed. Murakami (1989) mentioned one such approach that is based on Vickers hardness for steels. The equation is as follows: 1.6HV 0. HV (2.6) wo 1 where σ wo and HV represent the axial fatigue strength and Vickers hardness, respectively. Murakami (1989) has shown that Equation 2.6 provides a valid linear relationship up until a hardness of 400 HV. Akiniwa et al. (2008) investigated the fatigue strength of an oil-tempered Si-Cr steel used for the manufacture of valve springs. The ultrasonic tested material had a Vickers hardness of 598, and all residual surface stresses were removed 9

26 prior to testing by electro-polishing. According to the investigators, both the axial and the torsion testing produced large scatter in the data despite the fact consistent hardness levels were measured for all tested specimens. The 957 MPa predicted axial fatigue limit from the Brinell hardness when computed by way of Equation 2.6 was much higher than the experimental data indicated. Axial runout testing in the giga cycle regime produced a fatigue strength in the range of 650 to 810 MPa, as shown in Figure 2-3. The tendency of the linear relationship to diminish with higher material hardness and ultimate tensile strength was recognized by Garwood et al. (1951). Figure 2-4 shows how hardness and fatigue strengths are related (Murakami et al., 1989). The research identifying six different steels was compiled from several difference sources. Materials having a hardness of about 60 HRC (Rockwell C-scale hardness) were found to have a fatigue strength between 800 MPa and 900 MPa. 2.2 Correlation of Axial and Torsion Data and Prediction of Torsion Fatigue Majority of the available fatigue data and material properties resemble axial loading rather than torsion. In addition, the available torsion data do not typically include materials exhibiting a high hardness similar to the materials tested in the current investigation. According to McClaflin and Fatemi (2004), the vast majority of the torsional data available included mostly ductile materials. Current database searches today still provide evidence that there is great need for studies related to pure torsion fatigue of high hardness steels. With limited torsion data available, there are many instances when data from axial fatigue testing is used to estimate the torsion stress-life or 10

27 strain-life curve. As a result, a key question requiring an answer is which relationship or method should be used to obtain the best prediction. In the study reported by McClaflin and Fatemi (2004), a high strength quenched and tempered spring steel was tested under pure torsion conditions. The material of interest had a hardness of 58 HRC, or 584 HB. Tensile testing produced an ultimate strength of 2950 MPa while resulting in a reduction of area and elongation of 4% and 3.9%, respectively. Due to the high strength and brittleness of the material, little to no plastic deformation occurred even in the low cycle fatigue regime. As a result, McClafin and Fatemi (2004) observed minimal differences in behavior between stress-life and strain-life curves, and a stress-life approach was considered due to the high strength of the material. McClaflin and Fatemi (2004) considered the von-mises, Tresca, and maximum principal stress criteria when comparing the torsional stress-life curves from axial data to the torsion data. The fatigue properties in the stress-life approach were computed from axial properties according to the von-mises criterion: ' '/ 3 and b0 b (2.7) f f the Tresca criterion: f ' f '/ 2 and b0 b (2.8) and the maximum principal stress criterion: f ' f ' and b0 b (2.9) where τ f and b o are the shear fatigue strength coefficient and shear fatigue strength exponent, respectively. The axial fatigue strength coefficient and axial fatigue strength 11

28 exponent were found to be 4108 MPa and , respectively. The shear fatigue coefficient and shear fatigue strength exponent are used in the following equation: b0 / 2 f '(2N f ) (2.10) where Δτ/2 is the shear stress amplitude. Equation 2.10 is analogous to Basquin s relation for axial loading given in Equation 2.1. Each prediction method was then compared against the experimental torsion data. The torsional best fit experimental curve and predicted curves can be seen in Figure 2-5. They found the three predictions to be unsatisfactory. In fact, the maximum principal stress criterion gave the most non-conservative result. Historically, the maximum principal stress or maximum principal strain criteria are usually considered as an adequate prediction method when considering brittle behaving materials that fail due to brittle fracture prior to yielding (for example, see Boresi and Schmidt (2003)). In addition, both the Tresca and von-mises criteria gave a non-conservative result up until the range of 10 4 to 10 5 reversals, as shown in Figure 2-5. McClaflin and Fatemi (2004) used the axial hardness life predictions from the Roessle-Fatemi hardness method to provide torsion fatigue life estimates. The von- Mises, Tresca, and maximum principal strain criteria were used to correlate the axial hardness and torsion predictions. The von-mises criterion in conjunction with the Roessle-Fatemi hardness equation is given by: [4.25( HB) 225] (2N 2 3G 3 E f ) [0.32( HB) 487( HB) ](2N f ) 0.56 (2.11) Based on the Tresca criterion: [4.25( HB) 225] (2N 2 2G 1.5 E f ) [0.32( HB) 487 ( HB) ](2N f ) 0.56 (2.12) 12

29 and based on the maximum principal strain criterion: [4.25( HB) 225] (2N 2 G(1 ) 2 E f ) [0.32( HB) 487( HB) ](2N f ) 0.56 (2.13) Figure 2-6 shows the experimental and predicted torsion results for the SAE 9254 AL FG 584 HB steel. McClaflin and Fatemi stated that the maximum principal strain criterion fit the data the best. However, they suggested that since the axial hardness predicted curve (Figure 2-1) was conservative when compared to the axial experimental results, the maximum principal strain criterion might have added a cancellation effect that coincidently provided the best results. Shear fatigue properties were also estimated from the Roessle-Fatemi hardness predicted uniaxial fatigue properties based on the equivalent strain (von-mises) criterion by Kim et al. (2002). The predicted life estimates provided satisfactory results with 90% of the data differing by a factor of three in life. Figure 2-7 shows the results for the eight steels that ranged in hardness from 153 to 327 HB. 2.3 Prediction of Fatigue Limit from Inclusion Size Murakami and Endo (1994) state that a geometrical parameter proposed in 1983 for both two and three dimensional defects built upon the observation of microscopic cracking and numerical stress analysis could predict the rotating bending or tensioncompression fatigue limit of a material. They derived the following empirical formula: n area C (2.14) w where σ w represents the fatigue limit, area signifies the geometrical parameter of a defect, and n and C are material constants determined from numerous fatigue tests. The 13

30 area is defined as the square root of the area of the inclusion or defect projected onto the plane perpendicular to the applied maximum tensile stress, as shown in Figure 2-8. Equation 2.14 was revisited and revised in 1986 for internal and surface defects (Murakami and Endo, 1994). The surface defect equation for fully-reversed loading (R = -1), where R is the stress ratio, is given by: 1/ 6 w 1.43 ( HV 120) /( area) (2.15) and the subsurface defect equation for fully-reversed loading (R = -1) is given by: 1/ 6 w 1.56 ( HV 120) /( area) (2.16) where the variables are as previously mentioned. The appropriate units for the Vickers hardness and area parameter in these equations are kgf mm -2 and µm, respectively. The revised equations by Murakami and Endo allow for the prediction of the material fatigue limit without the use of fatigue testing. Based on analyzing experimental data, Murakami and Endo (1994) concluded that the error from using the above surface and internal defect equations was usually less than 10 percent for notched and cracked specimens. However, their conclusions were based on the specimen having a area lower than 1000 µm and a hardness in the range of 70 to 720 HV. In addition, Equations 2.15 and 2.16 were further extended to predict the fatigue limit for stress ratios other than the fully-reversed (R = -1) loading conditions (Murakami et al., 1990). The revised equation for material surface defects is given by: ] 1.43 ( 120) /( ) 1/ 6 w HV area [(1 R) / 2 (2.17) while the following equation can be used for subsurface defects: ] 1.56 ( 120) /( ) 1/ 6 w HV area [(1 R) / 2 (2.18) 14

31 The exponent alpha (α) can be found from the following expression: HV (10 ) (2.19) The reported prediction error for fatigue limits was usually less than 15% for hardness levels in the range of 100 to 740 HV. Table 2.1 presents results of experimental data (Murakami, 2002) and compares the experimental data with the predicted fatigue strengths from Equation 2.16 for high hardness bearing steels. It can be observed from this table that the predictions are consistent with the experimental data in most cases. The area parameter was calculated at the fish-eye fracture in the shape of an ellipse. The ratio of the nominal bending stress at the inclusion failure site to the predicted fatigue limit ranges between 1 and 1.4 for this set of experimental rotating bending data. Additional interpretation of rotating bending fatigue data obtained by Konuma and Furukawa (1986) for two quenched and tempered steels with different carbon levels showed similar results (Murakami, 2002). The material hardness varied from 570 HV to 831 HV for the two steels. The ratio of the nominal bending stress at the inclusion failure site to the predicted fatigue limit ranged between and 1.2 for this set of experimental data. In a study reported by Nakajima et al. (2010), very high cycle fatigue testing was conducted on high carbon chromium steel JIS SUJ2. Subsurface fractures with distinct fish-eyes proved to be the dominant failure mode for all fully-reversed axial fatigue testing conducted. According to Nishijima and Kanazawa (1999), axial fatigue failure initiates on the surface of the material specimen in most instances. However, failure can initiate from the interior of the material specimen. In general, surface initiation failures 15

32 are related to high stress levels while subsurface initiation levels are realized under lower stress levels. Initiated subsurface failures according to Nishijima and Kanazawa (1999) are most often seen in the high cycle regime for case-hardened steels, quench-hardened steels prepared by induction heating, and surface-toughened steels prepared by shot peening. All additional testing conducted with an R ratio equal to 0.05 proved to be dominated by subsurface failure (Nakajima et al., 2010). The runout stress levels in terms of maximum stress were found to be 676 MPa and 988 MPa with a life duration of 5x10 8 cycles for the axial loading conditions of R = -1 and R = 0.05, respectively (Nakajima et al., 2010). The maximum stresses correspond to stress amplitudes of 676 MPa and 469 MPa, respectively. All subsurface fractures were observed in detail with a scanning electron microscope (SEM) to identify the non-metallic inclusion sizes and the associated granular areas surrounding the inclusion. Figure 2-9 shows the size distribution of the non-metallic inclusions that acted as the fracture origin. As a result, the investigators documented the average inclusion size to be 14.6 µm for all completed axial testing. From the gathered information, the area parameter model proposed by Murakami (Equation 2.16) was used to predict the axial fully-reversed fatigue limit. An extreme value statistics method was used to arrive at an appropriate inclusion standard area size of mm 2 and an inclusion size of 14.7 µm. The fatigue limit prediction of 877 MPa was calculated with a Vickers hardness of 760 HV. As a result, the prediction was considered non-conservative since the fully-reversed axial fatigue limit was found to be 676 MPa. 16

33 Murakami et al. (1998) performed an investigation regarding the effect of nonmetallic inclusions. An attempt was made to predict the fatigue strength of a quenched and tempered 0.46% carbon steel by way of the area parameter. The fully-reversed fatigue tests for the 650 HV material produced predominantly fish-eye failures. For high hardness steels, two plateaus often occur in the long life range and super-long regime (Murakami et al., 1998). Sakai et al. (2002) also observed evidence of two plateaus in the S-N curve for the high-carbon-chromium bearing steel studied in their investigation. The area parameter has been documented to produce a higher predicted fatigue limit than found through experimental testing when considering life regimes greater than 10 7 cycles (Murakami et al., 1998). The fatigue limit corresponding to a life of 5 x 10 8 cycles was predicted by use of Equations 2.15 and 2.16 for surface and subsurface failures, respectively. Figure 2-10 represents the fully-reversed axial fatigue test results for the carbon steel they used, showing two distinct plateau regions with respect to the S- N curve. Table 2.2 represents the information needed to use Equations 2.15 and 2.16 to predict the fatigue limit of the material. Note that the area values ranged from 33.8 to 95.7 µm. The distance (h) from the surface to the inclusion was directly related to the area parameter. The predicted fatigue limit ranged from 572 to 621 MPa. In addition, the investigators found the ratio of the applied stress to the predicted fatigue limit to vary from to 1.12, where a value less than 1.0 means that the specimen fractured at an applied stress lower than the predicted fatigue limit. The investigation by Murakami et al. (1998) was taken one step further by considering the hardness variation and residual stress levels within the material. They checked residual stress levels since fish-eye failures have suggested that large residual 17

34 compressive levels can exist on the specimen surface due to the effects of shot-peening. X-ray analysis found the residual stress level in the middle of the gage section on the specimen surface to have a tensile value of 150 MPa. Figure 2-11 shows the effects of residual stress when predicting the fatigue limit. Figure 2-11(a) describes a modified S-N curve that compares the ratio of the applied stress to the predicted fatigue limit. Figure 2-11(b) considers the tensile residual stress level by using Equations 2.17, 2.18, and 2.19 with R -1. As a result, the minimum ratio of the applied stress to predicted fatigue limit was found to be In general the area parameter was found to provide accurate predictions when considering internal inclusions. 2.4 Axial Mean Stress Effects Mean stress effect is another aspect of fatigue behavior that was examined in this investigation. In many practical situations, machine components are often subjected to loads that reflect nonzero mean stress conditions. The modified Goodman, Gerber, Morrow, and SWT models coupled with the monotonic and cyclic fatigue properties of the material have been used to determine the expected fatigue life for a nonzero mean stress condition. The modified Goodman model is given by (Stephens et al., 2000): a '(2N f f ) b m S u 1 (2.20) The Gerber model is given by (Stephens et al., 2000): a '(2N f f ) b m Su 2 1 (2.21) 18

35 The Morrow model is given by (Stephens et al., 2000): a '(2N f f ) b m f 1 (2.22) and the SWT stress model for elastic loading is given by (Stephens et al., 2000): b max a f '(2N f ) (2.23) In addition to the previously mentioned variables, σ max is the applied maximum stress, σ a is the alternating stress, σ m is the mean stress, S u is the ultimate tensile strength, and σ f is the monotonic true fracture stress. According to Karadag and Stephens (2003), many mechanical parts that undergo high tensile mean stresses include bolts, gas turbine blades, and airplane wings. Within their investigation, Karadag and Stephens examined the influence of high R ratios, and how the experimental data fit models designed to predict mean stress effects. The material of interest in their investigation was a unotched SAE 1045 hot-rolled steel. While R = 0.8 and R = 0.9 tests were considered for three different hardness levels, the 50 HRC level is of most interest in this current study. Scanning Electron Microscopy analysis showed that the 50 HRC specimens fractured in a very brittle manner. As shown in Figure 2-12, this material exhibited a higher fatigue strength for R = 0.8 than for R = 0.9. Figure 2-13 shows the predicted lives when plotted against the experimental cycles to failure for the 50 HRC steel in the Karadag and Stephens (2003) investigation. The triangular points in Figure 2-13 represent the 50 HRC steel with an ultimate strength of 2370 MPa, cyclic fatigue coefficient of 5786 MPa, and fatigue strength exponent of They concluded that the three models did a very poor job of predicting the fatigue 19

36 lives for such high R ratios. All three predictions for the 50 HRC material provided both conservative and non-conservative results. An investigation performed by Sakai et al. (2006) examined how changing stress ratios affected the life of a high strength carbon-chromium steel having a hardness range of 750 to 795 HV. As with other high strength steels mentioned in this investigation, the material was found to exhibit both surface and subsurface (fish-eye) failure modes with the ratios R = -1, R = 0, and R = 0.5. Inclusions were found to be present at the center of the fish-eye. They reported that high strength steels and surface-hardened steels can exhibit multiple distinct knee points within the S-N curve. Figure 2-14 shows their surface and subsurface fatigue test results. Note that in this figure solid lines correspond to surface induced fractures while dashed lines refer to subsurface induced failures. The investigators pointed out that there was a clear difference between the surface and subsurface S-N curves for the axial load conditions of R = -1 and R = 0, while minimal separation was seen for the R = 0.5 curves. The R = -1 and R = 0 fish-eye S-N curves also exhibited the same similar slope. Figure 2-15 shows the maximum stress against the cycles to failure for the same data in Figure Similar slopes were identified for the R = -1 and R = 0 ratios, pointing to a similar fatigue strength. As a result, the investigators identified that compressive stress had minimal effect on the fatigue life of the steel they investigated. Rather, they suggested that the predominant factor affecting fatigue life was the tension side of the stress range. One concluding result inferred that the fatigue limit tended to decrease in a proportional manner with an increase in mean stress over the range of -1 R 0.5. Likewise, the outcome showed that the fatigue strengths at 10 8 cycles were significantly lower than expected with the modified 20

37 Goodman criterion. This is shown in Figure 2-16, where experimental data fall much below the modified Goodman line. Mean stress effects regarding cyclic deformation and fatigue life of SAE 1045 hardened automotive steel with ultimate tensile strength of 2165 MPa were investigated by Wehner and Fatemi (1991). Smooth uniaxial fatigue specimens hardened to 55 HRC were subjected to both tensile and compressive mean stresses by using three mean strain ratios. Tensile mean stresses were generated with strain ratios, R ε, of 0.5 and 0, while a compressive mean stress was generated with a strain ratio of -2. The experimental mean stress results were also compared with the predicted results obtained from using the modified Goodman, Gerber, Soderberg, Morrow, and SWT parameters. Figure 2-17 illustrates how the mean stress implemented by different strain amplitudes influenced the fatigue life for the SAE 1045 hardened steel. Wehner and Fatemi stated that tensile mean stresses resulted in fatigue life reductions in the range of two orders of magnitude. Fatigue life increased by a factor of five in some cases with compressive mean stress. The modified Goodman and Gerber parameters (Equations 2.20 and 2.21) were used to develop mean stress life predictions for the SAE 1045 steel (Wehner and Fatemi, 1991). Figure 2-18 shows the predicted fatigue life from the modified Goodman parameter when plotted against the experimental results. Wehner and Fatemi stated that the degree of correlation was similar for both the tensile and compressive mean stress data. Figure 2-19 represents the mean stress fatigue life Gerber prediction results. They proposed changing the positive sign in Equation 2.21 to a negative sign so the equation could distinguish tensile and compressive mean stresses. However, they found larger scatter with the Gerber parameter and mostly non-conservative results. They also 21

38 implemented the SWT stress-strain parameter for mean stress predictions. The SWT equation plotted in Figure 2-20 is given by: 2 2b bc a max E ( f ') (2N f ) f ' f ' E(2N f ) (2.24) Figure 2-20 also shows a log-log linear model in addition to the bilinear model. Minimal differences were observed between the linear and bilinear models. As can be seen from this figure, better correlation was found in the low-cycle region than in the high cycle region with the linear SWT model, as expected. 2.5 Summary High strength steels play an important role in many practical applications. The ability to make predictions both quickly and accurately has remarkable benefits in the area of fatigue and engineering design. Significant effort has been put forth to develop such prediction methods and gain a better understanding of how high strength materials behave under different loading conditions. The Roessle-Fatemi hardness model can be used to estimate the axial S-N curve for a steel. Such a model requires only knowing the material hardness and modulus of elasticity, which can be easily obtained through nondestructive laboratory methods. As a result, the model has proved to provide relatively accurate predictions when the measured hardness is between 150 and 700 HB. Axial fatigue prediction results obtained from the Roessle-Fatemi model can then be combined with stress criteria such as the maximum principal stress, maximum principal strain, von-mises, or Tresca to develop torsional fatigue life predictions. Axial experimental results can also be combined with the above stress criteria to develop correlations with the torsional experimental data. 22

39 The area parameter model can be used to estimate the fatigue limit of a steel using material hardness, residual stress levels, and inclusion size. Equations are available for both surface and subsurface failure conditions. Numerous studies have been performed to determine the compatibility of the model with common steels. Murakami and Endo (1994) recommended the area parameter for specimens having a area lower than 1000 µm and a hardness in the range of 70 to 720 HV. Mean stress effects are very important when considering fatigue and realistic loading conditions. Models such as the modified Goodman, Gerber, Morrow, and SWT have been used to predict material behavior under mean stress loading conditions. The modified Goodman, Gerber, and Morrow parameters were found to offer poor predictions for high hardness steels with high R ratios. It is difficult to draw general conclusions regarding these mean stress parameters based on the limited available mean stress data for high hardness steels. 23

40 Table 2.1 Inclusion shape, size, and locations, nominal fracture stress, and estimated fatigue limit for individual fracture origins with the area parameter for subsurface failures of high hardness bearing steels (Murakami, 2002). 24

41 Table 2.2 Size and location of inclusions at fatigue fracture origin and the predicted fatigue limits for quenched and tempered 0.46% carbon steel having a hardness of 650 HV (Murakami et al., 1998). 25

42 Figure 2-1 Comparison of experimental axial curve to axial strain-life predictions by the Roessle-Fatemi hardness method for the SAE 9254 AL FG 58 HRC steel (McClaflin, 2001). Figure 2-2 Comparison of experimental and predicted uniaxial fatigue lives by the Roessle-Fatemi hardness method for eight steels (Kim et al., 2002). 26

43 Figure 2-3 Axial tension-compression experimental data for an oil-tempered Si-Cr spring steel with a hardness of 598 HV (Akiniwa et al., 2008). Figure 2-4 Relationship between hardness and fatigue strength for steels (Murakami et al., 1989). 27

44 Figure 2-5 Experimental and predicted shear stress amplitude versus fatigue life curves for a high strength quenched and tempered spring steel having a hardness of 58 HRC (McClaflin and Fatemi, 2004). Figure 2-6 Shear strain amplitude versus fatigue life from experiments and predictions using the Roessle-Fatemi hardness method for the SAE 9254 AL FG 58 HRC steel (McClaflin, 2001). 28

45 Figure 2-7 Comparison of experimental and predicted shear fatigue lives by the Roessle-Fatemi hardness method and equivalent strain (i.e. von-mises) criterion for eight steels (Kim et al., 2002). Figure 2-8 Definition of area (Murakami and Endo, 1994). 29

46 Figure 2-9 Distributions of size of non-metallic inclusions that acted as a fracture origin for high carbon chromium steel with a hardness of 760 HV (Nakajima et al., 2010). Figure 2-10 S-N curve [tension-compression, R = -1] for a quenched and tempered 0.46% carbon steel with a hardness of 650 HV (Murakami et al., 1998). 30

47 (a) (b) Figure 2-11 Ratio of experimental to predicted fatigue strength (a) without residual stress as a consideration, and (b) with residual stress as a consideration (Murakami et al., 1998). Figure 2-12 Stress amplitude versus cycles to failure of unnotched SAE 1045 HR steel with hardness variations for axial fatigue tests with R = 0.8 and R = 0.9 (Karadag and Stephens, 2003). 31

48 Figure 2-13 Comparison of calculated life versus experimental life for 1045 HR steel at R = 0.8 and 0.9 when using three S-N mean stress models (Karadag and Stephens, 2003). Figure 2-14 S-N diagram with R = -1, R = 0, and R = 0.5 for carbon chromium bearing steel having a hardness range of 750 to 795 HV (Sakai et al., 2006). 32

49 Figure 2-15 Maximum stress versus cycles to failure with R = -1, R = 0, and R = 0.5 for carbon chromium bearing steel having a hardness range of 750 to 795 HV (Sakai et al., 2006). Figure 2-16 Stress amplitude versus mean stress at 10 8 cycles with R = -1, R = 0, and R = 0.5 for carbon chromium bearing steel having a hardness range of 750 to 795 HV (Sakai et al., 2006). 33

50 Figure 2-17 Strain amplitude versus reversals to failure for all strain ratios employed on SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991). Figure 2-18 Predicted versus experimental fatigue life when using the modified Goodman parameter for the SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991). 34

51 Figure 2-19 Predicted versus experimental fatigue life when using the Gerber parameter for the SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991). Figure 2-20 Mean stress data correlation with the linear and bilinear SWT mean stress parameter for the SAE 1045 hardened steel with a hardness of 55 HRC (Wehner and Fatemi, 1991). 35

52 Chapter 3 3 Experimental Program The specimen geometries used are discussed along with specimen preparation in this chapter. The fatigue testing machines used are presented in conjunction with their specifications and capacities. The significance of machine alignment and the process utilized to avoid misalignment is also discussed. Monotonic and fatigue testing procedures used to obtain the experimental data are also described and presented in Chapter Specimen Geometries The HSS1, HSS2, and HSS3 steels are high strength steels with a hardness of 60 HRC. Specimen preparation for the HSS1 steel was completed prior to sending a significant portion of the specimens to undergo a superfinish surface process. Similar round hourglass specimens were used for both axial and torsion fatigue testing. The axial specimen configuration and dimensions are shown in Figure 3-1. Similar hourglass specimen geometry with larger dimensions that were used for the torsion tests can be seen in Figure 3-2. Both the axial and torsion specimens were designed to have a low stress concentration in the grip to gage section transition region. The stress 36

53 concentration, K t, is 1.02 for both specimen geometries. The arithmetical average surface roughness, R a, was found to be less than µm for the axial and torsion superfinished specimens. 3.2 Testing Equipment Uniaxial Testing Machines An INSTRON 8801 and MTS closed-loop servo-controlled hydraulic axial load frame, as shown in Figures 3-3(a) and 3-3(b), in conjunction with Fast-Track digital servo-controllers were used to conduct the axial fatigue testing. The MTS machine was used for all mean stress testing. The load cells had a capacity of 50 kn and 100 kn, respectively. Hydraulically operated grips using universal tapered 12.7 mm diameter collets were employed to secure the specimens ends in series with the load cell on the INSTRON 8801 machine. Hydraulically operated grips using universal tapered wedges were employed to secure the specimens ends in series with the load cell on the MTS machine Axial-Torsion Testing Machine An INSTRON 8822 closed-loop servo-controlled hydraulic axial-torsional load frame, as shown in Figure 3-3(c), in conjunction with digital servo-controllers was used to conduct the torsion and tensile tests. The axial and torsion channels are independent of each other and controlled by way of two separate channels. The capacity of the load cell is 1000 N m in torsion and 100 kn in the axial direction. Hydraulically operated grips using universal tapered 19 mm diameter collets were employed to secure the specimens 37

54 ends with the load cell. Universal tapered 12.7 mm diameter collets were employed for tensile testing Alignment Significant effort was put forth to align the load train (load cell, grips, specimen, and actuator) for both testing machines. Misalignment can result from both tilt and offset between the central lines of the load train components. In order to align the axial machine, a round strain-gage bar was used. The strain-gaged 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. The alignment for the axial-torsion machine was completed by using an actual test specimen with mounted longitudinal strain gages placed at four equidistant locations around the minimum diameter. The maximum bending strain determined from the gage specimens were within the allowable ASTM limit. Alignment for both testing machines was verified and completed in accordance with ASTM Standard E1012 (2007a). 3.3 Test Methods and Procedures Monotonic Axial Testing All monotonic tests during the duration of this project were performed using methods specified by ASTM E8 (2007e). One valid test was performed for each of the four materials, and the results were used to obtain the ultimate strength and percent reduction in area. INSTRON MAX software and the INSTRON 8822 axial-torsion load frame were used for all monotonic tension testing. A displacement rate of 0.08 mm/min 38

55 was documented as a reference value and transformed into a cyclic testing frequency of Hz. Under displacement control with the rotation channel set to zero rotation, adequate displacement was allotted so that the test would finish during the first quarter of the first cycle. Appropriate data recording strategies were employed to collect the necessary testing information. After the tension tests were concluded, the broken specimens were carefully reassembled. The final diameters of the fractured specimens were measured with a Vernier caliper having divisions of in. It should be noted that prior to the test, the initial diameter was measured with this same instrument Constant Amplitude Fatigue Tests All axial and torsion constant amplitude fatigue tests in this study were performed in load control. All specimens were checked for straightness, symmetry, and test section defects. A flat Starret Surface Plate was used to check straightness, while an optical comparator with 10X magnification was used to check the symmetry. Visual inspection under a light source was used to locate any test section defects. Grip and minimum test section diameters were measured using a Vernier caliper having divisions of 0.01 mm. Clear tape was attached to the caliper to ensure the surface of the specimen was not scratched. A ramp time was employed during testing to allow for a smooth, gradual transition from zero to maximum load. Ramp times were chosen in a manner to ensure maximum load was reached before 100 cycles were completed. 39

56 3.3.2 Axial Fatigue Tests All axial constant amplitude fatigue tests in this study were performed according to ASTM Standard E606 (2007b). For the HSS1 axial fatigue study, 22 specimens at 7 different stress amplitudes ranging from 900 MPa to 1400 MPa resulted in a life range of 5x10 3 to 2x10 7 cycles. For the HSS2 axial fatigue study, 23 specimens at 5 different stress amplitudes ranging from 800 MPa to 1000 MPa resulted in a life range of 1x10 4 to 1x10 7 cycles. For the HSS3 axial fatigue study, 24 specimens at 6 different stress amplitudes ranging from 775 MPa to 1000 MPa resulted in a life range of 5x10 3 to 1x10 7 cycles. INSTRON SAX software was used in all tests. All tests conducted at a frequency lower than 10 Hz used a triangular waveform, while frequencies equal to or greater than 20 Hz used a sinusoidal waveform pattern. Frequencies between 10 and 20 Hz were subject to either triangular or sinusoidal waveform patterns to maintain accurate testing control while sharing a hydraulic pump with another machine. Failure was defined as fracture and designated as either surface or subsurface. Some additional axial fatigue testing was also performed for the HSS2 and HSS3 materials to determine the effects of mean stress on the high hardness steels being used. The additional mean stress testing was performed with a R ratio of A stress amplitude of 900 MPa was selected to keep the duration of the test within the desirable fatigue life regime. The selected stress level and R ratio corresponds to a tensile mean stress level of 300 MPa Torsion Fatigue Tests All torsion constant amplitude fatigue tests in this study were performed according to ASTM Standard E2207 (2007c). For the HSS1 torsion fatigue study, 20 40

57 specimens at 7 different stress amplitudes ranging from 700 MPa to 1100 MPa resulted in a life range of 6x10 3 to 2x10 6 cycles. For the HSS2 torsion fatigue study, 26 specimens at 7 different stress amplitudes ranging from 625 MPa to 900 MPa resulted in a life range of 3x10 3 to 2x10 6 cycles. For the HSS3 torsion fatigue study, 22 specimens at 6 different stress amplitudes ranging from 650 MPa to 900 MPa resulted in a life range of 6x10 3 to 1x10 6 cycles. INSTRON MAX software was used in all torque-controlled tests. The machine axial channel was set to load control with a value of zero in order to accommodate the change in length during the torsion tests. All testing was conducted with a sinusoidal waveform pattern over a frequency range of 1 to 5 Hz. Failure was defined as fracture and crack location and orientation were recorded at the completion of the test. 41

58 Figure 3-1 Axial specimen configuration and dimensions (mm). Figure 3-2 Torsion specimen configuration and dimensions (mm). 42

59 (a) Load Cell Capacity: 50 kn (b) (c) Load Cell Capacity: 100 kn Load Cell Capacity: 100 kn, 1000 N m Figure 3-3 Testing machines used (a) Instron 8801 axial, (b) MTS axial, and (c) Instron 8822 axial-torsion. 43

60 Chapter 4 4 Experimental Results and Analysis Monotonic and fatigue test results obtained are presented and discussed in this chapter. Fully-reversed axial, fully-reversed torsion, and axial mean stress fatigue data are discussed. A statistical analysis was completed to quantify the expected probabilities of survival. A fractography section also features a discussion regarding pictures taken by a scanning electron microscope. Axial specimens from the three steels were used for the SEM analysis. 4.1 Monotonic Tension Deformation Behavior The ultimate tensile strength (S u ) and percent reduction in area (%RA) were the properties determined from the monotonic tension tests. The ultimate tensile strength was calculated according to the following equation: S P / (4.1) u max A original where P max refers to the maximum load obtained before fracture occurred for the test specimen, and A original refers to the original minimum cross-sectional specimen area. The percent reduction in area was calculated according to the following equation: 44

61 % original final original RA [( A A ) / A ] 100 (4.2) where A final represents the final cross-sectional area at fracture. The monotonic results can be found in Table 4.1. Figure 4-1 shows the tensile stress-displacement curves for the three materials. The nonlinear and linear relationships do not necessarily indicate plastic or only elastic deformation. The extreme brittleness of the materials and the possibility of damage from sudden fracture hindered the use of an extensometer. 4.2 Fully Reversed Constant Amplitude Fatigue Behavior Axial Fatigue Fatigue tests were performed to determine the stress-life curves for the HSS1, HSS2, and HSS3 steels. The axial fully-reversed test conditions and results are reported in Tables 4.2, 4.3, and 4.4. The HSS1 steel listed in Table 4.2 indicates that five nonsuperfinished surface specimens were tested at three different levels to determine if any difference in life resulted from the two different surface finish conditions. The test results indicated that there was no difference between the superfinished and nonsuperfinished specimens. Tables 4.2, 4.3, and 4.4 all indicate that some specimens failed in a premature failure mode. All eight axial premature failures from the three steels fractured in the grip to gage section transition region with an applied stress of approximately 150 MPa. The direct cause of the premature failures is thought to be linked to high tensile residual stress levels in the transition region resulting from 45

62 hardening heat treatment and/or grinding of the specimens and/or due to lower hardness and, therefore, lower strength at this section. The stress-life curves for the HSS1, HSS2, and HSS3 axially tested steels can be seen in Figures 4-2(a), 4-2(b), and 4-2(c), respectively. Symbol designations clearly identify superfinished and non-superfinished specimens for HSS1, as well as surface and subsurface failures for all steels. Stress was calculated as P/A original, where P represents load and A original represents the original minimum cross-sectional area. All tests were in the elastic regime, as indicated by the linear relation between load and displacement. The axial fatigue strength coefficient, f ', and axial fatigue strength exponent, b, are the intercept and slope of the best line fit to axial stress amplitude (/2) versus reversals to failure (2N f ) data in log-log scale: f ' 2 b 2N AN b f f (4.3) Coefficient A and axial fatigue strength coefficient, f ', are related by: f b A ' 2 (4.4) In accordance with ASTM Standard E739 (2007d), when performing the least squares fit, the stress amplitude (/2) was the independent variable and the cycles to failure (N f ) was the dependent variable. The best fit curve in Figure 4-2(a) for all the HSS1 axial data excludes the three tests at 1300 MPa that failed before 10 4 cycles. Within Figure 4-2(a), a second best fit line is fitted to the subsurface failure data exceeding a life of 97,000 cycles. It can be seen that there is very little difference between the two best fit lines. A distinct transition between surface and subsurface failures for the HSS1 material occurred in the 1200 MPa 46

63 to 1300 MPa stress amplitude range, or between 3x10 4 and 6x10 4 cycles. In addition, the HSS1 material did not produce any runout tests over the course of the seven stress amplitude levels tested. The best fit curves for the HSS2 and HSS3 steels in Figures 4-2(b) and 4-2(c) exclude tests at the runout level and the tests at the 1000, 950, 900, and 850 MPa stress amplitude levels that failed before 2.5x10 4 cycles. Both surface and subsurface failures occurred for three of the five stress levels tested for the HSS2 steel, while both surface and subsurface failures occurred for four of the six stress levels tested for the HSS3 steel. The HSS2 steel produced two runout tests defined as 10 7 cycles at the 800 MPa stress amplitude level, while the HSS3 steel produced one runout test defined as 10 7 cycles at the 775 MPa stress amplitude level. Table 4.8 provides a summary of the axial fully-reversed fatigue properties. The results show that the HSS1 material produced the highest axial fatigue strength coefficient. The axial fatigue strengths and axial fatigue strength exponents for the HSS2 and HSS3 steels were somewhat lower with about 16% lower fatigue strengths at 10 6 and 10 7 cycles than for the HSS1 material. As mentioned in the literature review, Equation 2.2 states that the fatigue limit is often estimated as 700 MPa when the ultimate strength is greater than 1400 MPa. For the HSS1, HSS2, and HSS3 steels in this study, this estimate would have been conservative. The estimate for the fatigue limit in Equation 2.6, based on a hardness of 697 HV, the equivalent of 60 HRC, produced a much higher result than found for the HSS1, HSS2, and HSS3 steels. This is similar to the findings for a valve spring steel having a hardness of 598 HV (Akiniwa et al., 2008). However, the relationship between hardness and 47

64 fatigue limit for steels as shown in Figure 2-4 compares favorably to the results found for the HSS1, HSS2, and HSS3 steels in this investigation Torsion Fatigue Fatigue tests were performed to determine the shear stress-life curves for the HSS1, HSS2, and HSS3 steels. The torsion fully-reversed test conditions and results are reported in Tables 4.5, 4.6, and 4.7. The HSS1 steel listed in Table 4.5 indicates that five non-superfinished specimens were tested at four different levels to determine if any difference in life resulted from the two different surface finish conditions. The test results indicated that there was no difference between the superfinish and non-superfinish specimens. Table 4.6 indicates that some of the HSS2 specimens failed in a premature failure mode and in an unusual manner after surviving a significant number of testing cycles. Three specimens failed near the grip to gage section transition region during the gripping or ungripping process prior to starting a test. A specimen that reached a runout cycle count of 2x10 6 failed in the grip to gage section transition region during the ungripping process. Failures of this nature did not occur in the HSS3 material, as shown in Table 4.7, while using common testing practices. The stress-life curves for the HSS1, HSS2, and HSS3 shear loaded steels can be seen in Figures 4-3(a), 4-3(b), and 4-3(c), respectively. Symbol designations clearly identify superfinish and non-superfinish surface finish specimens for HSS1. Stress was calculated as (16T/πD 3 original ) where T represents torque, and D original represents the original specimen test diameter. All torsion tests were in the elastic regime as indicated by the linear relationship between torque and angle. 48

65 The shear fatigue strength coefficient, τ f ', and shear fatigue strength exponent, b o, are the intercept and slope of the best line fit to shear stress amplitude (τ/2) versus reversals to failure (2N f ) data in log-log scale: f ' 2 b 2 0 b N A N 0 f o f (4.5) Coefficient A o and shear fatigue strength coefficient, τ f ', are related by: Ao b 2 0 ' (4.6) f In accordance with ASTM Standard E739 (2007d), when performing the least squares fit, the shear stress amplitude (τ/2) was the independent variable and the cycles to failure (N f ) was the dependent variable. The best fit curve in Figure 4-3(a) for the HSS1 torsion data includes all test data. The seven tested stress levels did not produce a runout test. The best fit curve for the HSS2 material in Figure 4-3(b) excludes seven torsion tests. The solid symbols in Figure 4-3(b) indicate all tests above the runout level not used to generate the τ f' and b o values in the shear stress-life diagram. One runout equivalent to 2x10 6 cycles was found at the 650 MPa stress amplitude level. The second runout indicated test failed in the grip to gage section transition region after 5.4x10 5 cycles. Significant scatter with both runout and failure tests at the 650 MPa stress amplitude level prompted a test at the 625 MPa stress amplitude level. The best fit curve for the HSS3 material in Figure 4-3(c) utilized all tests except both runout levels to obtain the best fit curve. The six stress levels produced runout tests defined as 10 6 cycles at the 700 and 650 MPa stress amplitude levels where fatigue failures occurred in both levels as well. 49

66 Table 4.8 provides a summary of the torsion fully-reversed fatigue properties. The results showed that the HSS1 material produced the highest shear fatigue strength coefficient. The shear fatigue strengths and shear fatigue strength exponents for the HSS2 and HSS3 steels were somewhat lower with about 8% and 12% lower fatigue strengths at 10 6 and 10 7 cycles, respectively, than for the HSS1 material Failure Location and Mode Figures 4-4(a), 4-4(b), and 4-4(c) show the tested specimens for the three materials arranged according to the applied stress level and cycles to failure. Figure 4-4 shows that in some instances the axial specimens did not fail at the minimum diameter. The calculated area at fracture, however, was within five percent of the area at the minimum diameter in most cases. The left specimen half in each case in Figure 4-4 represents the portion of the specimen placed in the lower grip during testing. Figure 4-4 shows a random pattern for which side of the minimum diameter the specimens broke, which indicates that misalignment within the load train of the machine was not responsible for such failures. As mentioned previously in discussing Figure 4-2, a distinct transition from surface to subsurface failure in the HSS1 axial testing occurred in the range of 3x10 4 to 6x10 4 cycles to failure, where the axial stress amplitude was between 1200 MPa and 1300 MPa. A likely source of subsurface failure for through hardened specimens is surface compressive residual stress. Figure 4-5 shows both surface and subsurface (fisheye) failures for the HSS1 steel. Figures 4-6 and 4-7 also show that the location of the fish-eye failure was random with respect to the outer edge of the specimen for the HSS2 and HSS3 steels. The stress level controlled the failure type (i.e. surface versus 50

67 subsurface), but the inclusions played a role in determining the subsurface location of the failure. The location of the surface failure was random with respect to the specimen circumference and with respect to the testing machine. This indicates no effect of any misalignment (i.e. bending stress) during the axial tests. Figures 4-8(f), 4-9(f), and 4-10(f) show consistent surface spiral cracking at 45 in the HSS1, HSS2, and HSS3 torsion fatigue tests, respectively. This indicates that failure occurred on the maximum principal plane. Several attempts were made to observe a crack prior to failure, but they were unsuccessful. Video recorded by a camera capturing 30 frames per second showed that failure occurred in less than one second for several HSS1 shear specimens. No crack growth was observed because of low fracture toughness. A high yield or ultimate strength generally results in a lower fracture toughness. Figures 4-8, 4-9, and 4-10 also show the fractured torsion specimens arranged by applied shear stress level. The 1100 MPa applied shear stress amplitude level for the HSS1 specimens, as shown in Figure 4-8(a), fractured into multiple pieces while maintaining a spiral fracture pattern. The hardness and brittle material properties resulted in a large amount of energy being released upon fracture. In addition, Figures 4-8, 4-9, and 4-10 all indicate that fracture occurred in a random location with respect to the specimen circumference. This indicated that there was no effect of any misalignment (i.e. bending stress) during the torsion testing. 51

68 4.3 Tensile Mean Stress Effects on Axial Fatigue Behavior Twelve constant amplitude mean stress tests were performed for the HSS2 and HSS3 materials with an R ratio of This R ratio produces a tensile mean stress which is one third of the stress amplitude. The load-controlled testing was performed to determine the effects of applying a tensile mean stress to high hardness steels. Table 4.9 shows the test conditions and results at the stress amplitudes of 900 and 850 MPa for the two steels tested. Majority of the specimens produced a surface failure similar to the results observed from the fully-reversed axial fatigue testing. One of the HSS3 specimens produced a subsurface (fish-eye) failure. In addition, two of the HSS3 specimens failed in the grip section after surviving 427,904 and 515,380 cycles. A rather high tensile residual stress and a lower hardness in the grip section could be the reason for such a failure. The hardness was measured to be about 42 HRC on the grip end surface, while a lower value of 30 HRC was measured at the center of the grip section diameter. As was seen with the fully-reversed fatigue testing, Figure 4-11 shows that the specimens did not always break at the minimum gage section diameter. Figure 4-12 shows the results of the mean stress testing as compared with the fully-reversed data for the HSS2 and HSS3 steels. The median life for the fully-reversed 900 MPa stress amplitude level was 143,184 cycles. The median life for the mean stress tests at this stress amplitude level was 8,811 cycles. A factor of about 16 difference in life resulted from introducing the mean stress in the HSS2 and HSS3 axial fatigue tests. 52

69 4.4 Statistical Analysis The axial and torsion data for the HSS1, HSS2, and HSS3 materials show significant scatter in some instances and necessitates a statistical evaluation. Minitab Statistical software was used to evaluate the relationship between probabilities of failure and fatigue life for a given axial or shear stress amplitude level. The Normal, Lognormal, and Weibull distributions were considered within the individual distribution identification function in Minitab. Only stress amplitude levels with a minimum of three data points were used to develop such plots. Minitab automatically established a plotting position based on the number of data points for each stress amplitude level. Minitab reported an Anderson-Darling Statistic for each of the three distributions considered. The Anderson-Darling Statistic is defined as a way to measure how well the data follows the selected distribution type. The smaller the Anderson-Darling Statistic, the better the data fits the selected distribution. Tables 4.10 and 4.11 describe the Anderson-Darling results obtained for the Normal, Lognormal, and Weibull distributions for the axial and torsion fatigue data, respectively. Bold and italicized values indicate where the smallest Anderson-Darling Statistic occurred. The Normal distribution fits the data the best for the HSS1 axial data while each distribution fit some of the HSS2 axial fatigue data. The Weibull distribution failed as an acceptable way to interpret the torsion data for all three steels. The experimental data were found to follow the Lognormal distribution the best since the stress amplitude levels fitting the Lognormal distribution typically occurred where the larger number of data points considered appeared. The Anderson-Darling Statistic varied between and for the axial stress amplitude Lognormal distribution, while it 53

70 varied between and for the shear stress amplitude Lognormal distribution. Linearity and variation of the Lognormal line fit for the different axial and shear stress amplitude levels of the three steels can be seen in Figures 4-13 and 4-14, repectively. Representations of both the best and worst cases are shown in these figures. The plots also represent the variation in the number of points used to determine the Anderson Darling Statistic. Minitab was also used to determine the 50%, 75%, 90%, and 95% probabilities of survival at each stress amplitude level for the axial and torsion test results of the three steels. A 90% confidence level was used. Tables 4.12 and 4.13 list the probabilities of survival for each stress amplitude level and steel, while Figures 4-15 and 4-16 show the data for each steel for axial and torsion loading, respectively. The smaller scatter in the HSS1 axial and torsion data resulted in the best R-squared correlation coefficients that raged in values from to The R-squared correlation coefficient was found to significantly decrease with the increase in probability of survival for the HSS1 axial data. The R-squared correlation coefficient for the HSS1 torsion data increased with an increase in probability of survival. 4.5 Fractography Visual macroscopic examination and scanning electron microscopy (SEM) were used to study the fractographic features of the fracture surface and subsurface failures for the three steels loaded in the axial direction. Figure 4-17(a) shows a surface failure specimen of the HSS1 steel under axial loading where the arrow points to a small region of pitting which was observed on the 54

71 surface of the gage section. The 18 µm long and 8 µm wide pitted region was found to have been associated with the fatigue initiation site. The arrow in Figure 4-17(b) points to a subsurface linear string of shallow porosity that was approximately 20 µm long in the HSS1A-03 subsurface failure specimen. The string was identified to have been associated with the fatigue initiation site. Figure 4-17(c) shows a subsurface (fish-eye) failure for the HSS1 material. A surface inclusion with major and minor elliptical dimensions of 10 µm and 7 µm, respectively, was found at the initiation site for the HSS1 axial surface failure seen in Figure 4-18(a). The propagation away from the inclusion is evident. A subsurface failure from a specimen at the same stress amplitude level is shown in Figure 4-18(b). The arrow in the figure points to a subsurface linear string of shallow porosity. Figure 4-18(b) indicates the same initiation pattern found in Figure 4-17(b). The variation in the initiation patterns provide a means for explaining the scatter and different failure types observed at the 1225 MPa stress level for the HSS1 steel. There was a factor of about 3.5 difference in the fatigue lives at this stress level. Figure 4-19(a) shows a highly magnified image reflecting an inclusion found at the initiation site of a HSS2 subsurface failure specimen. The major and minor elliptical dimensions were measured to be 34 µm and 28 µm, respectively. Figure 4-19(b) shows a similar inclusion for a HSS3 subsurface failure specimen. Figure 4-20 shows a SEM fractograph of a premature axial failure for the HSS1 steel. Figure 4-20(a) shows subsurface fracture origin near the center of the specimen. Figure 4-20(b) shows the subsurface fracture magnified. The circular subsurface fracture origin was identified to be approximately 1800 µm in diameter. Further magnification in 55

72 Figure 4-20(c) identified a small pore of approximately 5 µm in diameter at the center of the origin region. Hardness testing also revealed that the hardness was non-uniform throughout the specimen. The grip to gage transition section varied in hardness from 60 HRC on the surface to 50 HRC at the center of the cross-section of the specimen diameter. 56

73 Table 4.1 Summary of monotonic tensile test results. Specimen ID D original, mm D final, mm P max, kn S u, MPa %RA HSS1-23T HSS2-30T HSS3-33T

74 Table 4.2 Summary of fully-reversed (R = -1) axial fatigue test results for the HSS1 material. Specimen Surface Specimen Testing Load Stress Cycles Failure ID Finish Diameter Frequency Amplitude Amplitude to Failure Location Number Type (mm) (Hz) (kn) (MPa) (N f ) [a] [b] HSS1A-09 S ,710 Surface HSS1A-12 S ,267 Surface HSS1A-10 S ,480 Surface HSS1A-14 NS ,245 Surface HSS1A-17 NS ,053 Surface HSS1A-15 S ,849 Surface HSS1A-06 S ,251 Surface HSS1A-01 S ,950 Subsurface HSS1A-05 S Premature - HSS1A-13 NS Premature - HSS1A-08 S ,627 Surface HSS1A-16 S ,768 Subsurface HSS1A-07 S ,534 Subsurface HSS1A-02 S ,733 Unknown HSS1A-03 S ,075 Subsurface HSS1A-22 NS ,610 Subsurface HSS1A-04 S , ,158,912 Subsurface HSS1A-11 S ,311,054 Subsurface HSS1A-18 S ,533,123 Subsurface HSS1A-20 NS , ,298,238 Subsurface HSS1A-19 S ,320,716 Subsurface HSS1A-21 S ,185,370 Subsurface [a] S =Superfinished; NS = Non-superfinished [b] Premature is defined as fracture in the first load cycles before reaching the maximum load 58

75 Table 4.3 Summary of fully-reversed (R = -1) axial fatigue test results for the HSS2 material. Specimen Specimen Testing Load Stress Cycles Failure ID Diameter Frequency Amplitude Amplitude to Failure Location Number (mm) (Hz) (kn) (MPa) (N f ) HSS2A ,382 Surface HSS2A ,248 Surface HSS2A ,403 Subsurface HSS2A ,178 Surface HSS2A ,535 Subsurface HSS2A , ,329 Surface HSS2A , ,252,765 Surface HSS2A , 15, ,836,779 Subsurface HSS2A ,489 Surface HSS2A ,778 Surface HSS2A ,158 Surface HSS2A , 10, ,100 Surface HSS2A , 5, ,375 Surface HSS2A , ,870,027 Subsurface HSS2A ,271 Subsurface HSS2A ,271,286 Subsurface HSS2A , 20, ,872,201 Subsurface HSS2A , ,632,737 Subsurface HSS2A Premature [a] - HSS2A , 10, ,973,137 Subsurface HSS2A > 10,000,000 No Failure HSS2A > 10,000,000 No Failure HSS2A Premature [a] - [a] Premature is defined as fracture in the first load cycle before reaching the maximum load 59

76 Table 4.4 Summary of fully-reversed (R = -1) axial fatigue test results for the HSS3 material. Specimen Specimen Testing Load Stress Cycles Failure ID Diameter Frequency Amplitude Amplitude to Failure Location Number (mm) (Hz) (kn) (MPa) (N f ) HSS3A ,643 Surface HSS3A ,220 Subsurface HSS3A , ,199 Surface HSS3A Premature [a] - HSS3A ,572 Surface HSS3A ,754 Surface HSS3A ,290 Surface HSS3A , 10, 15, ,559,518 Subsurface HSS3A ,308 Surface HSS3A ,268 Surface HSS3A , ,178 Surface HSS3A , 10, 15, ,033,176 Subsurface HSS3A Premature [a] - HSS3A ,944 Surface HSS3A ,765 Surface HSS3A ,213 Surface HSS3A ,580,153 Surface HSS3A , ,594,064 Subsurface HSS3A Premature [a] - HSS3A Premature [a] - HSS3A ,733,461 Subsurface HSS3A ,010,685 Subsurface HSS3A ,292,241 Subsurface HSS3A > 10,000,000 No Failure [a] Premature is defined as fracture in the first load cycles before reaching the maximum load 60

77 Table 4.5 Summary of fully-reversed (R = -1) torsion fatigue test results for the HSS1 material. Specimen Surface Specimen Testing Torque Shear Cycles Failure ID Finish Diameter Frequency Amplitude Stress to Failure Location and Number Type (mm) (Hz) (N m) Amplitude (N f ) Orientation [a] (MPa) HSS1-16 S ,574 Surface (Spiral) HSS1-15 S ,986 Surface (Spiral) HSS1-04 S ,101 Surface (Spiral) HSS1-02 NS ,709 Surface (Spiral) HSS1-12 S ,033 Surface (Spiral) HSS1-06 S ,540 Surface (Spiral) HSS1-08 S ,959 Surface (Spiral) HSS1-13 S ,804 Surface (Spiral) HSS1-01 NS ,359 Surface (Spiral) HSS1-14 S ,464 Surface (Spiral) HSS1-10 S ,839 Surface (Spiral) HSS1-07 S ,754 Surface (Spiral) HSS1-11 NS ,875 Surface (Spiral) HSS1-09 S ,726 Surface (Spiral) HSS1-03 NS ,346 Surface (Spiral) HSS1-05 S ,640 Surface (Spiral) HSS1-17 NS ,548 Surface (Spiral) HSS1-20 S ,510 Surface (Spiral) HSS1-18 S ,221,573 Surface (Spiral) HSS1-19 S ,886,995 Surface (Spiral) [a] S = Superfinished; NS = Non-superfinished 61

78 Table 4.6 Summary of fully-reversed (R = -1) torsion fatigue test results for the HSS2 material. Specimen Specimen Testing Torque Shear Cycles Failure ID Diameter Frequency Amplitude Stress to Failure Location and Number (mm) (Hz) (N m) Amplitude (N f ) Orientation (MPa) HSS ,788 Surface (Spiral) HSS Premature [a] - HSS ,581 Surface (Spiral) HSS ,608 Surface (Spiral) HSS ,077 Surface (Spiral) HSS ,645 Surface (Spiral) HSS ,386 Surface (Spiral) HSS ,358 Surface (Spiral) HSS ,096 Surface (Spiral) HSS Premature [a] - HSS ,973 Surface (Spiral) HSS ,811 Surface (Spiral) HSS ,776 Surface (Spiral) HSS ,085 Surface (Spiral) HSS ,934 Surface (Spiral) HSS ,842 Surface (Spiral) HSS ,566 Surface (Spiral) HSS ,648 Surface (Spiral) HSS ,386 Surface (Spiral) HSS Premature [a] - HSS ,333 Surface (Spiral) HSS ,893 Surface (Spiral) HSS , > 540,010 Ungrip [b] HSS ,867 Surface (Spiral) HSS > 2,000,000 No Failure [c] HSS ,191 Surface (Spiral) [a] Premature is defined as fracture during gripping or ungripping of specimen prior to test [b] Test was stopped at cycle count and specimen fractured during ungripping process [c] Test reached runout level and specimen fractured during ungripping process 62

79 Table 4.7 Summary of fully-reversed (R = -1) torsion fatigue test results for the HSS3 material. Specimen Specimen Testing Torque Shear Cycles Failure ID Diameter Frequency Amplitude Stress to Failure Location and Number (mm) (Hz) (N m) Amplitude (N f ) Orientation (MPa) HSS ,965 Surface (Spiral) HSS ,361 Surface (Spiral) HSS ,663 Surface (Spiral) HSS ,222 Surface (Spiral) HSS ,818 Surface (Spiral) HSS ,563 Surface (Spiral) HSS ,865 Surface (Spiral) HSS ,859 Surface (Spiral) HSS ,180 Surface (Spiral) HSS ,894 Surface (Spiral) HSS ,131 Surface (Spiral) HSS ,191 Surface (Spiral) HSS ,277 Surface (Spiral) HSS ,199 Surface (Spiral) HSS ,217 Surface (Spiral) HSS ,354 Surface (Spiral) HSS ,793 Surface (Spiral) HSS ,139 Surface (Spiral) HSS , ,314 Surface (Spiral) HSS , > 1,000,000 No Failure HSS ,605 Surface (Spiral) HSS > 1,000,000 No Failure 63

80 Table 4.8 Summary of fully-reversed axial and torsion (R = -1) fatigue properties. Axial Fatigue Properties HSS1 HSS2 HSS3 Axial Fatigue Strength Coefficient, σ f 2501 MPa 2165 MPa 2177 MPa Axial Fatigue Coefficient at One Cycle, A 2401 MPa 2077 MPa 2085 MPa Axial Fatigue Strength Exponent, b Axial Fatigue Strength at 10 6 Cycles 1068 MPa 915 MPa 886 MPa Axial Fatigue Strength at 10 7 Cycles 933 MPa 798 MPa 768 MPa Torsion (Shear) Fatigue Properties HSS1 HSS2 HSS3 Shear Fatigue Strength Coefficient, τ f 2434 MPa 1914 MPa 2143 MPa Shear Fatigue Coefficient at One Cycle, A o 2299 MPa 1816 MPa 2021 MPa Shear Fatigue Strength Exponent, b o Shear Fatigue Strength at 10 6 Cycles 737 MPa 637 MPa 628 MPa Shear Fatigue Strength at 10 7 Cycles 610 MPa 535 MPa 517 MPa 64

81 Table 4.9 Summary of axial mean stress (R = -0.5) fatigue test results for the HSS2 and HSS3 materials. Specimen Specimen Testing Load Stress Mean Stress Cycles Failure ID Diameter Frequency Amplitude Amplitude Amplitude to Failure Location Number (mm) (Hz) (kn) (MPa) (MPa) (N f ) HSS2AM ,995 Surface HSS2AM ,055 Surface HSS2AM ,860 Surface HSS2AM ,811 Surface HSS3AM ,155 Surface HSS3AM ,333 Surface HSS3AM ,420 Surface HSS3AM , ,737 Subsurface HSS3AM , ,374 Surface HSS3AM > 427,904 Grip HSS3AM , ,573 Surface HSS3AM > 545,380 Grip 65

82 Table 4.10 Axial fatigue Anderson-Darling Statistic values for HSS1, HSS2, and HSS3. Material Stress Amplitude Number Anderson-Darling Statistic (MPa) of data Normal Lognormal Weibull HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS Table 4.11 Torsion fatigue Anderson-Darling Statistic values for HSS1, HSS2, and HSS3. Material Stress Amplitude Number Anderson-Darling Statistic (MPa) of data Normal Lognormal Weibull HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS HSS

83 Table 4.12 Projected axial fatigue lives of the HSS1, HSS2, and HSS3 steels at a given stress amplitude level for different probabilities of survival. Material Stress Amplitude Probability of Survival (Cycles) (MPa) 50% 75% 90% 95% HSS ,011 6,848 5,349 4,614 HSS ,590 7,865 4,249 2,940 HSS ,180 47,430 31,330 24,450 HSS , ,200 66,580 39,810 HSS ,240 11,360 4,208 2,322 HSS ,600 72,330 21,080 10,080 HSS ,600 24,760 6,046 2,600 HSS ,145,000 1,960, , ,200 HSS ,420 15,220 5,693 3,160 HSS ,200 21,070 4,271 1,643 HSS ,800 23,040 4,665 1,794 HSS ,300 13,570 1, HSS ,281,000 2,795,000 2,420,000 2,220,000 Table 4.13 Projected torsion fatigue lives of the HSS1, HSS2, and HSS3 steels at a given stress amplitude level for different probabilities of survival. Material Stress Amplitude Probability of Survival (Cycles) (MPa) 50% 75% 90% 95% HSS ,907 7,595 6,580 6,038 HSS ,770 19,140 17,040 15,900 HSS ,750 59,460 50,200 45,370 HSS , , , ,100 HSS ,830 32,320 27,400 24,820 HSS ,450 21,700 16,480 13,980 HSS ,150 15,370 6,625 4,004 HSS ,600 35,930 12,650 6,772 HSS ,170 9,949 6,426 4,947 HSS ,530 13,370 9,968 8,362 HSS ,330 66,410 56,590 51,420 HSS ,100 68,160 45,760 36,050 67

84 Stress (MPa) Stress (MPa) HSS1-23T Fracture Displacement (mm) (a) HSS2-30T HSS3-33T Fracture Displacement (mm) (b) Figure 4-1 Monotonic tensile stress-displacement curves showing ultimate tensile strength for (a) HSS1, and (b) HSS2 and HSS3. 68

85 Axial Stress Amplitude, /2 (MPa) Axial Stress Amplitude, /2 (MPa) Axial Stress Amplitude, /2 (MPa) Superfinished Surface Failure Superfinished Subsurface Failure Non-superfinished Surface Failure Non-superfinished Subsurface Failure Best Fit (No first 1300 MPa) Best Fit (Subsurface > 97,000) /2 = 2401(Nf) (2) (3) Cycles to Failure, N f (a) Surface Failure Subsurface Failure Best Fit (Runout Level and Failures less than 20,000 cycles not included) f '(N f ) b f ' = MPa b = (2) /2 = 2077 (Nf) Cycles to Failure, N f (b) Surface Failure Subsurface Failure Best Fit (Runout Level and Failures less than 25,000 cycles not included) f '(N f ) b f ' = MPa b = Figure 4-2 /2 = 2085 (Nf) Cycles to Failure, N f 69 (c) Fully-reversed (R = -1) axial fatigue stress-life plots with best fit lines for (a) HSS1, (b) HSS2, and (c) HSS3. f '(N f ) b f ' = MPa b =

86 Shear Stress Amplitude, /2 (MPa) Shear Stress Amplitude, /2 (MPa) Shear Stress Amplitude, /2 (MPa) 2000 Non-superfinished Failure Superfinished Failure Best Fit (2) (3) (2) /2 = 2299(Nf) Cycles to Failure, N f (a) Failure used in best fit Failure not used in best fit Best Fit (Runout Level not included) f '(N f ) b o f ' = MPa b o = /2 = 1816 (Nf) Cycles to Failure, N f (b) Failure Best Fit (Runout Levels Not Included) 800 (3) 700 f '(N f ) b o f ' = MPa b o = /2 = 2021 (Nf) Cycles to Failure, N f (c) Figure 4-3 Fully-reversed (R = -1) torsion fatigue stress-life plots with best fit lines for (a) HSS1, (b) HSS2, and (c) HSS3. 70 f '(N f ) b o f ' = MPa b o =

87 (a) (b) (c) Figure 4-4 Broken axial specimens (ordered by stress level and cycles to failure) for (a) HSS1, (b) HSS2, and (c) HSS3. 71

88 HSS1A-09 HSS1A-12 HSS1A-10 HSS1A-17 HSS1A-06 HSS1A-01 HSS1A-08 HSS1A-16 HSS1A-07 HSS1A-02 HSS1A-22 HSS1A-04 HSS1A-11 HSS1A-18 HSS1A-20 HSS1A-19 HSS1A-21 Figure 4-5 Surface and subsurface axial test specimen pictures of HSS1 ordered by stress level and cycles to failure (left to right and top to bottom). 72

89 HSS2A-23 HSS2A-22 HSS2A-21 HSS2A-14 HSS2A-17 HSS2A-16 HSS2A-19 HSS2A-13 HSS2A-05 HSS2A-01 HSS2A-06 HSS2A-12 HSS2A-04 HSS2A-15 HSS2A-20 HSS2A-11 HSS2A-08 HSS2A-10 HSS2A-03 Figure 4-6 Surface and subsurface axial test specimen pictures of HSS2 ordered by stress level and cycles to failure (left to right and top to bottom). 73

90 HSS3A-01 HSS3A-02 HSS3A-04 HSS3A-24 HSS3A-05 HSS3A-06 HSS3A-22 HSS3A-07 HSS3A-21 HSS3A-19 HSS3A-09 HSS3A-14 HSS3A-16 HSS3A-12 HSS3A-23 HSS3A-15 HSS3A-17 HSS3A-18 HSS3A-10 Figure 4-7 Surface and subsurface axial test specimen pictures of HSS3 ordered by stress level and cycles to failure (left to right and top to bottom). 74

91 (a) (b) (c) Figure 4-8 Broken HSS1 torsion specimens arranged by cycles to failure for shear stress amplitude level of (a) 1100 MPa, (b) 1000 and 950 MPa, (c) 900 MPa, (d) 825 MPa, (e) 750 and 700 MPa, and (f) spiral break pattern. (d) (e) (f) 75

92 (a) (b) (c) Figure 4-9 Broken HSS2 torsion specimens arranged by cycles to failure for shear stress amplitude level of (a) 900 and 850 MPa, (b) 800 MPa, (c) 775 MPa, (d) 700 MPa, (e) 650 and 625 MPa, and (f) spiral break pattern. (d) (e) (f) 76

93 (a) (b) (c) Figure 4-10 Broken HSS3 torsion specimens arranged by cycles to failure for shear stress amplitude level of (a) 900 MPa, (b) 850 MPa, (c) 800 MPa, (d) 750 MPa, (e) 700 and 650 MPa, and (f) spiral break pattern. (d) (e) (f) 77

94 Figure 4-11 HSS2 and HSS3 axial mean stress test specimens arranged by stress level and cycles to failure from left to right. 78

95 Median Life Surface Failure Subsurface Failure Broke in Grip Section HSS2 HSS3 HSS2 HSS3 = -1 = -0.5 R R Figure 4-12 Axial mean stress (R = -0.5) test results with superimposed fully-reversed axial fatigue test results for HSS2 and HSS3. Cycles to Failure, Nf 79

96 Probability of Failure (%) Probability of Failure (%) Probability of Failure (%) 99 AD = Life (Cycles) (a) AD = Life (Cycles) (b) AD = Life (Cycles) Figure 4-13 (c) Lognormal probability of failure versus axial fatigue life for (a) 1300 MPa stress amplitude and HSS1, (b) 850 MPa stress amplitude and HSS2, and (c) 1000 MPa stress amplitude and HSS3. 80

97 Probability of Failure (%) Probability of Failure (%) Probability of Failure (%) 99 AD = Life (Cycles) (a) 99 AD = Life (Cycles) (b) AD = Life (Cycles) (c) Figure 4-14 Lognormal probability of failure versus torsion fatigue life for (a) 1000 MPa stress amplitude and HSS1, (b) 775 MPa stress amplitude and HSS2, and (c) 800 MPa stress amplitude and HSS3. 81

98 Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) PWpyro53 Axial Survival 50% 75% 90% 95% Cycles to Failure (a) GM8 Axial Survival 50% 75% 90% 95% Cycles to Failure (b) GM4 Axial Survival 50% 75% 90% 95% Cycles to Failure (c) Figure 4-15 Stress amplitude versus cycles to failure at different probabilities of survival for the axial tested specimens of (a) HSS1, (b) HSS2, and (c) HSS3. 82

99 Stress Amplitude (MPa) Stress Amplitude (MPa) Stress Amplitude (MPa) PWpyro53 Torsion Survival 50% 75% 90% 95% Cycles to Failure (a) GM8 Torsion Survival 50% 75% Cycles to Failure (b) GM4 Torsion Survival 50% 75% 90% 95% Cycles to Failure (c) Figure 4-16 Stress amplitude versus cycles to failure at different probabilities of survival for the torsion tested specimens of (a) HSS1, (b) HSS2, and (c) HSS3. 83

100 (a) (b) (c) Figure 4-17 SEM fractographs for axial loading of (a) HSS1A-14 specimen with surface failure, (b) HSS1A-03 specimen with subsurface failure, and (c) HSS1 axial subsurface failure specimen. 84

101 (a) (b) Figure 4-18 SEM fractographs for axial loading of (a) HSS1A-08 specimen with surface failure, and (b) HSS1A-07 specimen with subsurface failure. 85

102 (a) (b) Figure 4-19 SEM fractographs for axial loading of (a) HSS2A-15 specimen with subsurface failure, and (b) HSS3A-09 specimen with subsurface failure. 86

103 (a) (b) (c) Figure 4-20 SEM fractograph of an axial premature failure specimen of HSS1 material showing (a) subsurface failure at low magnification, (b) subsurface failure at high magnification, and (c) small pore magnification. 87