High Cycle Fatigue: A Mechanics of Materials Perspective part 16 pdf

136 Introduction and Background and 0.11% carbon, normalized. While most of the materials show an increase of fatigue limit strength as a function of frequency, 0.86% carbon steel and, to a lesser extent Armco iron, show a maximum stress at a frequency of approximately 10 kHz. The early results of Jenkin [72] were obtained using a resonance technique on simply supported beams excited electromagnetically, but the specimen dimensions were much smaller than those used by Lomas et al., thereby producing a range of resonant frequencies that were much higher. Later, Jenkin and Lehmann [73] further extended the frequency range by using even smaller bend specimens excited pneumatically with pressure pulses. The first experiments of Jenkin [72] on copper, Armco iron and mild steel were able to easily cover a frequency range up to 1 kHz. Their results showed that “materials ( similar to those tested) gain slightly in their strength to resist fatigue as the speed goes up, but for most practical speeds the gain is insignificant.” Jenkin and Lehmann [73] achieved frequencies up to nearly 20 kHz and showed significant frequency effects. They question, however, their own mathematical analysis of the strains based on beam deflection (contributed by Prof. Love) and the purely elastic behavior of the materials which might affect the smaller bar (higher frequency) tests in a systematic manner. The results of the tests by Lomas et al. [71], shown in Figure 3.48, were obtained from resonance tests on cantilever beams of different dimensions in order to achieve a wide range of natural frequencies. Of note is the characteristic shape of the curves where the fatigue limit strength, corresponding to 10 8 cycles, increases with frequency up to a maximum and then decreases with further increase in frequency for almost all of the ferrous alloys tested. As pointed out by the authors, the grave difference in the results with those of Jenkin is that the peak is obtained at a very different frequency. In Figure 3.48, the peak is seen to occur in the 1–2 kHz regime compared to 10 kHz for Jenkin (Figure 3.47) for a similar class of alloys. While these results are cited sometimes as an example of frequency effects on the fatigue or endurance limit (see Collins [74] for example), it is this author’s opinion that aspects of the resonance methods used may be responsible for the apparent effects and discrepancies between investigators. Of greatest concern is that there exists a maximum value of fatigue limit strength with frequency among several different alloys, yet this maximum occurs near the same frequency for each of the alloys. Of unknown significance is that the data point at each frequency is obtained with a different size cantilever beam, but the same geometry beam is used for each of the materials at a given frequency. The observed behavior, however, is in contradiction with observed strain rate effects in many metallic materials [70] and the modeling of such effects where a monotonically increasing effect of strength with strain rate is the norm. ∗ While it is not the intent of this book to critique the referenced observations in detail, ∗ As pointed out earlier, strain rate effects in metals have been studied almost exclusively in the inelastic regime of material behavior and constitute the field of dynamic plasticity. Strain rate effects under nominally elastic conditions are widely considered to be nonexistent. Accelerated Test Techniques 137 12% Ni – 25% Cr 36% Ni – 12% Cr FREQUENCY-CYCLES PER SEC. ENDURANCE LIMT-TONS PER SQ. IN. AT 10 8 CYCLES En 56A En 8A En 3A En 30A, 30 tons per sq in 2.5% Cr-Mo-W-V, Heat treat B 2.5% Cr-Mo-W-V, Heat treat A 19 20 21 22 23 24 25 26 27 28 28 29 30 31 32 33 34 35 36 37 38 39 18 19 20 21 22 23 24 25 26 27 100 300 1,000 3,000 a b c Figure 3.48. Endurance stress as a function of frequency for several materials [71]. 138 Introduction and Background it is important to point out some of the potential problems that might be encountered when using resonance tests on simple structural components for obtaining fatigue limit strengths. Of the many concerns, hysteretic heating can lead to changes in behavior even though Morrissey and Nicholas [75] have shown that, in 20 kHz resonance tests on titanium, the effect of temperature rise when running tests without external cooling is negligible. Other issues that have to be considered in conducting resonance tests are the material damping, the structural damping from the experimental apparatus such as supports or grips, and the aerodynamic damping when conducting high frequency tests in air. Of prime concern is that the geometry of the specimen has to be different for each frequency tested in order to achieve different resonant frequencies. This can also raise potential issues regarding the effective stressed area or volume or the stress gradient in bending for different thickness specimens. It should also be noted that these types of tests are not pure resonance tests but, rather, are forced vibrations of lightly damped systems, conducted at or near the resonant frequencies of the test article. The analysis that leads to interpretation of the experimentally observed quantities such as peak displacements is quite complicated, and the ability to maintain the test at a resonant frequency under constant conditions is very difficult. The cited observations of Lomas et al. [71] and the comparisons of his data with similar data from Jenkin and Lehmann [73] serve to point out the need to carefully analyze and interpret experimental findings when using resonance techniques for determination of fatigue limit strengths. REFERENCES 1. Morgan, J.M. and Milligan, W.W., “A 1 kHz Servohydraulic Testing System”, High Cycle Fatigue of Structural Materials, W.O. Soboyejo, and T.S. Srivatsan, eds, The Minerals, Metals & Materials Society, 1997, pp. 305–312. 2. 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Gallagher, J.P. et al., “Improved High Cycle Fatigue Life Prediction”, Report # AFRL-ML- WP-TR-2001-4159, University of Dayton Research Institute, Dayton, OH, January, 2001 (on CD ROM). 24. Gallagher, J. et al., “Advanced High Cycle Fatigue (HCF) Life Assurance Methodologies”, Report # AFRL-ML-WP-TR-2005-4102, Air Force Research Laboratory, Wright-Patterson AFB, OH, July 2004. 25. Ruschau, J.J., Nicholas, T., and Thompson, S.R., “Influence of Foreign Object Damage (FOD) on Fatigue Life of Simulated Ti-6Al-4V Airfoils”, Int. Jour. Impact Engng, 25, 2001, pp. 233–250. 26. Bellows, R.S., Muju, S., and Nicholas, T., “Validation of the Step Test Method for Generating Haigh Diagrams for Ti-6Al-4V”, Int. J. Fatigue, 21, 1999, pp. 687–697. 27. Bathias, C., “Relation Between Endurance Limits and Thresholds in the Field of Gigacycle Fatigue”, Fatigue Crack Growth Thresholds, Endurance Limits, and Design, ASTM STP 1372, American Society for Testing and Materials, West Conshohocken, PA, 2000, pp. 135–154. 28. Bellows, R.S., Bain, K.R., and Sheldon, J.W., “Effect of Step Testing and Notches on the Endurance Limit of Ti-6Al-4V”, Mechanical Behavior of Advanced Materials, MD-Vol. 84, D.C. Davis et al., eds, ASME, New York, 1998, p. 27. 140 Introduction and Background 29. Morrissey, R.J., McDowell, D.L., and Nicholas, T., “Frequency and Stress Ratio Effects in High Cycle Fatigue of Ti-6Al-4V”, Int. J. Fatigue, 21, 1999, pp. 679–685. 30. Moshier, M.A., Hillberry, B.M., and Nicholas, T., “The Effect of Low-Cycle Fatigue Cracks and Loading History on the High Cycle Fatigue Threshold”, Fatigue and Fracture Mechanics: 31st Volume, ASTM STP 1389, G.R. Halford, and J.P. Gallagher, eds, American Society for Testing and Materials, West Conshohocken, PA, 2000, pp. 427–444. 31. Golden, P.J., Bartha, B.B., Grandt, A.F., Jr., and Nicholas, T., “Measurement of the Fatigue Crack Propagation Threshold of Fretting Cracks in Ti-6Al-4V”, Int. J. Fatigue, 26, 2004, pp. 281–288. 32. Caton, M.J., “Predicting Fatigue Properties of Cast Aluminum by Characterizing Small-Crack Propagation Behavior”, PhD Dissertation, University of Michigan, 2001. 33. Nicholas, T., “Step Loading for Very High Cycle Fatigue”, Fatigue Fract. Engng. Mater. Struct., 25, 2002, pp. 861–869. 34. Lin, S K., Lee, Y L., and Lu, M W., “Evaluation of the Staircase and the Accelerated Test Methods for Fatigue Limit Distributions”, Int. J. Fatigue, 23, 2001, pp. 75–83. 35. Dixon, W.J. and Mood, A.M., “A Method for Obtaining and Analyzing Sensitivity Data”, J. Amer. Stat. Assn., 43, 1948, pp. 109–126. 36. Finney, D.J., Probit Analysis, 3rd ed., Cambridge University Press, 1971. 37. Fisher, R.A., Statistical Methods for Research Workers, 14th Edition, Oliver and Boyd Ltd, Edinburgh, 1969. 38. A Guide for Fatigue Testing and the Statistical Analysis of Fatigue Data, ASTM STP 91-A, 2nd ed., American Society for Testing and Materials, 1963, pp. 12–13. 39. Braam, J.J. and van der Zwaag, S., “A Statistical Evaluation of the Staircase and the ArcSin √ P Methods for Determining the Fatigue Limit”, Journal of Testing and Evaluation, JTEVA, 26, 1998, pp. 125–131. 40. Davoli, P., Bernasconi, A., Filippini, M., Foletti, S., and Papadopoulos, I.V., “Independence of the Torsional Fatigue Limit Upon a Mean Shear Stress”, Int. J. Fatigue, 25, 2003, pp. 471–480. 41. Little, R.E. and Jebe, E.H., Statistical Design of Fatigue Experiments, Applied Science Pub- lishers, Essex, 1975. 42. Brownlee, K.A., Hodges, J.L. Jr., and Rosenblatt, M., “The Up-and-Down Method with Small Samples”, J. Amer. Stat. Assn., 48, 1953, pp. 262–277. 43. Dixon, W.J., “The Up-and-Down Method for Small Samples”, J. Amer. Stat. Assn., 60, 1965, pp. 967–978. 44. Efron, B. and Tibshirani, R.J., An Introduction to the Bootstrap, Chapman and Hall, New York, 1993. 45. Morrissey, R.J. and Nicholas, T., “Staircase Testing of Titanium in the Gigacycle Regime”, presented at 3rd International Conference on Very High Cycle Fatigue (VHCF-3), Ritsumeikan University, Shiga, Japan, 16–19 September 2004. 46. Pascual, and Meeker, “Estimating Fatigue Curves with the Random Fatigue-Limit Model”, Technometrics, 41, No. 4, with comments, November 1999, pp. 277–302. 47. MIL-HDBK-5G, Metallic Materials and Elements for Aerospace Vehicle Structures, 2,1 November 1994, pp. 9–100. 48. Berens, A.P. and Annis, C., “Characterizing Fatigue Limits for Haigh Diagrams”, Proceedings of the 5th National Turbine Engine High Cycle Fatigue Conference, Chandler, AZ, 7–9 March 2000 (see also [24 Appendix B]). 49. Meeker, W.Q. and Escobar, L.A., Statistical Methods for Reliability Data, John Wiley & Sons, New York, 1998. Accelerated Test Techniques 141 50. Annis, C. and Griffiths, J., “Staircase Testing and the Random Fatigue Limit”, Proceedings of the 6th National Turbine Engine High Cycle Fatigue Conference, Jacksonville, FL, 6–8 March 2001. 51. Smith, K.N., Watson, P., and Topper, T.H., “A Stress-Strain Function for the Fatigue of Metals”, Journal of Materials, JMLSA, 5, No. 4, December 1970, pp. 767–778. 52. Doner, M., Bain, K.R., and Adams, J.H., “Evaluation of Methods for the Treatment of Mean Stress Effects on Low-Cycle Fatigue,” Journal of Engineering for Power, 1981, pp. 1–9. 53. Loren, S., “Fatigue Limit Estimated using Finite Lives”, Fatigue Fract. Engng. Mater. Struct., 26, 2003, pp. 757–766. 54. ASTM E739-91, Standard Practice for Statistical Analysis of Linear or Linearized Stress-Life (S–N) and Strain-Life (e-N) Fatigue Data, 1998. 55. Beretta, S., Clericic, P., and Matteazzi, S., “The Effect of Sample Size on the Confidence of Endurance Fatigue Tests”, Fatigue Fract. Engng. Mater. Struct., 18, 1995, pp. 129–139. 56. Nelson, W., “Fitting of Fatigue Curves with Nonconstant Standard Deviation to Data with Run-outs”, Journal of Testing and Evaluation, JTEVA, 12, 1984, pp. 69–77. 57. Nelson, W., Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, John Wiley & Sons, New York, 1990. 58. Berens, A., University of Dayton Research Institute, 2004, private communication. 59. George, T.J., Seidt, J., Shen, M H. H., Nicholas, T., and Cross, C.J., “Development of a Novel Vibration-Based Fatigue Testing Methodology”, Int. J. Fatigue, 26, 2004, pp. 477–486. 60. Sendeckyj, G.P., Bibliography on the History of Fatigue, Air Force Research Laboratory, Materials Directorate 1997 (unpublished). 61. Bernhard, R.K., “Testing Materials in the Resonance Range”, Proc. ASTM, 41, 1941, pp. 747–757. 62. Nowack, H., “Fatigue Test Machines”, Fatigue Test Methodology, AGARD Lecture Series No. 118, North Atlantic Treaty Organization, October 1981, pp. 3-1–3-23. 63. Memmler, K. and Laute, K., “Dauerversuche an der Hochfrequenz-Zuf-Druck-Maschine, Bauert-Schenck [Fatigue tests with the Schenck high frequency tension-compression machine]”, Forschungsarbeiten a. d. Gebiete d. Ingenieur-wesens, No. 329, 1930, p. 32; Abstract: Z. Ver. dtsch. Ing, 8 February, 1930, 74, pp. 189–190; Z. Metallk., 1930 July, 22, pp. 249–250. 64. Herzog, A., “Six ton Schenck Fatigue Testing Machine”, Tech. Rep. U.S. Army Air Force, No. 5623, 15 August, 1947, p. 24. 65. Rawlins, R.E., “Fatigue Tests at Resonant Speed”, Metal Prog., 1947, 47, pp. 265–267. 66. Fehr, R.O. and Schabtach, C., “Resonant Vibration Testing”, Steel, 109, 1941, pp. 64–65, 96, 102. 67. Symposium on Large Fatigue Testing Machines and Their Results, ASTM STP 216, American Society for Testing and Materials, Philadelphia, 1958. 68. Fairbairn, W., “Experiments to Determine the Effect of Impact Vibratory and Long-Continued Changes of Load on Wrought-Iron Girders”, Phil. Trans. Roy. Soc., London, 154, 1864, pp. 311–326. 69. Morrissey, R.J., Golden, P., and Nicholas, T., “The Effect of Stress Transients on the HCF Endurance Limit”, Int. J. Fatigue, 25 , 2003, pp. 1125–1133. 70. Nicholas, T., “Material Behavior at High Strain Rates”, Impact Dynamics, Chapter 8, J. Zukas et al., eds, Wiley, New York, 1982, pp. 277–332. 71. Lomas, T.W., Ward, J.O., Rait, J.R., and Colbeck, E.W., “The Influence of Frequency of Vibration on the Endurance Limit of Ferrous Alloys at Speeds up to 150,000 Cycles per Minute Using a Pneumatic Resonance System”, Proceedings of the International Conference on Fatigue of Metals, Inst. Mech. Engrs, London, 1956, pp. 375–385. 142 Introduction and Background 72. Jenkin, C.F., “High Frequency Fatigue Tests”, Proc. Roy. Soc., A, 109, 1925, pp. 119–143. 73. Jenkin, C.F. and Lehmann, G.D., “High Frequency Fatigue”, Proc. Roy. Soc., A, 125, 1929, pp. 83–119. 74. Collins, J., Failure of Materials in Mechanical Design, John Wiley and Sons, New york, 1993, p. 224. 75. Morrissey, R.J. and Nicholas, T., “Fatigue Strength of Ti-6A1-4V at Very Long Lives,” Int. J. Fatigue, 27, 2005, pp. 1608–1612. Part Two Effects of Damage on HCF Properties The following four chapters deal with the general subject of the effects of damage on HCF material capability. While HCF alone is a subject that has been well covered in the literature, the effects of damage on the HCF properties of materials have received much less attention. Of concern in design is the effect of any potential damaging mechanism in the form of fatigue cracking, for example, on the fatigue limit strength (FLS) of a material. The terminology HCF implies a potentially very high number of cycles so that HCF capability is discussed here in terms of FLS corresponding to an endurance limit or a threshold for crack propagation when damage can be characterized in terms of an actual fatigue crack. Damage can be in the form of any loading or service event that degrades the properties of a material, whether it be in the form of fatigue cracks or deformation due to creep or corrosion. Chapter 4 starts with a discussion of the influence of LCF cycles on the HCF limit stress of a material. The LCF cycling is loosely categorized here as cycling at higher amplitudes than the HCF limit stress in an undamaged material. HCF cycles that have occasional transients above the FLS also constitute a combined loading spectrum that can be considered as LCF–HCF. The general condition of LCF superimposed with HCF is also considered to be a spectrum load condition where the HCF is subjected to periodic underloads (negative overloads). From both an experimental point of view and a service condition, the LCF loading can occur before any HCF loading or, in the more usual spectrum type loading, can be intermixed with the HCF loads. Causes of damage other than LCF, such as cracks forming at notches or stress concentrations, fretting fatigue that may produce cracks, or FOD, all produce similar conditions where HCF capability may be degraded. All of these subjects are discussed here in Part Two of this book. This page intentionally left blank Chapter 4 LCF–HCF Interactions 4.1. SMALL CRACKS AND THE KITAGAWA DIAGRAM Of primary concern in HCF design is the material capability after it has been subjected to service conditions that may degrade capability over time and cycles. LCF loading, while accounted for in design and not leading to failure during the design life, may degrade the capability of the material regarding its HCF resistance. One other form of potential damage, which is due to transient stresses above the fatigue limit during HCF loading, must also be considered. A practical problem arises when, in designing against HCF, the occurrence of stress transients above the FLS becomes a possibility. Both stress transients above the FLS and prior or combined loading, under conditions where part of the loading is above the HCF limit, constitute conditions that will be referred to as LCF–HCF loading. The LCF portion of the loading is designated as such irrespective of the frequency of loading and is not necessarily restricted to true LCF conditions that normally involve strain-control testing, a low number of cycles to failure, and inelastic deformation in a typical load-displacement loop. It is simply used to designate loading conditions that are different than the HCF conditions being evaluated. Research into the interactions of LCF with HCF thresholds has spanned the range from tests on smooth bars under LCF loading to the initiation of cracks under LCF, usually in a notched specimen, to determine the threshold for subsequent crack propagation in terms of a threshold stress intensity. In many of these studies, and to bridge the gap between no observable cracks and measurable cracks from prior LCF loading, the concept of a small crack arises. In work reviewed in [1], the threshold for continued fatigue after LCF loading involved analysis of many data points corresponding to crack depths below 100 m, with many of those below 50m, in a titanium alloy. These crack lengths tend towards the region that is commonly referred to as the small or short crack regime. In this regime, it is found that the threshold stress intensity for crack propagation is lower than the long crack threshold, and the behavior is termed “anomalous” by many researchers. An effective way of plotting threshold data for small cracks is to use the Kitagawa diagram [2] shown schematically in Figure 4.1, where stress at threshold is plotted against crack length. The diagram shows a region below the threshold stress intensity and the endurance limit stress, joined by a correction due to El Haddad et al. [3], where cracks 145 . 12–13. 39. Braam, J.J. and van der Zwaag, S., A Statistical Evaluation of the Staircase and the ArcSin √ P Methods for Determining the Fatigue Limit”, Journal of Testing and Evaluation, JTEVA, 26, 1998,. capability is discussed here in terms of FLS corresponding to an endurance limit or a threshold for crack propagation when damage can be characterized in terms of an actual fatigue crack. Damage. 1969. 12. Maennig, W W., “Planning and Evaluation of Fatigue Tests”, ASM Handbook, Volume 19, Fatigue and Fracture, ASM International, Materials Park, 1996, pp. 303–313. 13. Moore, H.F. and Wishart,