Mode I and Mode II Stress Intensity Factors for a Surface Cracked in TiN/Steel Under Hertzian Rolling Contact

Hertzian 접촉하중시 TiN/Steel의 표면균열에 대한 모드 I과 모드 II 응력확대계수

  • Published : 2001.08.01


The two dimensional problem of a layered tribological system(TiN/Steel) containing a vertical surface breaking crack and subject to rolling contact is considered in this study. Using finite elements and stress extrapolation method, a series of preliminary models are developed. Preliminary results indicate that the extrapolation technique is valid to determine Modes I and II stress intensity factors for cracks. In the case of TiN/Steel medium, KI and KII were determined for variations in crack length, layer thickness, and load location. The results show that KII reaches maximum values when the contact is adjacent to the crack where Mode I stresses are compressive. KII values decrease with decreased crack length and significantly decrease for reduced layer thickness.


Stress Intensity Factor;Finite Element Analysis;Crack Propagation;Coating/Layer;Stress Method;Hertzian Contact


  1. Bhushan, B. and Gupta, B. K., 1991, Handbook of Tribology, McGraw-Hill, Inc.
  2. Tada, H., 1973, The Stress Analysis of Cracks Handbook, Del Research Corp., St. Louis
  3. Johnson, K. L., 1989 'Contact Mechanics,' Cambridge: University Press
  4. 김병수, 김위대, 부명환, 2000, '유한요소를 이용한 TiN/Steel 코팅재 표면균열의 파괴거동에 대한 해석,' 대한기계학회, 2000 부산지부 춘계학술대회 논문집, pp. 1-8
  5. Salehizadeh, H. and Saka, N., 1992, 'Crack Propagation in Rolling Line Contacts,' ASME Journal of Tribology, Vol. 114, pp. 690-697
  6. COSMOS/M Finite Element analysis System, 1995, Version 1.75, User Guide, 1, Structural Research and Analysis Corporation, Pittsburgh, PA.
  7. Kim, B. S. and Eberhardit, A. W., 'Linear and Nonlinear Extrapolation of Stress Intensities for Edge Cracks in Mixed-Node Loading,' Engineering Fracture Mechanics, V. 57, No. 4, pp. 715-720
  8. Chan, S. K., Tuba, I. S. and Wilson, W. K., 1970, 'On the Finite Element Method in Linear Fracture Mechanics,' Engineering Fracture Mechanics, Vol. 2, pp. 1-17
  9. Eberhardt, A. W. and Peri, S., 1995, 'Surface Cracks in Layered Hertzian Contact with Fraction,' Tribology Transactions, Vol. 38, pp. 299-304
  10. Kim, S. H., Keer, L. M. and Cheng, H. S., 1990, 'Loss of Adhesion of a Layer Bonded to an Elastic Half space Caused by a Concentrated Contact,' Tribology Transactions, Vol 33, pp. 53-59
  11. 이억섭, 김동준, 류황희, 1999, '혼합모드하주하에서의 피로균열전파방향과 피로수명 예측,' 대한기계학회논문집, 제23권, 제9호, pp. 1550-1558
  12. 김정규, 이종선, 김철수, 1999, '단일 및 혼합모드 하중하에서의 레일강의 파괴조건 및 피로균열진전거동,' 대한기계학회논문집, 제23권, 제6호, pp. 1039-1047
  13. Kaneta, M., Yatsuzuka, H. and Murakami, Y., 1985, 'Mechanism of Crack Growth on Lubricated Rolling/Sliding Contact,' ASLE Transactions., Vol. 28, pp. 407-414
  14. Bower, A. F., 1988, 'The Influence of Crack Face Friction and Tappered Fluid on Surface Initiated Rolling Contact Fatigue Cracks,' ASME Journal of Tribology, Vol. 110, pp. 704-711
  15. Kuo, C. H. and Keer, L. M., 1995, 'Three-Dimensional Analysis of Cracking in a Multilayered Composite,' ASME Journal of Applied mechanics., Vol. 62, pp. 273-281
  16. Hanson, M. T. and Keer, L. M., 1992, 'An Analytical Life Prediction Model for the Crack Propagation Occurring in Contact Fatigue Failure,' Tribology Transactions, Vol. 35, pp. 451-461
  17. Keer, L. M. and Bryant, M. D., 1983, 'A Pitting Model for Rolling Contact Fatigue,' Journal of Lubrication Technology, Vol. 105, pp. 198-205
  18. Keer, L.M., Bryant, M.D., and Haritos, G.K.,1982, 'Subsurface and Surface Cracking Due to Hertzian Contact,' Journal of Lubrication Technology, Vol. 104, pp. 347-351
  19. Rosenfield, A. R., 1980, 'A Fracture Mechanics Approach to Wear,' Wear, Vol. 61, pp. 125-132
  20. Shieh, W. T., 1977, 'Compressive Maximum Shear Crack Initiation and Propagation,' Engineering Fracture Mechanics, Vol. 9, pp. 37-54
  21. Komvopoulos, K., 1988, 'Finite Element analysis of a Layered Elastic Solid in Normal Contact With a Rgid Surface,' Journal of Tribology, Vol. 110, pp. 477-485
  22. Kramer, B. M., 1988, 'Predicting the Wear Resistance of Hard Coatings,' in Engineered Materials for Advanced Friction and Wear Applications, Schmidt, F. A. and Blau, P. J., eds., pp. 101-108
  23. Erdemir, A., 1992, 'Rolling-Contact Fatigue and Wear Resistance of Hard Coating on Bearing-Steel Substrates,' Surface and Coating Technology, Vol. 54, pp. 482-489
  24. Cheng, H. S., Chang, T. P. and Sproul, W. D., 1990, 'A Morphological Study of Contact Fatigue of TiN Coated Rollers,' in Mechanics of Coatings, Dowson, D., Taylor, C. M., and Goldet, M.(eds.)., pp. 81-88
  25. Erdemir, A., 1986, 'A Study of Surface Metallurgical Characteristics of TiN Coated Bearing Steels,; Ph. D. Dissertation, Georgia Institue of Technology, Atlanta, GA.
  26. Kastsov, K. B., Zhitomirskii, V. N., and Khrunik, R. A., 1986, 'Contact Fatigue of High-Speed Steel with Wear-Resistant Nitride Coatings in a Corrosive Medium,' Soviet materials Science (English Translation of Fiziko-Khimicheskaya Mekhanika Materialov) Vol. 22 No. 5 Sep-Oct, pp. 534-535
  27. Hochman, R. F., Erdemir, A., Dolan, F. J., and Thom, R. L., 1985, 'Rolling-contact Fatigue of Cu and TiN Coatings on Bearing Steel Substrates,' Journal of Vacuum Science, Vol. 3, pp. 2348-2353
  28. Chang, T. P., Cheng, H. S., Chiou, W. A., and Sproul, W. D., 1991, 'A Comparison of Fatigue Failure Morphology Between TiN Coated and Uncoated Lubricated Rollers,' Tribology Transaction, Vol. 34, pp. 408-416