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Stress Intensity Factors and Possible Crack Propagation Mechanisms for a Crack Surface in a Polyethylene Tibia Component Subject to Rolling and Sliding Contact

구름마찰 접촉하중시 Polyethylene Tibia 표면균열의 응력확대계 수와 복합전파거동에 관한 연구

  • 김병수 (인제대학교 기계자동차공학부) ;
  • 문병영 (부산대학교 항공우주공학과)
  • Published : 2003.12.01

Abstract

Pitting wear is a dominant from of polyethylene surface damage in total knee replacements, and may originate from surface cracks that propagate under repeated tribological contact. In this study, stress intensity factors, K$\_$I/and $_{4}$, were calculated for a surface crack in a polyethylene-CoCr-bone system under the rolling and/or sliding contact pressures. Crack length and load location were considered in determination of probable crack propagation mechanisms and fracture modes. Positive K$\_$I/ values were obtained for shorter cracks in rolling contact and for all crack lengths when the sliding load was apart from the crack. $_{4}$ was the greatest when the load was directly adjacent to the crack (g/a=${\pm}$1). Sliding friction caused a substantial increase of both K$\_$I/$\^$max/ and $_{4}$$\^$max/. The effective Mode I stress intensity factors, K$\_$eff/, were the greatest at g/a=${\pm}$1, showing the significance of high shear stresses generated by loads adjacent to surface cracks. Such behavior of K$\_$eff/ suggests mechanisms for surface pitting by which surface cracks may propagate along their original plane under repeated rolling or sliding contact.

Keywords

Stress Intensity Factor;Surface Crack;Contact;Finite Element Analysis

References

  1. Bower, A. F., 1988, 'The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Crack,' ASME Journal of Tribology, Vol.110, pp.704-711 https://doi.org/10.1115/1.3261717
  2. Rimnac, C. M., Wright, T. M., and Klein, R. W., 1989, 'The Effect of Waveform on the Fatigue Crack Propagation Behavior of Ultra Molecular Weight Polyethylene,' Advances in Fracture Research, Proc. 7th International Conference on Fracture, pp.1305-1311
  3. Broek, D., 1986, 'Elementary Engineering Fracture Mechanics, 4th ed., Martinus Nijhoff, Dordrecht, Netherlands
  4. Kim, B.S., and Eberhardt, A. W., 1997, 'Linear and Nonlinear Extrapolation of Stress Intensities for Edhe Cracks in Mixed-Mode Loading,' Engineering Fracture Mechanics, Vol.57, No.4, pp.715-720 https://doi.org/10.1016/S0013-7944(97)00060-X
  5. Chan, S. K., Tube, I. S., and Wilson, W. K., 1970, 'On the Finite Element Method in Linear Fracture Mechanics,' Engineering Fracture Mechanics, Vol.1, pp.1-17
  6. Arnell, R. D., Davies, P. B., Halling, J., and Wholmes, T. L., 1991, Tribology: Principles and Design Applications, Springer-Verlag
  7. McKellop, H., Clarke, K. L., Markolf, X. X., Amstuts, H. C., 1978, 'Wear Characteristics of UHMW Polyethylene: A Method for Accurately Measuring Extremely Low Wear Rates,' Journal of Biomedical Materials Research, Vol.12, pp.895-927 https://doi.org/10.1002/jbm.820120611
  8. Banks-Sills, L., and Sherman, D., 1986, 'Comparison of Methods for Calculating Stress Intensity Factors with Quarter Point Elements,' International Journal of Fracture Mechanics, Vol.32, pp.127-140 https://doi.org/10.1007/BF00019788
  9. Balasubramian, V., Doehring, T. C., Rubash, H. E., and Shanbhag, A. S., 1996, 'Stress Analysis of the Ultra High Molecular Weight Polyethylene(UHMWPE) Tibial Linear,' Pittsburgh Orthopaedic Journal, Vol.7, pp.42-43
  10. Kim, B. S., and Kim, W. D., 2001, 'Mode I and Mode II Stress Intensity Factors for a Surface Cracked in TiN/Steel Under Hertzian Rolling Contact,' Transactions of Korean society of Mechanical Engineers(A), Vol.25, No.8, pp.1163-1172
  11. COSMOS/M Finite Element Analysis System: Version 1.75, 1995, User Guide, Vol.1
  12. Estupinan, J. A., Bartel, D. L., and Wright, T. M., 1998, 'Simulation of Surface Crack Propagation in UHMWPE,' Proc. 43rd Annual Meeting, Orthopaedic Research Society, p.70
  13. Keer, L. M., Bryant, M. D., and Haritos, G. K., 1982, 'Subsurface and Surface Cracking Due to Hertzian Contact,' ASME Journal of Lubrication Technology, Vol.104, pp.347-351 https://doi.org/10.1115/1.3253217
  14. Rose, R. M., Ries, M. D., Paul, I. L., Crugnola, A. M., and Ellis, E., 1984, 'On the True Wear Rate of Ultrahigh Molecular Weight Polyethylene in the Total Knee Prosthesis,' Journal of Biomedical Materials Research, Vol.18, pp.207-224 https://doi.org/10.1002/jbm.820180209
  15. Kaneta, M., Yatsuzuka, H., and Murakame, Y., 1985, 'Mechanism of Crack Growth in Lubricated Rolling/Sliding Contact,' ASLE Transactions, Vol.28, pp.407-414 https://doi.org/10.1080/05698198508981637
  16. Elbert, K. E., Wright, T. M., Rimnac, C. M., Klein, R. W., Ingraffea, A. R., Gunsallus. K., and Bartel, D. L., 1994, 'Fatigue Crack Propagation Behavior of Ultra High Molecular Weight Polyethylene Under Mixed Mode Conditions,' Journal of Biomedical Materials Research, Vol.28, pp.181-187 https://doi.org/10.1002/jbm.820280207
  17. Pruitt, L., Koo, J., Rimnac, C. M., Suresh, S., and Wright, T. M., 1995, 'Cyclic Compressive Loading Results in Fatigue Cracks in Ultra High Molecular Weight Polyethylene,' Journal of Orthopaedic Research, Vol.13, pp.143-146 https://doi.org/10.1002/jor.1100130121
  18. Natarajan, R. N., Schroeder, U., Andreacchi, T. P., and Wimmer, M., 1997, 'Effect of Cofficient of Friction on Shear Stress Distribution in a UHMWPE Component of a TKR,' ASME Bioengineering Conference Proceedings, Vol.35, pp.107-108
  19. Wimmer, M. A., and Andriacchi, T. P., 1997, 'Tractive Forces During Rolling Motion of the Knee: Implications for Wear in Thtal Knee Replacement,' Journal of Biomechanics, Vol.30, pp.131-137 https://doi.org/10.1016/S0021-9290(96)00112-1
  20. Rose, R. M., Crugnola, A. M., Ries, M., Cimino, W. R., Paul, I., and Radin, E. L., 1979, 'On the Origins of High in Vivo Wear Rates in Polyethylene Components of Total Joint Prostheses,' Clinical Orthopedics and Related Research, Vol.145, pp.277-286
  21. Wright, T. M., and Bartel, D. L., 1986, 'The Problem of Surface Damage in Polyethylene Total Knee Components,' Clinical Orthopaedics and Related Research, Vol.205, pp.67-74
  22. Walker, P. S., Blunn, G. W., and Lilley, P. A., 1996, 'Wear Testing of Materials and Surfaces for Total Knee Replacement,' Journal of Biomedical Materials Research, Vol.33, pp.159-175 https://doi.org/10.1002/(SICI)1097-4636(199623)33:3<159::AID-JBM6>3.0.CO;2-P
  23. Blunn, G. W., Walker, P. S,, Joshi, A., and Hardinge, K., 1991, 'The Dominance of Cyclic Sliding in Producing Wear in Total Knee Replacements,' Clinical Orthopaedics and Related Research, No.273, pp.253-260
  24. AAOS, 1996, 'Implant Wear: The Future of Total Joint Replacement,' Wright and Goodman, eds., Amer. Acad. Orth. Surg
  25. Hood, R. W., Wright, T. M., and Burstein, A. H., 1983, 'Retrieval Analysis of Total Knee Prostheses: a Method and Its Applications to 48 Condylar Prostheses,' Journal of Biomedical Materials Research, Vol.17, pp.829-842 https://doi.org/10.1002/jbm.820170510