Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Higher Order Eigenfields in Mode II Cracks Under Elastic-Plastic Deformation

  • Insu Jeon (Department of Mechanical Engineering, KAIST Science Town) ;
  • Lee, Yongwoo (Department of Mechanical Engineering, KAIST Science Town) ;
  • Seyoung Im (Department of Mechanical Engineering, KAIST Science Town)
  • Published : 2003.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

The explicit formulation of the J-integral and the M-integral is constructed in terms of the stress intensity factor and the higher order stress coefficients for Mode II cracks under small or large scale yielding. Furthermore, the stress intensity factor and the higher order stress coefficients as well are computed with the aid of the two-state J- and the M-integral, which is found to be accurate and efficient. It is found that the contribution from the higher order singularities to the J-integral is closely related to the configuration of the plastic zone.

Keywords

References

  1. Betagon, C. abd Hancock, J. W., 1991, 'Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields,' ASME J. Appl. Mech., Vol. 58, pp. 104-110 https://doi.org/10.1115/1.2897135
  2. Bibly, B. A., Cardew, G. E., Goldthorpe, M. R. and Howard, I. C., 1986, 'A Finite Lement Investigation of the Effects of Specimen Geometry on the Fields of Stress and Strain at the Tips of Stationary Cracks,' Size Effects in Fracture I, pp. 37-46
  3. Chen, F. H. K. and Shield, R. T., 1977, 'Conservation Laws in Elasticity of the J-Integral Type,' Z. Angw. Math. Phys. (ZAMP), Vol. 28, pp. 1-22 https://doi.org/10.1007/BF01590704
  4. Chen, Y. H. and Hasebe, N., 1994a, 'Further Investigation of Comninou's EEF for an Interface Crack With Completely Closed Faces,' Int. J. Engng Sci., Vol. 32, pp. 1037-1046 https://doi.org/10.1016/0020-7225(94)90069-8
  5. Chen, Y. Z. and Hasebe, N., 1994b, 'Eigenfunction Expansion and Higher Order Weight Fuctions of Interface Cracks,' ASME J. Appl. Mech., Vol. 61, pp. 843-849 https://doi.org/10.1115/1.2901566
  6. Chen, Y. H. and Hasebe, N., 1997, 'Explicit Formulation of the J-Integral Considering Higher Order Singular Terms in Eigenfunction Expansion Forms. Part Ⅰ. Analysis Treatments,' Int. J. Fract., Vol. 85, pp. 11-34 https://doi.org/10.1023/A:1007486727751
  7. Cho, Y. J., Beom, H. G. and Earmme, Y. Y., 1994, 'Application of a Conservation Integral to an Interface Crack Interaction with Singularities,' Int. J. Fract., Vol. 65, pp. 63-73 https://doi.org/10.1007/BF00017143
  8. Choi, N. Y. and Earmme, Y. Y., 1992, 'Evaluation of Stress Intensity Factors in a Circular Arc-shaped Interfacial Crack using L-integral,' Mech. Materials, Vol. 14, pp. 141-153 https://doi.org/10.1016/0167-6636(92)90011-2
  9. Eshelby, J. D., 1956, 'The Continuum Theory of Lattice Defects,' Solid State Phisics, Vol. III, pp. 79-144
  10. Hui, C. Y. and Ruina, A., 1995, 'Why K ? High Order Singularities and Small Scale Yielding,' Int. J. Fract., Vol. 72, pp. 97-120 https://doi.org/10.1007/BF00042823
  11. Im, S. and Kim, K. S., 2000, 'An Application of Two-State M-Integral for Computing the Intensity of the Singular Near-Tip Field for a Generic Wedge,' J. Mech. Phys. Solids, Vol. 48, pp. 129-151 https://doi.org/10.1016/S0022-5096(99)00023-X
  12. Jeon, I., Cha, B. W. and Im, S., 1996, 'Edge Delamination in a Laminated Composite Strip Under Generalized Plane Deformations,' Int. J. Fract., Vol. 77, pp. 95-110 https://doi.org/10.1007/BF00037232
  13. Jeon, I. and Im, S., 2001, 'The Role of Higher Order Eigenfields in Elastic-Plastic Cracks,' J. Mech. and Phys. Solids, Vol. 49, pp. 2789-2819 https://doi.org/10.1016/S0022-5096(01)00097-7
  14. Kfouri, A. P., 1986, 'Some Evaluation of Elastic T- Term Using Eshelby's Method,' Int. J. Fract., Vol. 30, pp. 301-315 https://doi.org/10.1007/BF00019710
  15. Kim, Y. J. and Lee, H. Y., 'Decomposition of Interfacial Crack Driving Forces in Dissimilar Joints,' KSME Int. J., Vol. 14, pp. 30-38 https://doi.org/10.1007/BF03184768
  16. Knowles, J. K. and Sternberg, E., 1972, 'On a Class of Conservation Laws in a Linearized and Finite Elastostatics,' Arch. Rat. Mech. Anal., Vol. 44, pp. 187-211 https://doi.org/10.1007/BF00250778
  17. Li, F. Z., Shin, C. F. and Needleman, A., 1985, 'A Comparison of Methods for Calculating Energy Release Rates,' Engr. Fract. Mech., Vol. 21, pp. 401-421 https://doi.org/10.1016/0013-7944(85)90029-3
  18. P. G. and Drory, M. D., 1989, 'A Method for Calculating Stress Intensities in Bimaterial Fracture,' Int. J. Fract., Vol. 40, pp. 235-254 https://doi.org/10.1007/BF00963659
  19. McMeeking, R. M., 1977, 'Finite Deformation Analysis of Crack-Tip Opening in Elastic-Plastic Materials and Implications for Fracture,' J. Mech. and Phys. Solids, Vol. 25, pp. 357-381 https://doi.org/10.1016/0022-5096(77)90003-5
  20. Rice, J. R., 1968, 'A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,' ASME J. Appl. Mech., Vol. 35, pp. 379-386 https://doi.org/10.1115/1.3601206
  21. Timoshenko, S. P. and Goodier, J. N., 1987, 'Theory of Elasticity,' Mcgraw-Hill International Editions (3rd Edition)