Abstract
Using Beom and Atluri's complete eigen-function solutions for stresses and displacements near the tip of an interfacial crack between dissimilar anisotropic media, a hybrid crack tip finite-element is developed. This element, as well as a mutual integral method are used to determine the stress intensity factors for an interfacial crack between dissimilar anisotropic media. The hybrid element has, for its Galerkin basis functions, the eigen-function solutions for stresses and displacements embedded within it. The “mutual integral” approach is based on the application of the path-independent J integral to a linear combination of two solutions: one, the problem to be solved, and the second, an “auxiliary” solution with a known singular solution. A comparison with exact solutions is made to determine the accuracy and efficiency of both the methods in various mixed mode interfacial crack problems. The size of the hybrid element was found to have very little effect on the accuracy of the solution: an acceptable numerical solution can be obtained with a very coarse mesh by using a larger hybrid element. An equivalent domain integral method is used in the application of the “mutual” integral instead of the line integral method. It is shown that the calculated mutual integral is domain independent. Therefore, the mutual integral can be evaluated far away from the crack-tip where the finite element solution is more accurate. In addition, numerical examples are given to determine the stress intensity factors for a delamination crack in composite lap joints and at plate-stiffener interfaces.
Similar content being viewed by others
References
Atluri, S. N.; Nakagaki, M. 1975: Analysis of two-dimensional fracture problems involving large-scale yielding: A displacement-hybrid finite element method. Proc. 12th Annual Meeting Soc. of Engng. Science, Austin, Texas. pp. 381–386
Atluri, S. N.; Kobayashi, A. S.; Nakagaki, M. 1975: An assumed displacement hybrid finite element model for linear fracture mechanics. Int. J. of Fracture. 11: 257–271
Beom, H. G.; Atluri, S. N. 1994: Near-tip fields and stress intensity factors for interfacial cracks in dissimilar anisotropic media. Center for Computational Mechanics, Georgia Institute of Technology, March 1994
Brezzi, F. 1974. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO 8 (R2): 129–151
Chen, F. H. K.; Shield, R. T. 1977: Conservation laws in elasticity of j-integral type. ZAMP J. Appl. Math. Phys. 28: 1–22
Cho, Y. J.; Beom, H. G.; Earmme, Y. Y. 1994: Application of a conservation integral to an interface crack interaction with singularities. Int. J. Fracture 65: 63–73
Kathireson, K.; Atluri, S. N. 1978: Homogeneous and bimaterial crack elements for analysis of solid rocket motor grains. Vol 1 AFRPL-TR-78-286, pp. 200, Edwards Airforce Base, CA.
Knowles, J. K.; Sternberg, E. 1972: On a class of conservation laws in linearized and finite elastostatics. Arch. Ration. Mech. Analysis. 44: 187–211
Li, F. Z.; Shih, C. F.; Needleman, A. 1985: A comparison of methods for calculating energy release rates. Engng. Fracture Mech. 21: 495–421
Lin, K. Y.; Mar, J. W. 1976: Finite element analysis of stress intensity factors for cracks at a bi-material interface. Int. J. Fracture. 12: 521–531
Nikishkov, G. P.; Atluri, S. N. 1987: An equivalent domain integral method for computing crack-tip integral parameters in non-elastic, thermo-mechanical fracture. Engng. Fract. Mech. 26: 851–867
Qu, J.; Bassani, J. L. 1993: Interfacial fracture mechanics for anisotropic bimaterials. J. Appl. Mech. 60: 422–431
Qu, J.; Li, Q. 1991: Interfacial dislocation and its application to interface cracks in anisotropic bimaterials. J. Elasticity 26: 169–195
Rice, J. R. 1968: A path-independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35: 379–386
Rice, J. R.; Sih, G. C. 1965: Plane problems of cracks in dissimilar media. J. Appl. Mech. 32: 403–410
Rice, J. R. 1968: Elastic fracture mechanics concepts for interfacial cracks. J. Appl. Mech. 55: 98–103
Rubinstein, R., Punch, E. F.; Atluri, S. N. 1983: an analysis of, and remedies for, kinematic modes in hybrid-stress finite elements: selection of stable, invariant stress fields. Comp Meth. in Appl. Mech. and Engng. 38: 63–92
Tong, P., Pian, T. H. H.; Lasry, S. 1973: A hybrid-element approach to crack problems in plane elasticity. Int. J. Num. Meth. Engng. 7: 297–308
Williams, M. L. 1959: The stresses around a fault or crack in dissimilar media. Bull. Seismol. Soc. America 49: 199–204
Wu, K. C. 1989: Representations of stress intensity factors by path-independent integrals, J. Appl. Mech. 56: 780–785
Wu, K. C. 1990: Stress intensity factor and energy release rate for interfacial cracks between dissimilar anisotropic materials. J. Appl. Mech. 57: 882–886
Yeh, C. S.; Shu, Y. C.; Wu, K. C. 1993: Conservation laws in anisotropic elasticity I. Basic frame work. Proc. R. Soc. Lond. A433: 139–151
Author information
Authors and Affiliations
Additional information
Communicated by S. N. Atluri, 2 may, 1994
This work was supported by a grant from the NASA Langley Research Center.
Rights and permissions
About this article
Cite this article
Chow, W.T., Beom, H.G. & Atluri, S.N. Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media, using a hybrid element method and the mutual integral. Computational Mechanics 15, 546–557 (1995). https://doi.org/10.1007/BF00350267
Issue Date:
DOI: https://doi.org/10.1007/BF00350267