Abstract：A numerical method is presented for obtaining the stress intensity factors of cracks terminating at a bimaterial interface based on extended finite element method (XFEM). A new 6-term crack tip displacement enrichment function is derived. Based on the analytical solution of the stress and displacement fields around the crack tip, the expression of the path independent integral Jkε and the stress intensity factors KⅠ and KⅡ, is established. The XFEM numerical solution is used to calculate the integral Jkε, and the stress intensity factors are obtained by using the above expression. Finally, the maximum circumferential stress criterion is used to request the crack propagation angle θp. Results of the numerical simulations show that propagation problems of vertical crack at the bimaterial interface can be solved efficiently by the combination of the integral Jkε method and the XFEM. The crack propagation angle θp is smaller when the crack propagates from a softer material into a harder material, but θp is larger when the crack propagates from a harder material into a softer material. In the case of the four-point bending test, the crack propagation angle θp is independent of the ratio of the Poisson's ratios (v1/v2) of materials on both sides of the interface, but θp and the logarithm of the ratio of elasticity modulus lg(E1/E2) meet an exponential relation.
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2014, Vol. 32 
