基于扩展有限元法，提出了双材料界面上垂向裂纹应力强度因子的计算方案。导出由6 项组成的新型裂纹尖端位移增强函数，基于裂尖应力场和位移场的解析解，建立路径无关Jkε积分与应力强度因子KⅠKⅡ的关系式，利用扩展有限元法计算Jkε积分，通过上述关系式求得应力强度因子，用最大周向应力准则确定裂纹扩展角θp。数值计算表明，Jkε积分与XFEM 结合可有效解决垂直于双材料界面的裂纹扩展问题；当裂纹由弹模较小材料朝着弹模较大材料扩展时，裂纹扩展角θp较小，而由弹模较大材料朝着弹模较小材料扩展时，θp较大；4 点弯曲试验结果表明，裂纹扩展角θp与界面两侧材料的泊松比比值v1/v2无关，而与弹性模量比值的对数lg（E1/E2）成指数关系。
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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