基于小波内聚力模型的界面裂纹扩展
Interface crack growth based on wavelet cohesive zone model

利用区间B样条小波良好的局部化性能，将内聚力模型（CZM）引入小波有限元法（WFEM）数值分析中，以区间B样条小波尺度函数作为插值函数，构造小波内聚力界面单元，推导了小波内聚力界面单元刚度矩阵，基于虚拟裂纹闭合技术（VCCT）计算界面裂纹应变能释放率（SERR），采用β-Κ断裂准则，实现界面裂纹扩展准静态分析。将WFEM和传统有限元法（CFEM） 的SERR数值分析结果与理论解进行比较，结果表明：采用WFEM和CFEM计算的SERR分别为96.60 J/m2 和 101.43 J/m2，2种方法的SERR数值解与理论解相对误差分别为1.85%和3.06%，这明确表明WFEM在计算界面裂纹扩展方面能用较少单元和节点数获得较高的计算精度和效率。在此基础上，探讨了界面裂纹初始长度和双材料弹性模量比对界面裂纹扩展的影响，分析结果表明：界面裂纹尖端等效应力随界面裂纹初始长度的增加而增加；双材料弹性模量比相差越大，界面裂纹越易于扩展，且裂纹扩展长度也越大，因此可通过调节双材料弹性模量比来延缓界面裂纹扩展。 Cohesive zone model(CZM) was applied to numerical analysis of wavelet finite element method(WFEM) by using the excellent localization properties of interval B-spline wavelet, interface elements of wavelet cohesive zone were constructed by regarding interval B-spline wavelet scaling functions as the interpolation functions, stiffness matrix of interface elements of wavelet cohesive zone was derived, and strain energy release rate(SERR) of interface crack was calculated by using virtual crack closure technique(VCCT), and the quasi-static analysis of interface crack growth was achieved by taking β-Κ fracture criterion. The numerical analyzed results of SERR by WFEM and conventional finite element method(CFEM) were compared with theoretical results, and the results show that the SERR calculated by WFEM and CFEM are 96.60 J/m2 and 101.43 J/m2, respectively, and the relative errors of SERR between numerical and theoretical results of two method are 1.85% and 3.06%, respectively. It clearly indicates that WFEM can obtain higher accuracy and efficiency of calculating interface crack growth with less numbers of elements and nodes. On this basis, we studied the influence of initial interface crack length and bi-material elastic modulus ratio on interface crack growth. It is found that the equivalent stress at interface crack tip tends to increase with the increase of initial interface crack length. The difference of bi-material elastic modulus ratio is greater, interface crack is easier to expand, and the length of interface crack growth is also greater, therefore, interface crack growth can be slowed by adjusting bi-material elastic modulus ratio. 黑龙江省科技厅重大专项（GA13A402）；黑龙江省教育厅科技项目（12541091）