Abstract A semi-analytical method is presented to investigate fracture behavior of a mode-I crack in a thin ductile plate. In the part of theoretical analysis, a total deformation theory of plasticity, in conjunction with a power law hardening stress-strain relation, is employed. Three-dimensional Maxwell stress functions, the minimum complementary potential energy principle and three dimensional J-integrals are used to obtain crack front stress fields. In the part of numerical analysis, three dimensional finite element simulations are carried out to obtain J-integrals, the out-of-plane constraint level and crack front stress fields. Comparison with numerical results of crack front stress fields shows the analytic solutions for crack front stress fields are valid. Numerical and analytic results show that the value of the opening stress ahead of the crack front deceases with increasing z (approaching the free surface) and lies between the corresponding plane strain and plane stress solutions.

中文翻译：

---

薄裂纹硬化板三维断裂分析

摘要 提出了一种研究延性薄板I型裂纹断裂行为的半解析方法。在理论分析部分，采用塑性全变形理论，结合幂律硬化应力应变关系。三维麦克斯韦应力函数、最小互补势能原理和三维J-积分用于获得裂纹前沿应力场。在数值分析部分，通过三维有限元模拟得到J积分、面外约束水平和裂纹前沿应力场。与裂纹前缘应力场的数值结果对比表明，裂纹前缘应力场的解析解是有效的。