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混合型裂纹断裂能(GF)是裂纹扩展的判据之一,是裂纹扩展方向分析的基础。以往平面问题断裂能J积分方法的研究只是局限于Ⅰ型或是Ⅱ型,裂纹方向为水平方向。推导了Ⅰ-Ⅱ混合型裂纹任意角度时线弹性材料J积分与应力强度因子(SIF)K之间的关系,提出将比例边界有限元法(SBFEM)用于J积分的求解。在数值计算中,通过用SBFEM、有限元法(FEM)和用推导公式计算J积分的对比,验证推导公式的正确性,同时也说明SBFEM计算J积分是精确的、方便的。根据数值计算的结果,对计算边界与裂纹的距离、计算单元的尺寸以及积分路径等诸因素对精度的影响进行一定分析。
Mixed crack fracture energy (GF) is one of the criteria for crack propagation and is the basis of crack propagation direction analysis. In the past, the study on the integral method of fracture energy in plane problem was only limited to type I or type II, and the crack direction was horizontal. The relationship between J integral and stress intensity factor (SIF) K of linear elastic material at any angle of I-Ⅱ mixed crack is deduced. Proportional boundary finite element method (SBFEM) is proposed to solve J integral. In the numerical calculation, the correctness of the derivation formula is verified by comparing the J integral calculated by SBFEM, FEM and the derivation formula, and also shows that the calculation of J integral by SBFEM is accurate and convenient. According to the result of numerical calculation, the influence of the factors such as the distance between the boundary and the crack, the size of the calculation unit and the integral path are analyzed.