基于SBFEM任意角度混合型裂纹断裂能计算的J积分方法研究

J integral method for calculation of fracture energy of mixed mode inclined cracks based on SBFEM

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。

The fracture energy of mixed mode cracks（GF） serves as one of the criterion for crack extension.The J integral is often used for the determination of the direction of crack propagation.Most of the previous studies on the calculation of fracture energy through J integral dealt either with the mode I crack or mode II crack only,and the crack is usually assumed to be in the horizontal direction,which causes some inconvenience in the numerical analysis.In this paper,the relationship between the value of J integral and the stress intensity factors（SIF） K for mixed mode inclinde cracks in the elastic material are determined.The scaled boundary finite element method（SBFEM） is put forward for the J integral calculation.Numerical examples are provided to verify the proposed formulae.Results are compared with those obtained by finite element method（FEM）.It is revealed that the SBFEM approach is effective and efficient,and higher accuracy can be achieved.In addition,factors that affect the accuracy of the results such as the selection of the size of outer boundary of the calculated domain,the size of the discretized element and the position of integral path are examined.