含裂纹复合材料板J积分的复变函数方法

Complex Function Method On J-integral of Mixed Mode Crack-Tip for Anisotropic Fiber Composite Plate

采用复变函数方法讨论了无限大各向异性纤维复合材料单层板I+II混合型裂纹尖端的J-积分。在给出各向异性复合材料单层板J-积分对坐标的曲线积分表示式基础上,通过将裂纹尖端的应力和位移代入该表示式得到了J-积分的复形式———复变函数积分的实部,根据柯西—古萨基本定理证明了该J-积分的路径无关性,借助柯西积分公式推出了该J-积分的理论计算公式。

By using a complex function method in this paper, the complex form of mixed mode crack tip J-integral for linear elastic anisotropic fiber composite plate is divied. The path-independent of this J-integral is proved. The concrete computing formula of this J-integral is obtained. The results derived in this paper are important in fracture analysis.