两相材料倾斜裂纹的界面应力场

采用Muskhelishvili复变函数的方法，将两相材料倾斜裂纹问题归结以裂纹表面位错密度函数和未知量的Cauchy型奇异积分方程的求解。通过Cauchy型奇异积分的主部分析，得到倾斜裂纹接触界面时性态指数的特征方程，给出的数值结果可对奇异积分方程进行数值求解。根据两相材料倾斜裂纹在界面上产生的应力场与位错密度函数的关系，得到界面常规应力场及奇性应力场表达式。最后对两相材料的界面应力场进行了数值求解和分析，数值结果令人满意。

The Interface Stress Fields of Bimaterial Incline Crack

By using Muskhelishvili complex function methods, the problem of bimaterial incline crack was induced to the solving of Cauchy singular integral equations, in which the unknown functions are the dislocation density functions. The singular index characteristic equation was obtained through the principal value analysis and numerically solved. Thus the singular integral equations were solved numerically. The equations of the interface normal and singular stress fields were obtained according to the relations between the interface stress fields caused by the bimaterial incline crack and the dislocation density functions. Finally, the bimaterial interface stress fields were analyzed numerically and the solution is satisfactory.