弹塑性双材料界面裂纹的渐近分析

ASYMPTOTIC FIELDS FOR INTERFACE CRACK IN ELASTIC-PLASTIC MATERIALS

本文通过精确的数学分析,对于遵循塑性形变理论的幂硬化材料界面裂纹,求得了裂纹面面力自由和裂纹面无摩擦接触两种情况下的分离变量形式的全连续HRR 型奇性渐近解,这种全连续的奇性渐近解只对特殊的混合参数M'才存在.对任意指定的混合参数M',我们进一步求得了含弱间断的分离变量形式的HRR 型奇性渐近解(?)我们得到的所有解均保证了界面处的面力连续条件和位移连续条件,且不出现弹性双材料界面裂纹问题中所常见的应力振荡奇性和裂纹面相互嵌入的不合理现象.

Exact mathematical analyses are presented for interface crack between dissimilar elastic-plastic ma-terials.The deformation theory of plasticity is used.For two kinds of boundary conditions on crack faces:(1)traction free and(2)frictionless contact,the asymptotic separable solutions of the HRR typewith full continuity are obtained,which exist only for special mixity parameter M^(?).For any assignedM^(?),the separable solutions of the HRR type which contained weak discontinued line are further ob-tained.All of our results not only satisfy the continuity of displacements and the continuity of tractionson the interface,but also are free of oscillatory singularity and interpenetration of crack faces.