物理弱间断线上Ⅲ型斜交裂纹高阶渐近场

针对功能梯度材料层/均匀材料基体的物理弱间断线上斜交裂纹,通过分离变量和级数展开法构造位移函数,求得了裂纹尖端高阶渐近场。其界面裂纹尖端高阶渐近应力场具有与均匀材料相同的r-1/2的奇异性。由高阶项的表达式可知：材料非均匀性对应力场有显著影响。数学上,该解为此类问题的特征函数,能够描述此类材料各种含裂纹结构的整个应力场和位移场,当非均匀参数为零时,它可以退化到均匀材料反平面裂纹问题经典的W il-liam s解。

Higher Order Asymptotic Fields of Mode m Crack Oblique to the Physical Weak-discontinuous Line

Considering an arbitrarily oriented mode Ⅲ crack with its tip on the physical weak-discontinuous line between FGMs（functionally graded materials） layer and the matrix of homogeneous material,the crack tip higher order asymptotic fields are obtained by applying the separation variable method and asymptotic series expansion.The results show that the stress field is equipped with the same square root singularity as one of homogeneous materials.Moreover,the non-homogeneity has a great effect on the stress fields according to the expressions of higher order terms.Further,the solution is eigen-function of this kind of problems mathematically and can be used to describe the whole stress and displacement fields of any cracked structure of the materials.As non-homogeneous parameter is zero,it will become the same as the Williams′ solutions to the homogeneous materials.