各向同性与各向异性三相材料接头应力奇异性研究

Study of stress singularities of three-material junctions formed from isotropic and anisotropic wedges

研究了各向同性与各向异性三相材料接头的应力奇性指数,通过引入奇异点附近区域位移场渐近展开的典型项,将各向同性与各向异性组合材料接头的控制方程和径向边界条件转化为变系数常微分方程的特征值问题;再利用插值矩阵法求解所建立的特征方程,得到接头端部的应力奇性指数和特征角函数。对由两个各向异性材料和一个各向同性材料以任意楔形角组成的三相接头结构的奇异性进行了研究,并比较了它们的应力奇性指数。计算结果表明:对于粘结接头,各向同性材料刚度越大应力奇异性越强;对于剥离接头,各向同性材料楔形角或材料刚度越大,第一阶应力奇异性越弱。计算结果与已有文献的结果对比吻合良好,证明了本文方法的有效性。

In this paper,the stress singularity order for three-material junctions formed from isotropic and anisotropic wedges are investigated.By introducing the typical terms in the asymptotic expansions of the displacement field near the singular point,the governing equations and radial boundary conditions of three-material junctions are transformed into the characteristic ordinary differential equations with varying coefficients.The singularity order and characteristic angular function of the junction are yielded by applying the interpolating matrix method to solve the established characteristic equations.Consequently,the singularities for the junctions in three-phase structure formed from two anisotropic wedges and one isotropic intermediate wedge with arbitrary angles are evaluated and their singularity orders are compared.In general,it can be seen that harder intermediate material induces stronger singularity with regard to bonded junctions,and that the first stress singularity order becomes weaker as isotropic intermediate wedge angle is larger or isotropic intermediate material is stiffer with regard to disbonded junctions.Simultaneously,the validity of the present method is confirmed by comparing with the existed results in the numerical examinations.