功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载的响应分析

在忽略界面裂尖端裂纹面相互叠入的条件下,对功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载响应问题进行了分析。利用傅立叶变换,将问题的求解转换为对以裂纹面上位移差为未知函数的对偶积分方程的求解。为了求解对偶积分方程,将裂纹面上的位移差函数展开为雅可毕多项式的级数形式。最终给出了裂纹长度、入射波频率和材料性质对应力强度的影响。结果表明,当界面材料不连续时,获得了具有普通1/2奇异性的近似解。

The Dynamic Behavior of an Interface Crack Between two Dissimilar Half-Planes of the Functionally Graded Materials and the Homogeneous Materials for the Opening Crack Mode

The dynamic behavior of an interface crack between two dissimilar half-planes of functionally graded materials(FGMs)and homogeneous materials subjected to harmonic dynamic loading is investigated by means of the Schmidt method under an assumption-the effect of the crack surface overlapping very near the crack tips is negligible.By use of the Fourier transform,the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces.To solve the dual integral equations,the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials.Numerical examples are provided to show the effects of the length of the crack,the circular frequency of incident waves and the material constants upon the stress intensity factors of the crack.It can be shown that the stress singularities of the approximate solution of the present paper are similar with the ones for the ordinary crack in bomogeneous materials.