具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子
DynamicStress Intensity Factors around Two Cracks near an Interface of Two Dissimilar EIastic Half-PIanes under In-plane Shear Impact Load
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摘要: 本文研究了两个异材半无限弹性平板的接合面附近存在与接合面平行的双裂纹、并承受剪切冲击时的瞬态应力.运用付里叶(Fourier)和拉普拉斯(Laplce)变换,将问题归结为求解二元积分方程.求解时将裂纹所在面上、下的位移差展成级数,并让其自动满足裂纹面外的位移差为零的条件,利用裂纹面上的边界条件和施密特(Schmidt)方法求解级数中的待定系数.在拉普拉斯像空间中,求得动应力强度因子,并将其数值地逆变换至物理空间中.本文对由陶瓷材料与钢板接合而成的复合材料进行了数值计算.Abstract: Transient stresses around two collinear cracks which lie in parallel with the interface of the two dissimilar half-planes are studied in this article.The surfaces of the cracks are sheared suddenly.Application of the Fourier and Laplace transforms technique reduces the problem to that of solving dual integrai equations.To solvethese,the differences of the crack surface displacements are expanded in a series of functions which are automatically zero outside of the cracks.The unknown coefficients accompanied in the series are determined by the Schmidt method.The stress intensity factors are defined in the Laplace transform domain and these are inverted numerically in the physical space.As an example,the dynamic stress intensity factors around two cracks in a ceramic and steel bonded composite are numerically.
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