Transient dynamic stress intensity factors around two rectangular cracks in a nonhomogeneous interfacial layer between two dissimilar elastic half-spaces under impact load

Abstract

Transient dynamic stresses around two rectangular cracks in a nonhomogeneous interfacial layer sandwiched between two dissimilar elastic half-spaces are examined. The material properties vary continuously in the layer within a range from those of the upper half-space to those of the lower half-space. An incoming shock stress wave impinges perpendicular on the crack surfaces. In order to solve the problem, the interfacial layer is divided into several homogeneous layers that have different material properties. Application of Laplace and Fourier transforms reduces the problem to the solution of a pair of dual integral equations. To solve the equations, the differences in the crack surface displacements are expanded into a series of functions that vanish outside the crack. The unknown coefficients in the series are solved using the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted numerically in physical space. Numerical calculations are carried out for composite materials made of a ceramic half-space and a steel half-space.