Dynamic stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar elastic half-planes subject to an impact load

Some composite materials are constructed of two dissimilar half-planes bonded by a nonhomogeneous elastic layer. In the present study, a crack is situated at the interface between the upper half-plane and the bonding layer of such a material, and another crack is located at the interface between the lower half-plane and the bonding layer. The material properties of the bonding layer vary continuously from those of the lower half-plane to those of the upper half-plane. Incoming shock stress waves impinge upon the two interface cracks normal to their surfaces. Fourier transformations were used to reduce the boundary conditions for the cracks to two pairs of dual integral equations in the Laplace domain. To solve these equations, the differences in the crack surface displacements were expanded in a series of functions that are zero-valued outside the cracks. The unknown coefficients in the series were solved using the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors were defined in the Laplace domain and were inverted numerically to physical space. Dynamic stress intensity factors were calculated numerically for selected crack configurations.