Transient response of several cracks in a nonhomogeneous half-layer bonded to a magneto-electro-elastic coating

Abstract In this study, we examine the fracture analysis of a non-homogeneous half-layer reinforced by a magneto-electro-elastic (MEE) coating with multiple interface and embedded cracks in a non-homogeneous substrate under impact loadings. Material properties of the functionally graded (FG) orthotropic substrate are assumed to vary exponentially in the thickness direction of the half-layer. First, the analytical solution is developed by considering a dynamic mechanical dislocation with time-dependent Burgers vector be situated at the substrate and interface by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the medium containing embedded and interface cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the dynamic stress intensity factors (DSIFs). The effects of crack spacing, the length and position of the cracks and FGM exponent as well as crack interaction are studied.