On Deformation peculiarities of two thin strips with a microcrack at the Interface

Abstract

This study examines the problem of plane strain in a crack between two isotropic, linearly elastic layers, one of which is rigidly fixed. The Fourier integral transform method was applied, reducing the initial system of differential equations to a system of ordinary differential equations. A system of singular integral equations (SIE) was constructed to satisfy the boundary conditions of the problem. By discretizing this system, it was further reduced to a system of linear algebraic equations (SLAE). Analytical expressions were obtained for the crack opening and stress distribution along the interface, allowing the calculation of the energy release rate (ERR) at the crack tips. A numerical illustration of the results was conducted, including graphs of crack opening and stress dependence for various layer thicknesses and Young's moduli. Comparison between analytical and numerical solutions, obtained using the finite element method (FEM), showed good agreement for the case of a microcrack with variable characteristics of the thin coating and the lower layer. A significant influence of the coating thickness on the energy release rate was identified.