Stress concentration in ultra-thin coating with undulated surface profile

Abstract

The uniaxial loading of an isotropic film-substrate system with a sinusoidal surface profile and planar interface is considered under plain strain conditions. We for- mulate the corresponding boundary value problem involving two-dimensional constitutive equations for bulk materials and one-dimensional equations for membrane-type surface and interface with the extra elastic constants as well as the residual surface stresses. The mixed boundary conditions consist of the generalized Young–Laplace equations and rela- tions describing the continuous of displacements across the surface and interphase regions. Using the linear perturbation technique combined with the Goursat–Kolosov complex po- tentials and the superposition principle, the original boundary value problem is reduced to the analytical solution of the integral equations system.