A multilayer film coating with slightly curved boundary

Surface irregularity is often a source of stress concentrations. They can be reduced by proper matching of dissimilar surface layers. In this connection, a 2-D model of an isotropic multilayer film-substrate composite with rough surface is considered, in order to examine an influence of physical and geometrical properties of the components on the stress state of a boundary. Using the complex variable representations and boundary perturbation technique, the problem is reduced to the set of Fredholm integral equations of the second kind for an arbitrary shape of the boundary. The solution is given in terms of Fourier series for the periodic shape. In the case of a bilayer film coating, numerical results obtained with the use of the first-order approximation demonstrate effects of the boundary shape, thickness and elastic properties of the layers and the substrate on the stress state of a rough surface.