Analytical modeling of edge effects on the residual stresses within the film/substrate systems. Ⅱ. Normal stresses

摘要

For the film/substrate bimaterial system, some considerable efforts have been made to predict the stress distribution in the film. However, only the normal stress in the film at the position away from the edge is usually considered. Moreover, the stress gradient through the thickness in the film and the stress in the substrate are often ignored. In this paper, an analytical model is developed to analyze the edge effects on the stress gradients in the film and the substrate. In order to obtain the closed-form solutions for the stresses in the film and the substrate, the shear lag model in the planar geometry is used to solve the stress transfer problem. By comparing the results from the present model with those from the existing analytical models, finite element analysis, and the experimental measurements, it can be concluded that the present analytical model is very rigorous.