Analytical modeling of edge effects on the residual stresses within the film/substrate systems. Ⅰ. Interfacial stresses

摘要

Several analytical models have been developed to derive the closed-form solutions for the residual stresses at the interface when a film was overlaid on a substrate. In these models, the film edge effects on the interfacial stresses were analyzed. However, some of the existing models do not yield good results, and sometimes, they err in a fundamental manner in the prediction of the interfacial stress distribution. In this paper, an analytical model is developed to derive the closed-form solutions for the interfacial stress distributions along the film width. Compared to the existing analytical models, the present model is more rigorous and the analytical results agree better with the finite element results.