Abstract
An analytical model is developed to analyze the effects of viscous flow on residual stresses in film/substrate systems. This is achieved by utilizing the analogy between the governing field equation of elasticity and the Laplace transform with respect to time of the viscoelastic field equation. While viscous flow can occur in either the film or the substrate, analyses of how viscous flow in the substrate relaxes residual stresses in the film have not been performed. Also, the film thickness is often ignored in analyzing stress relaxation due to viscous flow in the film. The above two issues are studied in the present analysis. For the case of viscous flow in the film, the stress relaxation rate decreases with increasing film thickness. Conversely, for the case of viscous flow in the substrate, the stress relaxation rate increases with increasing film thickness. Compared to viscous flow in the film, viscous flow in the substrate results in slower stress relaxation in the system.
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