Abstract
Residual stresses in elastic multi-layer film/elastic substrate systems were derived in closed-form solutions. There are always three unknowns to be solved and three equilibrium conditions to be satisfied. The special case of an elastic single nano-film deposited on an elastic substrate was demonstrated to analyze the viscoelastic stress relaxation. Two models of Maxwell and Kelvin were described the viscoelastic body. Two cases of viscoelastic film/elastic substrate and elastic film/viscoelastic substrate are considered. The stress in the elastic body in the space coordinates has the same form as the stress in the viscoelastic body in the Laplace transform coordinates. According to this analogy, we solve the residual stress in nano-film/substrate system. For the case of viscous flow in the film, both models show that the stress relaxation rate increases with decreasing film thickness. However, both models for the case of viscous flow in the substrate exhibit the opposite trend to those for the case of viscous flow in the film. The Maxwell model has full stress relaxation, but the Kelvin has not.
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