Ratcheting-induced wrinkling of an elastic film on a metal layer under cyclic temperatures

Abstract

This paper develops a theoretical model for wrinkling of an elastic film on an elastic–plastic metal layer caused by cyclic temperatures. The film is compressively strained and bonded to the metal layer, which in turn lies on a thick substrate. The thermal expansion mismatch between the metal and the substrate induces a biaxial stress, which is assumed to be large enough to cause the metal to deform plastically during each cycle. Wrinkling of the film induces normal and shear tractions at the film–metal interface, which bias the plastic flow of the metal. Consequently, the metal ratchets, namely, accumulates plastic deformation in the same directions as the temperature cycles. Concomitantly, the wrinkle of the film grows. The model reveals an analogy between ratcheting and creep. Analytical solutions are obtained for linear perturbation analysis and equilibrium states. Numerical simulations show evolution of wrinkles under various conditions and the effect of elastic constraint.