Curvature of a Film-Substrate System in the Nonlinear Deformation Range

Abstract

The physical system considered is a thin film bonded to the surface of an initially flat circular substrate, in the case when a residual stress exists due to an incompatible mismatch strain in the film. The magnitude of the mismatch strain is often inferred from a measurement of the curvature it induces in the substrate. This discussion is focused on the limit of the linear range of the relationship between the mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch strain. Results are obtained on the basis of both simple models and more detailed finite element simulations. Preliminary full-field observations are reported on deformation of a 6 μm thick Al film deposited onto a 100 μm thick Si substrate subjected to thermal cycling.