Stress and shape evolution of irregularities in oxide films on elastic–plastic substrates due to thermal cycling and film growth

Abstract

Initial geometric imperfections in oxide films on elastic–plastic substrates often develop local shape irregularities upon thermal cycling, even though the same system shows no such shape change under similar constant temperature exposure. This paper outlines a mechanics-based explanation of the evolution of such irregularities during thermal cycling, based on reversed plasticity in the material surrounding the irregularity and stress-dependent oxide film growth. Idealized models consisting of spherical or cylindrical elastic shells embedded in an elastic–plastic matrix are used to identify regimes where thermal strains, cyclic reversed plasticity, geometry and oxide growth combine to promote rapid evolution of irregularities. The entirely closed-form solutions for stress and displacements during temperature cycling allow for quick evaluation of the role of various parameters, including: the temperature amplitude, size of the irregularity, oxide thickness, yield stress of the substrate and stress-dependent oxide growth strains. The usefulness of the solutions is illustrated by comparing two oxide film-growth scenarios with preliminary experimental results on a representative thermal barrier system that exhibits significant feature growth. The comparison demonstrates that oxide growth enhanced by tensile stresses created during reversed plastic deformation may be a significant factor in accounting for the large geometry changes observed in experiments.