A theory for stress-driven interfacial damage upon cationic-selective oxidation of alloys

Imagine a void at an interface, separating an outwardly growing oxide and a substitutional solid solution of two metallic elements A and B. Assume the metal interface oxidizes, but the void-free surface does not. Interdiffusion inside the metal, and misfit dislocation activities at the oxidizing interface, both generate a stress-free strain rate field. The compositional and material constraints in the presence of a non-oxidizing void give rise to a multi-axial tensile stress field, while a viscoplastic strain field arises to relax stress. The tensile stress at the interface enforces a concave curvature near the void tip through the continuity condition of the chemical potential. Atoms interflow along the void surface under the combined action of curvature, stress and composition gradients. They enter the metal/oxide interface and flow under the action of local stress, curvature and composition fields. The void grows. The stress at the interface relaxes, and the interface recedes partially and non-uniformly. Interfacial voiding upon cationic-selective oxidation is a long-standing topic in the world of thermal barrier coating and interconnect systems. This paper develops governing equations, within the alloy, for stress generation upon composition evolution and induced plastic strain. Governing equations at the interface and the void surface are next formulated to describe a moving boundary problem that accounts for the simultaneous void extension and interface recession. These governing equations are boundary conditions for the bulk formulation.