Elastoplastic deformation of multilayered materials during thermal cycling

Analytical models are presented for the elastoplastic deformation of multilayered materials subjected to fluctuating temperatures. The layered structure comprises an elastic-perfectly plastic ductile material sandwiched between two elastic brittle materials. With creep, heat transfer, and edge effects excluded, closed-form solutions for different characteristic temperatures for thermal cycling are presented as a function of the layer geometries and the thermomechanical properties of the constituent phases. The evolution of curvature, the generation of thermal residual stresses within each layer, and the onset and spread of plasticity in the ductile layer are also examined. It is theoretically shown that reversals of curvature in the layered solid can occur during monotonic changes in temperature, even when the thermomechanical properties of the layer do not vary significantly with temperature. The predictions of the analytical model are seen to compare favorably with experimental observations of curvatures during thermal cycling in the limiting case of bilayer composite with Al–Al₂O₃ layers and Al–Si layers and in a Si–Al–SiO₂ trilayer system. Case studies of the effects of the relative variations in the geometry, elastic properties, and plastic response of the constituent phases on the overall deformation are examined for two practically significant layered systems: a Si–Al–SiO₂ layered solid with extensive applications in the electronics industry and a Cr₂O₃-coated steel with an interlayer of a Ni–Al alloy which is used in structural applications.