Elastoplastic deformation of multilayered materials during thermal cycling
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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 A1-A12O3 layers and Al-Si layers and in a Si-Al-SiO 2 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-SiCh 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.
I. INTRODUCTION Multilayered structures have a wide variety of applications in modern technology. Layers comprising metallic, ceramic, or polymeric materials are extensively used to achieve desirable functions in integrated circuits, semiconductor lasers, optical devices, and multichip modules for electronic packaging. Layered coatings of dissimilar solids are also widely used in engineering structural components with the objective of improving the mechanical, thermal, chemical, and tribological performance. In advanced structural materials such as fiber-reinforced composites, layers of coatings on the surface of reinforcing fibers are often used to enhance adherence, to serve as diffusion barriers, or to avoid degradation due to chemical reactions at the reinforcement-matrix interface. In any type of multilayered structures, the differences in the coefficients of thermal expansion (CTE) between dissimilar materials inevitably generate thermal residual stresses during temperature excursions. Control of the thermal stresses, the extent of elastoplastic deformation, and the accompanying changes in configuration (e.g., bending) are essential for ensuring the structural integrity of the layered component during manufacturing and in service.
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to whom correspondence should be addressed. J. Mater. Res., Vol. 10, No. 5, May 1995
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