Small and large deformation of thick and thin-film multi-layers: Effect of layer geometry, plasticity and compositional gradients

The thermomechanical response of multi-layered materials subjected to small and large deformation during temperature excursions is examined in this paper. General bilayer and trilayer plates with comparable layer thicknesses, as well as the limiting cases of thin films on thicker substrates with and without compositionally graded interfaces are examined, all within the context of the classical Kirchoff theory for thin plates. Closed-form analytical formulations for small elastic deformation are presented whereby explicit expressions for stress/curvature relations are obtained for any general bilayer or graded trilayer with isotropic elastic properties, but anisotropic strains. The effects of the variation of Poisson ratio through the thickness of layered and compositionally graded materials on the evolution of multiple curvatures are analyzed. New theoretical results are presented on the effects of layer geometry, plastic flow and compositional gradation on large deformation (small strains and small rotations) in bilayer and trilayer systems comprising thick or thin-film layers. It is shown that the small deformation theory predictions for the generalized plane strain slate provide an upper bound for curvature evolution among all the cases considered. By recourse to analytical methods and three-dimensional finite element modeling involving shell elements, particular attention is devoted to the occurrence of bifurcation in the solution for curvature evolution and the associated geometry changes in the thermoelastoplastic response of layered materials during thermal excursions. The model systems chosen for analyses include Ni-Al2O3 layers with a sharp or compositionally graded interfaces, Al/Si thin-film bilayers and a compositionally graded interlayer sandwiched between layers in In0.12Ga0.88As and GaAs for applications in microelectronics and optoelectronics, and a carbon/epoxy laminated composite.