Micromechanical Modeling of Functionally Graded Materials

Abstract

Thermoelastic response of graded composite material is examined for both uniform changes in temperature and steady-state heat conduction in the gradient direction. Detailed finite element studies of the overall response and local fields in the discrete models were conducted, using large plane-array domains with simulated skeletal and particulate microstructures. Homogenized layered models with the same composition gradient and effective properties, derived from the Mori-Tanaka and/or self-consistent methods, were analyzed under identical boundary conditions. Comparisons of temperature distributions and the overall and local fields predicted by the discrete and homogenized models were made using a C/SiC composite system with very different Young’s moduli of the phases, and relatively steep composition gradients. Close agreement with the discrete model predictions is observed for homogenized models which derive effective properties estimates from several averaging methods: In those parts of the graded microstructure which have a well-defined continuous matrix and discontinuous reinforcement, the effective moduli, expansion coefficients and heat conductivities are approximated by the Mori-Tanaka estimates. In skeletal microstructures that often form transition zones between clearly defined matrix and reinforcement phases, the effective properties are approximated by the self-consistent estimates. Subject to these selection rules, the averaging methods originally developed for statistically homogeneous aggregates under uniform overall fields may be applied to graded material subjected to nonuniform overall loads. A complete description of this investigation was presented by T. Reiter, G. J. Dvorak and V. Tvergaard, J. Mech. Phys. Solids, 45, 1281–1302, and in a forthcoming paper in the same volume. The results do not suggest that nonlocal or new micromechanical theories are needed for modeling functionally graded materials. Such theories appear appropriate only in those limited volumes of the material where the field averages are very small and their gradients very large.