Micromechanical models for graded composite materials : ii. thermomechanical loading

Abstract

Thermoelastic response of several discrete and homogenized models of unconstrained graded composite layers 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 are conducted, using large plane-array domains containing 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, are analyzed under identical boundary conditions. Comparisons of temperature distributions, and of overall and local stress and strain fields predicted by the discrete and homogenized models are made in the C\\SiC composite system, with very different phase properties and relatively steep composition gradient, that was used in the first part of this study (T. Reiter, G. J. Dvorak and V. Tvergaard, J. Mech. Phys. Solids, Vol. 45, pp. 1281–1302, 1997). Homogenized models of combined microstructures which employ only a single averaging method do not provide reliable agreements with the discrete model predictions. However, close agreement with the discrete models is shown by 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 appropriate 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. The results do not support the proposition that nonlocal or new micromechanical theories are required for modeling of graded microstructures.