Micromechanical modelling of functionally graded materials

Abstract

The problems in design of functionally graded materials (FGMs) are outlined and their modelling approaches are reviewed. Due to the concentrational or structural gradients in FGMs, the “normal” approximations and models, used for traditional composites, are not directly applicable to graded materials. The goal is to show the efficiency of the simplest models to provide the most accurate estimates of the properties and even to make simple elasto-plastic analysis of FGM components without vast computations by FEMs or an array of empirical fitting parameters. The development of a micromechanical model for FGMs with an arbitrary non-linear 3D-distribution of phases and corresponding properties is presented and the model application is discussed in comparison with other similar approaches. The model allows the prediction of basic properties of a 3-D FGM, computations of thermal stresses, and, in some limits, it may be used for pre-design evaluation of dynamic strain/stress distribution and inelastic behaviour. Since all equations of the model are expressed in a simple analytical form, the model is rather flexible for computations and may be easily implemented. As an example, results for W–Cu FGM are presented for application of upper divertor plates for the international experimental thermonuclear reactor (ITER).