Micromechanical Modeling of Elastic and Thermoelastoplatic Deformations of Functionally Graded Metal Matrix Composites

The subject of this research is a fundamental problem of solid mechanics consisting in the prediction of the effective elastic-plastic behavior, i.e. the formulation of the incremental macroscopic material law, of Functionally Graded Metal Matrix Composites (FGMMCs) with random microstructure from microstructural information such as mechanical properties of the constituent phases and their microtopology. In general the behavior of such composites is mainly characterized by the statistical distribution of the inclusions, by thermo-mechanical interactions, and by the inhomogeneity of the stresses and the elastic and plastic strains in the components. Numerical analyses of these effects require very fine discritizations and, hence, extreme computational efforts. They are limited to material characterization and to relatively simple microtopologies. The crucial point of the project is the analytical description of the statistically inhomogeneous random structure of FGM and its influence on the nonlocal effective material behavior. This description and following analyses are based on the use of the multiparticle effective field method (MEFM), put forward and developed by the applicant. The MEFM is based on the theory of functions of random variables and Green`s functions. Within this method one constructs a hierarchy of statistical moment equations for conditional averages of the stresses in the inclusions. The hierarchy is cut by introducing the notion of an effective field. This way the interaction of diffrent inclusions is taken into account. The estimations of second moments of stresses in the constituents of the composite are used in the elastoplastic analysis. For this purpose a new method of integral equations is proposed, which is based on the consideration of both binary and triple interaction of the inclusions. Another essential point for defining efficient algorithms for the elastoplastic analysis of FGMs is the use of the proposed local model of plasticity of random structure composites, in which each inclusion consists of an elastic core and a thin coating. The mechanical properties of both the matrix and the coating are the same but with different plastic strains. Homogeneous plastic strains are assumed inside the remaining matrix and in each of the separate subdomains of the coating. This way a discrete variation of the plastic strains in the matrix material of a composite with uncoated elastic inclusions is introduced. A general theory of plasticity is developed for arbitrary loading based on incremental elastoplastic analysis. The consideration of the inhomogeneity of plastic strains in the coating enables to obtain some principally new effects of elastoplastic deformations in FGMs. The next step of the improvement of the proposed model is a consideration of statistical average of the second moment of stresses in the matrix as well as in the coating.