Abstract
A two-phase, pixelized representation of a simple composite microstructure is used as a basis for comparing the accuracy of models that extract local information for use on a larger scale. The local microstructure is homogenized on the meso-scale, using a moving window Generalized Method of Cells (GMC) homogenization technique [1]. Effective elastic constitutive behavior is modeled, and several possible representations of the local yield surface of the composite are compared. The goal of this work is to determine a simple and accurate method to approximate a meso-scale yield surface based on the material microstructure, such that the approximation can be used in a macro-scale analysis.
In order to determine the accuracy of the homogenized models, each is compared with an analytical study. The problem of a single elasto-plastic circular inclusion in an elasto-plastic matrix under radial loading at an infinite boundary is considered. A benchmark solution to this problem is developed based on the work of Mendelson [2].
Investigation is made into the effect of the variation of several model parameters. The pixel resolution of the digitized circular fiber image, and the moving window size used within the analysis are both varied. The yield surface of the meso-scale element is also varied, according to two different requirements: first yield in the microstructure, or an averaged yield in the matrix microstructure. According to the definition of yield in the material, the yield surface is then fitted with parameters to match the behavior of the material, and to describe the material on the meso-scale. These yield parameters are first defined as those of Hill's anisotropic yield criterion [3]. The Hill's yield criterion is chosen for its simplicity as an anisotropic generalization of the Mises yield criterion. A second set of modified Hill's parameters is also defined, which can be applied to highly anisotropic materials for which the Hill's criterion is undefined.
A finite element analysis is carried out on each meso-scale model, with varying degrees of homogenization. The internal energy and degree of plasticity in these models are compared against the results of the Mendelson benchmark. It is shown that the Hill's criterion parameters can be successfully modified. A subcell initial yield criterion is shown to be most effective in a material that exhibits high stress concentrations, while a matrix average yield criterion is shown to be more effective in a material with lower stress concentrations. (C) 2008 Elsevier B.V. All rights reserved.