Macro-mechanical material model for fiber reinforced metal matrix composites

Abstract

Abstract The stress–strain behavior of a metal matrix composite reinforced with unidirectional, continuous and periodic fibers is investigated. Three-dimensional micro-mechanical analyses of a unit cell by means of the finite element method and homogenization–localization are carried out. These calculations allow the determination of material behavior of the in-plane, as well as the fiber directions. The fibers are assumed to be elastic and the matrix elasto-plastic. The matrix material is governed by a von Mises yield surface, isotropic hardening and an associated flow rule. With the aid of these analyses, the foundation to a macro-mechanical material model is presented which is employed to consider an elementary problem. The model includes an anisotropic yield surface with isotropic hardening and an associated flow rule. A beam in bending containing square fibers under plane strain conditions is analyzed by means of the model. Two cases are considered: one in which the fibers are symmetric with respect to the unit cell and one in which they are rotated by an angle of π/6 with respect to the horizontal axis. Good agreement is found between the macro-mechanical analyses and full finite element analyses of the beam. The aim here is to develop an initial macro-mechanical material model which can be extended to include more realistic aspects of the composite elasto-plastic behavior. As part of this model, a family of effective stress-effective plastic strain curves are obtained. An important aspect of this investigation is the implementation of the homogenization–localization technique for elasto-plastic material behavior of non-symmetric unit cells.