Numerical Modeling of Plasticity in Metal Matrix Fiber Composites

This paper presents micromechanical analyses of an orthogonally reinforced composite with new constitutive equations of kinematic plastic hardening. The homogenization of plastic properties was performed through a numerical analysis of a representative volume using the finite element method. A modification of Prager’s theory was used to construct physical relations for an equivalent orthotropic material. In the proposed version of the theory, a special tensor for back stresses is introduced, which takes into account the difference in the rate of hardening for different types of plastic deformation. For boron–aluminum orthogonally reinforced composite with known mechanical properties of fibers and matrix, all material parameters of the theory were determined, deformation diagrams were constructed, and the equation for a plasticity surface in a six-dimensional stress space was obtained. The advantage of the developed method of numerical homogenization is that it only requires a minimal amount of experimental data. The efficiency of micromechanical analysis makes it possible to optimally design metal matrix composites with the required plastic properties.