An Eshelby inclusion-based model for the study of stresses and plastic strain localization in metal matrix composites I: General formulation and its application to round particles

The Eshelby model has been extended to handle incipient plastic deformation following a Prandlt—Reuss plastic law. The current model is a modification of a previous integro-differential model also based in a discretization of the Eshelby one. It has been modified to perform the calculations starting from an integral equation on strain tensor instead of an integro-differential equation on displacements. It allows us, through the use of a novel convergence criterion, to find the solution for the elastoplastic field in the general case of ellipsoidal particles under thermal and mechanical loads. Both modifications greatly improve the ability of the model to handle composites with high ratios between matrix and inclusion shear moduli. The formulation is applied to a model case of Al matrix reinforced with SiC round particles. Both matrix and particles are considered elastic and thermally isotropic. The particle behavior is purely elastic and the matrix flows when it reaches an isotropic yield stress. It is found that the results agree with previous finite element method (FEM) calculations and the method allows us to study local plastic relaxation when mechanical load is below the matrix macroscopic yield stress.