Micromechanics versus macromechanics: a combined approach for metal matrix composite constitutive modelling

Abstract

The cyclic constitutive behaviour description of long fibre metal matrix composites needs to take into account viscoplasticity of the matrix, damage of the constituents and interfaces, manufacture residual stresses and damage deactivation effects. In order to incorporate in the model the main constituent characteristics and the composite parameters (volume fractions, fibre shape and arrangements) a combined approach is proposed, i.e. that of using a micromechanics-based analysis for the thermo-elastoviscoplasticity of the composite with damaging effects when the damage is active (i.e. when the microcracks are open). The developed model is based on transformation field analysis and on the effective stress-effective strain space within the continuum damage mechanics of the constituents. The particularization to a two-phase material permits an explanation of the macroscopic constitutive operators of the composite. The obtained macroscopic model is then formulated in such a way as to describe the damage deactivation effects that take place under cyclic conditions for compressive-like loadings. The formalism is extended from that developed previously for elastic brittle ceramic matrix composites, taking into account the possible deactivation for a given (or varying) non-zero strain. The deactivation criterion ensures the continuity of the stress-strain response for any multiaxial loadings. The proposed model is then applied to a SiC/Ti metal matrix composite, with unidirectional long fibres.