Plasticity dependent damage evolution in composites with strain-gradient effects

Abstract

A unit cell approach is adopted to numerically analyze the effect of reinforcement size on fracture evolution in metal matrix composites. The matrix material shows plastic size-effects and is modeled by an anisotropic version of the single parameter strain-gradient (higher-order) plasticity model by Fleck and Hutchinson (2001). The fracture process along the fiber–matrix interface is modeled using a recently proposed cohesive law extension, where plasticity affects the fracture process as both the average as well as the jump in plastic strain across the interface are accounted for Tvergaard et al. (2013). In this study the reinforcement is assumed perfectly stiff and consequently only one new cohesive material parameter is introduced. Results are shown for both conventional isotropy as well as plastic anisotropy with higher-order material behavior. Due to fiber–matrix decohesion a sudden stress-drop is seen in the macroscopic stress–strain response curve, which defines the failure strain of the composite. It is shown, that decreasing the value of the new cohesive material length parameter will monotonically decrease the failure strain. On the other hand, the material length scale parameter of the matrix affects the failure strain in a non-monotonic manner. Depending on the degree of anisotropy a maximum failure strain is predicted for a length scale corresponding to 10–15% of the reinforcement radius.