Grain size–inclusion size interaction in metal matrix composites using mechanism-based gradient crystal plasticity

Metal matrix composites (MMCs) comprising nano/microcrystalline matrices and reinforcements exhibit impressive mechanical behaviors derived by exploiting the size effects due to development of geometrically necessary dislocations. In such nanostructured MMCs intricate interactions between the grain size dg and inclusion size di may exist in their overall response, but are difficult to isolate in experiments and are also not accounted for in the size-dependent homogenized models. In this paper, we computationally investigate the grain size–inclusion size interaction in model MMCs architectures wherein the grains and inclusions are explicitly resolved. A mechanism-based slip-gradient crystal plasticity formulation (Han et al., 2005a) is implemented in a finite element framework to model polycrystalline mass as an aggregate of randomly oriented single crystals that host elastic inclusions. The slip gradients that develop across grain boundaries and at inclusion–grain interfaces during deformation result in length-scale dependent responses that depend on both dg and di, for a fixed inclusion volume fraction f. For a given di and f, the overall hardening exhibits a nonlinear dependence on grain size for dg ⩽ di indicating that interaction effects become important at those length-scales. Systematic computational simulations on bare polycrystalline and MMC architectures are performed in order to isolate the contributions due to grain size, inclusion size and the interaction thereof. Based on these results, an analytical model developed for the interaction hardening exhibits a Hall–Petch type dependence on these microstructural sizes that can be incorporated into homogenized approaches.