Multiresolution modeling of ductile reinforced brittle composites

Tungsten carbide–cobalt (WC–Co) is an important ductile reinforced brittle composite used in a range of important applications. The relationship between microstructure and mechanical properties of WC–Co is truly multiscale; micromechanical processes interact at different scales, resulting in permanent plastic deformation, damage accumulation and final failure of the composite. The goal of the current paper is to develop a continuum-based model, which captures the progressively finer scales of strain localization observed in WC–Co composites during plastic deformation and failure. This is achieved via a set of multiresolution governing equations; a microstress is introduced at each scale of strain localization, which represents the resistance to inhomogeneous strain localization at that scale. The extra constitutive models associated with these microstresses can be elucidated from the average response of separate computational cell models of a representative microstructure. The final multiresolution continuum model is capable of capturing the important length scales of deformation during the plastic stage of deformation without resorting to modeling microstructural scale features directly. The result is a more realistic continuum model; in particular the fracture toughness prediction is more physical when these length scales are incorporated compared to a conventional continuum approach.