The effective fracture strength and fracture toughness of solids with energy dissipation confined to localized strips

Abstract

Inelastic localized deformation in front of a crack tip dissipates energy and toughens the material. Such concentrated deformation could be resulted from plastic localization in solids, such as interfacial sliding in composites composing of heterogeneous layers, or by shear banding as seen in bulk metallic glasses (BMGs). The mechanisms of the localized deformation and the size of such events are crucial for the effective fracture properties of those particular solids. In this paper, we investigate the effective fracture strength and fracture toughness of solids where dissipation is dominantly contributed from plasticity in narrow strips by shear banding or interfacial sliding. We derive the analytical solutions in solids where energy dissipation occurs in co-planar elastic-perfectly plastic strips with strain softening, and also give approximate formulas of the effective strength and toughness for the solids with symmetric plastic strips. The toughening as a function of branching angle, thickness, yield stress, strength-softening ratio and local fracture toughness of the strips is determined quantitatively. The theory is also verified using finite-element (FE) simulations. These theoretical and finite element analysis supply a base for the design of strong and tough materials in which the plastic deformation is restricted within strips.