Fracture toughness of soft solids with Mullins dissipation

Abstract

The fracture toughness of soft polymeric materials can be enhanced by inducing energy dissipation. While dissipation may be introduced through various chemical or physical mechanisms, at the continuum scale it is manifested in the hysteresis under a loading-unloading cycle. Such inelastic behavior, resembling the Mullins effect in filled rubber, may lead to ambiguities in the interpretation of fracture toughness measurements. Here we use finite element simulations to elucidate the mechanics of crack growth in soft inelastic solids. Specifically, we consider the pure shear configuration and adopt a phenomenological model to capture the Mullins effect. It is found that the apparent energy release rate continues to increase after the crack growth is initiated, resulting in a crack growth resistance curve. The physical origin of the resistance curve is attributed to the formation and expansion of a damage zone surrounding the crack tip. We use the simulation results to illustrate how the resistance curve is related to the force-stretch curve as well as their dependence on sample dimensions. Moreover, we discuss the interpretation of fracture toughness based on the resistance curve and the force-stretch curve. Our results can provide guidance to experimental characterization of fracture toughness in soft inelastic solids.