How hidden 3D structure within crack fronts reveals energy balance

Abstract

Griffith's energetic criterion, or `energy balance', has for a century formed the basis for fracture mechanics; the energy flowing into a crack front is precisely balanced by the dissipation (fracture energy) at the front. If the crack front structure is not properly accounted for, energy balance will either appear to fail or lead to unrealistic results. Here, we study the influence of the secondary structure of low-speed crack propagation in hydrogels under tensile loading conditions. We first show that these cracks are bistable; either simple (cracks having no secondary structure) or faceted crack states (formed by steps propagating along crack fronts) can be generated under identical loading conditions. The selection of either crack state is determined by the form of the initial `seed' crack; perfect seed cracks generate simple cracks while a small local mode~III component generates crack fronts having multiple steps. Step coarsening eventually leads to single steps that propagate along crack fronts. As they evolve, steps locally change the instantaneous structure and motion of the crack front, breaking transverse translational invariance. In contrast to simple cracks, faceted cracks can, therefore, no longer be considered as existing in a quasi-2D system. For both simple and faceted cracks we simultaneously measure the energy flux and local dissipation along these crack fronts over velocities, $v$, spanning $0<v<0.2c_R$ ($c_R$ is the Rayleigh wave speed). We find that, in the presence of secondary structure within the crack front, the implementation of energy balance must be generalized for 3D systems; faceted cracks reveal energy balance, only when we account for the local dynamic dissipation at each point along the crack front.