Spatial heterogeneity of flaw-sensitivity in tough hydrogels

Tough double-network (DN) hydrogels are widely regarded as promising soft materials for load-bearing applications due to their exceptional fracture resistance. However, the spatial heterogeneity in their fracture behavior, particularly how flaw-sensitivity varies across structurally distinct regions such as necked and un-necked zones, remains poorly understood. Here, we systematically investigate the flaw-sensitivity of DN hydrogels using single-edge notch tests (SENT) combined with real-time birefringence imaging and true stress analysis. By introducing controlled internal damage via pre-stretching, we generate gels exhibiting both necked and un-necked regions and assess the critical stretch ratio, engineering stress, and strain energy density at crack initiation. We uncover two distinct crack propagation scenarios governed by whether necking precedes or follows crack growth, and identify spatially dependent flaw-sensitivity with remarkably larger transition crack length c*_{I to II} in un-necked regions than in necked ones. Remarkably, the true stress at fracture follows a unified scaling σ_true,c∝c₀⁻¹ across all regions and pre-damage levels, deviating significantly from linear elastic fracture mechanics predictions. We rationalize this behavior within an elastic-plastic fracture framework, demonstrating that the observed scaling is a hallmark of Large-Scale Yielding (LSY) and a Limit Load condition. In this regime, the fracture process is governed by a stress-limited cohesive zone where energy dissipation is capped by the necking plateau, akin to an elastic-perfectly plastic solid. Our findings reveal that the fracture resistance of DN gels is not uniform but is highly localized, governed by the interplay between microstructural damage and non-linear deformation, and provide critical insights for the design of flaw-tolerant soft materials.