Falling through the Cracks: Energy Storage along Segmented Brittle Crack Fronts

During brittle crack propagation, a smooth crack front curve frequently becomes disjoint, generating a stepped crack and a material ligament that unites the newly formed crack fronts. These universal features fundamentally alter the singular field structure and stability of propagating cracks; however, a quantitative analysis of their mechanics is lacking. Here, we perform in situ 3D measurements to resolve the deformation field around stepped cracks, and crucially, within the ligament feature. The 3D kinematic data are obtained by scanning a thin laser sheet through the brittle hydrogel samples, while recording the scattered intensity from the embedded tracer particles. We find that the ligament concentrates the strain energy density. We introduce the "Ligament Equivalent Energy" and demonstrate that the macroscopic fracture energy increases linearly with this volumetric quantity when normalized by the ligament rupture area. Furthermore, by extracting an effective traction-separation law from the local stress fields, we reveal that the ligament functions as an effective cohesive zone.