Size selection of crack front defects: Multiple fracture-plane interactions and intrinsic lengthscales

Material failure is mediated by the propagation of cracks, which in realistic 3D materials typically involve multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures, such as step defects on tensile fracture surfaces. Steps form once a slowly moving, distorted crack front segments into disconnected overlapping fracture planes separated by a stabilizing distance $h_{\mathrm{m}\mathrm{a}\mathrm{x}}$. Our experiments on numerous brittle hydrogels reveal that $h_{\mathrm{m}\mathrm{a}\mathrm{x}}$ varies linearly with both a nonlinear elastic length $\mathrm{\Gamma }(v)\mathrm{/}\mu$ and a dissipation length $\xi$. Here, $\mathrm{\Gamma }(v)$ is the measured crack velocity $v$-dependent fracture energy and $\mu$ is the shear modulus. These intrinsic lengthscales point the way to a fundamental understanding of multiple-crack interactions in 3D that lead to the formation of stable out-of-plane fracture structures.