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

Abstract: 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 $h_{\rm max}$. Our experiments on numerous brittle hydrogels reveal that $h_{\rm max}$ varies linearly with both a nonlinear elastic length $\Gamma(v)/\mu$ and a dissipation length $\xi$. Here, $\Gamma(v)$ 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.