Size Selection of Crack Front Defects: Multiple Fracture-Plane Interactions and Intrinsic Length Scales

Material failure is mediated by the propagation of cracks which, in realistic 3D materials, typically involves 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_{max}. Our experiments on numerous brittle hydrogels reveal that h_{max} varies linearly with both a nonlinear elastic length Γ(v)/μ and a dissipation length ξ. Here, Γ(v) is the measured crack velocity v-dependent fracture energy, and μ is the shear modulus. These intrinsic length scales 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.