Optimal scaling laws for ductile fracture derived from strain-gradient microplasticity

We perform an optimal-scaling analysis of ductile fracture in metals. We specifically consider the deformation up to failure of a slab of finite thickness subject to monotonically increasing normal opening displacements on its surfaces. We show that ductile fracture emerges as the net outcome of two competing effects: the sublinear growth characteristic of the hardening of metals and strain-gradient plasticity. We also put forth physical arguments that identify the intrinsic length of strain-gradient plasticity and the critical opening displacement for fracture. We show that, when Jc is renormalized in a manner suggested by the optimal scaling laws, the experimental data tends to cluster—with allowances made for experimental scatter—within bounds dependent on the hardening exponent but otherwise material independent.