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 J_c 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.
© 2013 Elsevier Ltd. Received 5 November 2013. Received in revised form 5 November 2013. Accepted 6 November 2013. Available online 7 November 2013. L.F. and M. O. gratefully acknowledge the support of the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. L.F. and M.O. also gratefully acknowledge the support of the U.S. National Science Foundation through the Partnership for International Research and Education (PIRE) on Science at the Triple Point Between Mathematics, Mechanics and Materials Science, Award Number 0967140. L.F. gratefully acknowledges support provided by the Hausdorff Trimester Program "Mathematical challenges of materials science and condensed matter physics: From quantum mechanics through statistical mechanics to nonlinear PDEs", Hausdorff Research Institute for Mathematics (HIM), University of Bonn, Germany.