

Origin of Plasticity Length-Scale Effects in Fracture and Deformation
Abstract
Engineering design of essentially all metallic components used in structural applications – aircraft structures, cars, bridges, pacemakers, hip implants, computer chip packages, turbine disks, among others - relies heavily on the long-standing framework of continuum plasticity. However, many experiments now show that the plastic flow stress in metals increases in material volumes on the micron scale and below. Micro and nano indentation hardness of metals, the flow strength of nanocrystalline metals, nano- and micro- pillar, nano-asperities, and thin films, all obey the mantra of “smaller is stronger†and highlight the failure of conventional continuum plasticity. These issues have spurred new approaches to plasticity such as phenomenological strain-gradient plasticity (SGP) models and discrete-dislocation models, aimed at capturing the effects of “geometrically necessary dislocationsâ€. While these models show size effects, there is no clear physical identification of the material length scales controlling size-dependence, in spite of wide speculation on possible length scales. Here, we use a new discrete-dislocation/cohesivezone model to unambiguously demonstrate that the spacing between obstacles to dislocation motion is one dominant material length scale controlling the fracture toughness of plastically deforming metals. Our results support one SGP model and provide a physical interpretation for that model’s phenomenological length scale. We then propose a new “stress gradient plasticity†concept based on the behavior of dislocations in a “pile-up†at an obstacle under a stress gradient. “Stress gradient plasticity†helps rationalize our fracture results. More importantly, applied to bending, it predicts an increase in the initial flow stress and is consistent with discrete-dislocation simulation studies. We then implement “stress gradient plasticity†within a low-order continuum plasticity framework and demonstrate size effects in bending, torsion, indentation, and void expansion, and explain observed size effects—both strengthening and hardening—in recent bending and torsion experiments.