An interpretation of size-scale plasticity in geometrically confined systems

The mesoscopic constitutive behavior of face-centered cubic metals as a function of the system characteristic dimension recently has been investigated experimentally. Strong size effects have been identified in both polycrystalline submicron thin films and single crystal micro pillars. The size effect is manifested as an increase in strength and hardening rate as the system dimensions are decreased. In this article, we provide a mechanistic interpretation for the observed mesoscopic behavior. By performing 3D discrete dislocation dynamics simulations of grains representative of the system microstructure and associated characteristic dimensions, we show that the experimentally observed size effects can be qualitatively described. In these simulations, a constant density of dislocation sources per unit of grain boundary area is modeled by sources randomly distributed at grain boundaries. The source length (strength) is modeled by a Gaussian distribution, in which average and standard deviation is independent of the system characteristic dimension. The simulations reveal that two key concepts are at the root of the observed plasticity size effect. First, the onset of plasticity is governed by a dislocation nucleation-controlled process (sources of various length, i.e., strengths, in our model). Second, the hardening rate is controlled by source exhaustion, i.e., sources are active only once as a result of the limited dislocation mobility arising from size and boundary effects. The model postulated here improves our understanding of why smaller is stronger and provides predictive capabilities that should enhance the reliable design of devices in applications such as microelectronics and micro/nano-electro-mechanical systems.