Multiscale unified prediction of size/scale and Hall-Petch effects in the mechanics of polycrystalline materials

Abstract Materials show size effects in their strength, i.e., improved strength as size decreases. Size effects have been studied extensively at a wide range of scales, from atomistic to continuum. Size effects depend on the scale of reference, as the physics change with increasing or decreasing scale. The work reported herein concentrates at scales near the average grain size in polycrystalline solids, where they are examined in conjunction with Hall-Petch effects. It presents a process for isolating physical information on a problem at specific spatial or temporal scales and applies it to Hall-Petch and size effects in one spatial dimension, extendable to higher dimensions. Importantly, the scale-isolated information captures the interactions among scales. As material failure and Hall-Petch effects are highly stochastic, a probabilistic approach to the present work is more appropriate than a deterministic one.