Multiscale Dislocation Plasticity: Discrete to Continuum

Hussein Zbib
Washington State University

The miniaturization of structural components to the sub-micrometer scale has created a significant challenge when attempting to engineer such structures using conventional models and simulation tools that are based solely on continuum approaches. Although there has been progress in strain-gradient continuum theories to model the mechanical behavior of metallic systems at small length scales, these theories fail to represent the variety of physical mechanisms involved in dislocation motion in small volumes where dislocations are scarce. The major difficulty in these theories lies in the notion that physical mechanisms which arise from dislocation motion that occur at the micrometer scale, and are intrinsically discrete events, can be represented in the form of continuum variables at the macro-meter length scale. This drastic jump between scales may be statistically meaningful for relatively large volumes but loses all sense when the volume is so small such that dislocations become in short supply. This situation, in turn, has brought about the need to develop novel multiscale material models and simulation tools that may enable engineers to design and analyze multiscale structures at such small scales. In parallel, this also necessitates the need to develop novel experimental techniques to determine and verify mechanical properties at the sub-micrometer scale for use in such models. In this presentation we will discuss a multliscale method bridging discrete dislocation dynamics with continuum plasticity, and how we use this approach not only to investigate small scale deformation phenomena, but also to develop a dislocation-based mesoscale crystal plasticity model, including dislocation densities, hardening laws based on dislocation-dislocation interactions, and a set of mechanisms-based evolution laws.

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