A Perspective on Dislocation Dynamics

Abstract

A fundamental description of plastic deformation has been recently pursued in many parts of the world as a result of dissatisfaction with the limitations of continuum plasticity theory. Although continuum models of plastic deformation are extensively used in engineering practice, their range of application is limited by the underlying database. The reliability of continuum plasticity descriptions is dependent on the accuracy and range of available experimental data. Under complex loading situations, however, the database is often hard to establish. Moreover, the lack of a characteristic length scale in continuum plasticity makes it difficult to predict the occurrence of critical localized deformation zones. Although homogenization methods have played a significant role in determining the elastic properties of new materials from their constituents (e.g., composite materials), the same methods have failed to describe plasticity. It is widely appreciated that plastic strain is fundamentally heterogenous, displaying high strains concentrated in small material volumes, with virtually undeformed regions in-between. Experimental observations consistently show that plastic deformation is heterogeneous at all length-scales. Depending on the deformation mode, heterogeneous dislocation structures appear with definitive wavelengths. A satisfactory description of realistic dislocation patterning and strain localization has been rather elusive. Attempts aimed at this question have been based on statistical mechanics, reaction-diffusion dynamics, or the theory of phase transitions. Much of the efforts have aimed at clarifying the fundamental origins of inhomogeneous plastic deformation. On the other hand, engineering descriptions of plasticity have relied on experimentally verified constitutive equations.