Plastic deformation of metals proceeds by crystallographic slip, which involves complex motion and interaction of large numbers of crystal dislocations. Such complex dynamics lead to highly heterogeneous distribution of the dislocations and slip activity, manifested in the form of dislocation and deformation patterns. Although the basic mechanisms of deformation have been known for a long time, attempts to model the collective dynamics of dislocations have only begun relatively recently with the introduction of dislocation dynamics simulations. Work on this technique has stimulated the development of statistical models of dislocation systems, which are cast along the lines of the classical kinetic theory and in which dislocation systems are described in terms of scalar density fields governed by kinetic equations representing their dynamics and interactions. In parallel, attempts to provide closure for the classical continuum theory of dislocation fields have been carried out, which model the dislocations by density fields of tensor type. The last few years have witnessed significant development and integration of these collective dislocation dynamics approaches among themselves and with crystal mechanics. In the context of developing continuum models of discrete dislocation systems, other statistical aspects of plastic deformation of metals, such as spatial correlations and scale invariance of dislocation patterns and elastic and plastic distortion fields, have also become important topics. Together with the fundamental question of how to represent dislocation dynamics in terms of dislocation densities, these statistical aspects of plastic deformation have been the subject of a few international meetings: a research workshop on Statistical Mechanics of Plasticity, Trieste, Italy, March 2002, a symposium on Statistical Mechanics of Plasticity and Related Materials Instabilities, part of the International Conference on Multiscale Materials Modeling, Los Angeles, October 2004, and an international conference with the same title in Bangalore, India, August 2005. Two guest editors of the current special issue, Anter El-Azab and Michael Zaiser, have been involved in the organization of these and other related meetings.
As progress in this direction continues, it has been felt that there is a need to compile a special journal issue dedicated to the general topic of statistical and continuum aspects of plastic deformation of metals. The idea of this special issue is not only to discuss key aspects of density-based modelling of dislocations and to document the state-of-the-art approaches in this emerging area, but also to include contributors from the larger community working on mesoscale aspects of metal deformation. Selection of authors in this special issue has been done in such a way that all leading theoretical modelling approaches of mesoscale deformation and collective dynamics of dislocations are represented (see contributions by lead authors R. Sedlacek, M. Hochrainer, A. Acharya, C. J. Bayley, I. Groma, F. Akasheh, M. Koslowski, M. Zaiser and A. El-Azab). An experimental contribution by lead author A. E. Larson highlights the recent developments in using X-ray techniques to perform spatially resolved, sub-micrometer scale measurements of elastic strain and dislocation density tensor in heavily deformed crystals. The technique furnishes a critically needed capability to acquire data at the same scale considered in the theoretical approaches. The experimental investigation of J. A. Weiss also uses X-ray methods, but focuses on the investigation of long-range correlated density fluctuations in dislocation patterns and the concomitant problems in defining average densities. Another contribution by lead author M. Kempf addresses surface strain mapped at the nano-to-macroscale range in plastically deformed metals. A two-part contribution by lead author A. Zeghadi on the use of classical crystal plasticity theory to investigate strain heterogeneity in polycrystalline metals is also included in this special issue, providing some contrast between a more conventional approach and the density-based models.
Due to the diverse collection of authors, this special issue presents a variety of perspectives on the development of new and, hopefully, more efficient approaches to dislocation dynamics and mesoscale plastic deformation in metals. These approaches still require extensive development, but they are now viewed to be on the path towards predictive mesoscale metal deformation theories that start from rigorous mathematical treatment of the dynamics and interactions of the underlying crystal dislocation systems.