Dislocation patterning: tochastic approach to mesoscale modeling
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Joint Research Centre of the European Commission, Institute for Advanced Materials, NL-1755 ZG Petten, The Netherlands ABSTRACT
Plastic deformation by dislocation glide is known to be associated with the spontaneous formation of mesoscopic patterns of various types, e.g. cellular dislocation structures during unidirectional deformation and quasi-periodic persistent slip band structures during cyclic deformation. While it is recognized that dislocation patterning represents a dissipative far-from-equilibrium process, theoretical modelling of those phenomena is complicated by the long-range nature of dislocation interactions inducing collective dislocation behaviour on a mesoscopic scale. In this paper the problem is addressed using a stochastic approach with random uctuations acting on the evolution of the dislocation ensemble. The intensity of the uctuations is determined self-consistently from dynamic dislocation interactions and, hence, re ects correlated dislocation motion. It is shown that those uctuations may induce dislocation patterns by stabilizing non-uniform dislocation distributions. Microstructure-based models are presented for unidirectional and cyclic plastic deformation. In the rst case fractal dislocations distributions corresponding to hierarchically organized dislocation cell structures are obtained, while in the latter case a decomposition into dislocation-rich walls or veins and depleted channels is found, which are associated with the formation of persistent slip bands and matrix structures. The good agreement with experimental observations in single-crystalline f.c.c. metals points at the importance of collective dislocation e ects in the self-organization of those structures. INTRODUCTION
Dislocation dynamics approaches to plastic ow of metals and alloys may provide the physical base to the constitutive viscoplastic laws used in continuum mechanics, and give access to the characteristic length and time scales that are important for modelling the spatio-temporal aspects of plastic deformation. Moreoever, dislocation dynamical modelling is indispensable for understanding the spontaneous formation of dislocation patterns [1, 2, 3] which are examples of self-organization in complex systems far from equilibrium [4]. For theoretical modelling purposes, however, fundamental problems are due to the long-range interactions between dislocations. They are the reason why in dislocation dynamics systems various characteristic length scales may not clearly separate, as to allow averaging (coarse graining) procedures to be applicable. Instead, the correlation length over which mobile dislocations behave in a collective way is of the same order of magnitude as the characteristic wavelength of the spontaneously emerging dislocation patterns. This situation distinguishes dislocation patterning from other self-organization phenomena, for instance the convection patterning associated with the Benard instability which is observed in viscous liquids heated from below. In this case patterns emerge on a 3macrosc
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