Dislocation Patterning: From Micro- to Mesoscale Description

Abstract

During the plastic deformation of crystalline material the dislocations, being the carriers of the plastic flow, tend to form different patterns. Because of the long range nature of dislocation-dislocation interaction, the origin of this self-ordering phenomenon is still an open question. The paper presents a stochastic two-dimensional model derived directly from the properties of individual dislocations making it possible to investigate the problem on a mesoscale. Numerical results obtained in double slip configuration indicate the development of cell structure with fractal character.

Dislocation Patterns and the Similitude Principle: 2.5D Mesoscale Simulations

“…3, which indicates that short-range interactions are sufficient to obtain pattern formation in multislip conditions. This aspect is absent from current models, which consider patterning as only related to long-range stresses [5,6]. In addition, we show that two features that are never modeled, the volume fraction of walls and the wall thickness, exhibit well-defined types of behavior.…”

“…Elastic interactions between dislocations, which are long-ranged, also necessarily play a role. The cross-slip of screw dislocations stabilizes dislocation tangles, accounts for the threedimensional dissemination of slip, and governs the selforganization kinetics.Dislocation patterns can be more easily obtained in 2D, but in drastically simplified conditions [5]. As a consequence, none of the existing 2D studies lead to patterns that consistently verify the scaling relations commonly found in deformed fcc metals.…”

“…Dislocation patterns can be more easily obtained in 2D, but in drastically simplified conditions [5]. As a consequence, none of the existing 2D studies lead to patterns that consistently verify the scaling relations commonly found in deformed fcc metals.…”

“…[4] for a review), it was realized 20 years ago that dislocation patterning is an example of self-organization in a system driven far from equilibrium. In the models that were further developed, the main difficulty consists in accounting for long-range interaction stresses between dislocations, which were assumed to be at the origin of patterning phenomena [5,6]. The specific features of such models are, however, still under discussion, as they do not account for a few essential properties of dislocations.…”

Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations

“…20,26,27,21 A stochastic generalization of Groma's model which takes into account microscopic stress fluctuations in terms of a random stochastic process was shown to yield fractal dislocation patterns. 27 However, these studies also demonstrated that the neglection of correlations which is inherent in any mean-field approach makes it impossible to solve the problem of length scale selection. In the present investigation, we therefore consider explicitly the evolution of correlations in the dislocation arrangement.…”