Dislocation dynamics. I. A proposed methodology for deformation micromechanics

Abstract

A new methodology in computational micromechanics, dislocation dynamics (DD), is introduced.Dislocation dynamics is developed for examining the dynamic behavior of dislocation distributions in solid materials. Under conditions of externally applied stress, dislocations exhibit glide with a velocity proportional to a power of the applied stress 0. and climb motion with a velocity that is a function of the applied stress and temperature. These motions result from long-range force fields, comprising both externally applied stress and long-range interactions between individual dislocations. Short-range reactions are represented as discrete events. The DD methodology is to be differentiated from particle methods in statistical mechanics (e.g. , molecular dynamics and the Monte Carlo method) in two respects. First, DD is developed to study the dynamical behavior of "defects" in the solid. Generally, the density of defects is less than that of the particles that make up the solid. Second, the small number of dislocations allows for a complete dynamical representation of the evolution of dislocations in the material medium without the requirement of statistical averaging. The purpose of the DD methodology is to bridge the gap between experimentally observed phenomena and theoretical descriptions of dislocation aggregates, particularly the evolution of self-organized dislocation structures under temperature, stress, and irradiation conditions.

Intermittent dislocation flow in viscoplastic deformation

“…Analytical methods and sophisticated 'dislocation-dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation [2][3][4][5][6][7][8][9]. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed.…”

“…This long-range stress is responsible for mutual interactions among dislocations which are important in all dislocation dynamics models [4][5][6][7]. Under a constant external stress σ e , dislocation i performs an overdamped motion along the x direction described by the following equation…”

“…This general picture implies that the experimental phenomenology should be reproducible in simple numerical simulations of discrete dislocation dynamics that preserve the relevant characteristics of the system under study. As in previous dislocation dynamics models [4][5][6][7], we consider a two-dimensional cross-section of the crystal (that is, the xy plane), and randomly place N straight-edge dislocations gliding along a single slip direction parallel to their respective Burgers' vectors b (that is, the x direction). This implies that we have point-like dislocations moving along fixed lines parallel to the x axis.…”

A Simple Model on Dislocation Dynamics

“…Over the past decade several numerical investigations have been performed to study the dynamical properties of dislocation systems [1][2][3][4][5][6][7][8]. One of the most interesting questions stimulating these works is to understand the origin of dislocation patterning.…”

A new fast finite element method for dislocations based on interior discontinuities

“…Roughly speaking, dislocations models can be categorized as either continuum based, such as the method of van der Giessen and Needleman [4], or discrete, such as the methods of Amodeo and Ghoniem [5], Schwarz and Tersoff [6], Kubin and co-workers [7], and Zbib et al [8].…”