A method for solving small-strain plasticity problems with plastic flow represented by the collective motion of a large number of discrete dislocations is presented. The dislocations are modelled as line defects in a linear elastic medium. At each instant, superposition is used to represent the solution in terms of the infinite-medium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions on the finite body. The complementary solution is nonsingular and is obtained from a finite-element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation and annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-strain boundary value problems are solved for a solid having edge dislocations on parallel slip planes. Monophase and composite materials subject to simple shear parallel to the slip plane are analysed. Typically, a peak in the shear stress versus shear strain curve is found, after which the stress falls to a plateau at which the material deforms steadily. The plateau is associated with the localization of dislocation activity on more or less isolated systems. The results for composite materials are compared with solutions for a phenomenological continuum slip characterization of plastic flow.

/pdf/discrete-dislocation-plasticity-a-simple-planar-model-3yaflv8n1m.pdf

Discrete dislocation plasticity: a simple planar model

The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. 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. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behaviour of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials. Moreover, it should provide a framework for discussing fundamental aspects of plasticity that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.

Intermittent dislocation flow in viscoplastic deformation

Atomistic modeling of interfaces and their impact on microstructure and properties

This review examines the size effects observed in the mechanical strength of thin metal films and small samples such as single-crystalline pillars, whiskers, and wires. Experimental results from mechanical testing and electron mi- croscopy studies, as well as recent insights from discrete dislocation dynam- ics simulations, are presented. The size dependency of deformation may be separated into three regimes: the nanometer regime of roughly 100 nm and below, an intermediate regime between 100 nm and approximately 1 μm, and a bulk-like regime. We argue that there is no scaling law with one uni- versal power-law exponent encompassing the entire range. Instead, there are a number of different mechanisms and underlying effects, e.g., the initial dislocation microstructure or loading conditions. The complex interaction of these mechanisms leads to the typically observed scaling behavior.

Plasticity in Confined Dimensions

http://li.mit.edu/Archive/Papers/10/Wang10.pdf

Phase field modeling of defects and deformation

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 ${\mathrm{\ensuremath{\sigma}}}^{\mathit{m}}$ 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.

Dislocation dynamics. I. A proposed methodology for deformation micromechanics.

The dynamic organization of dislocations into spatially heterogeneous substructures is demonstrated by applying the principles of dislocation dynamics that were outlined in the preceding paper. Here it is shown that the formation of persistent slip bands is a consequence of the competition between dipole formation and annihilation of dislocations of opposite Burgers vectors in the absence of temperature-enhanced climb recovery under cyclic stress conditions. Planar arrays, which are also uniaxial structures, are shown to arise from enhanced dislocation multiplication and the formation of stable dipole configurations along a slip plane at lower temperatures where climb is unimportant. Biaxial dislocation systems experience additional degrees of freedom compared with uniaxial systems because of available motion along additional slip systems. It is demonstrated that for a system of orthogonal slip directions at high temperatures in which climb and glide motion are competitive, dislocation cellular structures form as a result of immobile dipole and junction formation and by the internal elastic strain energy minimization caused by long-range self-shielding. It is shown that the internal elastic strain energy is reduced by the self-organization process. However, the short-range nonlinear processes (i.e., dipole and junction formation) are shown not to allow absolute elastic energy minimization.

R. J. Amodeo

Papers

Dislocation dynamics. I. A proposed methodology for deformation micromechanics.

Dislocation dynamics. II. Applications to the formation of persistent slip bands, planar arrays, and dislocation cells