D. Weygand

Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics

A three-dimensional discrete dislocation dynamics plasticity model is presented. The approach allows realistic boundary conditions on the specimen, as both stress and displacement fields of the dislocations are incorporated in the formulation. Emphasis is placed on various technical details in the formulation as well as on the implementation. The current implementation includes features necessary to model conservative motion of dislocations in presence of surfaces. These include details of the discretization of the evolving dislocation structure, the handling of junction formation and destruction, cross-slip and boundary conditions. Special attention is given to the treatment of dislocations that partly glide out of the material, including the treatment of image forces via the finite-element method.

A vertex dynamics simulation of grain growth in two dimensions

Abstract A vertex model including real and virtual vertices is presented. Equations for the dynamics are derived and applied in their complete form. Details of the implementation in two dimensions are discussed. It is shown that the mobility and the energy of grain boundaries, and consequently the simulation time, are the usual real quantities. The model is then applied to the simulation of normal grain growth and compared with the Potts model and the Kawasaki et al. vertex models. The present model proved to be successful in reproducing classical laws related to static and dynamic features. In particular, it provides a value of the pre-factor constant in the law describing the evolution of the mean grain size against time.

Zener pinning and grain growth : A two-dimensional vertex computer simulation

Abstract A vertex dynamics model is applied to the two-dimensional simulation of grain growth in the presence of pinning particles. We study the influence of pinning force and particle density, considered as independent parameters, on the kinetics to reach the saturation state.

Three-dimensional grain growth: A vertex dynamics simulation

Abstract The evolution of a three-dimensional (3D) grain structure is simulated by a vertex dynamics method. Normal grain growth is simulated and two-dimensional (2D) sections and the 3D structure are analysed and compared with a 2D simulation. It is shown that 2D sections of a 3D structure can be distinguished from a pure 2D situation.

Submicron Plasticity: Yield Stress, Dislocation Avalanches, and Velocity Distribution

The existence of a well-defined yield stress, where a macroscopic crystal begins to plastically flow, has been a basic observation in materials science. In contrast with macroscopic samples, in microcrystals the strain accumulates in random bursts, which makes controlled plastic formation difficult. Here we study by 2D and 3D simulations the plastic deformation of submicron objects under increasing stress. We show that, while the stress-strain relation of individual samples exhibits jumps, its average and mean deviation still specify a well-defined critical stress. The statistical background of this phenomenon is analyzed through the velocity distribution of dislocations, revealing a universal cubic decay and the appearance of a shoulder due to dislocation avalanches.

Discrete dislocation modeling in three-dimensional confined volumes

Abstract Plastic deformation of micron-sized specimens or smaller cannot be described by continuum plasticity, as the discrete nature of the dislocations can no longer be ignored. This paper presents a three-dimensional dislocation dynamics plasticity method developed for the study of plasticity of such small specimens. The approach includes two components: (i) plasticity is described by the dynamics of individual, discretized three-dimensional dislocation loops; (ii) a finite element model supplies ‘image fields’ that incorporate traction or displacement boundary conditions on the specimen. A circular dislocation loop is used to validate the chosen discretization of the dislocation. The critical stress for activating a Frank–Read source confirms the used line-tension description. A tensile test of a free-standing thin film illustrates the incorporation of the boundary conditions into the model. Particular attention is given to the treatment of dislocation loops that have glided partly out of the body, leaving a step at the surface.

A generalized vertex dynamics model for grain growth in three dimensions

A generalized three-dimensional (3D) vertex dynamics model for simulating grain growth is presented. In this approach, grain boundaries (GB) are triangulated and the microstructural evolution is driven by the minimization of the GB energy. The generalized model includes misorientation and inclination dependent GB energies and mobilities. The model systems considered are SrTiO3 ceramics.The paper describes the derivation of the equations for the dynamics and the algorithm for handling topological changes in the GB network in detail. For isotropic grain growth, the numerical results for the volume change rate of embedded grains are in excellent agreement with the MacPherson–Srolovitz relation which can be interpreted as the 3D analogue of the von Neumann–Mullins law. The inclination dependent GB energy yields a torque contribution on the GB shape. This is illustrated by means of 2D cross-sections of structures modelled with and without inclination dependence showing rather flat GBs for the energetically favourable GB inclinations.

Discrete dislocation dynamics simulations of dislocation interactions with Y2O3 particles in PM2000 single crystals

In oxide dispersion strengthened steels the interactions between dispersoids and dislocations determine the materials plasticity. Using three-dimensional Discrete Dislocation Dynamics simulations, the effect of Y2O3 dispersoids on the motion of dislocations in BCC single crystal PM2000, a commercial alloy candidate for gas-cooled reactors, has been studied. The dispersoid distribution used in this model has been derived from experimental TEM observations of PM2000. As screw dislocations are predominant in the studied material, the behaviour of a single screw dislocation under shear loading in a distribution of spherical Y2O3 dispersoids is studied. The critical resolved shear stress, the minimum value of the external stress needed to move the dislocation through the obstacle field, is found to be only slightly lower than the experimentally determined value revealing that dispersoids are the main hardening contributions.

Influence of a reduced mobility of triple points on grain growth in two dimensions

Abstract A vertex dynamics model is applied to the two-dimensional simulation of grain growth including a limited mobility of triple points. It is shown that a recent experiment on a triple node is well reproduced by the proposed model. This model is then applied to the grain growth of polycrystals to investigate the possible consequences of a reduced mobility of triple nodes. It is shown how this effect can be detected through a careful examination of the grain growth kinetics and grain size distribution function.

Analysis of dislocation pile-ups using a dislocation-based continuum theory

The increasing demand for materials with well-defined microstructure, accompanied by the advancing miniaturization of devices, is the reason for the growing interest in physically motivated, dislocation-based continuum theories of plasticity. In recent years, various advanced continuum theories have been introduced, which are able to described the motion of straight and curved dislocation lines. The focus of this paper is the question of how to include fundamental properties of discrete dislocations during their motion and interaction in a continuum dislocation dynamics (CDD) theory. In our CDD model, we obtain elastic interaction stresses for the bundles of dislocations by a mean-field stress, which represents long-range stress components, and a short range corrective stress component, which represents the gradients of the local dislocation density. The attracting and repelling behavior of bundles of straight dislocations of the same and opposite sign are analyzed. Furthermore, considering different dislocation pile-up systems, we show that the CDD formulation can solve various fundamental problems of micro-plasticity. To obtain a mesh size independent formulation (which is a prerequisite for further application of the theory to more complex situations), we propose a discretization dependent scaling of the short range interaction stress. CDD results are compared to analytical solutions and benchmark data obtained from discrete dislocation simulations.