Dislocation patterning in a 2D continuum theory of dislocations

Abstract

Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a 2D continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusion like terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning.

References in corpus (6)

• Thermodynamically consistent continuum dislocation dynamics
• Scaling Properties of Dislocation Simulations in the Similitude Regime
• Local density approximation for the energy functional of three-dimensional dislocation systems
• Density-based crystal plasticity : from the discrete to the continuum
• Scale-free phase field theory of dislocations
• Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum plasticity theory

Cited by in corpus (19)

• Avalanches and Plastic Flow in Crystal Plasticity: An Overview
• Taming intermittent plasticity at small scales
• Density-based crystal plasticity : from the discrete to the continuum
• Deterministic and stochastic models of dislocation patterning
• On the implementation of dislocation reactions in continuum dislocation dynamics modeling of mesoscale plasticity
• Crystal plasticity modeling of non-Schmid yield behavior: from Ni3Al single crystals to Ni-based superalloys
• The Emergence and Role of Dipolar Dislocation Patterns in Discrete and Continuum Formulations of Plasticity
• On the dynamics of curved dislocation ensembles
• Continuum dynamics of the formation, migration and dissociation of self-locked dislocation structures on parallel slip planes
• Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations
• Convergence and non-convergence of many-particle evolutions with multiple signs
• Data-mining of dislocation microstructures: concepts for coarse-graining of internal energies
• A computationally efficient implementation of continuum dislocation dynamics: Formulation and application to ultrafine-grained Mg polycrystals
• Dynamic Length Scale and Weakest Link Behavior in Crystal Plasticity
• Efficient numerical method to handle boundary conditions in 2D elastic media
• A First Experiment at Interfacing Crystal Plasticity and Continuum Dislocation Dynamics
• Cell structure formation in a two-dimensional density-based dislocation dynamics model
• Cyclic-loading microstructure-property relations from a mesoscale perspective: An example of single crystal Nickel-based superalloys
• Variational approach to determine the properties of dislocations at finite deformation