Scaling Properties of Dislocation Simulations in the Similitude Regime

Abstract

Dislocation systems exhibit well known scaling properties such as the Taylor relationship between flow stress and dislocation density, and the "law of similitude" linking the flow stress to the characteristic wavelength of dislocation patterns. Here we discuss the origin of these properties, which can be related to generic invariance properties of the equations of evolution of discrete dislocation systems, and their implications for a wide class of models of dislocation microstructure evolution. We demonstrate that under certain conditions dislocation simulations carried out at different stress, dislocation density, and strain rate can be considered as equivalent, and we study the range of deformation conditions ("similitude regime") over which this equivalence can be expected to hold. In addition, we discuss the restrictions imposed by the formulated invariance properties for density-based, nonlocal or stochastic models of dislocation microstructure evolution, and for dislocation patterns and size effects.

References in corpus (2)

• Depinning transition of dislocation assemblies: pileup and low-angle grain boundary
• Dislocations Jam At Any Density

Cited by in corpus (23)

• Strain rate dependency of dislocation plasticity
• An analysis of the influence of grain size on the strength of FCC polycrystals by means of computational homogenization
• Dislocation Avalanches: Earthquakes on the Micron Scale
• Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization
• Taming intermittent plasticity at small scales
• Multipole expansion of continuum dislocations dynamics in terms of alignment tensors
• Dislocation patterning in a 2D continuum theory of dislocations
• Local density approximation for the energy functional of three-dimensional dislocation systems
• Quenched pinning and collective dislocation dynamics
• Deterministic and stochastic models of dislocation patterning
• Microstructural Comparison of the Kinematics of Discrete and Continuum Dislocations Models
• Grain boundary strengthening of FCC polycrystals
• A link between microstructure evolution and macroscopic response in elasto-plasticity: formulation and numerical approximation of the higher-dimensional Continuum Dislocation Dynamics theory
• Ice : The paradigm of wild plasticity
• Plastic yielding and deformation bursts in the presence of disorder from coherent precipitates
• Fluctuations in crystalline plasticity
• On the dynamics of curved dislocation ensembles
• The Emergence and Role of Dipolar Dislocation Patterns in Discrete and Continuum Formulations of Plasticity
• Microplasticity and yielding in crystals with heterogeneous dislocation distribution
• The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity
• 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
• On the effect of slip transfer at grain boundaries on the strength of FCC polycrystals