A Continuum Model for Dislocation Climb

Abstract

Dislocation climb plays an important role in understanding plastic deformation of metallic materials at high temperature. In this paper, we present a continuum formulation for dislocation climb velocity based on densities of dislocations. The obtained continuum formulation is an accurate approximation of the Green's function based discrete dislocation dynamics method (Gu et al. J. Mech. Phys. Solids 83:319-337, 2015). The continuum dislocation climb formulation has the advantage of accounting for both the long-range effect of vacancy bulk diffusion and that of the Peach-Koehler climb force, and the two longrange effects are canceled into a short-range effect (integral with fast-decaying kernel) and in some special cases, a completely local effect. This significantly simplifies the calculation in the Green's function based discrete dislocation dynamics method, in which a linear system has to be solved over the entire system for the long-range effect of vacancy diffusion and the long-range Peach-Koehler climb force has to be calculated. This obtained continuum dislocation climb velocity can be applied in any available continuum dislocation dynamics frameworks. We also present numerical validations for this continuum climb velocity and simulation examples for implementation in continuum dislocation dynamics frameworks.

References in corpus (10)

• Power-Law Creep from Discrete Dislocation Dynamics
• Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion
• Dislocation climb models from atomistic scheme to dislocation dynamics
• A coupled model of diffusional creep of polycrystalline solids based on climb of dislocations at grain boundaries
• Microstructural constitutive model for polycrystal viscoplasticity in cold and warm regimes based on continuum dislocation dynamics
• On the implementation of dislocation reactions in continuum dislocation dynamics modeling of mesoscale plasticity
• A continuum model for dislocation dynamics in three dimensions using the dislocation density potential functions and its application in understanding the micro-pillar size effect
• Dislocation dynamics formulation for self-climb of dislocation loops by vacancy pipe diffusion
• On the computational solution of vector-density based continuum dislocation dynamics models: a comparison of two plastic distortion and stress update algorithms
• The Role of Grain Boundaries under Long-Time Radiation