Enabling strain hardening simulations with dislocation dynamics

Abstract

Numerical algorithms for discrete dislocation dynamics simulations are investigated for the purpose of enabling strain hardening simulations of single crystals on massively parallel computers. The algorithms investigated include the ′(N) calculation of forces, the equations of motion, time integration, adaptive mesh refinement, the treatment of dislocation core reactions, and the dynamic distribution of work on parallel computers. A simulation integrating all of these algorithmic elements using the Parallel Dislocation Simulator (ParaDiS) code is performed to understand their behavior in concert, and evaluate the overall numerical performance of dislocation dynamics simulations and their ability to accumulate percents of plastic strain.

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

“…However, as experimental capabilities mature they will provide the possibility of direct, quantitative, non-destructive comparisons between experiments and discrete dislocation dynamics predictions (Devincre et al, 2011;Ghoniem et al, 2000;Arsenlis et al, 2007). Of course, such direct, one-to-one comparisons between theoretical predictions and experimental measurements for stochastic processes such as dislocation generation and evolution can be performed quantitatively only through quantitative, statistical based analyses of simulations and experimental measurements.…”

The role of free surfaces on the formation of prismatic dislocation loops

“…In this formulation, the stress fields due to dislocations in an infinite perfect crystal are combined with those obtained from a solution of an auxiliary boundary value problem with suitable traction boundary conditions. We utilize the Parallel Dislocation Simulator (ParaDiS) [11] for the former and a parallel finite element code for the latter [12,13]. The material considered is a model face-centered cubic (fcc) crystal of aluminum with shear modulus l ¼ 27 GPa, Poisson's ratio m ¼ 0:35 and Burgers vector magnitude jbj ¼ 2:86Å.…”

Matrix compression by common subexpression elimination

“…Dislocation dynamics [5,6] is a method used to study plasticity and defects in materials. The paper [6] describes a fast multipole method [4] for the long range interaction between dislocations.…”

“…The motivation is that there are many cases of matrices with similarities which have not been studied by hand, and thus no efficient multiplication algorithm exists. This work is in fact the result of an attempt to optimize certain linear operators with unknown structure that are used in the fast multipole method for dislocations, developed in [6]. The results for these matrices were quite impressive, and are discussed in the results section.…”

“…multiplied with a vector) very many times. Two examples of this are how the fast Fourier transform and its inverse are used in every timestep in a time dependent fast Poisson solver, and how the far field to near field conversion operators are used in the fast multipole algorithm [4,6].…”