Statistical characterization of dislocation ensembles

Abstract

A method of studying spatial and orientation statistics of dislocations in deforming crystals is presented in this paper. This method is based on the use of the concept of a stochastic fibre process to model dislocations. Orientation-dependent statistical measures of the dislocation density, velocity and flux have been introduced, and the connection between these statistical measures and the dislocation density tensor and rate of plastic distortion in deforming crystals has been established. The Parallel Dislocation Simulator (ParaDiS) code has been used to conduct a simulation of dislocation systems in a body-centred cubic crystal and the numerical data of the simulated dislocation systems have been used to compute the statistical measures introduced here. The orientation distributions of the density, velocity and flux of dislocations, as well as the dislocation correlations, have been computed as functions of strain and strain rate. The results reveal previously unknown features of these distributions, which illustrates the importance of the statistical method introduced here in understanding the collective behaviour of dislocation systems and building density-based models of dislocation dynamics.

Acknowledgements

JD has been supported in part by the LDRD Program of Oak Ridge National Laboratory under the UT-Battelle LLC contract number 4000040123 at Florida State University. The work of Meijie Tang was performed under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory (LLNL) under contract number W-7405-ENG-48. The authors wish to thank the ParaDiS code team of LLNL for making the code available for use during the course of this study. The comments provided by the referees led to a significant improvement of this paper.