Stochastically forced dislocation density distribution in plastic deformation


The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such type of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical") of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem but all nonlinear processes, both Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time τ. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information:
Uncontrolled Keywords: Stochastic,gradient mechanics,dislocation density,materials modelling,Statistical and Nonlinear Physics,Statistics and Probability,Condensed Matter Physics
Publication ISSN: 1550-2376
Last Modified: 15 Apr 2024 07:18
Date Deposited: 23 Sep 2016 07:11
Full Text Link: http://journals ... sRevE.94.022139
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2016-08
Published Online Date: 2016-08-26
Accepted Date: 2016-08-13
Submitted Date: 2016-05-19
Authors: Chattopadhyay, Amit K. (ORCID Profile 0000-0001-5499-6008)
Aifantis, Elias C.



Version: Accepted Version

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