Stochastically forced dislocation density distribution in plastic deformation

Amit K. Chattopadhyay*, Elias C. Aifantis

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Article number022139
Number of pages8
JournalPhysical Review E
Volume94
Issue number2
Early online date26 Aug 2016
DOIs
Publication statusPublished - Aug 2016

Fingerprint

Plastic Deformation
Dislocation
plastic deformation
density distribution
Randomness
Ornstein-Uhlenbeck process
Decay
Dislocation Dynamics
Stochastic Perturbation
Colored Noise
Fokker-Planck
Linear Process
Structural Dynamics
Ornstein-Uhlenbeck Process
Nonlinear Process
Wiener Process
decay
Random Effects
residual stress
Instantaneous

Bibliographical note

http://dx.doi.org/10.1103/PhysRevE.94.022139

Keywords

  • Stochastic
  • gradient mechanics
  • dislocation density
  • materials modelling

Cite this

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Stochastically forced dislocation density distribution in plastic deformation. / Chattopadhyay, Amit K.; Aifantis, Elias C.

In: Physical Review E, Vol. 94, No. 2, 022139, 08.2016.

Research output: Contribution to journalArticle

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