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Stochastically forced dislocation density distribution in plastic deformation.

Amit K Chattopadhyay1, Elias C Aifantis2

  • 1Mathematics, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom and Aston Materials Centre, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom.

Physical Review. E
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Summary
This summary is machine-generated.

This study introduces finite noise decay time into models of plastic deformation, revealing that nonlinear dislocation dynamics are significantly affected by this previously ignored factor, unlike linear processes.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Plastic deformation in metals involves deterministic applied loads and stochastic internal stress fluctuations.
  • Existing models often assume instantaneous relaxation of perturbations, which is physically unrealistic.
  • This simplification overlooks the impact of finite noise decay time on dislocation dynamics.

Purpose of the Study:

  • To investigate the influence of finite noise decay time on the dynamical evolution of dislocations.
  • To bridge the gap in existing models by incorporating colored noise (Ornstein-Uhlenbeck noise).
  • To analyze how this affects both linear and nonlinear dislocation processes.

Main Methods:

  • Mapping dislocation dynamics onto linear and nonlinear Wiener and Ornstein-Uhlenbeck processes.
  • Utilizing a Fokker-Planck model for mathematical analysis.
  • Introducing Ornstein-Uhlenbeck noise to represent colored noise with finite decay time (τ).

Main Results:

  • Linear Wiener processes in dislocation dynamics are unaffected by the noise decay time.
  • Nonlinear Wiener and Ornstein-Uhlenbeck processes exhibit scaling behavior dependent on the noise decay time (τ).
  • The finite decay time of stochastic perturbations plays a crucial role in nonlinear systems.

Conclusions:

  • The assumption of instantaneous relaxation in previous models is a significant limitation.
  • Finite noise decay time is a critical parameter for accurately modeling nonlinear dislocation dynamics.
  • Findings are expected to enhance experimental observations and guide future research in plasticity modeling.