Continuum approximation of dislocation correlations for systems of curved dislocations
A Jason Marx1,2, Stefan Sandfeld2, Thomas Hochrainer3
1Fachbereich Produktionstechnik, Fachgebiet 15, Universität Bremen, Bibliothekstraße 1, Bremen, 28359 Germany.
Journal of Materials Science. Materials Theory
|February 4, 2026
Summary
This study analyzes dislocation self-correlations in crystal plasticity, revealing their dominance in simulations. Understanding these correlations is crucial for developing accurate continuum plasticity theories.
Area of Science:
- Materials Science
- Condensed Matter Physics
- Solid Mechanics
Background:
- Crystal plasticity is governed by dislocation motion and interactions.
- Continuum plasticity theories can emerge from statistical mechanics of dislocations.
- Long-range elastic interactions necessitate considering dislocation correlations.
Purpose of the Study:
- To derive analytical expressions for dislocation self-correlations.
- To analyze pair correlations in dislocation configurations.
- To investigate dislocation radius distributions and their relation to curvature.
Main Methods:
- Derivation of analytical expressions for self-correlations in circular dislocation loop configurations.
- Analysis of pair correlations in dipole-like dislocation configurations.
- Comparison of discrete dislocation dynamics simulations with maximum information entropy models.
Main Results:
- Analytical expressions for self-correlations in various dislocation configurations were derived.
- Self-correlations were found to dominate numerical correlation data.
- Dislocation radius distributions from simulations match entropy models incorporating curvature.
Conclusions:
- Self-correlations are critical for understanding crystal plasticity and require careful theoretical treatment.
- A curvature-related variable is necessary for physically meaningful radius distributions in continuum dislocation dynamics.
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