Inertial and retardation effects for dislocation interactions

TL;DR

This paper introduces a new formulation for dislocation interactions considering inertial and retardation effects, showing improved accuracy in modeling high strain rate behaviors and revealing complex dislocation phenomena.

Contribution

A novel equation of motion for dislocations incorporating inertial, kinetic, and retardation effects, validated against numerical solutions and revealing new dislocation interaction mechanisms.

Findings

Good agreement with Peierls-Nabarro Galerkin simulations

Retardation effects significantly influence dislocation interactions

Discovery of a renucleation mechanism during dislocation annihilation

Abstract

A new formulation for the equation of motion of interacting dislocations is derived. From this solution it is shown that additional coupling forces, of kinetic and inertial origin, should be considered in Dislocation Dynamics (DD) simulations at high strain rates. A heuristic modification of this general equation of motion enables one to introduce retardation into inertial and elastic forces, in accordance with a progressive rearrangement of fields through wave propagation. The influence of the corresponding coupling terms and retardation effects are then illustrated in the case of dislocation dipolar interaction and coplanar annihilation. Finally, comparison is made between the modified equation of motion and a precise numerical solution based on the Peierls-Nabarro Galerkin method. Good agreement is found between the Peierls-Nabarro Galerkin method and the EoM including retardation effects for a dipolar interaction. For coplanar annihilation, it is demonstrated that an unexpected mechanism, involving a complex interplay between the core of the dislocations and kinetics energies, allows a renucleation from the completely annihilated dislocations. A description of this phenomenon that could break the most favourable reaction between dislocations is proposed.