Inertial and retardation effects for dislocation interactions

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 is then illustrated in the case of the 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 equation of motion including retardation effects for a dipolar interaction. For coplanar annihilation, it is demonstrated that an unexpected mechanism, involving a complex inter-play 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.

Keywords:

• dislocation interactions
• elastic waves
• plasticity of metals
• inertial effect

Acknowledgements

The authors gratefully thank Y.P. Pellegrini for insightful discussions about the equations of motion, B. Devincre for precious comments on this manuscript and R. Madec for discussions.