Core energy and regularization parameters of non-singular continuum theories of dislocations using atomistic simulations

TL;DR

This paper investigates how different regularization parameters in continuum dislocation theories affect simulation results, using atomistic simulations to determine core energies and parameters for various dislocation models.

Contribution

It provides a systematic analysis of core energy and regularization parameters in non-singular dislocation theories using atomistic data, highlighting their influence on simulation accuracy.

Findings

Regularization parameters significantly influence DDD simulation results.

Different methods require different numbers of energy parameters for accurate core energy description.

Core energy must be included for CAWB and gradient elasticity methods to be valid.

Abstract

The dislocation core is an important region as it controls many important properties of materials. Elasticity breaks down in the core and the stress, force, and energy diverge at the dislocation line. We consider three commonest methods employed in Discrete Dislocation Dynamics (DDD) simulations to eliminate these singularities: (1) considering a cutoff parameter, (2) spreading the Burgers vector (CAWB theory), and (3) using gradient elasticity. Each of these methods includes an extra length parameter to regularize the elastic fields. In this article, we show that these regularization parameters can significantly influence the results of the DDD simulations. We use atomistic simulations for mixed dislocations to find the radius and energy of the dislocation core and find the regularization parameter and its variations with the dislocation character angle in each of the three methods. We have also considered if an arbitrary constant is chosen for the regularization parameter how the core energy should be added to the simulation codes. We have concluded that while the core energy in classical elasticity with a cutoff parameter can be described by one parameter, the other two methods need two energy parameters (core energy of edge and core energy of screw) for describing the variation of the core energy with the character angle. We have shown that no regularization parameter can be selected for the CAWB theory or gradient elasticity if no core energy is included.