A Mesh-Independent Brute-Force Approach for Traction-Free Corrections in Dislocation Problems

Abu Bakar Siddique,Tariq Khraishi

doi:10.4236/mnsms.2021.111001

Abstract

Simulation of dislocation dynamics opens the opportunity for researchers and scientists to observe in-depth many plastic deformation phenomena. In 2D or 3D media, modeling of physical boundary conditions accurately is one of the keys to the success of dislocation dynamics (DD) simulations. The scope of analytical solutions is restricted and applies to specific configurations only. But in dynamics simulations, the dislocations’ shape and orientation change over time thus limiting the use of analytical solutions. The authors of this article present a mesh-based generalized numerical approach based on the collocation point method. The method is applicable to any number of dislocations of any shape/orientation and to different computational domain shapes. Several verifications of the method are provided and successful implementation of the method in 3D DD simulations have been incorporated. Also, the effect of free surfaces on the Peach-Koehler force has been computed. Lastly, the effect of free surfaces on the flow stress of the material has been studied. The results clearly showed a higher force with increased closeness to the free surface and with increased dislocation segment length. The simulations’ results also show a softening effect on the flow stress results due to the effect of the free surfaces.

Highlights

Simulation of dislocation dynamics opens the opportunity for researchers and scientists to observe in-depth many plastic deformation phenomena
The correction term is derived by introducing image dislocations to treat the boundary condition of the free surface, which is analogous to the electrostatic problem of a line charge in a medium of non-homogeneous dielectric constant [4]
The dynamic case implements the method in a 3D dislocation dynamics simulation code that can generate a stress-strain curve

Summary

Introduction

The dislocation is a type of defect and a source of stress in crystalline materials. Dislocation theory explains plastic deformation in a material. The correction term is derived by introducing image dislocations to treat the boundary condition of the free surface, which is analogous to the electrostatic problem of a line charge in a medium of non-homogeneous dielectric constant [4]. For a linear dislocation segment perpendicular and parallel to a free surface, [9] [10] derived the correction term in an isotropic medium that was half-infinite. In the references indicated earlier [24] [25] [26], correction terms to satisfy the traction-free surfaces were generated for dislocation segments using a surface-attached coordinate systems They were transformed to a global coordinate system in order to calculate the stress evolution problem. The dynamic case implements the method in a 3D dislocation dynamics simulation code that can generate a stress-strain curve

Theory

Solving the System of Equations

Solution Time

Findings

Conclusion