Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments

Abstract

We obtain the singular asymptotic behavior of the stress field in the vicinity of a non-planar dislocation in three dimensions and the nearly singular behavior of the full self-force of the dislocation including both glide and climb forces, using asymptotic analysis. We also derive asymptotic formulas for the stress field in the vicinity of a curved dislocation segment. Numerical examples are presented to examine the asymptotic formulas. The obtained formulas can be used for qualitative understanding of the stress tensor associated with dislocations and efficient and accurate calculation of the stress tensor in dislocation dynamics simulations.

Keywords:

• dislocations
• dislocation dynamics
• stresses
• singularity
• asymptotic analysis

Acknowledgments

This work was partially supported by Hong Kong Research Grants Council General Research Funds 604604 and 603807, HKUST Postdoctoral Fellowship Matching Fund, and the Nanoscience and Nanotechnology Program at HKUST. The work of H.Q. Wang is also supported by the National Natural Science Foundation of China no. 10901134.