Dislocation loops in anisotropic elasticity: displacement field, stress function tensor and interaction energy

Abstract

The aim of the present paper is to give a clear and straightforward derivation of the displacement field, stress function tensor and interaction energy of dislocations in the theory of incompatible anisotropic elasticity. The displacement field caused by a dislocation loop in an elastically anisotropic medium can be written as the sum of a line integral plus a purely geometric part. This is the anisotropic generalization of the Burgers formula. Formulae for the first-order stress function tensor and the interaction energy between two dislocation loops in anisotropic media are derived.

Keywords:

• anisotropic elasticity
• dislocation loop
• Green tensor
• Burgers formula
• interaction energy

Acknowledgements

M.L. gratefully acknowledges the grants of the Deutsche Forschungsgemeinschaft (Grant Nos. La1974/2-1, La1974/3-1). M.L. wishes to express his gratitude to Dr. Eleni Agiasofitou for her constructive and helpful remarks during the preparation of the paper.