Elastic energy of a straight dislocation and contribution from core tractions

Abstract

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.

Keywords:

• dislocation theory
• anisotropic elasticity
• core tractions
• elastic energy
• core energy

Acknowledgements

The author is grateful to V. Bulatov, L. Ventelon, and F. Willaime for stimulating discussions, as well as to B. Lemoine for his help with the atomic simulations.

Notes

Notes

1. For a review, see 7.

2. For a more detailed presentation of the sextic formalism, cf. Chap. 13 in 20, 7 or 22.

3. We use the same sign convention as Hirth and Lothe 20. Eshelby et al. 4 and Stroh 5,6 use the opposite sign in Equation (6).

4. The degeneracy can be lifted by adding some noise to the elastic constants.

5. The expression used by Li et al. 9, based on the work of Cai et al. 8, is different from Equation (17). Li obtained , whereas Equation (17) can be rewritten . Both definitions may be equivalent in the case of a screw dislocation studied by Li et al., but we could not demonstrate this.