Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis

A numerical methodology to incorporate anisotropic elasticity into three-dimensional dislocation dynamics codes has been developed, employing theorems derived by Lothe [J. Lothe, Philos. Mag. 15 (1967) 353], Brown [L.M. Brown, Philos. Mag. 15 (1967) 363], Indenbom and Orlov [V.L. Indenbom, S.S. Orlov, Sov. Phys. Crystallogr. 12 (6) (1968) 849], and Asaro and Bamett [R.J. Asaro, D.M. Barnett, in: R.J. Arsenault, J.R. Beeler Jr., J.A. Simmons (Eds.), Computer Simulation for Materials Applications, Part 2. Nuclear Metallurgy, Vol. 20, p. 313]. The formalism is based on the stress field solution for a straight dislocation segment of arbitrary orientation in three-dimensional space. The general solution is given in a complicated closed integral form. To reduce the computation complexity, look-up tables are used to avoid heavy computations for the evaluation of the angular stress factor (Σij) and its first derivative term (Σij′). The computation methodology and error analysis are discussed in comparison with known closed form solutions for isotropic elasticity. For the case of Mo single crystals, we show that the difference between anisotropic and isotropic elastic stress fields can be, for some components of the stress tensor, as high as 15% close to the dislocation line, and decrease significantly away from it. This suggests that short-range interactions should be evaluated based on anisotropic elasticity, while long-range interactions can be approximated using long-range elasticity.