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

A numerical methodology to incorporate anisotropic elasticity into three-di mensional 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. Orlo v, Sov. Phys. Crystallogr. 12 (6) (1968) 849], and Asaro and Bamett [R.J. A saro, D.M. Barnett, in: R.J. Arsenault, J.R. Beeler Jr., J.A. Simmons (Eds. ), Computer Simulation for Materials Applications, Part 2. Nuclear Metallur gy, Vol. 20, p. 313]. The formalism is based on the stress field solution f or a straight dislocation segment of arbitrary orientation in three-dimensi onal space. The general solution is given in a complicated closed integral form. To reduce the computation complexity, look-up tables are used to avoi d heavy computations for the evaluation of the angular stress factor (Sigma (ij)) and its first derivative term (Sigma ' (ij)). The computation method ology 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 tenser, as high as 15% clo se to the dislocation line, and decrease significantly away from it. This s uggests that short-range interactions should be evaluated based on anisotro pic elasticity, while long-range interactions can be approximated using lon g-range elasticity (C) 2001 Elsevier Science B.V. All rights reserved.