M. Rhee et al., Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis, MAT SCI E A, 309, 2001, pp. 288-293
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.