3D DISCRETE DISLOCATION DYNAMICS APPLIED TO ... - NUMODIS

Chapter 2
Description of the simulation method
THE discrete dislocation dynamics (DDD) method initially proposed in [Canova & Kubin 91] has
been improved much in its numerical precision and applicability to problems involving complex
boundary conditions over the past 15 years. The purpose of this chapter is to review the theoretical
backgrounds and methodologies of the DDD method, and also to describe the author’s contributions
: computation of displacement fields, implementation of internal interfaces and the periodic boundary
conditions and acceleration of the code using the revised box method.
The DDD method used in this thesis only deals with perfect dislocations in face-centered cubic (FCC)
metals. Sec. 2.1 introduces the simulation lattice and the discretization of a dislocation line of the DDD
model, and the model is compared with other dislocation dynamics models. Although the focus is given
on the FCC lattice, the methodology is quite general. The extension of the method to the other cubic
crystals is also discussed briefly.
Computation of the effective stress of each dislocation segment is presented in Sec. 2.2. The method
used for computing the displacement field of a dislocation loop is detailed also, and the extension of the
method to more general dislocation structures can be found in Sec. 4.3.5. The stress and displacement
solutions are all based on the theory of linear elasticity in isotropic frame.
Sec. 2.3 introduces the motion of dislocation segments. This section includes a description of the several
local rules needed to handle interactions between dislocations.
New boundary conditions are explained in Sec. 2.4. Representation of internal interfaces is discussed
in both a simple method using facets and a more rigorous way with full elastic interactions. The
implementation of periodic boundary conditions is also detailed.
The performance of the DDD code is improved by revising the box method which was first described in
[Verdier et al. 98]. The computational efficiency of the method is significantly increased by using the