Introduction of a hybrid model for the discrete 3D simulation of dislocation dynamics

Abstract

A hybrid model is suggested to discretely consider self forces and non-conservative effects in 3D dislocation dynamics. The dislocations are idealized as line defects in a homogeneous linear elastic medium. Each dislocation line consists of interconnected straight segments. The displacement and stress fields associated with the segments are formulated for general anisotropy and arbitrary crystal symmetry using Brown's theorem and the integral formalism in the version of Asaro and Barnett. The stress field of each dislocation is then computed through a linear superposition of the stress contributions of all segments. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. The differential equations of the individual segments are coupled through the line tension which is discretely considered by calculating the self interaction force among the segments that belong to the same dislocation according to the concept of Brown. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the climbing segment. The influence of temperature is introduced by regarding the crystal as a canonical ensemble and by including a stochastic Langevin force as proposed by Rönnpagel.