On the consideration of climb in discrete dislocation dynamics

A concept is outlined to incorporate dislocation climb in a discrete three-dimensional model of dislocation dynamics. Each dislocation line consists of a sequence of interconnected piecewise straight segments which are embedded in a homogeneous linear elastic medium. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the climbing segment. The osmotic force on each segment depends on the local point defect concentration. The mechanical structure evolution law must thus be complemented with a chemical structure evolution equation. Corresponding formulations are derived using the continuity equation and Fick's first law of diffusion.