Dislocation-density kinematics: a simple evolution equation for dislocation density involving movement and tilting of dislocations

In this paper, a simple evolution equation for dislocation densities moving on a slip plane is proven. This equation gives the time evolution of dislocation density at a general field point on the slip plane, due to the approach of new dislocations and tilting of dislocations already at the field point. This equation is fully consistent with Acharya's evolution equation and Hochrainer et al.'s "continuous dislocation dynamics" (CDD) theory. However, it is shown that the variable of dislocation curvature in CDD is unnecessary if one considers one-dimensional flux divergence along the dislocation velocity direction.