A Non-Linear Multiple Slip Theory in Continuum Dislocation Dynamics

Crystal plasticity is the result of the motion and complex and effectively non-linear interactions of dislocations. The collective behaviour of dislocations plays a prominent role both for the evolution of dislocation structures and as origin of strain hardening. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional dislocation density tensor was defined which overcomes some drawbacks of earlier dislocation density measures. The evolution equation for this tensor can be considered as a continuum version of dislocation dynamics. We use this tensor to develop a non-linear theory of multiple slip deformation. Starting from the rate of dislocation cutting events per volume, we deduce the m ean area swept by dislocations between cutting events and the closely related mean free segment length. If the mean dislocation velocity depends on the mean free segment length this leads to an important non-linearity which we illustrate by means of a simple example.