Examining the evolution of the internal length as a function of plastic strain

Recent studies have successfully related gradient plasticity with discrete dislocation dynamics (DDD), providing estimates for the internal length scale parameter and relating it to characteristics of deformation such as the dislocation source length and dislocation source spacing. In those studies the internal length was taken to be a constant throughout plastic deformation, which however may not be physically the case as the dislocation structure evolves with deformation and there have been theoretical models suggesting an internal length that is a function of the plastic strain. In the present study, hence, when fitting the gradient plasticity expressions to the DDD data, the internal length was treated as a 'free' fit parameter for different strain levels, providing different values for the internal length throughout deformation. The results indicate that when deformation occurred in a hardening manner, the internal length decreased with increasing deformation, since the dislocation structure became denser. If however, deformation occurred in a perfectly plastic manner the internal length remained relatively constant throughout the different strain levels.