The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip

A recent continuum dislocation dynamics formalism (Xia and El-Azab 2015 Model. Simul. Mater. Sci. Eng. 23 055009) has been enriched by incorporating an improved cross slip model. 3D discrete dislocation dynamics simulations were used to collect cross slip rate data in the form of time series that were analysed to estimate the correlation time for cross slip, which was subsequently used as a time scale for local window averaging of the collected cross slip rate data. This time averaging filters out the cross slip rate fluctuations over time intervals less than the correlation time, thus resulting in relatively smoother time series for the cross slip rates. The coarse grained series were further cast in the form of smooth trends with superposed fluctuations and implemented in continuum dislocation dynamics simulations using a Monte Carlo scheme. This approach resulted in a significant improvement of the predicted stress-strain response and a more realistic dislocation cell structure evolution. The similitude law for the average cell size evolution with inverse of stress, however, remains unaffected by the cross slip rates used in continuum dislocation dynamics.