  Dislocation slip is a general deformation mode and governs the strength of
metals. Via discrete dislocation dynamics and molecular dynamics simulations,
we investigate the strain rate and dislocation density dependence of the
strength of bulk copper single crystals using 192 simulations spanning over 10
orders of magnitude in strain rate and 9 orders of magnitude in dislocation
density. Based on these large set of simulations and theoretical analysis, a
new analytical relationship between material strength, dislocation density,
strain rate and dislocation mobility is proposed, which is in excellent
agreement with the current simulations as well as with experimental data. The
results show that the material strength is a non-monotonic function of
dislocation density and displays two universal regimes (first decreasing, then
increasing) as the dislocation density increases. The first regime is a result
of strain rate hardening, while the second regime is dominated by the classical
Taylor forest hardening. Accordingly, the strength displays universally, as a
function of strain rate, a rate-independent regime at low strain rates
(governed by forest hardening) followed by a rate hardening regime at high
strain rates (governed by strain rate hardening). All the results can be
captured by a single scaling function. Finally, the fluctuations of dislocation
flow are analyzed in terms of the strain rate dependent distribution of
dislocation segment velocities. It is found that the fluctuations are governed
by another universal scaling function and diverge in the rate independent
limit, indicating a critical behavior. The current analysis provides a
comprehensive understanding on how collective dislocation motions are governed
by the competition between the internal elastic interactions of dislocations,
and the stress required to drive dislocation fluxes at a given externally
imposed strain rate.
