  We present a dislocation density-based strain hardening model for single
crystal copper through a systematic coarse-graining analysis of more than 200
discrete dislocation dynamics (DDD) simulations of plastic deformation under
uniaxial tension. The proposed constitutive model has two components: a
generalized Taylor relation connecting resolved shear stresses to dislocation
densities on individual slip systems, and a generalized Kocks-Mecking model for
dislocation multiplication. The DDD data strongly suggests a logarithmic
dependence of flow stress on the plastic shear strain rate on each slip system,
and, equivalently, an exponential dependence of the plastic shear strain rate
on the resolved shear stress. Hence the proposed generalized Taylor relation
subsumes the Orowan relation for plastic flow. The DDD data also calls for a
correction to the Kocks-Mecking model of dislocation multiplication to account
for the increase of dislocation density on slip systems with negligible plastic
shear strain rate. This is accomplished by allowing the multiplication rate on
each slip system to include contributions from the plastic strain rates of the
two coplanar slip systems. The resulting constitutive model successfully
captures the strain hardening rate dependence on the loading orientation as
predicted by the DDD simulations, which is also consistent with existing
experiments.
