Plastic Flow Rule Based on Dislocation Link Velocity

We develop a theory for the plastic shear rate ${\dot{\gamma }}_i$ on each slip system $i$ of face-centered cubic (FCC) single crystals, by integrating the shear rate contributions ${\dot{\gamma }}_i(l)$ from dislocation links of length $l$. A generalized Orowan equation expresses ${\dot{\gamma }}_i(l)$ in terms of the link density $n_i(l)$ and the average link velocity $v_i(l)$. This model accurately reproduces the discrete dislocation dynamics (DDD) shear-rate data for all 12 slip systems across 99 loading orientations. In particular, it explains why the plastic shear rate depends exponentially on the resolved shear stress ${\tau }_i$, as reported previously, in the absence of any thermally activated mechanism. This dependence arises from the exponential tail of $n_i(l)$ filtered through the threshold-like velocity function $v_i(l)$. Furthermore, $v_i(l)$ is well approximated by a single two-dimensional function $v({\tau }_i,l)$ for all these slip systems. The link velocity is therefore governed mainly by ${\tau }_i$ and $l$, with only a minor effect from the complex interactions between slip systems. These interactions instead manifest themselves mainly through $n_i(l)$. As a demonstration of the effect of the link-length distribution on the slip rate, we show that even when ${\tau }_i$ is limited to a narrow window, the shear rates still span two orders of magnitude. The supply of long links is therefore the dominant factor controlling slip-system activity, outweighing the direct effect of ${\tau }_i$ on the link velocity.