Plastic Flow Rule Based on Dislocation Link Velocity
Abstract
We develop a theory for the plastic shear rate γ̇i on each slip system i of face-centered cubic (FCC) single crystals, by integrating the shear rate contributions γ̇i(l) from dislocation links of length l. A generalized Orowan equation expresses γ̇i(l) in terms of the link density ni(l) and the average link velocity vi(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 τi, as reported previously, in the absence of any thermally activated mechanism. This dependence arises from the exponential tail of ni(l) filtered through the threshold-like velocity function vi(l). Furthermore, vi(l) is well approximated by a single two-dimensional function v(τi,l) for all these slip systems. The link velocity is therefore governed mainly by τi and l, with only a minor effect from the complex interactions between slip systems. These interactions instead manifest themselves mainly through ni(l). As a demonstration of the effect of the link-length distribution on the slip rate, we show that even when τi 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 τi on the link velocity.
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BibTeX
@misc{zhai2026plastic,
title = {{Plastic Flow Rule Based on Dislocation Link Velocity}},
author = {Hanfeng Zhai and Sh. Akhondzadeh and Ryan B. Sills and Nicolas Bertin and Wei Cai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23674},
eprint = {2610.23674},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23674},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Plastic Flow Rule Based on Dislocation Link Velocity
AU - Hanfeng Zhai
AU - Sh. Akhondzadeh
AU - Ryan B. Sills
AU - Nicolas Bertin
AU - Wei Cai
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23674
UR - https://arxiv.org/abs/2610.23674
AB - We develop a theory for the plastic shear rate γ̇_i on each slip system i of face-centered cubic (FCC) single crystals, by integrating the shear rate contributions γ̇_i(l) from dislocation links of length l. A generalized Orowan equation expresses γ̇_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 τ_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(τ_i,l) for all these slip systems. The link velocity is therefore governed mainly by τ_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 τ_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 τ_i on the link velocity.
ER -