Volume 2, Issue 1
Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal

CSIAM Trans. Appl. Math., 2 (2021), pp. 175-194.

Published online: 2021-02

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• Abstract

The movement of dislocations and the corresponding crystal plastic deformation are highly influenced by the interaction between dislocations and nearby free surfaces. The boundary condition for inclination angle $θ$inc which indicates the relation between a dislocation line and the surface is one of the key ingredients in the dislocation dynamic simulations. In this paper, we first present a systematical study on $θ$inc by molecular static simulations in BCC-irons samples. We also study the inclination angle by using molecular dynamic simulations. A continuum description of inclination angle in both static and dynamic cases is derived based on Onsager's variational principle. We show that the results obtained from continuum description are in good agreement with the molecular simulations. These results can serve as boundary conditions for dislocation dynamics simulations.

• Keywords

Dislocation, dislocation dynamics, boundary conditions, analytical model, Onsager's variational principle.

65G05, 70G75

yuancheng@whu.edu.cn (Cheng Yuan)

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@Article{CSIAM-AM-2-175, author = {Shuyang and Dai and and 14475 and and Shuyang Dai and Fengru and Wang and and 14476 and and Fengru Wang and Yang and Xiang and and 14477 and and Yang Xiang and Jerry and Zhijian Yang and and 14478 and and Jerry Zhijian Yang and Cheng and Yuan and yuancheng@whu.edu.cn and 14479 and School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China. and Cheng Yuan}, title = {Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2021}, volume = {2}, number = {1}, pages = {175--194}, abstract = {

The movement of dislocations and the corresponding crystal plastic deformation are highly influenced by the interaction between dislocations and nearby free surfaces. The boundary condition for inclination angle $θ$inc which indicates the relation between a dislocation line and the surface is one of the key ingredients in the dislocation dynamic simulations. In this paper, we first present a systematical study on $θ$inc by molecular static simulations in BCC-irons samples. We also study the inclination angle by using molecular dynamic simulations. A continuum description of inclination angle in both static and dynamic cases is derived based on Onsager's variational principle. We show that the results obtained from continuum description are in good agreement with the molecular simulations. These results can serve as boundary conditions for dislocation dynamics simulations.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2020-0003}, url = {http://global-sci.org/intro/article_detail/csiam-am/18659.html} }
TY - JOUR T1 - Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal AU - Dai , Shuyang AU - Wang , Fengru AU - Xiang , Yang AU - Zhijian Yang , Jerry AU - Yuan , Cheng JO - CSIAM Transactions on Applied Mathematics VL - 1 SP - 175 EP - 194 PY - 2021 DA - 2021/02 SN - 2 DO - http://doi.org/10.4208/csiam-am.SO-2020-0003 UR - https://global-sci.org/intro/article_detail/csiam-am/18659.html KW - Dislocation, dislocation dynamics, boundary conditions, analytical model, Onsager's variational principle. AB -

The movement of dislocations and the corresponding crystal plastic deformation are highly influenced by the interaction between dislocations and nearby free surfaces. The boundary condition for inclination angle $θ$inc which indicates the relation between a dislocation line and the surface is one of the key ingredients in the dislocation dynamic simulations. In this paper, we first present a systematical study on $θ$inc by molecular static simulations in BCC-irons samples. We also study the inclination angle by using molecular dynamic simulations. A continuum description of inclination angle in both static and dynamic cases is derived based on Onsager's variational principle. We show that the results obtained from continuum description are in good agreement with the molecular simulations. These results can serve as boundary conditions for dislocation dynamics simulations.

Shuyang Dai, Fengru Wang, Yang Xiang, Jerry Zhijian Yang & Cheng Yuan. (2021). Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal. CSIAM Transactions on Applied Mathematics. 2 (1). 175-194. doi:10.4208/csiam-am.SO-2020-0003
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