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Chin. Phys. B, 2018, Vol. 27(7): 074601    DOI: 10.1088/1674-1056/27/7/074601

Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid

Xin Lv(吕鑫), Guan-Ting Liu(刘官厅)
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
Abstract  Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.
Keywords:  parallel screw dislocations      semi-infinite crack      magnetoelectroelastic solid      interaction  
Received:  18 November 2017      Revised:  23 February 2018      Published:  05 July 2018
PACS:  46.05.+b (General theory of continuum mechanics of solids)  
  46.50.+a (Fracture mechanics, fatigue and cracks)  
  61.72.Lk (Linear defects: dislocations, disclinations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11262017, 11262012, and 11462020), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2015MS0129), the Key Project of Inner Mongolia Normal University, China (Grant No. 2014ZD03), and the Graduate Research Innovation Project of Inner Mongolia Autonomous Region, China (Grant No. S20171013502).
Corresponding Authors:  Xin Lv, Guan-Ting Liu     E-mail:;

Cite this article: 

Xin Lv(吕鑫), Guan-Ting Liu(刘官厅) Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid 2018 Chin. Phys. B 27 074601

[1] Nan C W 1994 Phys. Rev. B 50 6082
[2] Sih G C, Jones R and Song Z F 2003 Theor. Appl. Fract. Mec. 40 161
[3] Gao C F, Kessler H and Balke H 2003 Int. J. Eng. Sci. 41 969
[4] Gao C F, Kessler H and Balke H 2003 Int. J. Eng. Sci. 41 983
[5] Wang B L and Mai Y W 2003 Eur. J. Mech. 22 591
[6] Wang B L and Mai Y W 2004 Mech. Res. Commun. 31 65
[7] Zhao M H, Wang H, Yang F and Liu T 2006 Theor. Appl. Fract. Mec. 45 227
[8] Wang B L and Mai Y W 2007 Int. J. Solid Struct. 44 387
[9] Zhong X C 2008 Study on Fracture of Magnetoelectroelastic Solid (Ph.D. Dissertation) (Hunan:Central South University) (in Chinese)
[10] Li G, Wang B L and Han J C 2010 Int. J. Solid Struct. 47 419
[11] Guo J H, Lu Z X and SIRI G L 2013 Acta Mater. Compos. Sin. 30 192 (in Chinese)
[12] Hao R J and Liu J X 2006 Mech. Res. Commun. 33 415
[13] Fang Q H, Liu Y W and Jiang C P 2005 Int. J. Eng. Sci. 43 1011
[14] Yu M, Fang Q H, Liu Y W and Zeng X 2012 Theor. Appl. Fract. Mech. 59 34
[15] Hu K Q and Li G Q 2005 Mech. Mater. 37 925
[16] Xiao Z M, Chen B J and Luo J 2010 Acta Mech. 214 261
[17] Liu X and Guo J H 2016 Theor. Appl. Fract. Mec. 86 225
[18] Liu G T and Yang L Y 2017 Chin. Phys. B 26 094601
[19] Qin Q H and Yang Q S 2006 Macro-Micro Theory on Multifield Coupling Behavior of Heterogeneous Materials (Vol. 1) (Beijing:Higher Education Press) p. 101 (in Chinese)
[20] Lin I H and Thomson R 1986 Acta Metall. 34 187
[21] Muskhelishvili N I 1953 Singular Integral Equations (Noordhoff:Groningen)
[22] Liu G T, Guo R P and Fan T Y 2003 Chin. Phys. B 12 1149
[23] Sih G C and Chen E P 2003 Theor. Appl. Fract. Mech. 40 1
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