The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

doi:10.1088/1674-1056/20/3/036102

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 36102-036102.doi: 10.1088/1674-1056/20/3/036102

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

范蕾¹, 范天佑²

(1)School of Life Science, Beijing Institute of Technology, Beijing 100081, China; (2)School of Science, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2010-10-29 修回日期:2010-11-25 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the National Natural Science Foundation of China(Grant Nos. 10372016 and 10672022).

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

Fan Tian-You (范天佑)^a)† and Fan Lei(范蕾)^b)

^a School of Science, Beijing Institute of Technology, Beijing 100081, China; ^b School of Life Science, Beijing Institute of Technology, Beijing 100081, China

Received:2010-10-29 Revised:2010-11-25 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the National Natural Science Foundation of China(Grant Nos. 10372016 and 10672022).

摘要/Abstract

摘要： The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the same results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy--momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.

关键词: quasicrystals, crack, plasticity, generalised Eshelby integral

Abstract: The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the same results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy--momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.

Key words: quasicrystals, crack, plasticity, generalised Eshelby integral

中图分类号:

61.44.Mr

范天佑, 范蕾. The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm[J]. 中国物理B, 2011, 20(3): 36102-036102.

Fan Tian-You (范天佑) and Fan Lei(范蕾). The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm[J]. Chin. Phys. B, 2011, 20(3): 36102-036102.

参考文献 19

[1]	Li X F and Fan T Y 2002 Chin. Phys. 11 266
[2]	Fan T Y, Li X F and Sun Y F 1999 Chin. Phys. 8 288
[3]	Fan T Y, Trebin H R, Messeschmidt U and Mai Y W, 2004 J. Phys.: Condens. Matter 16 3229
[4]	Fan T Y and Fan L 2008 Phil. Mag. 88(4) 305
[5]	Eshelby J D 1956 Solid State Physics (ed. by Seits F et al) (New York: Academic Press) Vol. 3
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[7]	Bilby B A, Cottrell A H, Smith E and Swinden K H 1964 Proc. R. Soc. A 279 1
[8]	Dugdale D S 1960 J. Mech. Phys. Solids 32 105
[9]	Barenblatt G I 1962 Advances in Applied Mechanics 7 55
[10]	Fan T Y 2010 Mathematical Theory of Elasticity of Quasicrystals and Its Applications (Beijing: Science Press/Heidelberg: Springer-Verlag) p 289
[11]	Fan T Y and Mai Y W 2004 Appl. Mech. Rev. 57 325
[12]	Zhu A Y and Fan T Y 2007 Chin. Phys. 16 1111
[13]	Fan T Y, Wang X F, Li Wu and Zhu A Y 2008 Phil. Mag. 88 601
[14]	Wang X F, Fan T Y and Zhu A Y 2009 Chin. Phys. B 18 709
[15]	Mong X M, Tong B Y and Wu Y K 1994 Acta Metallurgica Sinica A 30 61 (in Chinese)
[16]	Rice J R 1968 J. Appl. Mech. 35 379
[17]	Cherepanov G P 1969 Int. J. Solids and Structures 5 77
[18]	Begley G T and Landes J D 1972 Fracture Toughness, ASTM STP 514 (Philadelphia: American Society for Testing and Materials) p1
[19]	Landes J D and Begley G T 1972 Fracture Toughness, ASTM STP 514 (Philadelphia: American Society for Testing and Materials) p24 endfootnotesize

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

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