Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(11): 116201    DOI: 10.1088/1674-1056/20/11/116201
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Analytic solutions to a finite width strip with a single edge crack of two-dimensional quasicrystals

Li Wu(李梧)
Institute of Applied Mathematics, Xuchang University, Xuchang 461000, China
Abstract  In this paper, we investigate the well-known problem of a finite width strip with a single edge crack, which is useful in basic engineering and material science. By extending the configuration to a two-dimensional decagonal quasicrystal, we obtain the analytic solutions of modes I and II using the transcendental function conformal mapping technique. Our calculation results provide an accurate estimate of the stress intensity factors KI and KII, which can be expressed in a quite simple form and are essential in the fracture theory of quasicrystals. Meanwhile, we suggest a generalized cohesive force model for the configuration to a two-dimensional decagonal quasicrystal. The results may provide theoretical guidance for the fracture theory of two-dimensional decagonal quasicrystals.
Keywords:  transcendental function conformal mapping      quasicrystal      stress intensity factor  
Received:  12 April 2011      Revised:  14 June 2011      Accepted manuscript online: 
PACS:  62.20.D- (Elasticity)  
  61.44.Br (Quasicrystals)  
  62.20.M- (Structural failure of materials)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10802043).

Cite this article: 

Li Wu(李梧) Analytic solutions to a finite width strip with a single edge crack of two-dimensional quasicrystals 2011 Chin. Phys. B 20 116201

[1] Shechtman D, Blech I, Gratias D and Cahn J W 1984 Phys. Rev. Lett. 53 1951
[2] Hu C Z, Wang R H and Ding D H 2000 Rep. Prog. Phys. 63 1
[3] Gao Y, Zhao Y T and Zhao B S 2007 Physica B 394 56
[4] Li X F and Fan T Y 1998 Chin. Phys. Lett. 15 278
[5] Wang J B, Gastaldi J and Wang R H 2008 Chin. Phys. Lett. 18 88
[6] Mikulla R, Stadler J, Trebin H R, Krul F and Gumbsch P 1998 Phys. Rev. Lett. 81 3163
[7] Liu G T and Fan T Y 2004 Int. J. Solids Struct. 41 3949
[8] Edagawa K 2007 Phil. Mag. 87 2789
[9] Caillard D, Vanderschaeve G and Bresson L 2000 Phil. Mag. A 80 237
[10] Bohsung J and Trebin H R 1987 Phys. Rev. Lett. 58 1204
[11] Feuerbacher M, Bartsch M and Messerchmidt U 1997 Phil. Mag. Lett. 76 369
[12] Li L H 2010 Chin. Phys. B 19 046101
[13] Zhu A Y and Fan T Y 2008 J. Phys.: Condens. Matter 20 295217
[14] Wang J B, Mancini L, Wang R H and Gastaldi J 2003 J. Phys: Condens. Matter 15 L363
[15] Wang J B, Yang W G and Wang R H 2003 J. Phys.: Condens. Matter 15 1599
[16] Zhu A Y and Fan T Y 2007 Chin. Phys. 16 1111
[17] Wang X F, Fan T Y and Zhu A Y 2009 Chin. Phys. B 18 709
[18] Li W and Fan T Y 2011 Chin. Phys. B 20 036101
[19] Fan T Y and Fan L 2011 Chin. Phys. B 20 036102
[20] Shen D W and Fan T Y 2003 Eng. Fract. Mech. 70 813
[21] Fan T Y 1990 Chin. Phys. Lett. 7 402
[22] Yang X CH, Wang L and Fan T Y 1998 Chin. Phys. Lett. 15 117
[23] Fan T Y, Yang X C and Li H X 1999 Chin. Phys. Lett. 16 32
[24] Fan T Y 2010 Mathematical Theory of Elasticity of Quasicrystals and Its Applications (Heideberg: Springer-Verlag)
[1] Substitutions of vertex configuration of Ammann-Beenker tiling in framework of Ammann lines
Jia-Rong Ye(叶家容), Wei-Shen Huang(黄伟深), and Xiu-Jun Fu(傅秀军). Chin. Phys. B, 2022, 31(8): 086101.
[2] Non-Hermitian quasicrystal in dimerized lattices
Longwen Zhou(周龙文) and Wenqian Han(韩雯岍). Chin. Phys. B, 2021, 30(10): 100308.
[3] Bose-Einstein condensates in an eightfold symmetric optical lattice
Zhen-Xia Niu(牛真霞), Yong-Hang Tai(邰永航), Jun-Sheng Shi(石俊生), Wei Zhang(张威). Chin. Phys. B, 2020, 29(5): 056103.
[4] Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals
Dongsheng Yang(杨东升) and Guanting Liu(刘官厅)†. Chin. Phys. B, 2020, 29(10): 104601.
[5] Quantum anomalous Hall effect in twisted bilayer graphene quasicrystal
Zedong Li(李泽东) and Z F Wang(王征飞)†. Chin. Phys. B, 2020, 29(10): 107101.
[6] Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal
Guan-Ting Liu(刘官厅), Li-Ying Yang(杨丽英). Chin. Phys. B, 2017, 26(9): 094601.
[7] The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals
Li-Juan Jiang(姜丽娟), Guan-Ting Liu(刘官厅). Chin. Phys. B, 2017, 26(4): 044601.
[8] Diurnal cooling for continuous thermal sources under direct subtropical sunlight produced by quasi-Cantor structure
Jia-Ye Wu(吴嘉野), Yuan-Zhi Gong(龚远志), Pei-Ran Huang(黄培然), Gen-Jun Ma(马根骏), Qiao-Feng Dai(戴峭峰). Chin. Phys. B, 2017, 26(10): 104201.
[9] Analysis of composite material interface crack face contact and friction effects using a new node-pairs contact algorithm
Zhong Zhi-Peng (钟志鹏), He Yu-Bo (何郁波), Wan Shui (万水). Chin. Phys. B, 2014, 23(6): 064601.
[10] Finite size specimens with cracks of icosahedral Al–Pd–Mn quasicrystals
Yang Lian-Zhi (杨连枝), Ricoeur Andreas, He Fan-Min (何蕃民), Gao Yang (高阳). Chin. Phys. B, 2014, 23(5): 056102.
[11] Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow
Li Lian-He (李联和), Liu Guan-Ting (刘官厅). Chin. Phys. B, 2014, 23(5): 056101.
[12] Anti-plane problem analysis for icosahedral quasicrystals under shear loadings
Li Wu (李梧), Chai Yu-Zhen (柴玉珍). Chin. Phys. B, 2014, 23(11): 116201.
[13] Elastic fields around a nanosized elliptichole in decagonal quasicrystals
Li Lian-He (李联和), Yun Guo-Hong (云国宏). Chin. Phys. B, 2014, 23(10): 106104.
[14] A Dugdale–Barenblatt model for a strip with a semi-infinite crack embedded in decagonal quasicrystals
Li Wu (李梧), Xie Ling-Yun (解凌云). Chin. Phys. B, 2013, 22(3): 036201.
[15] Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole
Li Lian-He (李联和). Chin. Phys. B, 2013, 22(11): 116101.
No Suggested Reading articles found!