Crack problem under shear loading in cubic quasicrystal

  • Zhou Wang-min
  • Fan Tian-you
  • Yin Shu-yuan


The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. Based on the work, the analytic solutions of elastic field of cubic quasicrystal with a penny-shaped crack under the shear loading are found, and the stress intensity factor and strain energy release rate are determined.

Key words

cubic quasicryastal shear crack stress intensity factor 

Chinese Library Classification

O346.1 O346.1+

2000 MR Subject Classification

35Q72 74B99 74R10 


  1. [1]
    Shechtman D, Blech I, Gratias D,et al. Metallic phase with long-range orientational order and no translational symmetry[J].Phys Rev Lett, 198453(20):1951–1953.CrossRefGoogle Scholar
  2. [2]
    GUO Ke-xin. Five-fold symmetry and quasicrystal[J].Physics, 198614(8):449–451. (in Chinese)Google Scholar
  3. [3]
    ZHOU Wang-min, FAN Tian-you. Axisymmetric elasticity problem of cubic quasicrystal[J]Chin Phys, 20009(4):294–303.CrossRefGoogle Scholar
  4. [4]
    Ding D H, Yang W G, Hu C Z,et al. Generalized elasticity theory of quasicrystals[J].Phys Rev B, 199348(10):7003–7010.CrossRefGoogle Scholar
  5. [5]
    Yang W G, Wang R H, Ding D H,et al. Linear elasticity theory of cubic quasicrystals[J].Phys Rev B, 199348(10):6999–7002.CrossRefGoogle Scholar
  6. [6]
    De P, Pelcovits R A. Linear elasticity theory of pentagonal quasicrystals[J].Phys Rev B, 1987,35 (13):8609–8619.CrossRefGoogle Scholar
  7. [7]
    De P, Pelcovits R A. Disclinations in pentagonal quasicrystals[J].Phys Rev B, 198736(17): 9304–9307.CrossRefGoogle Scholar
  8. [8]
    LI Xian-fang, FAN Tian-you. New method for solving elasticity problems of some planar quasicrystals and solutions[J].Chinese Phys Lett, 199815(4):278–280.CrossRefGoogle Scholar
  9. [9]
    LI X F, Dun X Y, Fan T Y,et al. Elastic field for a straight dislocation in a decagonal quasicrystal[J].J Phys Condens Matter, 199911(3):703–711.CrossRefGoogle Scholar
  10. [10]
    FAN Tian-you, LI Xian-fang, SUN Ying-fei. A moving screw dislocation in one-dimensional hexagonal quasicrystals[J].Acta Physica Sinica (Overseas Edition), 19998(4):288–295.Google Scholar
  11. [11]
    ZHOU Wang-min, FAN Tian-you. Plane elasticity problem of two-dimensional octagonal quasicrystals and crack problem[J].Chin Phys, 200110(8):294–303.CrossRefGoogle Scholar
  12. [12]
    FAN Tian-you.Foundation of Fracture Mechanics[M]. Nanjing: Jiangsu Science and Technology Publishing House, 1978. (in Chinese)Google Scholar
  13. [13]
    MENG Xiang-min, TONG Bai-yun, WU Yu-kun. Mechanical properties of Al65Cu20Co15 quasicrystals[J].Acta Metal Sinica, 199430(1):61–64. (in Chinese)Google Scholar
  14. [14]
    Grriffith A A. The phenomenon of rupture and flow in solids[J].Philos Trans Roy Soc, Ser A, 1920221:163–197.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Zhou Wang-min
    • 1
    • 2
  • Fan Tian-you
    • 3
  • Yin Shu-yuan
    • 1
  1. 1.Department of Mathematics and PhysicsHebei Institute of Architectural Science & TechnologyHandan, HebeiP. R. China
  2. 2.Functional Materials DivisionCentral Iron & Steel Research InstituteBeijingP.R. China
  3. 3.Department of Applied PhysicsBeijing Institute of TechnologyBeijingP. R. China

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