Abstract
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.
Similar content being viewed by others
References
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.
GUO Ke-xin. Five-fold symmetry and quasicrystal[J].Physics, 198614(8):449–451. (in Chinese)
ZHOU Wang-min, FAN Tian-you. Axisymmetric elasticity problem of cubic quasicrystal[J]Chin Phys, 20009(4):294–303.
Ding D H, Yang W G, Hu C Z,et al. Generalized elasticity theory of quasicrystals[J].Phys Rev B, 199348(10):7003–7010.
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.
De P, Pelcovits R A. Linear elasticity theory of pentagonal quasicrystals[J].Phys Rev B, 1987,35 (13):8609–8619.
De P, Pelcovits R A. Disclinations in pentagonal quasicrystals[J].Phys Rev B, 198736(17): 9304–9307.
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.
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.
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.
ZHOU Wang-min, FAN Tian-you. Plane elasticity problem of two-dimensional octagonal quasicrystals and crack problem[J].Chin Phys, 200110(8):294–303.
FAN Tian-you.Foundation of Fracture Mechanics[M]. Nanjing: Jiangsu Science and Technology Publishing House, 1978. (in Chinese)
MENG Xiang-min, TONG Bai-yun, WU Yu-kun. Mechanical properties of Al65Cu20Co15 quasicrystals[J].Acta Metal Sinica, 199430(1):61–64. (in Chinese)
Grriffith A A. The phenomenon of rupture and flow in solids[J].Philos Trans Roy Soc, Ser A, 1920221:163–197.
Author information
Authors and Affiliations
Additional information
Communicated by Wupang Biao
Foundation item: the National Natural Science Foundation of China (19972011)
Biography: Zuphou Wang-min (1964∼)
Rights and permissions
About this article
Cite this article
Wang-min, Z., Tian-you, F. & Shu-yuan, Y. Crack problem under shear loading in cubic quasicrystal. Appl Math Mech 24, 720–726 (2003). https://doi.org/10.1007/BF02437874
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02437874