Abstract
Quasicrystals are potential materials to be developed for structural use, and their strength and toughness attract attention of researchers. Experimental observations[1],[2] have shown that quasicrystals are brittle. With common experience of conventional structural materials, we know that failure of brittle materials is mainly related to the existence and growth of cracks. Chapter 7 indicated that dislocations have been observed in quasicrystals, and the accumulation of dislocations will eventually lead to cracking of the material. Now let us study crack problems in quasicrystals that have both theoretical and practical value in the view of applications in future.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hu C Z, Yang W Z, Wang R H et al. Symmetry and physical properties of quasicrystals. Adv Phys, 1997, 17(4): 345–376 (in Chinese)
Meng X M, Dong B Y, Wu Y K. Mechanical property of quasi-crystal Al65Cu20Co15. Acta Metal Sinica, 1994, 30(2): 61–64 (in Chinese)
Kanninen M F, Popelar C H, Advanced Fracture Mechanics. Cambridge: Cambridge University Press, 1985; Fan T Y. Foundation of Fracture Theory. Beijing: Science Press, 2003 (in Chinese)
Fan T Y. Exact analytic solutions of stationary and fast propagating cracks in a strip. Science in China, A, 1991, 34(5): 560–569
Fan T Y. Mathematical Theory of Elasticity of Quasicrystals and Its Application. Beijing Institute of Technology Press. Beijing, 1999 (in Chinese)
Li L H, Fan T Y. Exact solutions of two semi-infinite collinear cracks in a strip of one-dimensional hexagonal quasicrystal. Applied Mathematics and Computation, 2008, 196(1): 1–5
Shen D W, Fan T Y. Exact solutions of two semi-infinite collinear cracks in a strip. Eng Fracture Mech, 2003, 70(8): 813–822
Li X F, Fan T Y, Sun Y F. A decagonal quasicrystal with a Griffith crack. Phil Mag A, 1999, 79(8): 1943–1952
Li L H, Fan T Y. Complex function method for solving notch problem of point group 10, 10 two-dimensional quasicrystals based on the stress potential function. J Phys: Condens Matter, 2007, 18(47): 10631–10641
Li X F. Defect problems and their analytic solutions of the theory of elasticity of quasicrystals. Dissertation. Beijing Institute of Technology, 1999 (in Chinese)
Zhou W M, Fan T Y. Plane elasticity problem of two-dimensional octagonal quasicrystal and crack problem. Chin Phys, 2001, 10(8): 743–747
Zhou W M. Mathematical analysis of elasticity and defects of two-and three-dimensional quasicrystals. Dissertation. Beijing: Beijing Institute of Technology, 2000 (in Chinese)
Li L H. Study on complex variable function method and analytic solutions of elasticity of quasicrystals. Dissertation. Beijing: Beijing Institute of Technology, 2008 (in Chinese)
Fan T Y, Guo R P. Three-dimensional elliptic crack in one-dimensional hexagonal quasicrystals. Appl Math Mech, submitted, 2009
Peng Y Z, Fan T Y. Elastic theory of 1D quasiperiodic stacking of 2D crystals. J Phys: Condens Matter, 2000, 12(45): 9381–9387
Liu G T, Fan T Y. The complex method of the plane elasticity in 2D quasicrystals point group 10mm ten-fold rotation symmetry notch problems. Science in China E, 2003, 46(3): 326–336
Liu G T. The complex variable function method of the elastic theory of quasicrystals and defects and auxiliary equation method for solving some nonlinear evolution equations. Dissertation. Beijing Institute of Technology, 2004 (in Chinese)
Muskhelishrili N I, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen: Noordhofltd, 1953
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2011 Science Press Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fan, T. (2011). Application II: Solutions of notch and crack problems of one-and two-dimensional quasicrystals. In: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14643-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-14643-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14642-8
Online ISBN: 978-3-642-14643-5
eBook Packages: EngineeringEngineering (R0)