Abstract
Quasicrystals are potential material to be developed for structural use, and their strength and toughness attract the attention of researchers. Experimental observations [Hu et al. in Adv Phy 17:345–376, 1997 1, Meng et al. in Acta Metal Sinica 30:61–64, 1994 2] have shown that quasicrystals are brittle under low and middle temperature.
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References
Hu C Z, Yang W H,Wang R H and Ding D H, 1997, Symmetry and physical properties of quasicrystals, Advances of Physics, 17(4), 345-376 (in Chinese).
Meng X M, Tong B Y and Wu Y Q, 1994, Mechanical properties of quasicrystals Al65Cu20Co15,Acta Metal Sinica, 30(2), 61-64 (in Chinese).
Fan T Y, 2014, Foundation of Defect and Fracture Theory of Solid and Soft Matter, Beijing, Science Press (in Chinese).
Fan T Y, 1991, Exact analytic solutions of stationary and fast propagating cracks in a strip. Science in China, A. 34(5), 560-569; Fan T Y, Mathematical Theory of Elasticity of Quasicrystals, Beijing, Beijing Institute of Technology Press, 1999 (in Chinese).
Li L H and Fan T Y, 2008, Exact solutions of two semi-infinite collinear cracks in a strip of one-dimensional hexagonal quasicrystal, Applied Mathematics and Computation, 196(1), 1-5.
Shen D W and Fan T Y, 2003, Exact solutions of two semi-infinite collinear cracks in a strip, Eng. Fracture Mech., 70(8), 813-822.
Li X F, Fan T Y, and Sun Y F, 1999, A decagonal quasicrystal with a Griffith crack. Phil Mag A, 79(8), 1943-1952.
Li L H and Fan T Y, 2007, 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, 18(47), 10631-10641.
Liu G T and Fan T Y, 2003,The complex method of the plane elasticity in 2D quasicrystals point group 10 mm ten-fold rotation symmetry notch problems, Science in China, E, 46(3), 326-336.
Li X F, 1999, Elastic fields of dislocations and cracks in one- and two-dimensional quasicrystals, Dissertation, Beijing Institute of Technology, in Chinese.
Zhou W M and Fan T Y, 2001, Plane elasticity problem of two-dimensional octagonal quasicrystal and crack problem, Chin. Phys., 10(8), 743-747.
Zhou W M, 2000, Mathematical analysis of elasticity and defects of two- and three-dimensional quasicrystals, Dissertation, Beijing Institute of Technology, in Chinese.
Li L H, 2008, Study on complex function method and analytic solutions of elasticity of quasicrystals,Dissertation, Beijing Institute of Technology, in Chinese.
Fan T Y and Tang Z Y, 2015, Bending problem for a two-dimensional quasicrystal with an elliptic notch and nonlinear analysis, submitted.
Muskhelishvili N I, 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff Ltd, Groningen.
Lokchine M A, Sur l’influence d’un trou elliptique dans la poutre qui eprouve une flexion. C.R.Paris, 1930, 190, 1178-1179.
Fan T Y and Tang Z Y, 2016, Crack solution of a strip in a two-dimensional quasicrystal, submitted.
Fan T Y, Yang X C , Li H X, 1998, Exact analytic solution for a finite width strip with a single crack, Chin Phys Lett, 18(1), 18-21.
Li W, 2011, Analytic solutions of a finite width strip with a single edge crack of two-dimensional quasicrystals, Chin Phys B Vol. 20(11), 116201.
FanTY, Guo R P, 2013, Three-dimensional elliptic crack in one-dimensional hexagonal quasicrystals, unpublished work.
Lamb H, Hydrodynamics, 1933, Dover, New York.
Green A E, Sneddon I N, 1950, The distribution of stress in the neighbourhood of a at elliptic crack in an elastic solid, Proc. Ca mb. Phil. Soc., 46(2), 159-163.
Peng Y Z, Fan T Y, 2000, Elastic theory of 1D quasiperiodic stacking of 2D crystals, J. Phys.: Condens. Matter, 12(45), 9381-9387.
Liu G T,2004, Elasticity and defects of quasicrystals and auxiliary function method of nonlinear evolution equations, Dissertation, Beijing Institute of Technology, in Chinese.
Li X Y, Fundamental solutions of a penny shaped embedded crack and half-infinite plane crack in infinite space of one-dimensional hexagonal quasicrystals under thermal loading, Proc Roy Soc A, 469, 20130023, 2013.
Messerschmidt U, 2010, Dislocation Dynamics during Plastic Deformation, Chapter 10, Springer-Verlag, Heidelberg.
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Fan, TY. (2016). 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 Series in Materials Science, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-10-1984-5_8
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DOI: https://doi.org/10.1007/978-981-10-1984-5_8
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