Abstract
Solid quasicrystals are brittle, and the study on fracture behaviour of the material is significant. In the previous chapters, many of crack problems are investigated, and the exact analytic, approximate and numerical solutions are constructed; this provides a basis for discussing the fracture theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Li X F, The defect problems and their analytic solutions in elasticity of quasicrystals, Dissertation, Beijing Institute of Technology, Beijing 1999; 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.
Fan T Y, 2000, Mathematical theory of elasticity and defects of quasicrystals, Advances of Mechanics, 30(2), 161-174 (in Chinese).
Fan T Y and Mai Y W, 2004, Theory of elasticity, fracture mechanics and some relevant thermal properties of quasicrystalline materials, Appl. Mech. Rev., 57(5), 235-244.
Rudhart C, Gumsch and Trebin H R, 2003, Crack propagation in quasicrystals, Quasicrystals, ed by Trebin H R, Berlin: Wiely Press.
Fan T Y and Guo L H, 2005, The final governing equation of plane elasticity of icosahedral quasicrystals, Phys. Ltte. A, 341(5), 235-239.
Zhu A Y and Fan T Y, 2007, Elastic analysis of Mode II Griffith crack in an icosahedral quasicrystal, Chinese Physics, 16(4), 1111-1118.
Li L H and Fan T Y, 2008, Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem, Science in China, G, 51(6), 1-8.
Fan T Y and Fan L, 2008, Plastic fracture of quasicrystals, Phil. Mag., 88(4), 323-335.
Fan T Y and Fan L, 2008, The relation between generalized Eshelby energy-momentum tensor and generalized BCS and DB models, Chinese Physics, to be published.
Zhu A Y and Fan T Y, 2008, Dynamic crack propagation of decagonal \( Al - Ni - Co \) decagonal quasicrystals, J. Phys.: Condens. Matter, 20(29), 295217.
Wang X F, Fan T Y and Zhu A Y, 2009, Dynamic behaviour of the icosahedral Al-Pd-Mn quasicrystals with a Griffith crack, Chin. Phys. B, 18(2), 709-714.
Meng X M, Tong B Y and Wu Y K, 1994, Mechanical behaviour of \( Al_{65} Cu_{20} Co_{15} \) quasicrystal, Acta Metallurgy Sinica (in Chinese), 30(1), 61-64.
Ma D L (ed), 1994, Handbook for Parameters of Fracture Mechanics Behaviour of General Black Metals, Beijing: Industrial Press (in Chinese).
Fan T Y, 2003, Foundation of Fracture Theory, Beijing: Science Press (in Chinese).
Li W and Fan T Y, 2009, Study on plastic analysis of crack problem decagonal Al-Ni-Co quasicrystals of point group 10, \( \overline{10} \), Int. Mod. Phys. Lett. B, 23(16), 1989-1999.
Fan T Y, Tang Z Y and Chen W Q, 2012, Theory of linear, nonlinear and dynamic fracture of quasicrystalline materials, Eng Fract Mech, 82(2), 185-194.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Science Press and Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Fan, TY. (2016). Fracture Theory of Solid 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_15
Download citation
DOI: https://doi.org/10.1007/978-981-10-1984-5_15
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1982-1
Online ISBN: 978-981-10-1984-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)