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Abstract

From Chapter 4 to Chapter 13 we mainly discussed the elasticity and relevant properties of quasicrystals, which belong to linear regime both physically and mathematically. Their mathematical treatment is relatively easy though the calculations are quite complex.

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References

  1. Calliard D. Dislocation mechanism and plasticity of quasicrystals: TEM observations in icosahedral Al-Pd-Mn. Materials Sci Forum, 2006, 509(1): 49–56

    Article  Google Scholar 

  2. Geyer B, Bartsch M, Wollgarten M et al. Plastic deformation of icosahedral Al-Pd-Mn single quasicrystals. Experimental results. Phil Mag A, 2000, 80(7): 1151–1164

    Article  Google Scholar 

  3. Messerschmidt U, Bartsch M, Wollgarten M et al. Plastic deformation of icosahedral Al-Pd-Mn single quasicrystals. II. Interpretation of experimental results. Phil Mag A, 2000, 80(7): 1165–1181

    Article  Google Scholar 

  4. Urban K, Wollgarten M. Dislocation and plasticity of quasicrstals. Materials Sci Forum, 1994, 150–151(2): 315–322

    Article  Google Scholar 

  5. Wollgarten M, Bartsch M, Messerschmidt U et al. In-situ observation of dislocation motion in icosahedral Al-Pd-Mn single quasicrystals. Phil Mag Lett, 1995, 71(1): 99–105

    Article  Google Scholar 

  6. Feuerbacher M, Metzmacher C, Wollgarten M et al. 1997, Plastic deformation of decagonal Al-Ni-Co quasicrystals. Phil Mag Lett, 76(4): 396–375

    Google Scholar 

  7. Messerschmidt U, Bartsch M, Feuerbacher M et al. Friction mechanism of dislocation motion in icosadedral Al-Pd-Mn single quasicrystals. Phil Mag A, 1999, 79(11): 2123–2135

    Article  Google Scholar 

  8. Fan T Y, Trebin H-R, Messerschmidt U et al. Plastic flow coupled with a Griffith crack in some one-and two-dimensional quasicrystals. J Phys: Condens Matter, 2004, 16(47): 5229–5240

    Article  Google Scholar 

  9. Feuerbacher M, Urban K. Platic behaviour of quasicrystalline materials. in: Quasicrystals, Trebin H R, Wiely Press, Berlin, 2003

    Google Scholar 

  10. Guyot P, Canova G. The plasticity of icosahedral quasicrystals. Phil Mag A, 1999, 79(11): 2815–2822

    Article  Google Scholar 

  11. Feuerbacher M, Schall P, Estrin Y et al. Aconstitntive model for quasicystal plasticity. Phil Mag Lett, 2001, 81(7): 473–482

    Article  Google Scholar 

  12. Estrin Y. in: Unified Constitutive Laws of Plastic Deformation, Krausz A, Krausz K, Academic Press. New York, 1996

    Google Scholar 

  13. Eshelby J D. The continuum theory of dislocations in crystals, Solid State Physics (ed by Seits F et al). Vol. 3. New York: Academic Press, 1956

    Google Scholar 

  14. Fan T Y, Fan L. Plastic fracture of quasicrystals. Phil Mag, 2008, 88(4): 523–535

    Article  Google Scholar 

  15. Dugdale D S. Yielding of steel sheets containing slits. J Mech Phys Solids, 1960, 32(2): 105–108

    Google Scholar 

  16. Barenblatt G I. The mathematical theory of equilibrium of crack in brittle fracture. Advances in Applied Mechanics. 1962, 7: 55–129

    Article  MathSciNet  Google Scholar 

  17. Fan T Y, Mai Y W. Elasticity theory, fracture mechanics and some relevant thermal properties of quasicrystalline materials. Appl Mech Rev, 2004, 57(5): 325–344

    Article  Google Scholar 

  18. Fan T Y, Fan L. Relation between generalized Eshelby integral and generalized BCS and generalized D B models for some one-and two-dimensional quasicrystals. Chin. Phys. B in press, 2010

    Google Scholar 

  19. Meng X M, Tong B Y, Wu Y K. Mechanical properties of quasicrystals Al65Cu20Co15. Acta Metallurgica Sinica A, 1994, 30(3): 61–64 (in Chinese)

    Google Scholar 

  20. Bilby B A, Cottrell A H, Swinden K H. The spread of plastic yield from a notch. Proc R Soc A, 1963, 272(2): 304–314

    Article  Google Scholar 

  21. Bilby B A, Cottrell A H, Smith E et al. Plastic yealding from sharp notches, ibid, 1964, 279(1): 1–9

    Article  Google Scholar 

  22. Rice J R. A path independent integral and approximate analysis of strain concentration by notches and cracks. J Appl Mech, 1968, 35(4): 379–386

    Google Scholar 

  23. Cherepanov G P. On crack propagation in solids. Int J Solids and Structures, 1969, 5(8): 863–871

    Article  Google Scholar 

  24. Begley G T, Landes J D. 1972, The J-integral as a fracture criterion, Fracture Toughness, ASTM STP 514, American Society for Testing and Materials, Philadelphia, 1–20

    Google Scholar 

  25. Landes J D, Begley G T. 1972, The effect of specimen geometry on J IC, Fracture Toughness, ASTM STP 514, American Society for Testing and Materials, Philadelphia, 24–29

    Google Scholar 

  26. Muskhelishvili N I. Singular Integral Equations. Groningen, Noordhoff, 1956

    Google Scholar 

  27. Li W, Fan T Y. Study on plastic analysis of crack problem in icosahedral quasicrystals. Phil. Mag., 2009, 89(31): 2823–2831

    Article  Google Scholar 

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© 2011 Science Press Beijing and Springer-Verlag Berlin Heidelberg

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Fan, T. (2011). Nonlinear behaviour of quasicrystals. In: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14643-5_14

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  • DOI: https://doi.org/10.1007/978-3-642-14643-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14642-8

  • Online ISBN: 978-3-642-14643-5

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