Collinear periodic cracks and/or rigid line inclusions ofantiplane sliding mode in one-dimensional hexagonal quasicrystal

For a one-dimensional (1D) hexagonal quasicrystal (QC), there is the periodic (x"1,x"2)-plane of atomic structures with the quasiperiodic direction x"3-axis along which there exists a phason displacement. The macroscopically collinear periodic cracks and/or rigid line inclusions are placed on the periodic (x"1,x"2)-plane for finding out the influence of phason displacement on the related physical quantities. These two models are reduced to the Riemann-Hilbert problem of periodic analytic functions to obtain the closed-form solutions for the antiplane sliding mode. It is found that the phonon and phason stress intensity factors of cracks as well as the phonon and phason stress field intensity factors of rigid line inclusions are not related to the coupling of phonon and phason fields. These mean that there is not the influence of phason displacement on both the phonon stress intensity factor (usual stress intensity factor) of cracks and the phonon stress field intensity factor of rigid line inclusions. However, the energy release rates of periodic cracks and/or rigid line inclusions are obtained and affected not only by the periodicity of cracks and/or rigid line inclusions but also by the phason displacement.

[1]  Zheng,et al.  A decagonal quasicrystal with an arc-shaped crack , 2003 .

[2]  Wenge Yang,et al.  Point and space groups and elastic behaviours of one-dimensional quasicrystals , 1997 .

[3]  Tian-You Fan,et al.  Exact solutions of two semi-infinite collinear cracks in a strip of one dimensional hexagonal quasicrystal , 2008, Appl. Math. Comput..

[4]  Weichen Shi.  Conservation integrals of any quasicrystal and application , 2007 .

[5]  Bak.  Symmetry, stability, and elastic properties of icosahedral incommensurate crystals. , 1985, Physical review. B, Condensed matter.

[6]  G. I. Barenblatt,et al.  On brittle cracks under longitudinal shear , 1961 .

[7]  Yang,et al.  Generalized elasticity theory of quasicrystals. , 1993, Physical review. B, Condensed matter.

[8]  J. Roth,et al.  Phason elastic constants of a binary tiling quasicrystal , 2002 .

[9]  Elser.  Comment on "Quasicrystals: A new class of ordered structures" , 1985, Physical review letters.

[10]  P. Steinhardt,et al.  Quasicrystals: a new class of ordered structures , 1984 .

[11]  P. Kramer,et al.  On Periodic and Non-periodic Space Fillings of E , 1984 .

[12]  Guo Yu-Cui,et al.  A mode-II griffith crack in decagonal quasicrystals , 2001 .

[13]  J. Cahn,et al.  Metallic Phase with Long-Range Orientational Order and No Translational Symmetry , 1984 .

[14]  D. Sahoo.  Elastic continuum theories of lattice defects: a review , 1984 .

[15]  T. Fan,et al.  Governing equations and general solutions of plane elasticity of one-dimensional quasicrystals , 2004 .

[16]  F. Tian-you,et al.  A decagonal quasicrystal with a Griffith crack , 1999 .

[17]  K. Chawla,et al.  Mechanical Behavior of Materials , 1998 .

[18]  H. Trebin.  Quasicrystals : structure and physical properties , 2003 .

[19]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[20]  Weichen Shi.  Conservation laws of a decagonal quasicrystal in elastodynamics , 2005 .