The Dugdale model for a semi-infinite crack in a strip of two-dimensional decagonal quasicrystals

Journal of Mathematical Physics (Impact Factor: 1.18). 05/2011; 52(5):053512-053512-5. DOI: 10.1063/1.3589242

ABSTRACT The problem of a semi-infinite crack in a strip is useful in materials science and engineering. The paper proposes a Dugdale model for the configuration of two-dimensional decagonal quasicrystals. Through the complex variable method, we obtain the exact solution of the problem. The plastic zone and the crack tip opening displacement and the most important physical quantity, stress intensity factor, can be expressed in quite a simple form.

1 Follower
  • [Show abstract] [Hide abstract]
    ABSTRACT: The present paper is concerned with the longitudinal shear elasticity of three-dimensional icosahedral quasicrystals. By virtue of the Dugdale hypothesis along with the method of complex potential theory, it involves two defect problems of the icosahedral quasicrystals. The first one is the calculation of stress intensity factors and the size of the cohesive force zone in a half-infinite crack. Meanwhile, the crack tip tearing displacements can be exactly derived. The other is the demonstration of the generalized stress intensity factors induced by a sharp V-notch as an extension of a crack. The generalized E-integral around the notch tip gives the energy release rate when the V-notch degenerates into a crack. Apart from their own usefulness in carrying out some simplified crack analyses, the results obtained in this work can particularly serve as a basis for fracture mechanics of anti-plane defect problems of icosahedral quasicrystals.
    Chinese Physics B 09/2014; 23(11):116201. DOI:10.1088/1674-1056/23/11/116201 · 1.39 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The present article concerns itself with three-dimensional analytical solutions for the phonon-phason field in an infinite space made of two-dimensional hexagonal quasi-crystal, which contains a planar crack subjected to a pair of equal but opposite phonon loadings on the upper and lower crack lips. Based on the general solutions in terms of harmonic functions, the method of potential theory is extended to the planar crack problems, in the context of elasticity of two-dimensional quasi-crystals. Five potentials are properly assumed and the boundary integro-differential equation governing the crack problem is established. For three common cracks (penny-shaped, external circular and half infinite planar), fundamental phonon-phason field variables in terms of elementary functions are obtained in a unified fashion. Important quantities in fracture mechanics, such as crack surface displacement, stress intensity factor and energy release rate, are explicitly presented. Furthermore, the fundamental solutions find some applications to the crack problems where distributed loadings are involved. Numerical calculations are preformed in order for a multiple purpose. The present analytical solutions can serve as benchmarks for numerous simplified analyses and various numerical codes in the future.
    International Journal of Solids and Structures 04/2015; 66. DOI:10.1016/j.ijsolstr.2015.04.013 · 2.04 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents fundamental solutions for an infinite space of one-dimensional hexagonal quasicrystal medium, which contains a penny-shaped or half-infinite plane crack subjected to two identical thermal loadings on the upper and lower crack lips. In view of the symmetry of the problem with respect to the crack plane, the original problem is transformed to a mixed boundary problem for a half-space, which is solved by means of a generalized method of potential theory conjugated with the newly proposed general solutions. When the cracks are under the action of a pair of point temperature loadings, fundamental solutions in terms of elementary functions are derived in an exact and complete way. Important parameters in crack analyses such as stress intensity factors and crack surface displacements are presented as well. The underlying relations between the fundamental solutions for the two cracks involved in this paper are discovered. The temperature fields associated with these two cracks are retrieved in alternative manners. The obtained solutions are of significance to boundary element analysis, and have an important role in clarifying simplified studies and serving as benchmarks for computational fracture mechanics can be expected to play.
    Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 04/2013; 469(2154):30023-. DOI:10.1098/rspa.2013.0023 · 2.00 Impact Factor