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

Journal of Mathematical Physics (Impact Factor: 1.24). 05/2011; 52(5):053512-053512-5. DOI: 10.1063/1.3589242


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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589242]

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    • "Furthermore, Dugdale crack model is generalized to materials with more complicated yield surfaces, where the Tresca or von Mises yield criterion is required to satisfy in the crack tip plastic zone [3] [16]. In recent years, some efforts on the Dugdale crack of QCs have been made by Fan and his coauthors [10] [23] [32], to investigate the size of plastic zone. To the best of authors' knowledge, however, the problem of the half-infinite Dugdale crack embedded in an infinite space of 1D hexagonal QC has not been studied. "
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    ABSTRACT: The present paper is devoted to determining the crack tip plasticity of a half-infinite Dugdale crack embedded in an infinite space of one-dimensional hexagonal quasicrystal. A pair of equal but opposite line loadings is assumed to be exerted on the upper and lower crack lips. By applying the Dugdale hypothesis together with the elastic results for a half-infinite crack, the extent of the plastic zone in the crack front is estimated. The normal stress outside the enlarged crack and crack surface displacements are explicitly presented, via the principle of superposition. The validity of the present solutions is discussed analytically by examining the overall equilibrium of the half-space.
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    ABSTRACT: The present study is to determine the solution of a strip with a semi-infinite crack embedded in decagonal quasicrystals, which transforms a physically and mathematically daunting problem. Then cohesive forces are incorporated into a plastic strip in the elastic body for nonlinear deformation. By superposing the two linear elastic fields, one is evaluated with internal loadings and the other with cohesive forces, the problem is treated in Dugdale-Barenblatt manner. A simple but yet rigorous version of the complex analysis theory is employed here, which involves a conformal mapping technique. The analytical approach leads to the establishment of a few equations, which allows the exact calculation of the size of cohesive force zone and the most important physical quantity in crack theory: stress intensity factor. The analytical results of the present study may be used as the basis of fracture theory of decagonal quasicrystals.
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    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.
    Full-text · Article · Apr 2013 · Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
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