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

Journal of Mathematical Physics (Impact Factor: 1.3). 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.

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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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