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Chin. Phys. B, 2008, Vol. 17(7): 2610-2620    DOI: 10.1088/1674-1056/17/7/044
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Guo Jun-Hong, Liu Guan-Ting
College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China
Abstract  Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors (SIFs) for mode III problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.
Keywords:  stress intensity factor      complex variable function method      one-dimensional hexagonal quasi-crystals      elliptic hole with asymmetric collinear cracks  
Received:  26 November 2007      Revised:  09 January 2008      Published:  09 July 2008
PACS:  61.44.Br (Quasicrystals)  
  46.50.+a (Fracture mechanics, fatigue and cracks)  
  62.20.M- (Structural failure of materials)  
  63.20.-e (Phonons in crystal lattices)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10761005) and the Inner Mongolia Natural Science Foundation of China (Grant No 200607010104).

Cite this article: 

Guo Jun-Hong, Liu Guan-Ting Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal 2008 Chin. Phys. B 17 2610

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