Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Inplane stress analysis of an isotropic strip containing several moving cracks

Authors
Abstract
In this paper, analyses of several finite cracks with constant length (Yoffe-type crack) propagating in an isotropic strip were studied. The distributed dislocation technique is used to carry out stress analysis in an isotropic strip containing moving cracks under in-plane loading. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. The solution of a moving edge dislocation is obtained in an isotropic strip by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. Finally several examples are solved and the numerical results for the stress intensity factor are obtained. The influences of the geometric parameters, the thickness of the isotropic strip, the crack size and speed have significant effects on the stress intensity factors of crack tips which are displayed graphically.
Keywords

[1] Volterra, V., “Sur Pe'quilibre Des Carps Elastiques Multiplement Connexes, Annales Scientifiques De l’Ecole Normale Superiure”, Paris, Series 3, Vol. 24, pp. 401-517, (1907).
 
[2] Das, S., and Patra, B., “Moving Griffith Crack at the Interface of Two Dissimilar Orthotropic Half Plane”, Engineering Fracture Mechanics Vol. 54. No. 4, pp. 523-531, (1996).
[3] Chen, Z. T., Karihaloo, B. L., and Yu, S. W., “A Griffith Crack Moving Along the Interface of Two Dissimilar Piezoelectric Materials”, International Journal of Fracture, Vol. 91, pp. 197-203, (1998).
 
[4] Das, S., and Patra, B., “Stress Intensity Factors for Moving Interfacial Crack between Bonded Dissimilar Fixed Orthotropic Layers”, Computers and Structures, Vol. 69, pp. 459-472, (1998).
 
[5] Li, X. F., and Wu, X. F., “A Moving Mode-III Crack at the Interface between Two Dissimilar Piezoelectric Materials”, International Journal of Engineering Science, Vol. 38, pp. 1219-1234, (2000).
 
[6] Gonzalez, C. R., and Mason, J. J., “Dynamic Stress Intensity Factor for a Propagating Semi-infinite Crack in Orthotropic Materials”, International Journal of Engineering Science, Vol. 39, pp. 15-38, (2001).
 
[7] Meguid, S. A., Wang, X. D., and Jiang, L. Y., “On the Dynamic Propagation of a Finite Crack in Functionally Graded Materials”, Engineering Fracture Mechanics, Vol. 69, pp. 1753-1768, (2002).
 
[8] Bi, X.S., Cheng, J., and Chen, X. L., “Moving Crack for Functionally Grated Material in an Infinite Length Strip under Anti-plane Shear”, Theoretical and Applied Fracture Mechanics, Vol. 39, pp. 89-97, (2003).
 
[9] Zhou, and Zeng, T., “Crack Propagation in a Functionally Graded Strip under the Plane Loading”, International Journal of Fracture Vol. 126, pp. 39-55, (2004).
 
[10] Das, S., “Interaction of Moving Interface Collinear Griffith Cracks under Anti-plane Shear”, International Journal of Solids and Structures, Vol. 43, pp. 7880-7890, (2006).
 
[11] Cheng, Z., and Zhong, Z., “Analysis of a Moving Crack in a Functionally Graded Strip between Two Homogeneous Layers”, International Journal of Mechanical Sciences, Vol. 49, pp. 1038-1046, (2007).
 
[12] Cheng, Z., ”Crack Propagating in Functionally Graded Coating with Arbitrarily Distributed Material Properties Bonded to Homogeneous Substrate”, Acta Mechanica Solida Sinica, Vol. 23, pp. 437-446, (2010).
 
[13] Cheng, Z., Gao, D., and Zhong, Z., “A Moving Interface Crack between two Dissimilar Functionally Graded Strips under Plane Deformation with Integral Equation Methods”, Engineering Analysis with Boundary Elements, Vol. 36, pp. 267-273, (2012).
 
[14] Bagheri, R., and Ayatollahi, M., “Multiple Moving Cracks in a Functionally Graded Strip”, Applied Mathematical Modelling, Vol. 36, pp. 4677–4686, (2012).
 
[15] Korsunsky, A. M., and Hills, D. A., “The Solution of Crack Problems by using Distributed Strain Nuclei”, Part C: Journal of Mechanical Engineering Science, Vol. 210, No.1, pp. 23-31, (1996).
 
[16] Erdogan, F., Gupta, G. D., and Cook, T. S., “Numerical Solution of Singular Integral Equations, Method of Analysis and Solution of Crack Problems”, Edited by G. C. Sih, Noordhoof, Leyden, Holland, (1973).
 
[17] Faal, R. T., Fotuhi, A. R., Fariborz, S. J., and Daghyani, H. R., “Antiplane Stress Analysis of an Isotropic Wedge with Multiple Cracks”, International Journal of Solids and Structures, Vol. 41, pp. 4535-4550, (2004).
Volume 16, Issue 1 - Serial Number 34
System Dyanamics and Solid Mechanics
Spring 2014
Pages 56-77

  • Receive Date 22 May 2014
  • Accept Date 23 August 2014