Abstract
This paper considers several finite moving cracks in a non-homogeneous material. The shear modulus and mass density of the plane are considered for a class of functional forms for which equilibrium equation has analytical solutions. The distributed dislocation technique is used to carry out stress analysis in a non-homogeneous plane containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in a non-homogeneous plane by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a plane weakened by moving cracks. Finally several examples are solved to show the effects of the material non-homogeneity and speed of cracks on the stress intensity factors.
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References
L. B. Freund, Dynamic fracture mechanics, Cambridge University Press (1998).
E. H. Yoffe, The moving Griffith crack, Philosophical Magazine, 42(330) (1951) 739–750.
C. Atkinson and R. D. List, Steady state crack propagation into media with spatially varying elastic properties, International Journal of Engineering Sciences, 16(10) (1978) 7171–730.
G. C. Sih and E. P. Chen, Moving cracks in layered composites, International Journal of Enginearing Sciences, 20(11) (1982) 1181–1192.
M. Nakagaki, H. Sasaki and S. Hagihava, A study of crack in functionally graded materials under dynamic loading, In: pvp-Dynamic Fracture, Failure and Deformations, ASME 300 (1995) 1–6.
X. D. Wang and S. A. Meguid, On the dynamic crack propagation in an interface with spatially varying elastic properties, International Journal of Fracture 69(1) (1995) 87–99.
C. Li and G. J. Weng, Yoffe-type moving crack in a functionally graded piezoelectric material, Proceedings Royal Society of London A 458 (2002) 381–399.
S. A. Meguid, X. D. Wang and L. Y. Jiang, On the dynamic propagation of a finite crack in functionally graded materials, Engineering Fracture Mechanics, 69(14–16) (2002) 1753–1768.
L. Y. Jiang and X. D. Wang, On the dynamic propagation in an interphase with spatially varying elastic properties under in-plane loading, International Journal of Fracture, 114(3) (2002) 225–244.
X. S. Bi, J. Cheng and X. L. Chen, Moving crack for functionally grated material in an infinite length strip under antiplane shear, Theoretical Applied Fracture Mechanics 39(1) (2003) 89–97.
X. F. Li, Griffith crack moving in a piezoelectric strip, Archive Applied. Mechanics, 72 (2003) 745–758.
S. M. Kwon, On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip, Acta Mechanica, 167(1–2) (2004) 73–89.
L. Ma, L. Z. Wu and L. C. Guo, On the moving Griffith crack in a non-homogeneous orthotropic strip, International Journal of Fracture, 136 (2005) 187–205.
S. Das, Interaction of moving interface collinear Griffith cracks under anti-plane shear, International Journal of Solids and Structures, 43(25–26) (2006) 7880–7890.
B. M. Singh, J. Rokne, J. Vrbik and R. S. Dhaliwal, Finite griffith crack propagating in a nonhomogeneous medium, European Journal of Mechanics-A/Solids, 25(5) (2006) 867–875.
W. Baolin and H. Jiecai, A moving crack in a nonhomogeneous material, Acta Mechanica Solida Sinica, 19(3) (2006) 223–230.
Z. Cheng and Z. Zhong, Analysis of a moving crack in a functionally graded strip between two homogeneous layers, International Journal of Mechanical Sciences, 49(9) (2007) 1038–1046.
Z. Yan and L. Y. Jiang, Study of a propagating finite crack in functionally graded piezoelectric materials considering dielectric medium effect, International Journal of Solids and Structures, 46 (2009) 1362–1372.
M. Ayatollahi, R. T. Faal and O. Tarkian, Anti-plane analysis of an orthotropic strip weakened by several moving cracks, Applied Mathematical Modelling, 36 (2012) 596–604.
J. Weertman, Dislocation based fracture mechanics, World Scientific Publishing Co., Singapore (1996).
D. G. Duffy, Transform method for solving partial differential equation, CRC press (1994).
J. Weertman and J. R. Weertman, Elementary dislocation theory, Oxford university press, New York (1992).
D. A. Hills, P. A. Kelly, D. N. Dai and A. M. Korsunsky, Solution of crack problems: The distributed dislocation technique, Kluwer Academic Publishers (1996).
F. Erdogan, G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations (1973).
F. Erdogan, The crack problem for bonded nonhomogeneous materials under anti-plane shear loading, Transaction of ASME Journal of Applied Mechanics, 52 (1985) 823–828.
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Mojtaba Ayatollahi is an associated professor of mechanical engineering at the Department of Engineering at University of Zanjan. Dr. Ayatollahi graduated with an Ph.D from Amirkabir University of Technology (Tehran Polytechnic) in Iran in 2007. His research is the fracture mechanics and he has published 20 papers in the well-known journals since 2009.
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Ayatollahi, M., Moharrami, R. Anti-plane analysis of functionally graded materials weakened by several moving cracks. J Mech Sci Technol 26, 3525–3531 (2012). https://doi.org/10.1007/s12206-012-0867-8
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DOI: https://doi.org/10.1007/s12206-012-0867-8