Effect of Heterogeneity and Reinforcement on Propagation of a Crack due to Shear Waves
Publication: International Journal of Geomechanics
Volume 14, Issue 4
Abstract
This paper investigates the effect of reinforcement and nonhomogeneity on the propagation of cracks caused by horizontally polarized shear waves in a heterogeneous fiber-reinforced medium. The effects of reinforcement and heterogeneity on the propagation of the crack are highlighted in this study. The stress intensity factor at the crack tip for a concentrated force of a constant intensity has been calculated and depicted by means of graphs for various cases. It is observed that fiber reinforcement and heterogeneity parameters decrease the stress intensity factor. Remarkably, the stress intensity factor decreases with the increase in the length and speed of the crack. Also, a comparative study was made for the stress intensity factor in reinforced medium over reinforced-free medium and heterogeneous medium over the homogeneous medium. Moreover, some important peculiarities were observed in graphs.
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Acknowledgments
The authors thank the Indian School of Mines, Dhanbad, for providing its best facilities for research and University Grants Commission, New Delhi, for providing financial support through a Start-Up Grant for the project titled Seismic Wave Propagation in Inhomogenous Anisotropic Layered Media.
References
Achenbach, J. D. (1970). “Extension of a crack by shear wave.” Z. Angew. Math. Phys., 21(6), 887–900.
Achenbach, J. D. (1975). Wave propagation in elastic solids, North Holland Publication Company, New York.
Achenbach, J. D., Bazant, Z. P., and Khetan, R. P. (1976). “Elastodynamic near-tip field for rapidly propagating interface crack.” Int. J. Eng. Sci., 14(9), 797–809.
Amarasiri, A., and Kodikara, J. (2013). “Numerical modeling of desiccation cracking using the cohesive crack method.” Int. J. Geomech., 213–221.
Belfield, A. J., Rogers, T. G., and Spencer, A. J. M. (1983). “Stress in elastic plates reinforced by fibers lying in concentric circles.” J. Mech. Phys. Solids, 31(1), 25–54.
Chattaraj, R., Samal, S., and Mahanti, N. (2013). “Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress.” Int. J. Geomech., 402–408.
Chattopadhyay, A., and Bandyopadhyay, U. (1986). “Diffraction of shear waves by a rigid strip in a medium of monoclinic type.” Acta Mech., 65(1–4), 27–40.
Chattopadhyay, A., and Bandyopadhyay, U. (1988). “Propagation of a crack due to shear wave in a medium of monoclinic type.” Acta Mech., 71(1–4), 145–156.
Chattopadhyay, A., and Chaudhury, S. (1990). “Propagation, reflection and transmission of magnetoelastic shear waves in a self reinforced medium.” Int. J. Eng. Sci., 28(6), 485–495.
Chattopadhyay, A., and Chaudhury, S. (1995). “Magnetoelastic shear waves in an infinite self-reinforced plate.” Int. J. Numer. Anal. Methods Geomech., 19(4), 289–304.
Chattopadhyay, A., Gupta, S., Chattopadhyay, A., and Singh, A. K. (2010). “The dispersion of shear wave in multilayered magnetoelastic self-reinforced media.” Int. J. Solids Struct., 47(9), 1317–1324.
Chattopadhyay, A., Gupta, S., Sahu, S., and Singh, A. (2012). “Torsional surface waves in a self-reinforced medium over a heterogeneous half space.” Int. J. Geomech., 193–197.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2013). “Dispersion of SH waves in an irregular non-homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium.” J. Vib. Control, 19(1), 109–119.
Chattopadhyay, A., Gupta, S., Samal, S., and Sharma, V. (2009). “Torsional waves in self-reinforced medium.” Int. J. Geomech., 9–13.
Chattopadhyay, A., Keshri, A., and Choudhury, S. (1994). “Propagation of a crack due to shear waves in a non-homogeneous medium of monoclinic type.” Ind. J. Pure App. Math, 25(11), 1195–1205.
Chattopadhyay, A., and Maugin, G. A. (1985). “Diffraction of magneto-elastic shear waves by a rigid strip.” J. Acoust. Soc. Am., 78(1), 217–222.
Chattopadhyay, A., and Singh, A. K. (2011). “G-type seismic waves in fibre reinforced media.” Meccanica, 47(7), 1775–1785.
Chattopadhyay, A., and Singh, A. K. (2012). “Propagation of magnetoelastic shear waves in an irregular self-reinforced layer.” J. Eng. Math., 75(1), 139–155.
Chattopadhyay, A., and Venkateswarlu, R. L. K. (1998). “Stresses produced in a fibre-reinforced half space due to moving load.” Bull. Cal. Math. Soc., 90, 337–342.
Chaudhary, S., Kaushik, V. P., and Tomar, S. K. (2005). “Transmission of shear waves through a self-reinforced layer sandwiched between two inhomogeneous viscoelastic half-spaces.” Int. J. Mech. Sci., 47(9), 1455–1472.
Chaudhary, S., Kaushik, V. P., and Tomar, S. K. (2006). “Plane SH-wave response from elastic slab interposed between two different self reinforced elastic solids.” Int. J. Eng. Sci., 11(4), 787–801.
Erdelyi, A., Oberhettinger, F., Magnus, W., and Tricomi, F. G. (1954). Tables of integral transforms, Vol. 1, McGraw Hill, New York.
Hool, G. A., and Kinne, W. S. (1924). Reinforced concrete and masonry structure, McGraw Hill, New York.
Loeber, J. F., and Sih, G. C. (1968). “Diffraction of antiplane shear wave by a finite crack.” J. Acoust. Soc. Am., 44(1), 90–98.
Mal, A. K. (1968). “Dynamic stress intensity factors for a non-axisymmetric loading of the penny shaped crack.” Int. J. Eng. Sci., 6(12), 725–733.
Mal, A. K. (1970). “Interaction of elastic waves with a penny shaped crack.” Int. J. Eng. Sci., 8(5), 381–388.
Markham, M. F. (1970). “Measurements of elastic constants of fibre composite by ultrasonics.” Composites, 1(3), 145–149.
Matczynski, M. (1973). “Quasi-static problem of a crack in an elastic strip subject to antiplane state of strain.” Arch. Mech. Stosow, 25, 851–860.
Noble, B. (1958). Methods based on Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press, London.
Sih, G. C., and Loeber, J. F. (1968). “Torsional vibration of an elastic solid containing a penny shaped crack.” J. Acoust. Soc. Am., 44(5), 1237–1245.
Singh, B. M., and Dhaliwal, R. S. (1983). “Diffraction of SH-wave by a moving crack.” Acta Mech., 48(1–2), 71–79.
Tait, R. J., and Moodie, T. B. (1981). “Complex variable methods and closed form solutions to dynamic crack and punch problems in the classical theory of elasticity.” Int. J. Eng. Sci., 19(2), 221–229.
Titchmark, E. C. (1939). Theory of Fourier integrals, Oxford University Press, London.
Tittmann, B. R. (1983). “Scattering of elastic waves from simple defects in solids.” Wave Motion, 5(4), 299–306.
Verma, P. D. S. (1986). “Magnetoelastic shear waves in self-reinforced bodies.” Int. J. Eng. Sci., 24(7), 1067–1073.
Verma, P. D. S., and Rana, O. H. (1983). “Rotation of a circular cylindrical tube reinforced by fibres lying along helices.” Mech. Mater., 2(4), 353–359.
Verma, P. D. S., Rana, O. H., and Verma, M. (1988). “Magnetoelastic transverse surface waves in self-reinforced elastic bodies.” Ind. J. Pure App. Math, 19(7), 713–716.
Yamamoto, K., Shimamoto, T., and Sukemura, S. (2004). “Multiple fracture propagation model for a three-dimensional hydraulic fracturing simulator.” Int. J. Geomech., 46–57.
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Published In
International Journal of Geomechanics
Volume 14 • Issue 4 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Feb 19, 2013
Accepted: Aug 28, 2013
Published online: Mar 26, 2014
Published in print: Aug 1, 2014
Discussion open until: Aug 26, 2014
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