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A Study of Crack-Face Boundary Conditions for Piezoelectric Strip Cut Along Two Equal Collinear Cracks

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  27 May 2016

R. R. Bhargava  and
Pooja Raj Verma
R. R. Bhargava*
Affiliation:
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee–247667, India
Pooja Raj Verma*
Affiliation:
Department of Applied Science, Madan Mohan Malaviya University of Technology, Gorakhpur–273001, India
*
*Corresponding author. Email:rajrbfma@iitr.ac.in (R. R. Bhargava), poojarajvs@gmail.com (P. R. Verma)
*Corresponding author. Email:rajrbfma@iitr.ac.in (R. R. Bhargava), poojarajvs@gmail.com (P. R. Verma)
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Abstract

A problem of two equal, semi-permeable, collinear cracks, situated normal to the edges of an infinitely long piezoelectric strip is considered. Piezoelectric strip being prescribed out-of-plane shear stress and in-plane electric-displacement. The Fourier series and integral equation methods are adopted to obtain analytical solution of the problem. Closed-form analytic expressions are derived for various fracture parameters viz. crack-sliding displacement, crack opening potential drop, field intensity factors and energy release rate. An numerical case study is considered for poled PZT–5H, BaTiO3 and PZT–6B piezoelectric ceramics to study the effect of applied electro-mechanical loadings, crack-face boundary conditions as well as inter-crack distance on fracture parameters. The obtained results are presented graphically, discussed and concluded.

Keywords

Collinear cracksFourier series methodpiezoelectric stripsemi-permeable crack

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 4 , August 2016 , pp. 573 - 587
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Parton, V. Z., Fracture mechanics of piezoelectric materials, Acta Astron., 3 (1976), pp. 671–683.Google Scholar
[2]Deeg, W. E. F., The Analysis of Dislocation, Crack and Inclusion Problems in Piezoelectric Solids, Ph.D. thesis, Stanford University, Stanford, 1980.Google Scholar
[3]Hao, T. H. and Shen, Z. Y., A new electric boundary condition of electric fracture mechanics and its applications, Eng. Frac. Mech., 47 (1994), pp. 793–802.Google Scholar
[4]Hang, Q., Daining, F. and Zhenhan, Y., Analysis of electric boundary condition effects on crack propagation in piezoelctric ceramics, Acta Mech. Sinica, 17 (2001), pp. 59–70.Google Scholar
[5]Zhang, T. Y. and Gao, C. F., Frcature behaviors of piezoelectric materials, Theo. Appl. Frac. Mech., 41 (2004), pp. 339–379.Google Scholar
[6]Ou, Z. C. and Chen, Y. H., On approach of crack tip energy release rate for a semi-permeable crack when electromechanical loads become very large, Int. Frac. Mech., 133 (2005), pp. 89–105.Google Scholar
[7]Li, Q. and Chen, Y. H., Solution for semi-permeable interface crack between two dissimilar piezoelectric material, J. Appl. Mech., 74 (2007), pp. 833–844.Google Scholar
[8]Zhou, Z. G., Wu, L. Z. and Du, S. Y., Non-local theory solution of two mode-I collinear cracks in the piezoelectric materials, Mech. Adv. Mater. Struct., 14 (2007), pp. 191–201.CrossRefGoogle Scholar
[9]Li, Y. D. and Lee, K. Y., Two collinear unequal cracks in a poled piezoelctric plane: Mode I case solved by a new approach of real fundamental solutions, Int. J. Frac., 165 (2010), pp. 47–60.Google Scholar
[10]Bhargava, R. R., Jangid, K. and Verma, P. R, Two semi-permeable equal collinear cracks weakening a piezoelectric plate–a study using complex variable technique, ZAMM-Int. J. Appl. Math. Mech., (2013), DOI 10.1002/zamm.201300109, pp. 1–11.Google Scholar
[11]Kwon, S. M., Electrical nonlinear anti-plane shear crack in a functionally graded piezoelectric strip, Int. J. Solids Struct., 40 (2003), pp. 5649–5667.CrossRefGoogle Scholar
[12]Ou, Z. C. and Wu, X., On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials, Int. J. Solids Struct., 40 (2005), pp. 7499–7511.Google Scholar
[13]Muskhelisvili, N., Singular Integral Equations, Noordhoff, Groningen, 1953.Google Scholar
[14]Ryzhik, I. M. and Gradshteyn, I. S., Table of Integrals, Series and Products, Academic Press, New York, 1965.Google Scholar