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Electroelastic Fields Induced by Two Collinear and Energetically Consistent Cracks in a Piezoelectric Layer

Published online by Cambridge University Press:  05 June 2014

X.-C. Zhong  and
K.-Y. Lee
X.-C. Zhong
Affiliation:
School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P.R., China
K.-Y. Lee*
Affiliation:
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, P.R., China
*
*[email protected]
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Abstract

Within the framework of linear piezoelectricity, the problem of two collinear electrically dielectric cracks in a piezoelectric layer is investigated under inplane electro-mechanical loadings. The energetically consistent crack-face boundary conditions are utilized to address the effects of a dielectric inside the cracks on the crack growth. The Fourier transform technique is applied to solve the boundary-value problem. Under the consideration of two-case electromechanical loadings, the electroelastic fields near the inner and outer crack tips are obtained through the Lobatto-Chebyshev collocation method. The special case of two collinear energetically consistent cracks in an infinite piezoelectric solid is analyzed and the closed-form solutions of the crack-tip electroelastic fields are further determined. Numerical results show the variations of stress intensity factors and energy release rates near the inner and outer crack tips on the applied electric fields, the geometry of cracks and the width of the piezoelectric layer in graphics. The observations reveal that the stress intensity factors are dependent not only on the adopted crack-face boundary conditions, but also on the applied mechanical loading.

Keywords

Piezoelectric layerEnergetically consistentTwo collinear cracksFourier transformCrack-tip fields
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 4 , August 2014 , pp. 361 - 372
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

1.McMeeking, R. M., “Crack Tip Energy Release Rate for a Piezoelectric Compact Tension Specimen,” Engineering Fracture Mechanics, 64, pp. 217–244 (1999).CrossRefGoogle Scholar
2.Yang, W., Mechatronic Reliability, Tsinghua University Press/Springer, Beijing (2001).Google Scholar
3.Qin, Q. H., Fracture Mechanics of Piezoelectric Materials, WIT Press, Southampton (2001).Google Scholar
4.Ding, H. J., Wang, H. M. and Chen, W. Q., “Analytical Solution of a Special Non-Homogeneous Pyro-electric Hollow Cylinder for Piezothermoelastic Axisymmetric Plane Strain Dynamic Problems,” Applied Mathematics and Computation, 151, pp. 423–441 (2004).CrossRefGoogle Scholar
5.Zhang, T. Y. and Gao, C. F., “Fracture Behaviors of Piezoelectric Materials,” Theoretical and Applied Fracture Mechanics, 41, pp. 339–379 (2004).CrossRefGoogle Scholar
6.Barboteu, M. and Sofonea, M., “Solvability of a Dynamic Contact Problem Between a Piezoelectric Body and a Conductive Foundation,” Applied Mathematics and Computation, 215, pp. 2978–2991 (2009).CrossRefGoogle Scholar
7.Kuna, M., “Fracture Mechanics of Piezoelectric Materials -Where are We Right Now?” Engineering Fracture Mechanics, 77, pp. 309–326 (2010).CrossRefGoogle Scholar
8.Guo, J. H., Lu, Z. X., Han, H. T. and Yang, Z. Y., “The Behavior of Two Non-Symmetrical Permeable Crack Semanating from an Elliptical Hole in a Piezoelectric Solid,” European Journal of Mechanics A/Solids, 29, pp. 654–663 (2010).CrossRefGoogle Scholar
9.Gao, H., Zhang, T. Y. and Tong, P., “Local and Global Energy Release Rate for an Electrically Yielded Crack in a Piezoelectric Ceramic,” Journal of the Mechanics and Physics of Solids, 45, pp. 491–510 (1997).CrossRefGoogle Scholar
10.Zhang, T. Y., Zhao, M. H. and Gao, C. F., “The Strip Dielectric Breakdown Model,” International Journal of Fracture, 132, pp. 311–327 (2005).CrossRefGoogle Scholar
11.Zhu, T. and Yang, W., “Toughness Variation of Ferroelectrics by Polarization Switch Under Nonuniform Electric Field,” Acta Materialia, 45, pp. 4695–4702 (1997).CrossRefGoogle Scholar
12.Hao, T. H. and Shen, Z. Y., “A New Electric Boundary Condition of Electric Fracture Mechanics and Its Application,” Engineering Fracture Mechanics, 47, pp. 793–802 (1994).Google Scholar
13.Landis, C. M., “Energetically Consistent Boundary Conditions for Electromechanical Fracture,” International Journal of Solids and Structures, 41, pp. 6291–6315 (2004).CrossRefGoogle Scholar
14.Ricoeur, A. and Kuna, M., “Electrostatic Tractions at Crack Faces and Their Influence on the Fracture Mechanics of Piezoelectrics,” International Journal of Fracture, 157, pp. 3–12 (2009).CrossRefGoogle Scholar
15.Schneider, G. A., Felten, F. and McMeeking, R. M., “The Electrical Potential Difference Across Cracks in PZT Measured by Kelvin Probe Microscopy and Implications for Fracture,” Acta Materialia, 51, pp. 2235–2241 (2003).CrossRefGoogle Scholar
16.Wang, B. L. and Mai, Y. W., “Impermeable Crack and Permeable Crack Assumptions, which One is More Realistic?” Journal of Applied Mechanics, ASME, 71, pp. 575–578 (2007).CrossRefGoogle Scholar
17.Wang, X. D. and Jiang, L. Y., “The Effective Electroelastic Property of Piezoelectric Media with Parallel Dielectric Cracks,” International Journal of Solids and Structures, 40, pp. 5287–5303 (2003).CrossRefGoogle Scholar
18.Wang, X. D. and Jiang, L. Y., “The Nonlinear Fracture Behavior of an Arbitrarily Oriented Dielectric Crack in Piezoelectric Materials,” Acta Mechanica, 172, pp. 195–210 (2004).CrossRefGoogle Scholar
19.Wang, X. D. and Jiang, L. Y., “Coupled Behaviour of Interacting Dielectric Cracks in Piezoelectric Materials,” International Journal of Fracture, 132, pp. 115–133 (2005).CrossRefGoogle Scholar
20.Chiang, C. R. and Weng, G. J., “Nonlinear Behavior and Critical State of a Penny-Shaped Dielectric Crack in a Piezoelectric Solid,” Journal of Applied Mechanics, ASME, 74, pp. 852–860 (2007).CrossRefGoogle Scholar
21.Li, X. F. and Lee, K. Y., “Fracture Analysis of Cracked Piezoelectric Materials,” International Journal of Solids and Structures, 41, pp. 4137–4161 (2004).CrossRefGoogle Scholar
22.Landis, C. M. and McMeeking, R. M., “Modeling of Fracture in Ferroelectric Ceramics,” Proceeding of SPIE, 3992, pp. 176–184 (2000).Google Scholar
23.Li, W., McMeeking, R. M. and Landis, C. M., “On the Crack Face Boundary Conditions in Electromechanical Fracture and an Experimental Protocol for Determining Energy Release Rate,” European Journal of Mechanics A/Solids, 27, pp. 285–301 (2008).CrossRefGoogle Scholar
24.Zhong, X. C. and Zhang, K. S., “Electroelastic Analysis of an Electrically Dielectric Griffith Crack in a Piezoelectric Layer,” International Journal of Engineering Science, 48, pp. 612–623 (2010).CrossRefGoogle Scholar
25.Eskandari, M., Moeini-Ardakani, S. S. and Shodja, H. M., “An Energetically Consistent Annular Crack in a Piezoelectric Medium,” Engineering Fracture Mechanics, 77, pp. 819–831 (2010).CrossRefGoogle Scholar
26.Fan, C. Y., Zhao, M. H., Meng, L. C., Gao, C. F. and Zhang, T. Y., “On The Self-Consistent, Energetically Consistent, and Electrostatic Traction Approaches in Piezoelectric Fracture Mechanics,” Engineering Fracture Mechanics, 78, pp. 2338–2355 (2011).CrossRefGoogle Scholar
27.Zhong, X. C., “Fracture Analysis of a Piezoelectric Layer with a Penny-Shaped and Energetically Consistent Crack,” Acta Mechanica, 223, pp. 331–345 (2012).CrossRefGoogle Scholar
28.Zhang, T. Y. and Hack, J. E., “Mode-III Crack in Piezoelectric Materials,” Journal of Applied Physics, 71, pp. 58–65 (1992).CrossRefGoogle Scholar
29.Hao, T. H., “Multiple Collinear Cracks in a Piezoelectric Material,” International Journal of Solids and Structures, 38, pp. 9201–9208 (2001).CrossRefGoogle Scholar
30.Liu, F. and Zhong, X. C., “Transient Response of Two Collinear Dielectric Cracks in a Piezoelectric Solid Under Inplane Impacts,” Applied Mathematics and Computation, 217, pp. 3779–3791 (2010).CrossRefGoogle Scholar
31.Wang, X. Y. and Yu, S. W., “Transient Response of a Crack in Piezoelectric Strip Subjected to the Mechanical and Electrical Impacts: Mode-I Problem,” Mechanics of Materials, 33, pp. 11–22 (2001).CrossRefGoogle Scholar
32.Wang, B. L., Nod, N., Han, J. C. and Du, S. Y., “A Penny-Shaped Crack in a Transversely Isotropic Piezoelectric Layer,” European Journal of Mechanics of A/Solids, 20, pp. 997–1005 (2001).CrossRefGoogle Scholar
33.Rice, J. M., Ben-Zion, Y. and Kim, K. S., “Three-Dimensional Perturbation Solution for a Dynamic Planar Crack Moving Unsteadily in a Model Elastic Solid,” Journal of the Mechanics and Physics of Solids, 42, pp. 813–843 (1994).CrossRefGoogle Scholar
34.Li, X. F. and Lee, K. Y., “Effects of Electric Field on Crack Growth for a Penny-Shaped Dielectric Crack in a Piezoelectric Layer,” Journal of the Mechanics and Physics of Solids, 52, pp. 2079–2100 (2004).CrossRefGoogle Scholar
35.Theocaris, P. S. and Ioakimidis, N. I., “Numerical Integration Methods for the Solution of Singular Integral Equations,” Quarterly of Applied Mathematics, 35, pp. 173–185 (1977).CrossRefGoogle Scholar
36.Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products, Academic Press, New York (1980).Google Scholar
37.Kumar, S. and Singh, R. N., “Effect of the Mechanical Boundary Condition at the Crack Surfaces on the Stress Distribution at the Crack Tip in Piezoelectric Materials,” Material Science Engineering: A, 252, pp. 64–77 (1998).CrossRefGoogle Scholar
38.Lowengrub, M. and Srivastava, K. N., “Two Coplanar Griffith Cracks in an Infinitely Long Elastic Strip,” International Journal of Engineering Science, 6, pp. 425–434 (1968).CrossRefGoogle Scholar