Cracked piezoelectric layer bounded between two orthotropic half-planes

Bastanfar, Marzieh; Ayatollahi, Mojtaba

Cracked piezoelectric layer bounded between two orthotropic half-planes

Document Type : Research Paper

Authors

¹ Faculty of Engineering, Department of Mechanical Engineering, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran

² Faculty of Engineering, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran

Abstract

This paper deals with the behavior of anti-plane shear crack in a piezoelectric layer bounded between two orthotropic half-planes within the framework of linear electroelasticity. The crack surfaces are assumed to be permeable or impermeable. The analysis is based on the stress fields caused by Volterra-type screw dislocation in the medium. Fourier transforms are used to reduce the dislocation problem to the solution of Cauchy-type singular integral equations, which are solved numerically for the dislocation density on the cracks. The dislocation densities are then employed to derive field intensity factors at the crack tips. The results show that the stress and the electric displacement intensity factors at the crack tips depend on the lengths and orientation of the cracks. It is also shown that, for a fixed value of the mechanical load, the field intensity factor can be either enhanced depending on the magnitude and direction of the applied electrical load. Furthermore, the interaction between the two cracks is investigated.

Keywords

20.1001.1.16059727.2018.19.1.5.4

Main Subjects

Fracture mechanics

References

[1] Narita, F., Shindo, Y., and Watanabe, K., "Anti-plane Shear Crack in a Piezoelectric Layer Bonded to Dissimilar Half-spaces", JSME International Journal Series A Solid Mechanics and Material Engineering, Vol. 42, pp. 66-72, (1999).

[2] Shin, J.W., and Lee, K.Y., "Eccentric Crack in a Piezoelectric Strip Bonded to Half-planes", European Journal of Mechanics A/solids, Vol. 19, pp. 989-994, (2000).

[3] Zhou, Z.G., Chen, J.Y., and Wang, B., "Analysis of Two Collinear Cracks in a Piezoelectric Layer Bonded to Two Half Spaces Subjected to Anti-plane Shear", Meccanica, Vol. 35, pp.443-456, (2000).

[4] Kwon, S.M., Son, M.S., and Lee, K.Y., "Transient Behavior in a Cracked Piezoelectric Layered Composite: Anti-plane Problem", Mechanics of Materials, Vol. 34, pp. 593-603, (2002).

[5] Ueda, S., "Crack in Functionally Graded Piezoelectric Strip Bonded to Elastic Surface Layers under Electro Mechanical Loading", Theoretical and Applied Fracture Mechanics, Vol. 40, pp. 225-236, (2003).

[6] Shenghu, D., and Xing, L., "The Periodic Crack Problem in Bonded Piezoelectric Materials", Acta Mechanica Solida Sinica, Vol. 20, pp. 171-179, (2007) .

[7] Ding, S.H., and Li, X., "Periodic Cracks in a Functionally Graded Piezoelectric Layer Bonded to a Piezoelectric Half-plane", Theoretical and Applied Fracture Mechanics, Vol. 49, pp. 313-320, (2008).

[8] Li, Y.D., and Lee, K.Y., "Crack Tip Shielding and Anti-shielding Effects of the Imperfect Interface in a Layered Piezoelectric Sensor", International Journal of Solids and Structures, Vol. 46, pp. 1736-1742, (2009).

[9] Ding, S.H., Li, X., and Guo, L.F., "Analysis of Bonded Piezoelectric Materials with a Crack Perpendicular to the Interface Subjected to In-plane Loading", Computational Material Science, Vol. 47, pp. 977-984, (2010).

[10] Li, Y.D., Zhao, H., and Zhang, N., "Mixed Mode Fracture of a Piezoelectric–piezomagnetic Bi-layer Structure with Two Un-coaxial Cracks Parallel to the Interface and each in a Layer", International Journal of Solids and Structures, Vol. 50, pp. 3610-3617, (2013).

[11] Mousavi, S.M., and Paavola, J., "Analysis of Cracked Functionally Graded Piezoelectric Strip", International Journal of Solids and Structures, Vol. 50, pp. 2449–2456, (2013).

[12] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., "Analysis of Cracked Piezoelectric Layer with Imperfect Non-homogeneous Orthotropic Coating", International Journal of Mechanical Sciences, Vol. 93, pp. 93-101, (2015).

[13] Nourazar, M., and Ayatollahi, M., "Analysis of an Orthotropic Strip Containing Multiple Defects Bonded between Two Piezoelectric Layers", Acta Mechanica, Vol. 227, pp. 1293-1306, (2016).

[14] Abramowitz, M., and Stegun, I.A., "Handbook of Mathematical Functions", Dover, New York, (1972).