Abstract
In this paper, the problem of multiple defects in an orthotropic layer bonded between two piezoelectric layers is considered. The analysis is based on the stress fields caused by Volterra-type screw dislocation in the orthotropic strip. The solution for the dislocation is obtained by means of the complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple defects. These equations, as a class of Cauchy singular equations, are solved numerically for dislocation density functions. A number of examples is given for various crack orientations and material properties. At the end, it is shown that the effect of the properties and defect geometries on the stress intensity factors and hoop stress for cavities can be highly significant.
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Kwon J.H., Lee K.Y.: Interface crack between piezoelectric and elastic strips. Arch. Appl. Mech. 70, 707–714 (2000)
Kwon J.H., Meguid S.A.: Analysis of a central crack normal to a piezoelectric–orthotropic interface. Int. J. Solids Struct. 39, 841–860 (2002)
Lee J.S., Kwon S.M., Lee K.Y., Kwon H.: Anti-plane interfacial Yoffe-crack between a piezoelectric and two orthotropic layers. Eur. J. Mech. A Solids 21, 483–492 (2002)
Kwon S.M., Son M.S., Lee K.Y.: Transient behavior in a cracked piezoelectric layered composite: anti-plane problem. Mech. Mater. 34, 593–603 (2002)
Ueda S.: Crack in functionally graded piezoelectric strip bonded to elastic surface layers under electro mechanical loading. Theor. Appl. Fract. Mech. 40, 225–236 (2003)
Chi S., Chung Y.L.: Cracking in coating-substrate composites with multi-layered and FGM coating. Eng. Fract. Mech. 70, 1227–1243 (2003)
Ding S.H., Li X.: Periodic cracks in a functionally graded piezoelectric layer bonded to a piezoelectric half-plane. Theor. Appl. Fract. Mech. 49, 313–320 (2008)
Cheng Z., Zhao X.: Fracture analysis of a functionally graded piezoelectric with viscoelastic interface. Int. J. Fract. 141, 63–73 (2009)
Li Y.D., Lee K.Y.: Crack tip shielding and anti-shielding effects of the imperfect interface in a layered piezoelectric sensor. Int. J. Solids Struct. 46, 1736–1742 (2009)
Peng X.L., Li X.F.: Transient response of the crack tip field in a magnetoelectroelastic half-space with a functionally graded coating under impacts. Arch. Appl. Mech. 79, 1099–1113 (2009)
Li X., Ding S.H.: Periodically distributed parallel cracks in a functionally graded piezoelectric (FGP) strip bonded to a FGP substrate under static electromechanical load. Comput. Mater. Sci. 50, 1477–1484 (2009)
Feng F.X., Lee K.Y., Li Y.D.: Multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate. Acta Mech. 221, 297–308 (2011)
Shin J.W., Lee Y.S.: Anti-plane moving crack in a functionally graded piezoelectric layer between two dissimilar piezoelectric strips. J. Mech. Sci. Technol. 26, 1017–1025 (2012)
Asadi E., Fariborz S.J., Fotuhi A.R.: Anti-plane analysis of orthotropic strips with defects and imperfect FGM coating. Eur. J. Mech. A Solids 34, 12–20 (2012)
Mousavi S.M., Paavola J.: Analysis of cracked functionally graded piezoelectric strip. Int. J. Solids Struct. 50, 2449–2456 (2013)
Bagheri R., Ayatollahi M., Asadi E.: Dynamic fracture analysis of multiple defects in an imperfect FGM coating-substrate layers. Int. J. Mech. Sci. 75, 55–65 (2013)
Ding S.H., Li X.: The collinear crack problem for an orthotropic functionally graded coating-substrate structure. Arch. Appl. Mech. 84, 291–307 (2014)
Bagheri R., Ayatollahi M., Mousavi S.M.: Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating. Int. J. Mech. Sci. 93, 93–101 (2015)
Erdogan F., Gupta G.D.: On the numerical solution of singular integral equations. Q. Appl. Math. 29, 525–534 (1972)
Lekhnitskii S.G.: Theory of Elasticity of an Anisotropic Elastic Body. Holden-Day, San Francisco (1963)
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Nourazar, M., Ayatollahi, M. Analysis of an orthotropic strip containing multiple defects bonded between two piezoelectric layers. Acta Mech 227, 1293–1306 (2016). https://doi.org/10.1007/s00707-015-1559-0
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DOI: https://doi.org/10.1007/s00707-015-1559-0