Abstract
In the present work, we investigate the problem of multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate. The method of dislocation simulation and singular integral equation are used to solve the crack problem. The theoretical derivation is verified by the classical result in a special case. Numerical results of the stress intensity factor are obtained, and thereby the effects of geometrical parameters and material orthotropy are surveyed. The optimal stiffness ratio of the orthotropic substrate is suggested for the purpose of interfacial fracture prevention, which is significant for the design and assessment of such a kind of smart structures.
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Li Y.D., Lee K.Y.: Crack tip shielding and anti-shielding effects of the imperfect interface in a layered piezoelectric sensor. Int. J. Solid. Struct. 46, 1736–1742 (2009)
Ru C.: Electrode-ceramic interfacial cracks in piezoelectric multilayer materials. J. Appl. Mech. 67, 255–261 (2000)
Govorukha V.B., Loboda V.V.: Contact zone models for an interface crack in a piezoelectric material. Acta Mech. 140, 233–246 (2000)
Gu B., Yu S.W., Feng X.Q.: Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts. Int. J. Solid. Struct. 39, 1743–1756 (2002)
Guo X.H., Fang D.N.: Simulation of interface cracking in piezoelectric layers. Int. J. Nonl. Sci. Num. Sim. 5, 235–242 (2004)
Huang G.L., Wang X.D.: On the dynamic behaviour of interfacial cracks between a piezoelectric layer and an elastic substrate. Int. J. Fract. 141, 63–73 (2006)
Li Q., Chen Y.H.: Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials. Acta Mech. Sin. 23, 681–687 (2007)
Tian W.Y., Rajapakse R.K.N.D.: Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system. Int. J. Fract. 141, 37–48 (2006)
Li Y.D., Lee K.Y.: Fracture analysis on the arc-shaped interface in a layered cylindrical piezoelectric sensor polarized along its axis. Eng. Fract. Mech. 76, 2065–2073 (2009)
Hausler C., Jelitto H., Neumeister P. et al.: Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading. Int. J. Fract. 160, 43–54 (2009)
Shin J.W., Lee Y.S.: A moving interface crack between two dissimilar functionally graded piezoelectric layers under electromechanical loading. Int. J. Solid. Struct. 47, 2706–2713 (2010)
Loboda V., Lapusta Y., Sheveleva A.: Limited permeable crack in an interlayer between piezoelectric materials with different zones of electrical saturation and mechanical yielding. Int. J. Solid. Struct. 47, 1795–1806 (2010)
Natroshvili D., Stratis I.G., Zazashvili S.: Interface crack problems for metallic-piezoelectric composite structures. Math. Meth. Appl. Sci. 33, 539–562 (2010)
Kwon J.H., Meguid S.A.: Analysis of a central crack normal to a piezoelectric-orthotropic interface. Int. J. Solid. Struct. 39, 841–860 (2002)
Kwon S.M., Lee K.Y.: Steady state crack propagation in a piezoelectric layer bonded between two orthotropic layers. Mech. Mater. 35, 1077–1088 (2003)
Chen Y.Z., Lin X.Y., Wang Z.X.: Antiplane elasticity crack problem for a strip of functionally graded materials with mixed boundary condition. Mech. Res. Commun. 37, 50–53 (2010)
Li Y.D., Lee K.Y.: Collinear unequal crack series in magnetoelectroelastic materials: mode I case solved via new real fundamental solutions. Eng. Fract. Mech. 77, 2772–2790 (2010)
Li Y.D., Lee K.Y.: Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions. Int. J. Fract. 165, 47–60 (2010)
Liebowitz H.: Fracture, An Advanced Treatise, Vol. 1 Microscopic and Macroscopic Fundamentals. Academic Press, New York (1968)
Yang J.S.: An Introduction to The Theory of Piezoelectricity. Springer Science+Business Media, Inc., Boston (2005)
Zhong X.C., Liu F., Li X.F.: Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts. Int. J. Solid. Struct. 46, 2950–2958 (2009)
Muskhelishvili N.I.: Singular Integral Equations. Noordhoff, Groningen (1953)
Li Y.D., Lee K.Y.: Effects of magneto-electric loadings and piezomagnetic/piezoelectric stiffening on multiferroic interface fracture. Eng. Fract. Mech. 77, 856–866 (2010)
Li X.F., Lee K.Y.: Closed-form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti-plane shear. ZAMM. Zeit. Fur. Ang. Math. Mech. 89, 370–382 (2009)
Matbuly M.S., Nassar M.: Analysis of multiple interfacial cracks in an orthotropic bi-material subjected to anti-plane shear loading. Eng. Fract. Mech. 76, 1658–1666 (2009)
Duan X.Y., Li X.F.: An interfacially-cracked orthotropic rectangular bi-material subjected to antiplane shear loading. Appl. Math. Comp. 174, 1060–1079 (2006)
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Feng, FX., Lee, K.Y. & Li, YD. Multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate. Acta Mech 221, 297–308 (2011). https://doi.org/10.1007/s00707-011-0506-y
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DOI: https://doi.org/10.1007/s00707-011-0506-y