Abstract
The scattering problem of the SH wave on a limited permeable crack in a functionally graded piezoelectric substrate bonded to a homogeneous piezoelectric strip is investigated. We adopted the limited permeable crack surface boundary condition. By using the Fourier cosine transform, this mixed boundary value problem is reduced to two pairs of dual integral equations, which are solved numerically by the Copson method. Numerical results showed the effects of gradient parameter, electric loading, electric boundary conditions, incident angle, thickness of PM strip, the distance from the crack to the interface, and wave number on the dynamic stress intensity factor.
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Li C., Weng G.J.: Antiplane crack problem in functionally graded piezoelectric materials. ASME J. Appl. Mech. 69, 481–488 (2002)
Chen J., Liu Z.X., Zou Z.Z.: The central crack problem for a functionally graded piezoelectric strip. Int. J. Fract. 121, 81–94 (2003)
Shin J.W., Kim T.U., Kim S.C.: Dynamic characteristics of an eccentric crack in a functionally graded piezoelectric ceramic strip. J. Mech. Sci. Technol. 18, 1582–1589 (2004)
Hu K., Zhong Z.: A moving mode-III crack in a functionally graded piezoelectric strip. Int. J. Mech. Mater. Des. 2, 61–79 (2005)
Yong H.D., Zhou Y.H.: A mode III crack in a functionally graded piezoelectric strip bonded to two dissimilar piezoelectric half-planes. Compos. Struct. 79, 404–410 (2007)
Jiang L.Y.: The fracture behavior of functionally graded piezoelectric materials with dielectric cracks. Int. J. Fract. 149, 87–104 (2008)
Shin J.W., Kim T.U., Kim S.J., Hwang I.H.: Dynamic propagation of a finite eccentric crack in a functionally graded piezoelectric ceramic strip. J. Mech. Sci. Technol. 23, 1–7 (2009)
Shin J.W., Lee Y.S.: A moving interface crack between two dissimilar functionally graded piezoe-lectric layers under electromechanical loading. Int. J. Solids Struct. 47, 2706–2713 (2010)
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 (2011)
Li X., Long Y.Y.: Thermal effect of functionally graded piezoelectric materials with crack by electric shock. Int. J. Mech. Res. 1, 1–7 (2012)
Zhou Y.T., Lee K.Y.: Investigation of frictional sliding contact problems of triangular and cylindrical punches on monoclinic piezoelectric materials. Mech. Mater. 69, 237–250 (2014)
Shen S.P., Kuang Z.B.: Wave scattering from an interface crack in laminated anisotropic media. Mech. Res. Commun. 25, 509–517 (1998)
Wang X.D., Meguid S.A.: Modeling and analysis of the dynamic behavior of piezoelectric materials containing interacting cracks. Mech. Mater. 32, 723–737 (2000)
Gu B., Yu S.W., Feng X.Q.: Elastic wave scattering by an interface crack between a piezoelectric layer and elastic substrate. Int. J. Fract. 116, L29–L34 (2002)
Ueda S.: Diffraction of antiplane shear waves in a piezoelectric laminate with a vertical crack. Euro. J. Mech. A Solids 22, 413–422 (2003)
Zhou Z.G., Wang B.: The scattering of harmonic anti-plane shear waves by an interface crack in magneto-electro-elastic composites. Appl. Math. Mech. 26, 17–26 (2005)
Ma L., Nie W., Wu L.Z., Guo L.C.: Scattering of anti-plane stress waves by a crack in a non-homogeneous orthotropic medium. Compos. Struct. 79, 174–179 (2007)
Li X., Liu J.Q.: Scattering of the SH wave from a crack in a piezoelectric substrate bonded to a half-space of functionally graded materials. Acta Mech. 208, 299–308 (2009)
Huang Y., Li X.F.: Shear waves guided by the imperfect interface of two magnetoelectric materials. Ultrasonics 50, 750–757 (2010)
Zhao J., Pan Y., Zhong Z.: Theoretical study of shear horizontal wave propagation in periodically layered piezoelectric structure. J. Appl. Phys. 111, 064906-1–064906-11 (2012)
Singh B.M., Rokne J.: Propagation of SH waves in layered functionally gradient piezoelectric–piezomagnetic structures. Philos. Mag. 93, 1690–1700 (2013)
Yang J., Li X.: Scattering of the SH wave by a crack magneto-electro-elastic material substrate bonded to piezoelectric material. Theor. Appl. Fract. Mech. 74, 109–115 (2014)
Hao T.H., Shen Z.Y.: A new electric boundary condition of electric fracture mechanics and its applications. Eng. Fract. Mech. 47, 793–802 (1994)
Kwon S.M.: On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip. Acta Mech. 167, 73–89 (2004)
Sun J.L., Zhou Z.G., Wang B.: Dynamic behavior of a crack in a functionally graded piezoelectric strip bonded to two dissimilar half piezoelectric material planes. Acta Mech. 176, 4–60 (2005)
Copson E.T.: On certain dual integral equations. Proc. Glasg. Math. Assoc. 5, 21–24 (1961)
Narita F., Shindo Y.: Dynamic anti-plane shear of a cracked piezoelectric ceramic. Theor. Appl. Fract. Mech. 29, 169–180 (1998)
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Yang, J., Li, X. The scattering of the SH wave on a limited permeable crack in a functionally graded piezoelectric substrate bonded to a homogeneous piezoelectric strip. Acta Mech 226, 3205–3219 (2015). https://doi.org/10.1007/s00707-015-1365-8
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DOI: https://doi.org/10.1007/s00707-015-1365-8