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2017 | OriginalPaper | Chapter

1. Introduction

Authors : Volodymyr Govorukha, Marc Kamlah, Volodymyr Loboda, Yuri Lapusta

Published in: Fracture Mechanics of Piezoelectric Solids with Interface Cracks

Publisher: Springer International Publishing

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Abstract

The piezoelectric effect, based on an electro-mechanical coupling, is quite common in nature and observed in certain anisotropic crystals such as quartz crystal, tourmaline and Rochelle salt. It is reversible and it can be direct and inverse.

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Literature
Akbarov, S.D., Yahnioglu, N.: Buckling delamination of a sandwich plate-strip with piezoelectric face and elastic core layers. Appl. Math. Model. 37, 8029–8038 (2013)MathSciNetCrossRef
Bakirov, V.F., Gol’dshtein, R.V.: The Leonov-Panasyuk-Dugdale model for a crack at the interface of the joint of materials. J. Appl. Math. Mech. 68(1), 153–161 (2004)CrossRef
Bakirov, V.F., Kim, T.W.: Analysis of a crack at the piezoceramic-metal interface and estimates of adhesion fracture energy. Int. J. Eng. Sci. 47, 793–804 (2009)CrossRef
Bardzokas, D.I., Filshtinsky, M.L., Filshtinsky, L.A.: Mathematical Methods in Electro-Magneto-Elasticity. Springer, Berlin (2007)MATH
Beom, H.G.: Permeable cracks between two dissimilar piezoelectric materials. Int. J. Solids Struct. 40, 6669–6679 (2003)CrossRefMATH
Beom, H.G., Atluri, S.N.: Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media. Int. J. Fract. 75, 163–183 (1996)CrossRef
Beom, H.G., Atluri, S.N.: Conducting cracks in dissimilar piezoelectric media. Int. J. Fract. 118, 285–301 (2002)CrossRef
Cady, W.G.: Piezoelectricity. MacDraw-Hill, New York (1946)
Chen, X., Mai, Y.W.: Fracture Mechanics of Electromagnetic Materials: Nonlinear Field Theory and Applications. Imperial College Press, London (2012)CrossRef
Chen, Y.H., Lu, T.J.: Cracks and fracture in piezoelectrics. Adv. Appl. Mech. 39, 121–215 (2003)CrossRef
Chen, Y.H., Hasebe, N.: Current understanding on fracture behaviors of ferroelectric/piezoelectric materials. J. Intell. Mater. Syst. Struct. 16, 673–687 (2005)CrossRef
Curie, J., Curie, P.: Development par compression de l’eletricite polaire dans les cristaux hemiedres a faces inclines. Bull. Soc. Mineral. France 3, 90–93 (1880)MATH
Deeg, W.F.: The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph.D. thesis, Stanford University, Stanford, California (1980)
Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)CrossRef
Duhem, P.: Die dauernden Änderungen und die Thermodynamic. Z. Phys. Chem. 22, 543–589 (1897)CrossRef
England, A.H.: A crack between dissimilar media. J. Appl. Mech. 32(2), 400–402 (1965)CrossRef
Erdogan, F.: Stress distribution in bonded dissimilar materials with cracks. J. Appl. Mech. 32(2), 403–410 (1965)CrossRef
Fang, D.N., Liu, J.X.: Fracture Mechanics of Piezoelectric and Ferroelectric Solids. Springer, Berlin (2013)CrossRefMATH
Fang, D.N., Soh, A.K., Liu, J.X.: Electromechanical deformation and fracture of piezoelectric/ferroelectric materials. Acta Mech. Sinica 17(3), 193–213 (2001)CrossRef
Gao, C.F., Wang, M.Z.: Collinear permeable cracks between dissimilar piezoelectric materials. Int. J. Solids Struct. 37, 4969–4986 (2000)CrossRefMATH
Gao, C.F., Haeusler, C., Balke, H.: Periodic permeable interface cracks in piezoelectric materials. Int. J. Solids Struct. 41, 323–335 (2004)CrossRefMATH
Gao, C.F., Tong, P., Zhang, T.Y.: Interaction of a dipole with an interfacial crack in piezoelectric media. Compos. Sci. Technol. 65, 1354–1362 (2005)CrossRef
Govorukha, V.B., Loboda, V.V.: Contact zone models for an interface crack in a piezoelectric material. Acta Mech. 140, 233–246 (2000)CrossRefMATH
Govorukha, V., Kamlah, M.: Asymptotic fields in the finite element analysis of electrically permeable interface cracks in piezoelectric bimaterials. Arch. Appl. Mech. 74, 92–101 (2004)CrossRefMATH
Govorukha, V., Kamlah, M.: Investigation of an interface crack with a contact zone in a piezoelectric bimaterial under limited permeable electric boundary conditions. Acta Mech. 178, 85–99 (2005)CrossRefMATH
Govorukha, V., Kamlah, M.: An analytically-numerical approach for the analysis of an interface crack with a contact zone in a piezoelectric bimaterial compound. Arch. Appl. Mech. 78, 575–586 (2008a)CrossRefMATH
Govorukha, V.B., Kamlah, M.: Pre-fracture zone modeling for an electrically impermeable interface crack in a piezoelectric bimaterial compound. J. Mech. Mater. Struct. 3, 1447–1463 (2008b)CrossRefMATH
Govorukha, V., Kamlah, M.: On contact zone models for an electrically limited permeable interface crack in a piezoelectric bimaterial. Int. J. Fract. 164, 133–146 (2010)CrossRefMATH
Govorukha, V.B., Kamlah, M., Munz, D.: On the singular integral equations approach to the interface crack problem for piezoelectric materials. Arch. Mech. 52, 247–273 (2000)MATH
Govorukha, V., Kamlah, M., Munz, D.: The interface crack problem for a piezoelectric semi-infinite strip under concentrated electromechanical loading. Eng. Fract. Mech. 71, 1853–1871 (2004)CrossRef
Govorukha, V.B., Loboda, V.V., Kamlah, M.: On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound. Int. J. Solids Struct. 43, 1979–1990 (2006)CrossRefMATH
Govorukha, V.B., Herrmann, K.P., Loboda, V.V.: Electrically permeable crack with contact zones between two piezoelectric materials. Int. Appl. Mech. 44(3), 296–303 (2008)MathSciNetCrossRefMATH
Govorukha, V., Kamlah, M., Loboda, V., Lapusta, Y.: Interface cracks in piezoelectric materials. Smart Mater. Struct. 25, 023001 (2016)
Gruebner, O., Kamlah, M., Munz, D.: Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Eng. Fract. Mech. 70, 1399–1413 (2003)CrossRef
Haeusler, C., Jelitto, H., Neumeister, P., Balke, H., Schneider, G.A.: Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading. Int. J. Fract. 160, 43–54 (2009)CrossRef
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)CrossRef
He, M.Y., Evans, A.G., Hutchinson, J.W.: Interface cracking phenomena in constrained metal layer. Acta Mater. 44, 2963–2971 (1996)CrossRef
Herrmann, K.P., Loboda, V.V.: Fracture-mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models. Arch. Appl. Mech. 70, 127–143 (2000)CrossRefMATH
Herrmann, K.P., Loboda, V.V., Govorukha, V.B.: On contact zone models for an electrically impermeable interface crack in a piezoelectric biomaterial. Int. J. Fract. 111, 203–227 (2001)CrossRef
Kaminskii, A.A., Kipnis, L.A., Kolmakova, V.A.: Slit lines at the end of a cut at the interface of different media. Int. Appl. Mech. 31(6), 491–495 (1995)CrossRefMATH
Kaminskii, A.A., Kipnis, L.A., Kolmakova, V.A.: On the Dugdale model for a crack at the interface of different media. Int. Appl. Mech. 35(1), 58–63 (1999)CrossRef
Kamins’kyi, A.O., Dudyk, M.V., Kipnis, L.A.: Stresses near crack tips on the boundary of two media in the presence of plastic strips. Mater. Sci. 37(3), 447–455 (2001)
Kaminskii, A.A., Kipnis, L.A., Dudik, M.V.: Initial development of the pre-fracture zone near the tip of a crack reaching the interface between dissimilar media. Int. Appl. Mech. 40(2), 176–182 (2004)CrossRef
Kelvin, L.: On the theory of pyro-electricity and piezo-electricity of crystals. Phil. Mag. Ser. 5, 36(222), 453–459 (1893)
Kozinov, S., Loboda, V., Lapusta, Y.: Periodic set of limited electrically permeable interface cracks with contact zones. Mech. Res. Commun. 48, 32–41 (2013)CrossRef
Kudriavtsev, B.A., Parton, V.Z., Rakitin, V.I.: Fracture mechanics of piezoelectric materials. Rectilinear tunnel crack on the boundary with a conductor. J. Appl. Math. Mech. 39(1), 136–146 (1975)MathSciNetCrossRefMATH
Kuna, M.: Finite element analyses of cracks in piezoelectric structures: a survey. Arch. Appl. Mech. 76, 725–745 (2006)CrossRefMATH
Kuna, M.: Fracture mechanics of piezoelectric materials—where are we right now? Eng. Fract. Mech. 77, 309–326 (2010)CrossRef
Kuo, C.M., Barnett, D.M.: Stress singularities of interfacial cracks in bonded piezoelectric half-spaces. In: Wu, J.J., Ting, T.C.T., Barnett, D.M. (eds.) Modern Theory of Anisotropic Elasticity and Applications, pp. 33–50. SIAM Proceedings Series, Philadelphia (1991)
Landis, C.M.: Energetically consistent boundary conditions for electromechanical fracture. Int. J. Solids Struct. 41, 6291–6315 (2004)CrossRefMATH
Lapusta, Y., Loboda, V.: Electro-mechanical yielding for a limited permeable crack in an interlayer between piezoelectric materials. Mech. Res. Commun. 36, 183–192 (2009)MathSciNetCrossRefMATH
Leonov, M.Y., Panasyuk, V.V.: The development of very shallow cracks in a solid. Prikl. Mekh. 5(4), 391–401 (1959)
Li, Q., Chen, Y.: Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials. Acta Mech. Sinica 23, 681–687 (2007a)CrossRefMATH
Li, Q., Chen, Y.: Analysis of crack-tip singularities for an interfacial permeable crack in metal/piezoelectric bimaterials. Acta Mech. Solida Sinca. 20, 247–257 (2007b)CrossRef
Li, Q., Chen, Y.H.: Solution for a semi-permeable interface crack between two dissimilar piezoelectric materials. J. Appl. Mech. 74, 833–844 (2007c)CrossRef
Li, Q., Chen, Y.H.: Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials. J. Appl. Mech. 75, 11010 (2008)
Li, Q., Chen, Y.H.: The Coulombic traction on the surfaces of an interface crack in dielectric/piezoelectric or metal/piezoelectric bimaterials. Acta Mech. 202, 111–126 (2009)CrossRefMATH
Lippmann, G.: Principe de conservation de l’electricite. Ann. Chim. Phys. 24, 145–178 (1881)
Liu, M., Hsia, K.J.: Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading. J. Mech. Phys. Solids 51, 921–944 (2003)CrossRefMATH
Loboda, V.V., Sheveleva, A.E.: Determining pre-fracture zones at a crack tip between two elastic orthotropic bodies. Int. Appl. Mech. 39(5), 566–572 (2003)CrossRefMATH
Loboda, V., Lapusta, Y., Sheveleva, A.: Analysis of pre-fracture zones for an electrically permeable crack in an interlayer between piezoelectric materials. Int. J. Fract. 142, 307–313 (2006)CrossRefMATH
Loboda, V., Lapusta, Y., Sheveleva, A.: Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric bimaterial. Int. J. Solids Struct. 44, 5538–5553 (2007)CrossRefMATH
Loboda, V., Lapusta, Y., Govorukha, V.: Mechanical and electrical yielding for an electrically insulated crack in an interlayer between piezoelectric materials. Int. J. Eng. Sci. 46, 260–272 (2008)CrossRefMATH
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. Solids Struct. 47, 1795–1806 (2010)CrossRefMATH
Loboda, V., Sheveleva, A., Lapusta, Y.: An electrically conducting interface crack with a contact zone in a piezoelectric bimaterial. Int. J. Solids Struct. 51, 63–73 (2014)CrossRef
Ma, L.F., Chen, Y.H.: Weight functions for interface cracks in dissimilar anisotropic piezoelectric materials. Int. J. Fract. 110, 263–279 (2001)CrossRef
Mason, W.P.: Piezoelectric crystals and their application to ultrasonics. Van Nostrand, New York (1950)
Mossakovskii, V.I., Rybka, M.T.: Generalization of the Grippith-Sneddon criterion for the case of a nonhomogeneous body. J. Appl. Math. Mech. 28(6), 1277–1286 (1964)CrossRefMATH
Ou, Z.C.: Singularity parameters ε and κ for interface cracks in transversely isotropic piezoelectric bimaterials. Int. J. Fract. 119, L41–L46 (2003)CrossRef
Ou, Z.C., Wu, X.: On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials. Int. J. Solids Struct. 40, 7499–7511 (2003)CrossRefMATH
Ou, Z.C., Chen, Y.H.: Near-tip stress fields and intensity factors for an interface crack in metal/piezoelectric bimaterials. Int. J. Eng. Sci. 42, 1407–1438 (2004a)CrossRef
Ou, Z.C., Chen, Y.H.: Interface crack problem in elastic dielectric/piezoelectric bimaterials. Int. J. Fract. 130, 427–454 (2004b)CrossRef
Ou, Z.C., Chen, Y.H.: Interface crack-tip generalized stress field and stress intensity factors in transversely isotropic piezoelectric bimaterials. Mech. Res. Commun. 31, 421–428 (2004c)CrossRefMATH
Pak, Y.E.: Linear electro-elastic fracture mechanics of piezoelectric materials. Int. J. Fract. 54, 79–100 (1992)CrossRef
Parton, V.Z.: Fracture mechanics of piezoelectric materials. Acta Astronaut. 3, 671–683 (1976)CrossRefMATH
Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach, New York (1988)
Pockels, F.: Über den Einfluss des Elektrostatischen Feldes auf das optische Verhalten piezoelektrischer Krystalle. Göttingen (1894)
Qin, Q.H.: Fracture Mechanics of Piezoelectric Materials. WIT Press, Southampton, Boston (2001)
Rice, J.R.: Elastic fracture mechanics concept for interfacial cracks. J. Appl. Mech. 55(1), 98–103 (1988)CrossRef
Rice, J.R., Sih, G.C.: Plane problem of cracks in dissimilar media. J. Appl. Mech. 32(2), 418–423 (1965)CrossRef
Ru, C.Q.: A hybrid complex-variable solution for piezoelectric/isotropic elastic interfacial cracks. Int. J. Fract. 152, 169–178 (2008)CrossRefMATH
Shen, S., Kuang, Z.B., Hu, S.: Interface crack problems of a laminated piezoelectric plate. Eur. J. Mech. A/Solids 18, 219–238 (1999)CrossRefMATH
Shen, S., Nishioka, T., Kuang, Z.B., Liu, Z.: Nonlinear electromechanical interfacial fracture for piezoelectric materials. Mech. Mater. 32, 57–64 (2000)CrossRef
Sheveleva, A.E.: Modeling of the near-tip zones of a crack between two anisotropic materials. Mater. Sci. 36(2), 187–197 (2000)CrossRef
Sladek, J., Sladek, V., Wuensche, M., Zhang, Ch.: Analysis of an interface crack between two dissimilar piezoelectric solids. Eng. Fract. Mech. 89, 114–127 (2012)CrossRef
Suo, Z., Kuo, C.M., Barnett, D.M., Willis, J.R.: Fracture Mechanics for Piezoelectric Ceramics. J. Mech. Phys. Solids 40, 739–765 (1992)MathSciNetCrossRefMATH
Tian, W.Y., Chen, Y.H.: Interaction between an interface crack and subinterface microcracks in metal/piezoelectric bimaterials. Int. J. Solids Struct. 37, 7743–7757 (2000)CrossRefMATH
Tiersten, H.F.: Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969)CrossRef
Voigt, W.: Lehrbuch der Kristallphysik. Leipzig (1910)
Voloshko, O., Lapusta, Y., Loboda, V.: Analytical and numerical study of cohesive zones for a crack in an adhesive layer between identical isotropic materials. Eng. Fract. Mech. 77, 2577–2592 (2010)CrossRef
Voloshko, O.I., Lapusta, Y., Loboda, V.V.: Construction of an approximating function in the pre-fracture zone for a crack in an adhesive interlayer between two isotropic materials. J. Math. Sci. 183(2), 131–149 (2012)CrossRefMATH
Wang, T.C., Han, X.L.: Fracture mechanics of piezoelectric materials. Int. J. Fract. 98, 15–35 (1999)CrossRef
Williams, M.L.: The stresses around a fault or cracks in dissimilar media. Bull. Seism. Soc. Am. 49(2), 199–204 (1959)MathSciNet
Zhang, T.Y., Gao, C.F.: Fracture behaviors of piezoelectric materials. Theor. Appl. Fract. Mech. 41, 339–379 (2004)CrossRef
Zhang, T.Y., Fu, R., Zhao, M.H., Tong, P.: Overview of fracture of piezoelectric ceramics. Key Eng. Mater. 183–187, 695–706 (2000)CrossRef
Zhang, T.Y., Zhao, M.H., Tong, P.: Fracture of piezoelectric ceramics. Adv. Appl. Mech. 38, 147–289 (2002)CrossRef
Zhou, Z., Wang, B.: Investigation of behavior of mode-I interface crack in piezoelectric materials by using Schmidt method. Appl. Math. Mech. Engl. Ed. 27, 871–882 (2006)CrossRefMATH
Metadata
Title
Introduction
Authors
Volodymyr Govorukha
Marc Kamlah
Volodymyr Loboda
Yuri Lapusta
Copyright Year
2017
Book
Fracture Mechanics of Piezoelectric Solids with Interface Cracks

Print ISBN: 978-3-319-53552-4

Electronic ISBN: 978-3-319-53553-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-53553-1_1

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