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Fracture Mechanics of Piezoelectric Solids with Interface Cracks

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 83))

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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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References

  • 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)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Bardzokas, D.I., Filshtinsky, M.L., Filshtinsky, L.A.: Mathematical Methods in Electro-Magneto-Elasticity. Springer, Berlin (2007)

    MATH  Google Scholar 

  • Beom, H.G.: Permeable cracks between two dissimilar piezoelectric materials. Int. J. Solids Struct. 40, 6669–6679 (2003)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Beom, H.G., Atluri, S.N.: Conducting cracks in dissimilar piezoelectric media. Int. J. Fract. 118, 285–301 (2002)

    Article  Google Scholar 

  • Cady, W.G.: Piezoelectricity. MacDraw-Hill, New York (1946)

    Google Scholar 

  • Chen, X., Mai, Y.W.: Fracture Mechanics of Electromagnetic Materials: Nonlinear Field Theory and Applications. Imperial College Press, London (2012)

    Book  Google Scholar 

  • Chen, Y.H., Lu, T.J.: Cracks and fracture in piezoelectrics. Adv. Appl. Mech. 39, 121–215 (2003)

    Article  Google Scholar 

  • Chen, Y.H., Hasebe, N.: Current understanding on fracture behaviors of ferroelectric/piezoelectric materials. J. Intell. Mater. Syst. Struct. 16, 673–687 (2005)

    Article  Google Scholar 

  • Comninou, M.: The interface crack. J. Appl. Mech. 44, 631–636 (1977)

    Article  MATH  Google Scholar 

  • 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  Google Scholar 

  • Deeg, W.F.: The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph.D. thesis, Stanford University, Stanford, California (1980)

    Google Scholar 

  • Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)

    Article  Google Scholar 

  • Duhem, P.: Die dauernden Änderungen und die Thermodynamic. Z. Phys. Chem. 22, 543–589 (1897)

    Article  Google Scholar 

  • England, A.H.: A crack between dissimilar media. J. Appl. Mech. 32(2), 400–402 (1965)

    Article  Google Scholar 

  • Erdogan, F.: Stress distribution in bonded dissimilar materials with cracks. J. Appl. Mech. 32(2), 403–410 (1965)

    Article  Google Scholar 

  • Fang, D.N., Liu, J.X.: Fracture Mechanics of Piezoelectric and Ferroelectric Solids. Springer, Berlin (2013)

    Book  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Gao, C.F., Wang, M.Z.: Collinear permeable cracks between dissimilar piezoelectric materials. Int. J. Solids Struct. 37, 4969–4986 (2000)

    Article  MATH  Google Scholar 

  • Gao, C.F., Haeusler, C., Balke, H.: Periodic permeable interface cracks in piezoelectric materials. Int. J. Solids Struct. 41, 323–335 (2004)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Govorukha, V.B., Loboda, V.V.: Contact zone models for an interface crack in a piezoelectric material. Acta Mech. 140, 233–246 (2000)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • Govorukha, V., Kamlah, M., Loboda, V., Lapusta, Y.: Interface cracks in piezoelectric materials. Smart Mater. Struct. 25, 023001 (2016)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • He, M.Y., Evans, A.G., Hutchinson, J.W.: Interface cracking phenomena in constrained metal layer. Acta Mater. 44, 2963–2971 (1996)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • Kelvin, L.: On the theory of pyro-electricity and piezo-electricity of crystals. Phil. Mag. Ser. 5, 36(222), 453–459 (1893)

    Google Scholar 

  • Kozinov, S., Loboda, V., Lapusta, Y.: Periodic set of limited electrically permeable interface cracks with contact zones. Mech. Res. Commun. 48, 32–41 (2013)

    Article  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • Kuna, M.: Finite element analyses of cracks in piezoelectric structures: a survey. Arch. Appl. Mech. 76, 725–745 (2006)

    Article  MATH  Google Scholar 

  • Kuna, M.: Fracture mechanics of piezoelectric materials—where are we right now? Eng. Fract. Mech. 77, 309–326 (2010)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • Landis, C.M.: Energetically consistent boundary conditions for electromechanical fracture. Int. J. Solids Struct. 41, 6291–6315 (2004)

    Article  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • Leonov, M.Y., Panasyuk, V.V.: The development of very shallow cracks in a solid. Prikl. Mekh. 5(4), 391–401 (1959)

    Google Scholar 

  • Li, Q., Chen, Y.: Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials. Acta Mech. Sinica 23, 681–687 (2007a)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Li, Q., Chen, Y.H.: Solution for a semi-permeable interface crack between two dissimilar piezoelectric materials. J. Appl. Mech. 74, 833–844 (2007c)

    Article  Google Scholar 

  • Li, Q., Chen, Y.H.: Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials. J. Appl. Mech. 75, 11010 (2008)

    Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Lippmann, G.: Principe de conservation de l’electricite. Ann. Chim. Phys. 24, 145–178 (1881)

    Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Ma, L.F., Chen, Y.H.: Weight functions for interface cracks in dissimilar anisotropic piezoelectric materials. Int. J. Fract. 110, 263–279 (2001)

    Article  Google Scholar 

  • Mason, W.P.: Piezoelectric crystals and their application to ultrasonics. Van Nostrand, New York (1950)

    Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Ou, Z.C.: Singularity parameters ε and κ for interface cracks in transversely isotropic piezoelectric bimaterials. Int. J. Fract. 119, L41–L46 (2003)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Ou, Z.C., Chen, Y.H.: Interface crack problem in elastic dielectric/piezoelectric bimaterials. Int. J. Fract. 130, 427–454 (2004b)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Pak, Y.E.: Linear electro-elastic fracture mechanics of piezoelectric materials. Int. J. Fract. 54, 79–100 (1992)

    Article  Google Scholar 

  • Parton, V.Z.: Fracture mechanics of piezoelectric materials. Acta Astronaut. 3, 671–683 (1976)

    Article  MATH  Google Scholar 

  • Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach, New York (1988)

    Google Scholar 

  • Pockels, F.: Über den Einfluss des Elektrostatischen Feldes auf das optische Verhalten piezoelektrischer Krystalle. Göttingen (1894)

    Google Scholar 

  • Qin, Q.H.: Fracture Mechanics of Piezoelectric Materials. WIT Press, Southampton, Boston (2001)

    Google Scholar 

  • Rice, J.R.: Elastic fracture mechanics concept for interfacial cracks. J. Appl. Mech. 55(1), 98–103 (1988)

    Article  Google Scholar 

  • Rice, J.R., Sih, G.C.: Plane problem of cracks in dissimilar media. J. Appl. Mech. 32(2), 418–423 (1965)

    Article  Google Scholar 

  • Ru, C.Q.: A hybrid complex-variable solution for piezoelectric/isotropic elastic interfacial cracks. Int. J. Fract. 152, 169–178 (2008)

    Article  MATH  Google Scholar 

  • Shen, S., Kuang, Z.B., Hu, S.: Interface crack problems of a laminated piezoelectric plate. Eur. J. Mech. A/Solids 18, 219–238 (1999)

    Article  MATH  Google Scholar 

  • Shen, S., Nishioka, T., Kuang, Z.B., Liu, Z.: Nonlinear electromechanical interfacial fracture for piezoelectric materials. Mech. Mater. 32, 57–64 (2000)

    Article  Google Scholar 

  • Sheveleva, A.E.: Modeling of the near-tip zones of a crack between two anisotropic materials. Mater. Sci. 36(2), 187–197 (2000)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Suo, Z., Kuo, C.M., Barnett, D.M., Willis, J.R.: Fracture Mechanics for Piezoelectric Ceramics. J. Mech. Phys. Solids 40, 739–765 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Tiersten, H.F.: Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969)

    Book  Google Scholar 

  • Voigt, W.: Lehrbuch der Kristallphysik. Leipzig (1910)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Wang, T.C., Han, X.L.: Fracture mechanics of piezoelectric materials. Int. J. Fract. 98, 15–35 (1999)

    Article  Google Scholar 

  • Williams, M.L.: The stresses around a fault or cracks in dissimilar media. Bull. Seism. Soc. Am. 49(2), 199–204 (1959)

    MathSciNet  Google Scholar 

  • Zhang, T.Y., Gao, C.F.: Fracture behaviors of piezoelectric materials. Theor. Appl. Fract. Mech. 41, 339–379 (2004)

    Article  Google Scholar 

  • Zhang, T.Y., Fu, R., Zhao, M.H., Tong, P.: Overview of fracture of piezoelectric ceramics. Key Eng. Mater. 183–187, 695–706 (2000)

    Article  Google Scholar 

  • Zhang, T.Y., Zhao, M.H., Tong, P.: Fracture of piezoelectric ceramics. Adv. Appl. Mech. 38, 147–289 (2002)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computational Mathematics, Dnipropetrovsk National University, Dnipropetrovsk, Ukraine

    Volodymyr Govorukha

  2. Institute for Applied Materials, Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, Germany

    Marc Kamlah

  3. Department of Theoretical and Applied Mechanics, Dnipropetrovsk National University, Dnipropetrovsk, Ukraine

    Volodymyr Loboda

  4. Université Clermont Auvergne, CNRS, SIGMA Clermont (ex- French Institute of Advanced Mechanics - IFMA), Institut Pascal, Clermont-Ferrand, F-63000, France

    Yuri Lapusta

Authors
  1. Volodymyr Govorukha
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  2. Marc Kamlah
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  3. Volodymyr Loboda
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  4. Yuri Lapusta
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Correspondence to Volodymyr Govorukha .

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Govorukha, V., Kamlah, M., Loboda, V., Lapusta, Y. (2017). Introduction. In: Fracture Mechanics of Piezoelectric Solids with Interface Cracks. Lecture Notes in Applied and Computational Mechanics, vol 83. Springer, Cham. https://doi.org/10.1007/978-3-319-53553-1_1

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