Abstract
The electroelasticity problem for an arbitrarily oriented disc-like crack under internal pressure in an orthotropic electroelastic material was considered. Generalizing of the Willis approach for an elastic material, using the Fourier transform of the Green’s function for an infinite anisotropic electroelastic space, the problem of electroelasticity is reduced to finding unknowns of the jumps of displacements and electric potential through the surface of a circular crack. Quadrature Gauss formulas were used to calculate one-dimensional integrals. Testing the approach in the particular case of the problem for which an exact solution is known confirms the effctiveness of the used approach. The distribution of stress intensity factors (SIF) along the boundary of a disc-shaped crack (under internal pressure) in a piezoelectric orthotropic material under various orientations of a crack was studied. A significant effect of the crack orientation on the SIF distributions was established.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen WQ, Lim CW (2005) 3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium. International Journal of Fracture 31(3):231–246
Chen WQ, Cai JB, Ye GR, Wang YF (2004) Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer. International Journal of Solids and Structures 41(18):5247–5263
Chiang CR, Weng GJ (2005) The nature of stress and electric-displacement concentrations around a strongly oblate cavity in a transversely isotropic piezoelectric material. International Journal of Fracture 134(3):319–337
Dai L, Guo W, Wang X (2006) Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids. International Journal of Solids and Structures 43(6):1818–1831
Dunn ML, Taya M (1994) Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. Journal of Applied Mechanics 61(4):474–475
Grinchenko VT, Ulitko AF, Shulga NA (1989) Electroelasticity (in Russ.), Mechanics of Coupled Fields in the Elements of Constructions, vol 5. Naukova Dumka, Kiev
Kaloerov SA (2007) Determining the intensity factors for stresses, electric-flux density, and electric-field strength in multiply connected electroelastic anisotropic media. International Applied Mechanics 43(6):631–637
Kirilyuk VS (2005) On the stress state of a piezoceramic body with a flat crack under symmetric loads. International Applied Mechanics 41(11):1263–1271
Kirilyuk VS (2006) Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads. International Applied Mechanics 42(2):152–161
Kirilyuk VS (2008) Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack. International Applied Mechanics 44(2):150–157
Kirilyuk VS, Levchuk OI (2017) Stress state of an orthotropic piezoelectric material with an elliptic crack. International Applied Mechanics 53(3):305–312
Lekhnitskii SG (1981) Theory of Elasticity of an Anisotropic Body. Mir, Moscow
Lin S, Narita F, Shindo Y (2003) Electroelastic analysis of a penny-shaped crack in a piezoelectric ceramic under mode I loading. Mechanics Research Communications 30(4):371–386
Podil’chuk YN (1998a) Electroelastic equilibrium of transversally isotropic, piezoceramic media containing cavities, inclusions, and cracks. International Applied Mechanics 34(10):1023–1034
Podil’chuk YN (1998b) Representation of the general solution of statics equations of the electroelasticity of a transversally isotropic piezoceramic body in terms of harmonic functions. International Applied Mechanics 34(7):623–628
Ricoeur A, Kuna M (2009) Electrostatic tractions at dielectric interfaces and their implication for crack boundary conditions. Mechanics Research Communications 36(3):330–335
Shang F, Kuna M, Kitamura T (2003) Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part I: Analitical development. Theoretical and Applied Fracture Mechanics 40(3):247–253
Shulga NA, Karlash VL (2008) Resonant Electromechanical Oscillations of Piezoelectric Plates (in Ukrain.). Naukova Dumka, Kiev
Sladek J, Sladek V, Wünsche M, Zhang C (2018) Effects of electric field and strain gradients on cracks in piezoelectric solids. European Journal of Mechanics - A/Solids 71:187–198
Wang YJ, Gao CF, Song H (2015) The anti-plane solution for the edge cracks originating from an arbitrary hole in a piezoelectric material. Mechanics Research Communications 65:17–23
Wang Z, Zheng B (1995) The general solution of three-dimensional problems in piezoelectric media. International Journal of Solids and Structures 32(1):105–115
Willis JR (1968) The stress field around an elliptical crack in an anisotropic elastic medium. International Journal of Engineering Science 6(5):253–263
Wippler K, Kuna M (2007) Crack analyses in three-dimensional piezoelectric structures by the BEM. Computational Materials Science 39(1):261–266
Wippler K, Ricoeur A, Kuna M (2004) Towards the computation of electrically permeable cracks in piezoelectrics. Engineering Fracture Mechanics 71(18):2567–2587
Xu CH, Zhou ZH, Xu XS, Leung AYT (2015) Electroelastic singularities and intensity factors for an interface crack in piezoelectric-elastic bimaterials. Applied Mathematical Modelling 39(9):2721–2739
Zhang QY, Fan CY, Xu GT, Zhao MH (2017) Iterative boundary element method for crack analysis of two-dimensional piezoelectric semiconductor. Engineering Analysis with Boundary Elements 83:87–95
Zhang TY, Gao CF (2004) Fracture behaviors of piezoelectric materials. Theoretical and Applied Fracture Mechanics 41(1):339–379
Zhao MH, Pan YB, Fan CY, Xu GT (2016) Extended displacement discontinuity method for analysis of cracks in 2d piezoelectric semiconductors. International Journal of Solids and Structures 94-95:50–59
Zhao MH, Yang CH, Fan CY, Xu GT (2018) Extended displacement discontinuity method for analysis of penny-shaped cracks in three-dimensional thermal piezoelectric semiconductors. European Journal of Mechanics - A/Solids 70:23–36
Zhou YY, Chen WQ, Lu CF (2010) Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections. Composite Structures 92(4):1009–1018
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kirilyuk, V.S., Levchuk, O.I., Altenbach, H. (2019). Calculation of Stress Intensity Factors for an Arbitrary Oriented Penny-shaped Crack Under Inner Pressure in an Orthotropic Electroelastic Material. In: Abali, B., Altenbach, H., dell'Isola, F., Eremeyev, V., Öchsner, A. (eds) New Achievements in Continuum Mechanics and Thermodynamics. Advanced Structured Materials, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-030-13307-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-13307-8_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13306-1
Online ISBN: 978-3-030-13307-8
eBook Packages: EngineeringEngineering (R0)