The problem of electric and stress state in a piezoelectric space with an arbitrary orientated elliptical crack under homogeneous force and electric loading is considered. The solution to this problem is obtained on the basis of the triple Fourier transformation and the Fourier transform of Green?s function for an infinite electroelastic space. Testing the approach against particular cases confirms its effectiveness. The numerical study is carried out, and the stress intensity factors along the elliptical crack front are studied for different crack orientations in the orthotropic electroelastic space under tension.
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V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, Mir, Moscow (1981).
M. P. Savruk, Stress Intensity Factors in Cracked Bodies, Vol. 2 of the four-volume Handbook V. V. Panasyuk (ed.), Fracture Mechanics and Strength of Materials [in Russian], Naukova Dumka, Kyiv (1988).
M. O. Shul’ga and V. L. Karlash, Resonant Electromechanical Vibrations of Piezoelectric Plates [in Ukrainian], Naukova Dumka, Kyiv (2008).
W. Q. Chen and C. W. Lim, “3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium,” Int. J. Fract., 131, No. 3, 231–246 (2005).
C. R. Chiang and G. J. Weng, “The nature of stress and electric-displacement concentrations around a strongly oblate cavity in a transversely isotropic piezoelectric material,” Int. J. Fract., 134, No. 3–4, 319–337 (2005).
M. L. Dunn and M. Taya, “Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids,” J. Appl. Mech., 61, No. 4, 474–475 (1994).
A. Y. Hodes and V. V. Loboda, “A contact zone approach for an arc crack at the interface between two electrostrictive materials,” Int. J. Solids Struct., 128, No. 1, 262–271 (2017).
S. A. Kaloerov, “Determination of intensity factors for stresses, induction and field strength in multi-connected electro-elastic anisotropic media,” Int. Appl. Mech., 43, No. 6, 631–637 (2007).
M. K. Kassir and G. Sih, Three-dimensional Crack Problems, Vol. 2, Mechanics of Fracture, Nordhoff International Publishing, Leyden (1975).
V. S. Kirilyuk, “On the stress state of a piezoceramic body with a flat crack under symmetric loads,” Int. Appl. Mech., 41, No. 11, 1263–1271 (2005).
V. S. Kirilyuk, “Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads,” Int. Appl. Mech., 42, No. 2, 152–161 (2006).
V. S. Kirilyuk, “Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion,” Int. Appl. Mech., 44, No. 7, 757–768 (2008).
V. S. Kirilyuk and O. I. Levchuk, “Stress state of an orthotropic piezoelectric body with a triaxial ellipsoidal inclusion subject to tension,” Int. Appl. Mech., 55, No. 3, 305–310 (2019).
L. V. Mol’chenko and I. I. Loos, “Thermomagnetoelastic deformation of flexible isotropic shells of revolution subject to Joule heating,” Int. Appl. Mech., 55, No. 1, 68–78 (2019).
L. V. Mol’chenko and I. I. Loos, “Thermomagnetoelastic deformation of a flexible orthotropic conical shell with electrical conductivity and Joule heat taken into account,” Int. Appl. Mech., 55, No. 5, 534–543 (2019).
Yu. N. Podil’chuk, “Representation of the general solution of statics equations of the electroelasticity of a transversally isotropic piezoceramic body in terms of harmonic functions,” Int. Appl. Mech., 34, No. 7, 623–628 (1998).
Yu. N. Podil’chuk, “Electroelastic equilibrium of transversally isotropic, piezoceramic media containing cavities, inclusions, and cracks,” Int. Appl. Mech., 34, No. 10, 1023–1034 (1998).
F. Shang, M. Kuna, and T. Kitamura, “Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part 1: Analytical development,” Theor. Appl. Fract. Mech., 40, No. 3, 237–246 (2003).
H. Sosa and N. Khutoryansky, “New developments concerning piezoelectric materials with defects,” Int. J. Solids Struct., 33, No. 23, 3399–3414 (1996).
Z. K. Wang and B. L. Zheng, “The general solution of three-dimension problems in piezoelectric media,” Int. J. Solids Struct., 32, No. 1, 105–115 (1995).
J. R. Willis, “The stress field around an elliptical crack in an anisotropic elastic medium,” Int. J. Eng. Sci., 6, No. 5, 253–263 (1968).
T. Y. Zhang and C. F. Gao, “Fracture behaviors of piezoelectric materials,” Theor. Appl. Fract. Mech., 41, No. 1 – 3, 339–379 (2004).
Translated from Prikladnaya Mekhanika, Vol. 57, No. 1, pp. 64–74, January–February 2021.
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
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Kyryliuk, V.S., Levchuk, O.I. Stress State of an Orthotropic Electroelastic Medium with an Arbitrarily Oriented Elliptic Crack Under Uniaxial Tension. Int Appl Mech 57, 53–62 (2021). https://doi.org/10.1007/s10778-021-01060-y
- orthotropic piezoelectric material
- flat elliptical crack
- arbitrary orientation
- stress intensity factors