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Magnetostrictive/electrostrictive fracture of the piezomagnetic and piezoelectric layers in a multiferroic composite: anti-plane case. (English) Zbl 1236.74081
Summary: The main purpose of the present work is to study the influences of magnetostriction, electrostriction and piezomagnetic/piezoelectric stiffening on the fracture behavior of a layered multiferroic composite. For comparison, it is assumed that there is a crack, parallel to the interface, in each layer. Methods of cosine transform and Cauchy singular integral equations are used to solve the crack problem. Numerical results of the stress intensity factor (SIF) are provided and the computational accuracy is demonstrated. Discussion on the numerical results indicates that the multiferroic composite consisting of cobalt ferrite and barium titanate layers are more prone to fracture under electric loading than under magnetic loading. In the case of magnetostriction, to increase the shear modulus of the piezomagnetic layer would raise the SIF; but to increase that of the piezoelectric layer would reduce the SIF; in the case of electrostriction, inverse results are obtained. Piezomagnetic stiffening can affect the SIF when the composite is under electrostriction; piezoelectric stiffening can influence the SIF if the composite is under magnetostriction. In addition, it is also revealed that two parallel equal cracks may shield each other even if an interface exists between them.

MSC:
74F15 Electromagnetic effects in solid mechanics
74R10 Brittle fracture
74E30 Composite and mixture properties
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[1] Bichurin, M. I.; Kornev, I. A.; Petrov, V. M.; Tatarenko, A. S.; Kiliba, Y. V.: Theory of magnetoelectric effects at microwave frequencies in a piezoelectric/magnetostrictive multilayer composite, Phys. rev. B 64, No. 9, 094409 (2001)
[2] Bichurin, M. I.; Petrov, V. M.; Srinivasan, G.: Theory of low-frequency magnetoelectric coupling in magnetostrictive – piezoelectric bilayers, Phys. rev. B 68, No. 5, 054402 (2003)
[3] Blackburn, J. F.; Vopsaroiu, M.; Cain, M. G.: Verified finite element simulation of multiferroic structures: solutions for conducting and insulating systems, J. appl. Phys. 104, No. 7, 074104 (2008)
[4] Huang, J. H.; Kuo, W. S.: The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions, J. appl. Phys. 81, No. 3, 1378-1386 (1997)
[5] Li, X. F.; Lee, K. Y.: Closed-form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti-plane shear, ZAMM-Z. Angew. math. Mech. 89, No. 5, 370-382 (2009) · Zbl 1162.74016 · doi:10.1002/zamm.200900233
[6] Li, Y. D.; Lee, K. Y.: Fracture analysis and improved design for a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties, Eng. fract. Mech. 75, No. 10, 3161-3172 (2008)
[7] Li, Y. D.; Lee, K. Y.: Dynamic responses of a crack in a layered graded magnetoelectroelastic sensor subjected to harmonic waves, Acta mech. 204, No. 3 – 4, 217-234 (2009) · Zbl 1165.74038 · doi:10.1007/s00707-008-0082-y
[8] Li, Y. D.; Lee, K. Y.: Crack tip shielding and anti-shielding effects of the imperfect interface in a layered piezoelectric sensor, Int. J. Solid. struct. 46, No. 7 – 8, 1736-1742 (2009) · Zbl 1217.74103 · doi:10.1016/j.ijsolstr.2008.12.023
[9] Li, Y. D.; Lee, K. Y.: Magnetostrictive fracture of a cylindrical multiferroic composite, Int. J. Eng. sci. 48, No. 2, 199-208 (2010)
[10] Li, Y. D.; Lee, K. Y.: Effects of magneto-electric loadings and piezomagnetic/piezoelectric stiffening on multiferroic interface fracture, Eng. fract. Mech. 77, No. 5, 856-866 (2010)
[11] Liu, G.; Nan, C. W.; Cai, N.; Lin, H. Y.: Calculations of giant magnetoelectric effect in multiferroic composites of rare-Earth – iron alloys and PZT by finite element method, Int. J. Solid. struct. 41, No. 16 – 17, 4423-4434 (2004) · Zbl 1079.74543 · doi:10.1016/j.ijsolstr.2004.03.022
[12] Liu, Y. L.; Lu, X. Y.; Wang, B.: Fracture toughness of multiferroic composite materials, Eng. fract. Mech. 75, No. 17, 4973-4977 (2008)
[13] Nan, C. W.; Liu, G.; Lin, Y. H.; Chen, H.: Magnetic-field-induced electric polarization in multiferroic nanostructures, Phys. rev. Lett. 94, No. 19, 197203 (2005)
[14] Ratwani, M.; Gupta, G. D.: Interaction between parallel cracks in layered composites, Int. J. Solid. struct. 10, No. 7, 701-708 (1974) · Zbl 0288.73072 · doi:10.1016/0020-7683(74)90034-1
[15] Theocaris, P. S.; Ioakimids, N. I.: Numerical integration methods for the solution of singular integral equations, Quart. appl. Math. 35, 173-183 (1977) · Zbl 0353.45016
[16] Wang, B. L.; Mai, Y. W.: Applicability of the crack-face electromagnetic boundary conditions for fracture of magnetoelectroelastic materials, Int. J. Solid. struct. 44, No. 2, 387-398 (2007) · Zbl 1178.74145 · doi:10.1016/j.ijsolstr.2006.04.028
[17] Wang, B. L.; Sun, Y. G.; Han, J. C.; Du, S. Y.: An interface electrode between two piezoelectric layers, Mech. mater. 41, No. 1, 1-11 (2009)
[18] Wang, X.; Pan, E.: Magnetoelectric effects in multiferroic fibrous composite with imperfect interface, Phys. rev. B 76, No. 21, 214107 (2007)
[19] Wang, X.; Pan, E.; Albrecht, J. D.: Two-dimensional Green’s functions in anisotropic multiferroic bimaterials with a viscous interface, J. mech. Phys. solid 56, No. 9, 2863-2875 (2008) · Zbl 1171.74347 · doi:10.1016/j.jmps.2008.04.004
[20] Zhang, C. L.; Chen, W. Q.; Xie, S. H.; Yang, J. S.; Li, J. Y.: The magnetoelectric effects in multiferroic composite nanofibers, Appl. phys. Lett. 94, No. 10, 102907 (2009)
[21] Zhou, Z. G.; Wang, B.: Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading, Int. J. Solid. struct. 41, No. 16 – 17, 4407-4422 (2004) · Zbl 1079.74621 · doi:10.1016/j.ijsolstr.2004.03.004
[22] Zhou, Z. G.; Zhang, P. W.; Li, G. Q.: Basic solution of four parallel non-symmetric permeable mode-III cracks in a piezoelectric/piezomagnetic composite plane, Phil. mag. 88, No. 8, 1153-1186 (2008)
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