An electrically impermeable and magnetically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under uniform magnetoelectromechanical loads. (English) Zbl 1278.74155
Summary: An interface crack with a frictionless contact zone at the right crack tip between two dissimilar magnetoelectroelastic materials under the action of remote mechanical, electrical and magnetic loads is considered. The open part of the crack is assumed to be electrically impermeable and magnetically permeable. Both the Dirichlet-Riemann boundary value problem and Hilbert problem have been formulated and solved exactly. Stress, electrical displacement and magnetic induction intensity factors as well as energy release rate are found in analytical forms. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived and analyzed. Some numerical results are plotted to show the effects of the applied loads on the contact zone length, stress intensity factor and energy release rate.
MSC:
| 74R10 | Brittle fracture |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74M15 | Contact in solid mechanics |
References:
| [1] | Atkinson, C., The interface crack with contact zone (an analytical treatment), Int. J. Fract., 18, 161-177 (1982) |
| [2] | Chen, X. H., Energy release rate and path-independent integral in dynamic fracture of magneto-electro-thermo-elastic solids, Int. J. Solids. Struct., 46, 2706-2711 (2009) · Zbl 1167.74544 |
| [3] | Chue, C. H.; Liu, T. J.C., Magneto-electro-elastic antiplane analysis of a bimaterial \(BaTiO_3-CoFe_2 O_4\) composite wedge with an interface crack, Theor. Appl. Frac. Mech., 44, 275-296 (2005) |
| [4] | Comninou, M., The interface crack, ASME J. Appl. Mech., 44, 631-636 (1977) · Zbl 0369.73092 |
| [5] | Dundurs, J.; Gautesen, A. K., An opportunistic analysis of the interface crack, Int. J. Fract., 36, 151-159 (1988) |
| [6] | Feng, W. J.; Li, Y. S.; Xu, Z. H., Transient response of an interfacial crack between dissimilar magnetoelectroelastic layers under magnetoelectromechanical impact loadings: mode-I problem, Int. J. Solids. Struct., 46, 3346-3356 (2009) · Zbl 1167.74547 |
| [7] | Feng, W. J.; Su, R. K.L., Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip, Int. J. Solids. Struct., 43, 5196-5216 (2006) · Zbl 1120.74751 |
| [8] | Feng, W. J.; Su, R. K.L.; Liu, J. X.; Li, Y. S., Fracture analysis of bounded magnetoelectroelastic layers with interfacial cracks under magnetoelectromechanical loads: plane problem, J. Intel. Mat. Syst. Str, 21, 581-594 (2010) |
| [9] | Feng, W. J.; Pan, E.; Wang, X., Dynamic fracture analysis of a penny-shaped crack in a magnetoelectroelastic layer, Int. J. Solids. Struct., 44, 7955-7974 (2007) · Zbl 1167.74548 |
| [10] | Feng, W. J.; Xue, Y.; Zou, Z. Z., Crack growth of an interface crack between two dissimilar magneto-electro-elastic materials under anti-plane mechanical and in-plane electromagnetic impact, Theor. Appl. Frac. Mech., 43, 376-394 (2005) |
| [11] | Gao, C. F.; Kessler, H.; Balke, H., Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack, Int. J. Eng. Sci., 41, 969-981 (2003) · Zbl 1211.74187 |
| [12] | Gao, C. F.; Kessler, H.; Balke, H., Crack problems in magnetoelectroelastic solids. Part II: general solution of collinear cracks, Int. J. Eng. Sci., 41, 983-994 (2003) · Zbl 1211.74188 |
| [13] | Gao, C. F.; Tong, P.; Zhang, T. Y., Interfacial crack problems in magneto-electric solids, Int. J. Eng. Sci., 41, 2105-2121 (2003) |
| [14] | Gao, C. F.; Tong, P.; Zhang, T. Y., Fracture mechanics for a mode III crack in a magnetoelectroelastic solid, Int. J. Solids. Struct., 41, 6613-6629 (2004) · Zbl 1179.74117 |
| [15] | Gao, C. F.; Noda, N., Thermal-induced interfacial cracking of magnetoelectroelastic material, Int. J. Eng. Sci., 42, 1347-1360 (2004) |
| [16] | 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) · Zbl 1030.74042 |
| [17] | Herrmann, K. P.; Loboda, V. V.; Govorukha, V. B., On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial, Int. J. Fract., 111, 203-227 (2001) |
| [18] | Herrmann, K. P.; Loboda, V. V.; Khodanen, T. V., An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial, Arch. Appl. Mech., 80, 651-670 (2010) · Zbl 1271.74390 |
| [19] | Hu, K. Q.; Li, G. Q., Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading, Int. J. Solids. Struct., 42, 2823-2835 (2005) · Zbl 1093.74550 |
| [20] | Kharun, I. V.; Loboda, V. V., A set of interface cracks with contact zones in combined tension-shear field, Acta. Mech., 166, 43-56 (2003) · Zbl 1064.74153 |
| [21] | Liu, J. X.; Liu, X. L.; Zhao, Y. B., Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack, Int. J. Eng. Sci., 39, 1405-1418 (2001) · Zbl 1210.74073 |
| [22] | Li, R.; Kardomateas, G. A., The mode III interface crack in piezo-electro-magneto-elastic dissimilar bimaterials, ASME J. Appl. Mech., 73, 220-227 (2006) · Zbl 1111.74509 |
| [23] | Li, R.; Kardomateas, G. A., The mixed mode I and II interface crack in piezoelectromagneto-elastic anisotropic bimaterials, ASME J. Appl. Mech., 74, 614-627 (2007) |
| [24] | Li, X. F., Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric magnetic impacts, Int. J. Solids. Struct., 42, 3185-3205 (2001) · Zbl 1142.74014 |
| [25] | Li, X. F.; Liu, G. L.; Lee, K. Y., Magnetoelectroelastic field induced by a crack terminating at the interface of a bi-magnetoelectric material, Philos. Mag., 89, 449-463 (2009) |
| [26] | Li, Y. D.; Lee, K. Y., Anti-plane crack intersecting the interface in a bonded smart structure with graded magnetoelectroelastic properties, Theor. Appl. Frac. Mech., 50, 235-242 (2008) |
| [27] | Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity (1975), Noordhoff, Leyden · Zbl 0297.73008 |
| [28] | Niraula, O. P.; Wang, B. L., A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading, Acta Mech., 187, 151-168 (2006) · Zbl 1151.76586 |
| [29] | Parton, V. Z.; Kudryavtsev, B. A., Electromagnetoelasticity (1988), Gordon and Breach Science Publishers: Gordon and Breach Science Publishers New York |
| [30] | Qin, Q. H.; Mai, Y. W., A closed crack tip model for interface cracks in thermopiezoelectric materials, Int. J. Solids. Struct., 36, 2463-2479 (1999) · Zbl 0932.74061 |
| [31] | Rice, J. R., Elastic fracture mechanics concept for interfacial cracks, ASME J. Appl. Mech., 55, 98-103 (1988) |
| [32] | Sih, G. C.; Jones, R.; Song, Z. F., Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials, Theor. Appl. Frac. Mech., 40, 161-186 (2003) |
| [33] | Sih, G. C.; Song, Z. F., Magnetic and electric poling effects associated with crack growth in \(BaTiO_3-CoFe_2 O_4\) composite, Theor. Appl. Frac. Mech., 39, 209-227 (2003) |
| [34] | Simonov, I. V., The interface crack in homogeneous field of stresses, Mech. Compos. Mater., 46, 969-976 (1985) |
| [35] | Singh, B. M.; Rokne, J.; Dhaliwal, R. S., Closed-form solutions for two anti-plane collinear cracks in a magnetoelectroelastic layer, Eur. J. Mech. A-Solids, 28, 599-609 (2009) · Zbl 1158.74456 |
| [36] | Song, Z. F.; Sih, G. C., Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation, Theor. Appl. Frac. Mech., 39, 189-207 (2003) |
| [37] | Tian, W. Y.; Gabbert, U., Multiple crack interaction problem in magnetoelectroelastic solids, Eur. J. Mech. A-Solids, 23, 599-614 (2004) · Zbl 1062.74044 |
| [38] | Tian, W. Y.; Gabbert, U., Macrocrack-microcrack interaction problem in magnetoelectroelastic solids, Mech. Mater., 37, 565-592 (2005) |
| [39] | Williams, M. L., The stresses around a fault or cracks in dissimilar media, Bull. Seismological. Soc. Am., 49, 199-204 (1959) |
| [40] | Wang, B. L.; Han, J. C.; Mai, Y. W., Mode III fracture of a magnetoelectroelastic layer: exact solution and discussion of the crack face electromagnetic boundary conditions, Int. J. Fract., 139, 27-38 (2006) · Zbl 1197.74140 |
| [41] | Wang, B. L.; Mai, Y. W., Applicability of the crack-face electromagnetic boundary conditions for fracture of magnetoelectroelastic materials, Int. J. Solids. Struct., 44, 387-398 (2007) · Zbl 1178.74145 |
| [42] | Wang, B. L.; Sun, Y. G.; Zhang, H. Y., Analysis of a penny-shaped crack in magnetoelectroelastic materials, J. Appl. Phys., 103, 0835301-0835308 (2008) |
| [43] | Wang, S. S.; Choi, I., The interface crack between two dissimilar anisotropic composite materials, ASME J. Appl. Mech., 50, 169-178 (1983) · Zbl 0511.73111 |
| [44] | Yong, H. D.; Zhou, Y. H., Transient response of a cracked manetoelectroelastic strip under anti-plane impact, Int. J. Solids. Struct., 44, 705-717 (2007) · Zbl 1123.74028 |
| [45] | Zhu, B. J.; Shi, Y. L.; Qin, T. Y.; Sukop, M.; Yu, S. H.; Li, Y. B., Mixed-mode stress intensity factors of 3D interface crack in fully coupled electromagnetothermoelastic multiphase composites, Int. J. Solids. Struct., 46, 2669-2679 (2010) · Zbl 1167.74436 |
| [46] | Zhao, M. H.; Li, N.; Fan, C. Y.; Xu, G. T., Analysis method of planar interface cracks of arbitrary shape in three-dimensional transversely isotropic magnetoelectroelastic bimaterials, Int. J. Solids. Struct., 45, 1804-1824 (2008) · Zbl 1159.74412 |
| [47] | Zhao, M. H.; Yang, F.; Liu, T., Analysis of a penny-shaped crack in a magneto-electro-elastic medium, Philos. Mag., 86, 4397-4416 (2006) |
| [48] | Zhong, X. C.; Li, X. F., T-stress analysis for a Griffith crack in a magnetoelectroelastic solid, Arch. Appl. Mech., 78, 117-125 (2007) · Zbl 1161.74480 |
| [49] | Zhong, X. C.; Liu, F.; Li, X. F., Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts, Int. J. Solids. Struct., 46, 2950-2958 (2009) · Zbl 1167.74414 |
| [50] | Zhong, X. C.; Zhang, K. S., Dynamic analysis of a penny-shaped dielectric crack in a magnetoelectroelastic solid under impacts, Eur. J. Mech. A-Solids, 29, 242-252 (2010) · Zbl 1478.74075 |
| [51] | Zhou, Z. G.; Wang, B.; Sun, Y. G., Two collinear interface cracks in magneto-electro-elastic composites, Int. J. Eng. Sci., 42, 1155-1167 (2004) · Zbl 1211.76107 |
| [52] | Zhou, Z. G.; Wang, J. Z.; Wu, L. Z., Two collinear mode-I cracks in piezoelectric/piezomagnetic materials, Struct. Eng. Mech., 29, 55-75 (2008) |
| [53] | Zhou, Z. G.; Wang, J. Z.; Wu, L. Z., The behavior of two parallel non-symmetric interface cracks in a magneto-electro-elastic material strip under an anti-plane shear stress loading, Int. J. Appl. Electromag. Mech., 29, 163-184 (2009) |
| [54] | Zhou, Z. G.; Zhang, P. W.; Wu, L. Z., The closed form solution of a mode-I crack in the piezoelectric/piezomagnetic materials, Int. J. Solids. Struct., 44, 419-435 (2007) · Zbl 1123.74043 |
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