Dynamic analysis of a penny-shaped dielectric crack in a magnetoelectroelastic solid under impacts. (English) Zbl 1478.74075
Summary: The transient response of a magneto-electro-elastic material with a penny-shaped dielectric crack subjected to in-plane magneto-electro-mechanical impacts is made. To simulate an opening crack with a dielectric interior, the crack-face electromagnetic boundary conditions are supposed to depend on the crack opening displacement and the jumps of electric and magnetic potentials across the crack. Four ideal crack-face electromagnetic boundary conditions involving a combination of electrically permeable or impermeable and magnetically permeable or impermeable assumptions can be reduced. The Laplace and Hankel transform techniques are further utilized to solve the mixed initial-boundary-value problem. Three coupling Fredholm integral equations are obtained and solved by the composite Simpson’s rule. Dynamic field intensity factors of stress, electric displacement, magnetic induction, crack opening displacement (COD), electric potential and magnetic potential are given in the Laplace transform domain. By means of a numerical inversion of the Laplace transform, numerical results are calculated to show the variations of the physical parameters of concern versus the normalized time in graphics. The effects of applied electric and magnetic loads on the dynamic intensity factors of stress and COD, and the dynamic energy release rate for a \(\mathrm{BaTiO_3}\)-\(\mathrm{CoFe_2O_4}\) composite with a penny-shaped vacuum crack are discussed in detail.
MSC:
| 74R10 | Brittle fracture |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
| 74M20 | Impact in solid mechanics |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
Keywords:
transient crack opening displacement; semi-permeable condition; dynamic intensity factor; Laplace transform; Hankel transformReferences:
| [1] | Balke, H.; Dresher, J.; Kemmer, G., Investigation of the mechanical stain energy release rate with respect to a fracture criterion for piezoelectric ceramics, International Journal of Fracture, 89, L59-L64 (1998) |
| [2] | Banks-Sills, L.; Motola, Y.; Shemesh, L., The M-integral for calculating intensity factors of an impermeable crack in a piezoelectric material, Engineering Fracture Mechanics, 75, 901-925 (2008) |
| [3] | Buchanan, G. R., Layered versus multiphase magneto-electro-elastic composites, Composites: Part B, 35, 413-420 (2004) |
| [4] | Chen, W. Q.; Lee, K. Y.; Ding, H. J., On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates, Journal of Sound and Vibration, 279, 237-251 (2005) |
| [5] | Deeg, W.F., 1980. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PhD thesis, Stanford University.; Deeg, W.F., 1980. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PhD thesis, Stanford University. |
| [6] | Devan, R. S.; Chougule, B. K., Effect of composition on coupled electric, magnetic, and dielectric properties of two phase particulate magnetoelectric composite, Journal of Applied Physics, 101, 014109 (2007) |
| [7] | Du, J. K.; Shen, Y. P.; Ye, D. Y.; Yue, F. R., Scattering of anti-plane shear waves by a partially debonded magneto-electro-elastic circular cylindrical inhomogeneity, International Journal of Engineering Science, 42, 887-913 (2004) |
| [8] | Dong, S. X.; Zhai, J. Y.; Li, J. F., Magnetoelectric gyration effect in \(Tb_{1-x}Dy_x Fe_{2-y} /Pb\)(Zr, \(Ti)O_3\) laminated composites at the electromechanical resonance, Applied Physics Letters, 89, 243512 (2006) |
| [9] | Feng, W. J.; Pan, E.; Wang, X., Dynamic fracture analysis of a penny-shaped crack in a magnetoelectroelastic layer, International Journal of Solids and Structures, 44, 7955-7974 (2007) · Zbl 1167.74548 |
| [10] | Feng, W. J.; Pan, E., Dynamic fracture behavior of an internal interfacial crack between two dissimilar magneto-electro-elastic plates, Engineering Fracture Mechanics, 75, 1468-1487 (2008) |
| [11] | Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series and Products (1980), Academic Press: Academic Press New York · Zbl 0521.33001 |
| [12] | Hao, T. H.; Shen, Z. Y., A new electric boundary condition of electric fracture mechanics and its application, Engineering Fracture Mechanics, 47, 793-802 (1994) |
| [13] | Hu, K. Q.; Li, G. Q., Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading, International Journal of Solids and Structures, 42, 2823-2835 (2005) · Zbl 1093.74550 |
| [14] | Hu, K. Q.; Kang, Y. L.; Li, G. Q., Moving crack at the interface between two dissimilar magnetoelectroelastic materials, Acta Mechanics, 182, 1-16 (2006) · Zbl 1112.74051 |
| [15] | Huang, J. H.; Chiu, Y. H.; Liu, H. K., Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions, Journal of Applied Physics, 83, 5363-5370 (1998) |
| [16] | Kumar, S.; Singh, R. N., Crack propagation in piezoelectric materials under combined mechanical and electrical loadings, Acta Materialia, 44, 173-200 (1996) |
| [17] | Kumar, S.; Singh, R. N., Energy release rate and crack propagation in piezoelectric materials. Part I: mechanical/electric load, Acta Materialia, 45, 849-857 (1997) |
| [18] | Kumar, S.; Singh, R. N., Energy release rate and crack propagation in piezoelectric materials. Part II: combined mechanical and electrical loads, Acta Materialia, 45, 859-868 (1997) |
| [19] | Landis, C. M., Energetically consistent boundary conditions for electromechanical fracture, International Journal of Solids and Structures, 41, 6291-6315 (2004) · Zbl 1120.74755 |
| [20] | Li, J. Y.; Dunn, M. L., Micromechanics of magnetoelectroelastic composite materials: average fields and effective behavior, Journal of Intelligent Material Systems and Structures, 9, 404-416 (1998) |
| [21] | Li, W.; McMeeking, R. M.; Landis, C. M., On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rate, European Journal of Mechanics A/Solids, 27, 285-301 (2008) · Zbl 1154.74378 |
| [22] | Li, X. F., Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric and magnetic impacts, International Journal of Solids and Structures, 42, 3185-3205 (2005) · Zbl 1142.74014 |
| [23] | Li, X. F.; Lee, K. Y., Fracture analysis of cracked piezoelectric materials, International Journal of Solids and Structures, 41, 4137-4161 (2004) · Zbl 1079.74613 |
| [24] | Li, X. F.; Lee, K. Y., Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer, Journal of the Mechanics and Physics of Solids, 52, 2079-2100 (2004) · Zbl 1081.74544 |
| [25] | McMeeking, R. M., Crack tip energy release rate for a piezoelectric compact tension specimen, Engineering Fracture Mechanics, 47, 793-802 (1999) |
| [26] | McMeeking, R. M., The energy release rate for a Griffith crack in a piezoelectric material, Engineering Fracture Mechanics, 71, 1149-1163 (2004) |
| [27] | Meguid, S. A.; Chen, Z. T., Transient response of a finite piezoelectric strip containing coplanar insulating cracks under electromechanical impact, Mechanics of Materials, 33, 85-96 (2001) |
| [28] | Nan, C. W., Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases, Physical Review B, 50, 6082-6088 (1994) |
| [29] | Pak, Y. E., Crack extension force in a piezoelectric materials, ASME Journal of Applied Mechanics, 57, 647-653 (1990) · Zbl 0724.73191 |
| [30] | Park, S.; Sun, C. T., Fracture criteria for piezoelectric ceramics, Journal of the American Ceramic Society, 78, 1475-1480 (1995) |
| [31] | Schneider, G. A.; Felten, F.; McMeeking, R. M., The electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and implications for fracture, Acta Materialia, 51, 2235-2241 (2003) |
| [32] | Shindo, Y.; Watanabc, K.; Narita, F., Electroelastic analysis of a piezoelectric ceramic strip with a central crack, International Journal of Engineering Science, 38, 1-19 (2000) |
| [33] | Soso, H., On the fracture mechanics of piezoelectric solids, International Journal of Solids and Structures, 29, 2613-2622 (1992) · Zbl 0775.73215 |
| [34] | Stehfest, H., Numerical inversion of Laplace transforms, Communications ACM, 13, 47-49 (1970), 624 |
| [35] | Su, R. K.L.; Feng, W. J.; Liu, J., Transient response of interface cracks between dissimilar magneto-electro-elastic strips under out-of-plane mechanical and in-plane magnto-electrical impact loads, Composite Structures, 78, 119-128 (2007) |
| [36] | Tian, W. Y.; Rajapakse, R. K.N. D., Field intensity factors of a penny-shaped crack in a magnetoelectroelastic layer, Journal of Alloys and Compounds, 449, 161-171 (2008) |
| [37] | Tupholme, G. E., Moving antiplane shear crack in transversely isotropic magnetoelectroelastic media, Acta Mechanics, 202, 153-162 (2009) · Zbl 1298.74216 |
| [38] | Wang, B. L.; Mai, Y. W., Applicability of the crack-face electromagnetic boundary conditions for fracture of magnetoelectroelastic materials, International Journal of Solids and Structures, 44, 387-398 (2007) · Zbl 1178.74145 |
| [39] | Wang, X.; Pan, E., Magnetoelectric effects in multiferroic fibrous composite with imperfect interface, Physical Review B, 76, 214107 (2007) |
| [40] | Wang, H.; Singh, R. N., Crack propagation in piezoelectric ceramics: effects of applied electric fields, Journal of Applied Physics, 81, 7471-7479 (1997) |
| [41] | Wang, X. Y.; Yu, S. W., Transient response of a crack in piezoelectric strip subjected to the mechanical and electrical impacts: mode-I problem, Mechanics of Materials, 33, 11-20 (2001) |
| [42] | Wang, B. L.; Sun, Y. G.; Zhang, H. Y., Analysis of a penny-shaped crack in magnetoelectroelastic materials, Journal of Applied Physics, 103, 083530 (2008) |
| [43] | Yong, H. D.; Zhou, Y. H., Transient response of a cracked magnetoelectroelastic strip under anti-plane impact, International Journal of Solids and Structures, 44, 705-717 (2007) · Zbl 1123.74028 |
| [44] | Zhang, T. Y.; Gao, C. F., Fracture behaviors of piezoelectric materials, Theoretical and Applied Fracture Mechanics, 41, 339-379 (2004) |
| [45] | Zheng, H.; Wang, J.; Lofland, S. E., Multiferroic \(BaTiO_3-CoFe_2 O_4\) nanostructures, Science, 303, 661-663 (2004) |
| [46] | Zhong, X. C.; Li, X. F., A finite length crack propagating along the interface of two dissimilar magnetoelectroelastic materials, International Journal of Engineering Science, 44, 1394-1407 (2006) |
| [47] | Zhong, X. C.; Li, X. F., Magnetoelectroelastic analysis for an opening crack in a piezoelectromagnetic solid, European Journal of Mechanics A/Solids, 26, 405-417 (2007) · Zbl 1150.74044 |
| [48] | Zhong, X. C.; Li, X. F., Fracture analysis of a magnetoelectroelastic solid with a penny-shaped crack by considering the effects of the opening crack interior, International Journal of Engineering Science, 46, 374-390 (2008) · Zbl 1213.74275 |
| [49] | Zhong, X. C.; Li, X. F.; Lee, K. Y., Transient response of a cracked magnetoelectric material under the action of in-plane sudden impacts, Computational Materials Science, 45, 905-911 (2009) |
| [50] | Zhong, X. C.; Liu, F.; Li, X. F., Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts, International Journal of Solids and Structures, 46, 2950-2958 (2009) · Zbl 1167.74414 |
| [51] | Zhou, Z. G.; Wu, L. Z.; Wang, B., The dynamic behaviour of two collinear interfaces cracks in magneto-electro-elastic materials, European Journal of Mechanics A/Solids, 24, 253-262 (2005) · Zbl 1069.74047 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
