Structural Engineering and Mechanics

  • 제29권1호
  • /
  • Pages.55-75
  • /
  • 2008
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Two collinear Mode-I cracks in piezoelectric/piezomagnetic materials

  • Zhou, Zhen-Gong (Center for Composite Materials and Structures, Harbin Institute of Technology) ;
  • Wang, Jia-Zhi (Center for Composite Materials and Structures, Harbin Institute of Technology) ;
  • Wu, Lin-Zhi (Center for Composite Materials and Structures, Harbin Institute of Technology)
  • 투고 : 2006.09.04
  • 심사 : 2008.02.28
  • 발행 : 2008.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the behavior of two collinear Mode-I cracks in piezoelectric/piezomagnetic materials subjected to a uniform tension loading was investigated by the generalized Almansi's theorem. Through the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations, in which the unknown variables were the jumps of displacements across the crack surfaces. To solve the triple integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials to obtain the relations among the electric displacement intensity factors, the magnetic flux intensity factors and the stress intensity factors at the crack tips. The interaction of two collinear cracks was also discussed in the present paper.

키워드

참고문헌

  1. Avellaneda, M. and Harshe, G. (1994), "Magnetoelectric effect in piezoelectric/magnetostrictive multiplayer (2-2) composites", J. Intel. Mat. Syst. Str., 5, 501-513 https://doi.org/10.1177/1045389X9400500406
  2. Benveniste, Y. (1995), "Magnetoelectric effect in fibrous composites with piezoelectric and magnetostrictive phases", Phys. Rev. B, 51, 16424-16427 https://doi.org/10.1103/PhysRevB.51.16424
  3. Chen, W.Q., Lee, K.Y. and Ding, H.J. (2004), "General solution for transversely isotropic magneto-electrothermo- elasticity and the potential theory method", Int. J. Eng. Sci., 42, 1361-1379 https://doi.org/10.1016/j.ijengsci.2004.04.002
  4. Chung, M.Y. and Ting, T.C.T. (1995), "The Green function for a piezoelectric piezomagnetic anisotropic elastic medium with an elliptic hole or rigid inclusion", Philos. Mag., 72, 405-410 https://doi.org/10.1080/09500839508242480
  5. Erdelyi, A. (ed) (1954), Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York
  6. Gao, C.F., Kessler, H. and Balke, H. (2003a), "Crack problems in magnetoelectroelastic solids. Part I: Exact solution of a crack", Int. J. Eng. Sci., 41(9), 969-981 https://doi.org/10.1016/S0020-7225(02)00323-3
  7. Gao, C.F., Kessler, H. and Balke, H. (2003b), "Crack problems in magnetoelectroelastic solids. Part II: General solution of collinear cracks", Int. J. Eng. Sci., 41(9), 983-994 https://doi.org/10.1016/S0020-7225(02)00324-5
  8. Gao, C.F., Kessler, H. and Balke, H. (2003c), "Fracture analysis of electromagnetic thermoelastic solids", Eur. J. Mech. A-Solid, 22(3), 433-442 https://doi.org/10.1016/S0997-7538(03)00047-0
  9. Gao, C.F., Tong, P. and Zhang, T.Y. (2003d), "Interfacial crack problems in magneto-electroelastic solids", Int. J. Eng. Sci., 41(18), 2105-2121 https://doi.org/10.1016/S0020-7225(03)00206-4
  10. Gradshteyn, I.S. and Ryzhik, I.M. (1980), Table of Integral, Series and Products, Academic Press, New York
  11. Harshe, G., Dougherty, J.P. and Newnham, R.E. (1993), "Theoretical modeling of 3-0/0-3 magnetoelectric composites", Int. J. Appl. Electrom., 4, 161-171
  12. Huang, J.H. and Kuo, W.S. (1997), "The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions", J. Appl. Phys., 81(3), 1378-1386 https://doi.org/10.1063/1.363874
  13. Li, J.Y. (2000), "Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials", Int. J. Eng. Sci., 38, 1993-2011 https://doi.org/10.1016/S0020-7225(00)00014-8
  14. Liu, J.X., Liu, X.L. and Zhao, Y.B. (2001), "Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack", Int. J. Eng. Sci., 39(12), 1405-1418 https://doi.org/10.1016/S0020-7225(01)00005-2
  15. Morse, P.M. and Feshbach, H. (1958), Methods of Theoretical Physics, Vol.n1, McGraw-Hill, New York
  16. Nan, C.W. (1994), "Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases", Phys. Rev. B, 50, 6082-6088 https://doi.org/10.1103/PhysRevB.50.6082
  17. Pan, E. (2002), "Three-dimensional Green's functions in anisotropic magneto-electro-elastic bimaterails", Zeitschrift fur Angewandte Mathematik und Physik, 53, 815-838 https://doi.org/10.1007/s00033-002-8184-1
  18. Parton, V.S. (1976), "Fracture mechanics of piezoelectric materials", ACTA Astronaut., 3, 671-683 https://doi.org/10.1016/0094-5765(76)90105-3
  19. Sih, G.C. and Song, Z.F. (2003), "Magnetic and electric poling effects associated with crack growth in $BaTiO3-CoFe_2O_4$ composite", Theor. Appl. Fract. Mec., 39, 209-227 https://doi.org/10.1016/S0167-8442(03)00003-X
  20. Song, Z.F. and Sih, G.C. (2003), "Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation", Theor. Appl. Fract. Mec., 39, 189-207 https://doi.org/10.1016/S0167-8442(03)00002-8
  21. Spyropoulos, C.P., Sih, G.C. and Song, Z.F. (2003), "Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation", Theor. Appl. Fract. Mec., 39(3), 281-289 https://doi.org/10.1016/S0167-8442(03)00021-1
  22. Van Suchtelen, J. (1972), "Product properties: A new application of composite materials", Phillips Res. Rep., 27, 28-37
  23. Wang, B.L. and Mai, Y.W. (2003), "Crack tip field in piezoelectric/piezomagnetic media", Eur. J. Mech. A-Solid, 22(4), 591-602 https://doi.org/10.1016/S0997-7538(03)00062-7
  24. Wang, B.L. and Mai, Y.W. (2004), "Fracture of piezoelectromagnetic materials", Mech. Res. Commun., 31(1), 65-73 https://doi.org/10.1016/j.mechrescom.2003.08.002
  25. Wang, X. and Shen, Y.P. (2002), "The general solution of three-dimensional problems in magnetoelectroelastic media", Int. J. Eng. Sci., 40, 1069-1080 https://doi.org/10.1016/S0020-7225(02)00006-X
  26. Wu, T.L. and Huang, J.H. (2000), "Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases", Int. J. Solids Struct., 37, 2981-3009 https://doi.org/10.1016/S0020-7683(99)00116-X
  27. Yang, F.Q. (2001), "Fracture mechanics for a Mode I crack in piezoelectric materials", Int. J. Solids Struct., 38, 3813-3830 https://doi.org/10.1016/S0020-7683(00)00244-4
  28. Zhou, Z.G. and Wang, B. (2004), "Two parallel symmetry permeable cracks in functionally graded piezoelectric/ piezomagnetic materials under anti-plane shear loading", Int. J. Solids Struct., 41, 4407-4422 https://doi.org/10.1016/j.ijsolstr.2004.03.004
  29. Zhou, Z.G. and Wang, B. (2006), The nonlocal theory solution for two collinear cracks in functionally graded materials subjected to the harmonic elastic anti-plane shear waves", Struct. Eng. Mech. 23(1), 63-74 https://doi.org/10.12989/sem.2006.23.1.063
  30. Zhou, Z.G., Wang, B. and Sun, Y.G. (2004), "Two collinear interface cracks in magneto-electro-elastic composites", Int. J. Eng. Sci., 42, 1157-1167
  31. Zhou, Z.G., Wang, B. and Wu, L.Z. (2005a), "Investigation of the behavior of a crack between two half-planes of functionally graded materials by using the Schmidt method", Struct. Eng. Mech., 19(4), 425-440 https://doi.org/10.12989/sem.2005.19.4.425
  32. Zhou, Z.G., Wu, L.Z. and Wang, B. (2005b), "The behavior of a crack in functionally graded piezoelectric/ piezomagnetic materials under anti-plane shear loading", Archive of Applied Mechanics, 74(8), 526-535 https://doi.org/10.1007/s00419-004-0369-y
  33. Zhou, Z.G., Wu, L.Z. and Wang, B. (2005c), "The dynamic behavior of two collinear interface cracks in magneto-electro-elastic composites", Eur. J. Mech. A-Solids, 24(2), 253-262 https://doi.org/10.1016/j.euromechsol.2004.10.006

피인용 문헌

  1. An electrically impermeable and magnetically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under uniform magnetoelectromechanical loads vol.32, 2012, https://doi.org/10.1016/j.euromechsol.2011.09.010
  2. X-FEM simulation for two-unequal-collinear cracks in 2-D finite piezoelectric specimen vol.8, pp.2, 2012, https://doi.org/10.1007/s10999-012-9182-x
  3. A magnetically impermeable and electrically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under concentrated magnetoelectromechanical loads on the crack faces vol.54, pp.9, 2011, https://doi.org/10.1007/s11433-011-4403-0
  4. Extreme value modeling of coincident lane load effects for multi-lane factors of bridges using peaks-over-threshold method vol.24, pp.3, 2021, https://doi.org/10.1177/1369433220960275