Abstract
This paper presents the domain form of interaction integrals based on three independent formulations for computation of stress intensity factors, electric displacement intensity factors and magnetic induction intensity factors for cracks in functionally graded magnetoelectroelastic materials. Conservation integrals of J-type are derived based on the governing equations for magnetoelectroelastic media and the crack tip asymptotic fields of homogeneous magnetoelectroelastic medium as auxiliary fields. Each of the formulations differs in the way auxiliary fields are imposed in the evaluation of interaction integrals and each of them results in a consistent form of the interaction integral in the sense that extra terms naturally appear in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded magnetoelectroelastic medium. The additional terms play an important role of ensuring domain independence of the presented interaction integrals. Comparison of numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of two examples.
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References
Ding HJ, Jiang AM (2004) A boundary integral formulation and solution for 2D problems in magneto-electro-elastic media. Comput Struc 82: 1599–1607. doi:10.1016/j.compstruc.2004.05.006
Dolbow J, Gosz M (2002) On the computation of mixed-mode stress intensity factors in functionally graded materials. Int J Solids Struct 39: 2557–2574. doi:10.1016/S0020-7683(02)00114-2
Eischen JW (1987) Fracture of nonhomogeneous materials. Int J Fract 34: 3–22
Feng WJ, Su RKL (2006) Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip. Int J Solids Struct 43: 5196–5216. doi:10.1016/j.ijsolstr.2005.07.050
Feng WJ, Su RKL (2007) Dynamic fracture behaviors of cracks in a functionally graded magneto-electro-elastic plate. Eur J Mech A Solids 26: 363–379
Gao CF, Kessler H, Balke H (2003a) Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack. Int J Eng Sci 41(9): 969–981. doi:10.1016/S0020-7225(02)00323-3
Gao CF, Kessler H, Balke H (2003b) Crack problems in magnetoelectroelastic solids. Part II: general solution of collinear cracks. Int J Eng Sci 41(9): 983–994. doi:10.1016/S0020-7225(02)00324-5
Garcia-Sanchez F, Rojas-Diaz R, Saez A, Zhang C (2007) Fracture of magnetoelectroelastic composite materials using boundary element method (BEM). Theor Appl Fract Mech Mech 47: 192–204. doi:10.1016/j.tafmec.2007.01.008
Hu KQ, Li GQ (2005) Electro-magneto-elastic analysis of a piezoelectromagnetic strip with a finite crack under longitudinal shear. Mech Mater 37: 925–934. doi:10.1016/j.mechmat.2004.03.006
Jin ZH, Noda N (1994) Crack tip singular fields in nonhomogeneous materials. Transactions of the ASME. J Appl Mech 61: 738–740. doi:10.1115/1.2901529
Kim JH, Paulino GH (2003) The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors. Int J Solids Struct 40: 3967–4001. doi:10.1016/S0020-7683(03)00176-8
Nan CW (1994) Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys Rev B 50(9): 6082–6088. doi:10.1103/PhysRevB.50.6082
Pan E, Han F (2005) Exact solution for functionally graded and layered magneto-electro-elastic plates. Int J Eng Sci 43: 321–339. doi:10.1016/j.ijengsci.2004.09.006
Paulino GH, Kim JH (2004) A new approach to compute T-stress in functionally graded materials by means of the interaction integral method. Eng Fract Mech 71: 1907–1950. doi:10.1016/j.engfracmech.2003.11.005
Rao BN, Rahman S (2003a) Meshfree analysis of cracks in isotropic functionally graded materials. Eng Fract Mech 70: 1–27. doi:10.1016/S0013-7944(02)00038-3
Rao BN, Rahman S (2003b) An interaction integral method for analysis of cracks in orthotropic functionally graded materials. Comput Mech 32: 40–51. doi:10.1007/s00466-003-0460-1
Sladek J, Sladek V, Zhang C, Solek P, Pan E (2007) Evaluation of fracture parameters in continuously nonhomogeneous piezoelectric solids. Int J Fract 145: 313–326. doi:10.1007/s10704-007-9130-1
Song ZF, Sih GC (2003) Crack initiation behavior in a magnetoelectroelastic composite under in-plane deformation. Theor Appl Fract Mech Mech 39: 189–207. doi:10.1016/S0167-8442(03)00002-8
Stroh AN (1958) Dislocations and cracks in anisotropic elasticity. Philos Mag 7: 625–646. doi:10.1080/14786435808565804
Tian WY, Gabbert U (2004) Multiple crack interaction problem in magnetoelectroelastic solids. Eur J Mech A Solids 23: 599–614
Tian WY, Gabbert U (2005) Macrocrack–microcrack interaction problem in magnetoelectroelastic solids. Mech Mater 37: 565–592. doi:10.1016/j.mechmat.2004.04.008
Tian WY, Rajapakse RKND (2005) Fracture analysis of magnetoelectroelastic solids by path independent integrals. Int J Fract 131: 311–335. doi:10.1007/s10704-004-5103-9
Tian WY, Rajapakse RKND (2008) Field intensity factors of a penny-shaped crack in a magnetoelectroelastic layer. J Alloy Comp 449: 161–171. doi:10.1016/j.jallcom.2005.11.097
Ting TCT (1996) Anisotropic elasticity: theory and application. Oxford Science, New York
Van Run AMJG, Terrell DR, Scholing JH (1974) An in situ grown eutectic magnetoelectric composite material. J Mater Sci 9: 1710–1714. doi:10.1007/BF00540771
Van Suchtelen J (1972) Product properties: a new application of composite materials. Phillips Res Rep 27: 28–37
Wang BL, Han JC (2007) Multiple cracking of magnetoelectroelastic materials in coupling thermo-electro-magneto-mechanical loading environments. Comput Mater Sci 39: 291–304. doi:10.1016/j.commatsci.2006.06.008
Wang BL, Mai YW (2003) Crack tip field in piezoelectric/piezomagnetic media. Eur J Mech A Solids 22(4): 591–602
Wang BL, Mai YW (2004) Fracture of piezoelectromagnetic materials. Mech Res Commun 31(1): 65–73. doi:10.1016/j.mechrescom.2003.08.002
Zhong XC, Li XF (2007) Magnetoelectroelastic analysis for an opening crack in a piezoelectromagnetic solid. Eur J Mech A Solids 26: 405–417
Zhong XC, Li XF (2008) Fracture analysis of a magnetoelectroelastic solid with a penny-shaped crack by considering the effects of the opening crack interior. Int J Eng Sci 46: 374–390. doi:10.1016/j.ijengsci.2007.11.005
Zhou ZG, Wang B (2004) Two parallel symmetric permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. Int J Solids Struct 41: 4407–4422. doi:10.1016/j.ijsolstr.2004.03.004
Zhou ZG, Wang B (2006) The scattering of the harmonic anti-plane shear stresswaves by two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material half infinite planes. Proc Inst Mech Eng C J Mech Eng Sci 220(2): 137–148. doi:10.1243/095440506X77562
Zhou ZG, Wu LZ, Wang B (2005) The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. Arch Appl Mech 74(8): 526–535. doi:10.1007/s00419-004-0369-y
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An erratum to this article can be found at http://dx.doi.org/10.1007/s10704-010-9446-0
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Rao, B.N., Kuna, M. Interaction integrals for fracture analysis of functionally graded magnetoelectroelastic materials. Int J Fract 153, 15–37 (2008). https://doi.org/10.1007/s10704-008-9285-4
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DOI: https://doi.org/10.1007/s10704-008-9285-4
Keywords
- Crack
- Functionally graded magnetoelectroelastic materials
- Interaction integral
- Nonequilibrium formulation
- Incompatibility formulation
- Constant constitutive tensor formulation
- Displacement extrapolation method
- Stress intensity factor
- Electric displacement intensity factor and magnetic induction intensity factor