Abstract
Anti-plane fracture analysis is performed for a micropolar material. The crack problem is reduced as Cauchy singular integral equations by Fourier integral transform. Numerical solutions of the stress intensity factors are obtained by the Lobatto–Chebyshev collocation method. Parametric studies indicate that the fracture behavior of the micropolar material depends on the coupling factor and the internal length scale. Larger coupling factor and internal length scale lead to stronger micropolar effect. The micropolarity is beneficial to reducing the driving force of a micro-crack, however, it may also prompt the propagation of a macro-crack.
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References
Chen YF, Erdogan F (1996) The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate. J Mech Phys Solids 44: 771–787. doi:10.1016/0022-5096(96)00002-6
Diegele E, Elsäßer R, Tsakmakis C (2004) Linear micropolar elastic crack-tip fields under mixed mode loading conditions. Int J Fract 129: 309–339. doi:10.1023/B:FRAC.0000049492.13523.5a
Erdogan F, Gupta GD (1972) On the numerical solution of singular integral equations. Q Appl Math 29: 525–534
Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 15: 909–
Eringen AC (1999) Microcontinuum field theories: I foundations and solids. Springer Verlag, New York
Han SY, Narasimhan MNL, Kennedy TC (1990) Dynamic propagation of a finite crack in a micropolar elastic solid. Acta Mech 85: 179–191. doi:10.1007/BF01181516
Li YD, Lee KY (2007) An anti-plane crack perpendicular to the weak/micro-discontinuous interface in a bi-FGM structure with exponential and linear non-homogeneities. Int J Fract 146: 203–211. doi:10.1007/s10704-007-9161-7
Li YD, Lee KY (2008) Fracture analysis and improved design for a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties. Eng Fract Mech. 75: 3161–3172. doi:10.1016/j.engfracmech.2007.12.005
Li YD, Lee KY, Dai Y (2008) Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface. Euro J Mech A/Solid 27: 808–823. doi:10.1016/j.euromechsol.2007.11.006
Li YD, Jia B, Zhang N, Tang LQ, Dai Y (2006) Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating. Int J Solids Struct 43: 4795–4809. doi:10.1016/j.ijsolstr.2005.07.030
Nowacki W (1970) Theory of Micropolar Elasticity. Springer Verlag, New York
Paul HS, Shridharan K (1980) The penny-shaped crack problem in micropolar elasticity. Int J Eng Sci 18: 1431–1448. doi:10.1016/0020-7225(80)90099-3
Shmoylova E, Potapenko S, Rothenburg L (2007) Stress distribution around a crack in plane micropolar elasticity. J Elast 86: 19–39. doi:10.1007/s10659-006-9078-9
Shmoylova E, Potapenko S (2008) Stress distribution around a crack in anti-plane micropolar elasticity. Math Mech Solid 13: 148–171. doi:10.1177/1081286506074881
Yadava RN, Roy A, Katiyar RAJK (1994) The effect of internal pressure on a penny-shaped crack at the interface of two bonded dissimilar micropolar elastic half-spaces. Int J Fract 65: 19–30. doi:10.1007/BF00017140
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Li, YD., Lee, K.Y. Fracture analysis in micropolar elasticity: anti-plane crack. Int J Fract 152, 163–168 (2008). https://doi.org/10.1007/s10704-008-9277-4
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DOI: https://doi.org/10.1007/s10704-008-9277-4