Abstract
Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deformation of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.
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References
Pao, Y.H., Yeh, C.S.: A linear theory for soft ferromagnetic elastic solids. International Journal of Engineering Science 11, 415–436 (1973)
Qin, F., Yan, D.M., Zhang, X.F.: Perturbed magnetic fields generated by deformation of structures in earth magnetic field. Acta Mechanic Sinica 38(6), 799–806 (2006) (in Chinese)
Qin, F., Yan, D.M., Zhang Y.: Analytical solution of the perturbed magnetic field induced in an infinite plate by a circinal hole under tension. Acta Mechanica Solida Sinica 28, 281–286 (2007) (in Chinese)
Qin, F., Yan, D.M.: Analytical solution of the perturbed magnetic fields of plates under tensile stress. Journal of Applied Mechanics 75(3), 0310041–6 (2008)
Yeh, C.S.: Magnetic fields generated by a tension fault. Bulletin of the College of Engineering, National Taiwan University 40, 47–56 (1987)
Shindo, Y., Sekiya, D., Narita, F., et al.: Tensile testing and analysis of ferromagnetic elastic strip with a central crack in a uniform magnetic field. Acta Materialia 52(15), 4677–4684 (2004)
Shindo, Y., Komatsu, T., Narita, F., et al.: Magnetic stress intensity factor for an edge crack in a soft ferromagnetic elastic half-plane under tension. Acta Mechanica 182(3/4), 183–193 (2006)
Lin, C.B., Yeh, C.S.: The magnetoelastic problem of a crack in a soft ferromagnetic solid. International Journal of Solids and Structures 39, 1–17 (2002)
Liang, W., Shen, Y.P., Fang, D.N.: Coupling field in an infinite soft ferromagnetic elastic plane with a through crack. Acta Mechanica Sinica 33, 758–766 (2001) (in Chinese)
Zhang, X.: Fracture and Damage Mechanics. Beijing University of Aeronautics and Astronautics Press, Beijing, 2006 (in Chinese)
Fan, T.Y.: Foundations of Fracture Theory. Science Press, Beijing, 2003 (in Chinese)
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The project was supported by the National Natural Science Foundation of China (10472004).
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Qin, F., Zhang, Y. & Liu, YN. Perturbed magnetic field of an infinite plate with a centered crack. Acta Mech Sin 27, 259–265 (2011). https://doi.org/10.1007/s10409-011-0418-z
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DOI: https://doi.org/10.1007/s10409-011-0418-z