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Plastic deformation is one of the most important features that affect the hysteresis magnetic properties of steels, because it changes the dislocation density and affects domain-wall movement and pinning. In order to model the effect of plastic deformation on the magnetic properties, the prevailing Jiles-Atherton (J-A) theory is extensively used. However, the J-A models in a series of papers published by Jiles et al. are not completely consistent. As a result, there exists no uniform formula of magneto-plastic model established by different researchers, based on different J-A models, and various versions given by different mathematic expressions of magneto-plastic model often create difficulty in discriminating the accuracies and effectivenesses of the analyzed results. Therefore, it is necessary to establish an accurate and reasonable magneto-plastic model. In this paper, on the basis of magnetization mechanism of ferrimagnet and plastic deformation model, the effects of plastic deformation on the magnetic characteristic parameters adopted in magneto-plastic model, such as dislocation density, pinning coefficient and scaling constant, are analyzed and the relationship between them is first established. Then, by contrasting the fitting formula of the anhysteretic magnetization curve, the energy conservation equation and the effective magnetic field equation established by different researchers, several queries are proposed, and the irrationality and inaccuracy of the existing magneto-plastic model are elucidated, such as the mixing of anhysteresis magnetization and magnetization, the unreasonably regarding the irreversible magnetization energy as actual total magnetization energy. Thus, the energy conservation equation, the effective magnetic field equation and the anhysteretic magnetization equation are modified, and the differential expression of the magneto-plastic model is re-derived finally. Comparing the results calculated by the existing magneto-plastic models with the experimental results, it is seen indeed that a more sharp change of magnetization appears at small plastic deformation, then, the values of magnetization decrease more slowly with the increase of plastic deformation than those from the models respectively proposed by Li Jian-Wei, Leng Jian-Cheng and Wang Zheng-Dao; the saturation magnetization and residual magnetization decrease with the increase of plastic deformation, the coercive force is increased oppositely and the trend to reach the saturation magnetization becomes gentler, which is more exactly consonant with experiment observation than that calculated by the Sablik's model; additionally, the hysteresis loops of the plastically deformed carbon-steel samples calculated by the modified magneto-plastic model are also in better agreement with the experimental results than those from the existing models. Consequently, the modification is effective, and the modified magneto-plastic model is more accurate to simulate the plastic deformation effect on the magnetic property of ferromagnetic material.
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Keywords:
- Jiles-Atherton model /
- hysteresis loop /
- magneto-plastic model /
- magneto-mechanical effect
[1] Li Z, Li Q M, Li C Y, Sun Q Q, Lou J 2011 Proc. Chin. Soc. Elect. Eng. 31 124 (in Chinese) [李贞, 李庆民, 李长云, 孙秋芹, 娄杰 2011 中国电机工程学报 31 124]
[2] Jiles D C, Atherton D L 1984 J. Appl. Phys. 55 2115
[3] Jiles D C, Atherton D L 1986 J.Magn. Magn. Mater. 61 48
[4] Jiles D C 1992 IEEE Trans. Magn. 28 27
[5] Jiles D C, Thoelke J B 1989 IEEE Trans. Magn. 25 3928
[6] Sablik M J, Jiles D C 1993 IEEE Trans. Magn. 29 2113
[7] Jiles D C 1995 J.Appl. Phys. 28 1537
[8] Jiles D C 1994 J.Appl. Phys. 76 5849
[9] Jiles D C, Li L 2004 J. Appl. Phys. 95 7058
[10] Sablik M J 2004 IEEE Trans. Magn. 40 3219
[11] Sablik M J, Geerts W J, Smith K, Gregory A, Moore C 2010 IEEE Trans. Magn. 46 491
[12] Sablik M J, Landgraf F J G, Paolo S Comparing grain size and dislocation density effects for hysteresis loops with the same maximum flux density in a magnetic hysteresis model https://wwwresearchgatenet /publication/265264412 [2017-03-08]
[13] Sablik M J, Rios S, Landgraf F J G 2005 J. Appl. Phys. 97 10E518
[14] Suliga M, Borowik L, Chwastek K 2015 Arch. Metall. Mater. 60 409
[15] Wang Z D, Deng B, Yao K 2011 J. Appl. Phys. 109 083928
[16] Li J W, Xu M Q, Leng J C, Xu M X 2012 J.Appl. Phys. 111 063909
[17] Leng J C, Liu Y, Zhou G Q 2013 NDT&E Int. 55 42
[18] Jiang P, Wang W 2009 Fundamentals of Engineering Mechanics(II): Mechanics of Materials (Beijing: Higher Education Press) pp61-63 (in Chinese) [蒋平, 王维 2009 工程力学基础(II): 材料力学(北京: 高等教育出版社) 第61—63页].
[19] Doubov A A K V G 2001 Proceedings of the Second International Conference ''Diagnostics of the Equipment and Constructions with Usage of Metal Magnetic Memory'' Moscow, Russia, February 26-28, 2001 p1
[20] Jiles D C 2000 J.Appl. Phys. 21 1196
[21] Makar J M, Tanner B K 1998 J. Magn. Magn. Mater. 184 193
[22] Iordache V E, Hug E, Buiron N 2003 Mat.Sci. Eng. A-Struct. 359 62
[23] Makar J M, Tanner B K 2000 J. Magn. Magn. Mater. 222 291
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[1] Li Z, Li Q M, Li C Y, Sun Q Q, Lou J 2011 Proc. Chin. Soc. Elect. Eng. 31 124 (in Chinese) [李贞, 李庆民, 李长云, 孙秋芹, 娄杰 2011 中国电机工程学报 31 124]
[2] Jiles D C, Atherton D L 1984 J. Appl. Phys. 55 2115
[3] Jiles D C, Atherton D L 1986 J.Magn. Magn. Mater. 61 48
[4] Jiles D C 1992 IEEE Trans. Magn. 28 27
[5] Jiles D C, Thoelke J B 1989 IEEE Trans. Magn. 25 3928
[6] Sablik M J, Jiles D C 1993 IEEE Trans. Magn. 29 2113
[7] Jiles D C 1995 J.Appl. Phys. 28 1537
[8] Jiles D C 1994 J.Appl. Phys. 76 5849
[9] Jiles D C, Li L 2004 J. Appl. Phys. 95 7058
[10] Sablik M J 2004 IEEE Trans. Magn. 40 3219
[11] Sablik M J, Geerts W J, Smith K, Gregory A, Moore C 2010 IEEE Trans. Magn. 46 491
[12] Sablik M J, Landgraf F J G, Paolo S Comparing grain size and dislocation density effects for hysteresis loops with the same maximum flux density in a magnetic hysteresis model https://wwwresearchgatenet /publication/265264412 [2017-03-08]
[13] Sablik M J, Rios S, Landgraf F J G 2005 J. Appl. Phys. 97 10E518
[14] Suliga M, Borowik L, Chwastek K 2015 Arch. Metall. Mater. 60 409
[15] Wang Z D, Deng B, Yao K 2011 J. Appl. Phys. 109 083928
[16] Li J W, Xu M Q, Leng J C, Xu M X 2012 J.Appl. Phys. 111 063909
[17] Leng J C, Liu Y, Zhou G Q 2013 NDT&E Int. 55 42
[18] Jiang P, Wang W 2009 Fundamentals of Engineering Mechanics(II): Mechanics of Materials (Beijing: Higher Education Press) pp61-63 (in Chinese) [蒋平, 王维 2009 工程力学基础(II): 材料力学(北京: 高等教育出版社) 第61—63页].
[19] Doubov A A K V G 2001 Proceedings of the Second International Conference ''Diagnostics of the Equipment and Constructions with Usage of Metal Magnetic Memory'' Moscow, Russia, February 26-28, 2001 p1
[20] Jiles D C 2000 J.Appl. Phys. 21 1196
[21] Makar J M, Tanner B K 1998 J. Magn. Magn. Mater. 184 193
[22] Iordache V E, Hug E, Buiron N 2003 Mat.Sci. Eng. A-Struct. 359 62
[23] Makar J M, Tanner B K 2000 J. Magn. Magn. Mater. 222 291
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