基于Jiles-Atherton理论的铁磁材料塑性变形磁化模型修正

Jiles-Atherton(J-A)模型在磁化建模领域应用广泛,但不同文献给出的J-A模型并不一致,致使采用不同表达式建立的塑性变形磁化模型存在多种版本,其正确性难以甄别.通过对无磁滞磁化方程、能量守恒方程和等效磁场强度方程的梳理与比较,发现原有模型中存在将磁化强度和无磁滞磁化强度混用、将不可逆磁化能量等效于全部的磁化能量、等效磁场强度中应力磁化项界定不清等问题.在此基础上,对上述方程进行了修正,推导了基于J-A模型的塑性变形磁化修正模型.将修正模型计算结果与原模型计算结果、相关文献中的试验结果进行对比,结果表明:与原有计算模型相比,修正模型计算结果的饱和磁化强度和剩余磁化强度随塑性变形增加而减小,矫顽力随塑性变形增大而增大,达到饱和磁化强度时的外磁场强度随塑性变形增大而增大的趋势有所减弱,更符合试验结果,可更准确地反映塑性变形对材料磁化的影响.

Modeling plastic deformation effect on the hysteresis loops of ferromagnetic materials based on modified Jiles-Atherton model

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.