A nonlinear magneto-elastoplastic coupling model based on Jiles–Atherton theory of ferromagnetic materials

Abstract

Abstract As seen in the Jiles–Atherton (J–A) model and its modified form, the linear relationship between the magnetization coefficient and the stress deviates significantly from the experimental results. It is necessary to introduce many parameters that are difficult to obtain or unknown to describe the effect of elastoplastic deformation on magnetization or hysteresis, such as shape coefficient, pinning coefficient, and molecular field coefficient. In this paper, a new nonlinear magneto-elastoplastic model for ferromagnetic materials is established based on the magneto-mechanical coupling effect, and both the sixth-order term of magnetization and the nonlinear equation of the magnetization coefficient are introduced into the magnetostriction equation. In the models established in this paper, the elastoplastic deformation equivalent magnetic field is introduced into the effective magnetic field, and the Frohlich–Kennelly equation is used to describe the anhysteretic magnetization. After comparing the prediction results of different models with the available experimental results, it is observed that the proposed model in this paper exhibits superior prediction ability for magnetostrictive strain, magnetization, and hysteresis phenomena under different stresses. This paper has also analyzed the mechanism of the effect of elasto-plastic loading and residual stress on the hysteresis in different models as well as the differences between them. The determination coefficient of the proposed model in this paper is closer to 1, which is better than the existing models, indicating that it has a better fitting effect and is of great significance to the development of quantitative non-destructive testing technology.