Analytical solution of magneto-mechanical magnetic dipole model for metal magnetic memory method

Abstract

Magnetic dipole theory has been widely and successfully used to explain the leakage magnetic field signals. Because the model parameter such as magnetic dipole density is not easy to quantify, magnetic dipole theory often needs normalizing in application, which is considered to be unsuitable for quantitatively analyzing the magnetic memory signals with the stress effect. In this paper, the theoretical model of magneto-mechanical coupling magnetic dipole is established, which is suitable for analyzing the stress effect on magnetic signals in magnetic memory testing method. Based on the ferromagnetic theory, the equivalent field under the combined action of the applied load and the magnetic field is determined. And then, the magneto-mechanical analytical model is obtained for the isotropic ferromagnetic material under the weak magnetic field based on the first-order magnetization approximation in the weak magnetization state. Under the assumptions of rectangular and V-shaped magnetic charge distribution for the two-dimensional magnetic signal problem, the theoretical analytical models of the magnetic memory signals from the smooth and cracked specimens, and the analytical models of the magnetic memory signal induced by the rectangular and V-shaped surface defect are established. Based on the analytical solution of the proposed magneto-mechanical magnetic dipole theory, the difference in signal between before and after the failure of the specimen, the signal from the rectangular and V-shaped defect, and other influencing factors and laws of the magnetic signal are analyzed in detail. In particular, the influence of stress, environmental magnetic field, defect morphology and size, lift-off effect, specimen size and other factors on magnetic memory signals can be described based on the analytical solution of magneto-mechanical magnetic dipole models proposed in this paper. The proposed analytical model of magneto-mechanical magnetic dipole in this paper is simple and easy to use, and the present research shows that the proposed analytical solution in this paper can explain some basic experimental phenomena and laws in magnetic memory testing experiments. In addition, the precise magneto-mechanical coupling quantitative model combined with the finite element analysis method is still needed for accurately analyzing the magnetic memory signals in experiment.