A magneto-mechanical model for the magnetic non-destructive evaluation of ferromagnetic materials

Abstract

In this paper, a new magneto-mechanical constitutive model is established based on the macro-thermodynamic relationship, the micro-magnetic domain theory and Jiles–Atherton–Sablic (J–A–S) theory. The fitting expression of magnetostriction newly describes the nonlinear stress dependence, which is extended to six-order magnetization terms. In particular, the new expressions of nonlinear functions related to the maximum point of magnetostriction (MPM) are introduced into the magnetostriction expression. In addition, the improved expressions of the plastic stress equivalent field and the three parameters (i.e., the inter-domain coupling parameter, the field relaxation factor and the loss coefficient) considering the nonlinear stress dependence are introduced into the magnetization expressions. Compared to the various experimental results and the theoretical results by the existing models, it is clearly perceived that the new model has an excellent prediction ability of the magnetostrictive and magnetic behaviors in ferromagnetic materials under the elasto-plastic stress and magnetic field. Furthermore, the prediction accuracy of the magnetic parameters related to the magnetic non-destructive evaluation (MNDE) is greatly improved. The integrative analysis of the magnetostrictive and magnetic behaviors in various ferromagnetic materials demonstrates that the presented model can be widely used in the quantitative study of the MNDE as well as in the research of the magneto-mechanical behavior and the application of ferromagnetic materials.