A magneto-mechanical coupling constitutive model for self-magnetic flux leakage stress detection in ferromagnetic materials

The initial magnetization state, magnetization history, stress loading history, and material type of ferromagnetic materials have significant effects on the self-magnetic flux leakage (SMFL) stress detection, which therefore needs to be clarified, and the key to clarifying these effects is to establish the magneto-mechanical coupling constitutive model accurately. Thus, mathematical descriptions of magneto-mechanical coupling are constructed, by combining the basic magnetization characteristics and hysteresis properties of ferromagnetic materials. The accuracy and validity of such fundamental theories are verified by experimental examples, allowing for an extended analysis of the working conditions. The results show that the proposed model is well suited to complex cross-coupling conditions of applied magnetic field H (involving constant excitation magnetic intensity H0) and tensile stress 6t(involving cyclic loading and unloading), predicting the stress-induced magnetization behaviour and its variation law in ferromagnetic materials effectively. The study here can further serve as an important theoretical basis for the work on numerical analog analysis, guiding the quantitative analysis of SMFL stress detection of ferromagnetic materials on the theoretical level.