Stress Dependent Magnetization and Vector Preisach Modeling in Low Carbon Steels

Measurements of magnetic properties have been performed on commercially available low carbon steels (Armco and non-oriented electrical steels) in order to construct and test a Preisach model for materials under stress. The measurements include hysteresis loops of samples under tensile stress taken during loading and after unloading at given strain levels. A vector Preisach model using the SW model as the elementary operator, superposition to account for easy axes dispersion and a weighed mixture of normal distributions to account for the long-range interactions established through the magnetoelastic coupling is proposed. The model reproduces the effect of applied stress, verifying the experimental finding that the permeability of a material under tensile stress decreases. The Preisach density is constructed in such a way as to account for the strong magnetostatic interactions observed in the high induction regions in the case of built-in stresses, so the model is also able to capture the effect of the residual compressive stresses in unloaded materials. The use of the differential permeability and its first derivative are proposed as parameters to be monitored in NDT applications.