Modeling microstructural effects on hysteresis loops with the same maximum flux density

Microstructural attributes such as grain size d and dislocation density ζ_d affect the hysteretic magnetic properties of steels because they affect domain wall movement and pinning. In an earlier paper, a model was proposed for computing hysteresis loops based on the effect of grain size and dislocation density. In that paper, hysteresis loops were compared that all had the same maximum field H_max. The result was that coercivity departed from linear relationships with inverse grain size (viz. 1/d) and ζ_d¹2/ for large values of 1/d and ζ_d¹2/. The same was true of hysteresis loss W_H, except that hysteresis loss even showed a peak, first increasing and then decreasing with increasing 1/d and ζ_d¹2/. This kind of behavior had not been seen by experimenters, particularly core-loss people. It was learned that the core-loss experimenters compared hysteresis loops of the same maximum flux density B_max instead of the same H_max. In this paper, we use the model previously formulated to produce hysteresis loops with the same B_max. Indeed, the appropriate linear relationships are found. The paper also addresses effects of uniaxial anisotropy on these microstructural magnetic effects and why two hysteresis parameters are affected by microstructural variation.