Modeling plastic deformation effects in steel on hysteresis loops with the same maximum flux density

Plastic deformation affects the hysteretic magnetic properties of steels because it changes the dislocation density, which affects domain-wall movement and pinning, and also because it places the specimen under residual strain. An earlier paper proposed a model for computing hysteresis loops on the basis of the effect of grain size d and dislocation density ζ_d. In that paper, hysteresis loops were compared that all had the same maximum flux density B_max. The result was that coercivity H_c exhibited a linear relationship with inverse grain size (1/d) and ζ_d¹2/. The same was true of hysteresis loss W_H. If one compared hysteresis loops all with the same H_max, these linear dependences were only approximately found. Because the relationships are simpler for loops of constant B_max, core loss experimenters compare loops that all have the same B_max. In this paper, we modify the model to study the effect of plastic tensile deformation on hysteresis loops with the same B_max. We found linear relationships between H_c and residual plastic strain ε_r and between W_H and ε_r. With increasing residual tensile strain, H_c increases (whereas with increasing elastic tensile strain, H_c decreases). Also, with increasing residual tensile strain, the slope of the hysteresis loop decreases (whereas with increasing elastic tensile strain, the slope increases). We also consider the effect of compressive plastic deformation.