Modeling of sharp change in magnetic hysteresis behavior of electrical steel at small plastic deformation

Abstract

In 2.2% Si electrical steel, the magnetic hysteresis behavior is sharply sheared by a rather small plastic deformation ͑0.5%͒. A modification to the Jiles-Atherton hysteresis model makes it possible to model magnetic effects of plastic deformation. In this paper, with this model, it is shown how a narrow hysteresis with an almost steplike hysteresis curve for an undeformed specimen is sharply sheared by plastic deformation. Computed coercivity and hysteresis loss show a sharp step to higher values at small strain due to an n =1/2 power law dependence on residual strain. The step is seen experimentally.

Fitting the flow curve of a plastically deformed silicon steel for the prediction of magnetic properties

“…It can be shown that the residual strain e r is equal to the ''plastic'' strain given as e pl ¼ e À s=Y , where Y is Young's modulus and e is the total deformation produced by stress s. The relationship between the strain-hardening stress and the residual strain e r is phenomenologically given as Ludwik's law, which states that s À s y is equal to a constant multiplied by the residual strain e r to some power n, where n is known as the Ludwik exponent and is material-dependent, and hence is an irrational number and not necessarily a rational fraction. We have shown that the magnetic properties are a function of this relationship [3], and hence it would not be surprising if hysteresis loss also satisfies a Ludwik-like relationship. We shall show that indeed they do exhibit such a relationship, but not with the same exponent as shown by the mechanical behavior.…”

“…[2,3], except that n ¼ 0:66 is used now for the Ludwik exponent used in computing the strain-hardening stress that enters into the model. This value of n ¼ 0:66 was extracted from the tensile mechanical data after using nonlinear extrapolation from the uniform strain region to obtain the Sy used in Ludwik's law.…”

“…It is known that in this steel, in rolled specimens, the magnetic hysteresis behavior is sharply sheared by what is considered to be a rather small plastic deformation (0.5%) [1]. A new modification [2] to the Jiles-Atherton hysteresis model has made it possible to model the magnetic effects of plastic deformation on the magnetic hysteresis B2H curve [3]. The flow curve of the steel, especially in the tensilely deformed specimens, shows evidence of discontinuous yield, which can be explained by a Cottrell atmosphere of carbon atoms initially pinning the dislocations [4]; hence, the ''apparent'' yield stress needed to start dislocation flow is actually greater than what is needed to continue dislocation flow.…”

Effect of deformation and annealing on the microstructure and magnetic properties of grain-oriented electrical steels

“…1 and 2), in a pattern that has been shown to occur in non-oriented steels [1,2]: a large increase in losses after a very small straining (less than 1%) followed by a less steep linear increase in losses for larger strains. The differences between the behaviour shown in Figs.…”

“…The magnetic hardening after rolling may be described using an analogy to Ludwik 0 s description [2] of the mechanical hardening: P ¼ P 0 +ke n , where P are power losses, P 0 are power losses without a plastic deformation, k is an experimental constant and n is the hardening exponent. For rolling in RD, we have found n ¼ 0.34 and for rolling in TD, n ¼ 0.71.…”