Modeling and experimental analysis of magnetostriction in high strength steels

Previous studies on the magnetostriction in high strength steels have ignored the internal anisotropies due to previous material handling. Cold-rolling an iron alloy will stretch and distort the magnetic domains in the direction of rolling. These altered domain shapes impact the magnetic characteristics of the alloy; adding an additional preferred direction of magnetization to the easy or hard axes within the crystalline structure. This paper presents data taken on rods of a high strength steel that have been machined parallel to the rolling direction; as well as simulated results using a Preisach-type magnetostriction model. The model, whose formulation is based on the DOK magnetization-based model, aims specifically to simulate the Villari reversal phenomenon observed in the magnetostriction measurements of high strength steels and some


Introduction
Magnetostriction is a mechanical strain caused by an applied magnetic field.High strength steels have magnetostrictions of 10 -30 x 10 -6 , which is one-half that of Ni for example.However, there are numerous situations in which the magnetostrictive properties of these steels are important; e.g. in torque sensing in shafts requiring high strength to weight ratios [1].
Steel shows inherently different material characteristics than giant magnetostrictive materials like Terfenol-D.A striking difference is shown in the "Villari reversal" seen in some high strength steels.This effect is characterized by the magnetostriction reaching a maximum value and then decreasing with larger applied fields instead of reaching a saturation value.Figure 1 illustrates an example of a Villari reversal, shown by the magnetostriction versus applied magnetic field for one of the parallel samples.
While previous work [1] took measurements principally in a single direction, we have taken into account directional anisotropies.Cold-rolling an iron alloy stretches and distorts the magnetic domains in the direction of rolling [2].These altered domain shapes impact the magnetic characteristics of the alloy; adding an additional preferred direction of magnetization to the easy or hard axes within the crystalline structure.Some previous measurements have mentioned directional anisotropies within rolled steels but did not characterize the differences [3].Our goal is to incorporate anisotropic stress-induced differences into a Preisach model.In a previous paper we have reported detailed measurement results for the magnetic properties of high strength steels oriented parallel, perpendicular and 45° to the rolling direction [4].

Joint European Magnetic Symposia 2012
The Preisach distribution of the model is incorporated in the A factor which is a function of the irreversible magnetization which in turn is calculated through the well-known Preisach function.For a DC-demagnetized single-quadrant material with a Gaussian Preisach function, the irreversible component of magnetization according to the DOK model is given by: where S is the squareness, Ms is the saturation magnetization, Hrem is the remanent coercivity and & is the standard deviation of the switching field.For detailed explanation of the model's parameters and the mathematical expressions, refer to [8].
In order to evaluate the validity of the proposed model, a comparison between the measurements and the model's output is presented.The unknown parameters of the model were selected manually, yet selectively, to model the measurements.A detailed identification process will be the subject of a separate paper.

Experimental Analysis & Comparisons
Figure 3 shows " as a function of increasing magnetic field for different applied compressive stresses.For stress magnitudes lower than 125 MPa, " decreases as the stress increases within the magnetostriction's steep rise region.Beyond this region (where the magnetostriction starts saturating), " behaves the same regardless of the stress magnitude.For stress magnitudes higher than 125 MPa, " is invariant with respect to stress magnitude.This observation is taken as a guide for choosing the value of ".The width of the flat region increases with the stress magnitude.We also observed that the aforementioned width is strongly correlated to the peak of the magnetic susceptibility.This observation shall be indicative of the shift parameter which will be introduced to the model later on to simulate the hysteresis phenomenon.Again, beyond 125 MPa the measurements are almost insensitive to the stress magnitude.

Conclusions
Our previous measurements show interesting differences between the cylinders depending on their orientation with respect to the rolling direction.However, these differences diminish beyond a critical compressive stress magnitude, in our case this value is 125 MPa.A Preisach-type, two-component model is presented to simulate the Villari reversal phenomenon observed in the magnetostriction measurements of high-strength steels under uniaxial compressive stress.The comparisons presented show that the model is able to simulate the Villari reversal observed in the measurements.Future work entails investigating the hysteretic properties of the model as well as exploring the inverse magnetostriction phenomenon.

Fig. 1 .
Fig. 1.Villari reversal in magnetostriction measurements of high strength steel under different compressive stress values.

Fig. 3 .
Fig. 3.The magnetoelastic coefficient (") as a function of increasing magnetic field (H)Figure4shows the magnetostriction measurements as a function of the increasing magnetic field for different compressive stresses in the region of minimum

Figures 5 -
Figures 5-8 show comparisons between the measurements and the model results for three compressive stress magnitudes.The model shows qualitatively good results.