Effect of mechanical stress on magnetization and magnetostriction strain behavior of non-oriented Si-Fe steels at different directions and under pseudo-DC conditions

Abstract

Soft ferromagnetic materials constitute the main components of magnetic circuits in electromechanical devices. However, their magnetic and magnetostrictive properties are strongly affected by mechanical loading. This can lead to a decrease in the performance and the efficiency of these devices and to a potential increase of the emitted noise. Aware of the importance of these factors, this paper proposes to study the effect of the mechanical stress on the magnetic and magneto-elastic properties of non-oriented electrical steel sheets. The stress dependency of permeability and Villari effect has been studied. Measurements of the magnetostrictive strain under applied stress are presented and the anisotropic behavior under stress is described. Moreover, the ΔE effect has been observed and analyzed. The novelty of this work is the extension of the measurements to many directions of cut with respect to the rolling direction under tensile and compressive stress, as well as the demonstration of the magnetic and magnetostrictive anisotropy under uniaxial stress.

Keywords

Magnetostriction magnetization mechanical stress magneto-elastic effect non-oriented electrical steel magnetic material anisotropy

1. Introduction

In the more-electric race, the development of electric systems is arousing great interests among the industrial and the scientific community worldwide. To succeed in this transition, a good mastery of electrical system technologies is required. Several factors enter into consideration in the design of these devices that can be divided into two categories: factors related to the structure and others related to the magnetic materials used. The second point is the subject of this article. Magnetic materials are at the center of interest because of their good magnetic and mechanical properties for fabrication of electrical devices such as power transformers and electrical motors, or for sensing and transducing applications. Nevertheless, their performances are strongly influenced by mechanical stress. The latter coupled with the magnetic behavior of the material, leads to a magneto-elastic coupling, which can be complicated to control. This phenomenon has two manifestations: the deformation caused by magnetostriction and the effect of stress on the magnetic behavior of the material. Among the existing magnetic materials, non-oriented (NO) Si-Fe steels constitute a good candidate for studying the magneto-elastic effects since they are widely used in rotating machine and embedded power transformer.

The study of the magnetostriction and the magnetic behavior of non-oriented electrical steel sheets has been the focus of several researches [1–5]. However, as mentioned previously, their magnetic and magnetostrictive characteristics are modified by the mechanical stress [6–10]. For applications such as rotating machines and transformers that use ferromagnetic materials, these factors need to be studied to better understand and control their behaviors because they can be an important source of noise and vibration [11–14]. In terms of experimental measurements of magnetostrictive strain under stress for non-oriented electrical steel, most of the studies are made in a specific direction, usually the rolling direction (RD) [9,15,16]. The author in [17] pushes it further to the transverse direction (TD).

Despite these efforts in this field, very few measurements of magnetostriction and magnetization of NO 3% Si-Fe under compressive and tensile stress are available for different directions of cut. Knowing the anisotropic behavior of NO steel sheets [1,18–20]; results found in the present work can be very useful for parameter identification when modeling the magnetostrictive and magnetic behavior of these materials, especially under rotating fields. Furthermore, most modeling strategies use a single direction of cut (RD in this case) to predict the magnetic behavior in the other directions of cut. These results can be considered as experimental references that will provide answers on the robustness of these models.

The paper is organized so that, Section 2 describes the experimental procedure and the setup used to measure the magnetostriction and magnetic properties under stress. Measurements results detailed in Section 3 provide observations and discussions on the magnetic behavior (Subsection 3.1) and the magnetostrictive deformation under stress (Subsection 3.2) as well as the ΔE effect (Subsection 3.2) for different directions of cut. Finally, a conclusion summarizes the important findings.

2. Experimental procedure setup description

The material under study is a non-oriented grain Si-Fe; further details on its magnetic characteristics are summarized in Table 1. Rectangular samples were cut in different directions with respect to the rolling direction (RD) with a water jet cutting machine and were tested in a single yoke tester under several magnitude of applied uniaxial stresses as illustrated in Fig. 1. The dimensions of the samples have been fixed in accordance with the standard IEC 60404-3 [21] adapted to our magnetizing yoke as illustrated in Fig. 2. In other words, the samples are 150 mm long, 30 mm wide and 0.35 mm thick. The longitudinal components of three quantities were measured locally in the middle of the samples: the magnetic field strength H, the flux density B and the magnetostriction strain 𝜆. They were measured respectively using an H-coil, B-coil, and strain gauges of 350 Ω (±2.5%) fitted in a quarter Wheatstone bridge. The geometric characteristics of these elements can be found in Table 2. Given the small thickness of the sample (0.35 mm), the magnetic field is expected to become homogenous at small distance of the yoke, hence, uniform conditions are considered in the middle of the sample. Besides, leaving the sample free to move generates a variation of the air gaps that can cause magnetic forces of Maxwell stress type to appear. Thus, a suitable tightening is put in place to avoid air gaps and therefore minimize the effect of these magnetic forces. As shown by authors in [22], controlling the contact between the yoke and the sample optimizes considerably the measurements results obtained by single-yoke system. All the elements of the setup and the samples were placed between a manual clamps to apply compressive and tensile stresses (Fig. 2). An excitation coil with 140 turns supplied with a programmable voltage source magnetizes the sample with different flux density amplitudes. A further description on the voltage control is reported in [23]. Knowing that the operating point of electrical machines is usually found around the bend of the B(H) characteristic, the samples were tested with a sinusoidal flux density of 1.4 T (the maximum achieved with waveform control). Also, in order to characterize the model and to get closer to the anhysteretic curves, the measurements are carried out under quasi-static regime (f = 6 Hz). Compared to real life AC operation (f = 50 Hz or 400 Hz), the total losses will increase whereas the magnetostriction is likely to decrease [17]. The applied stress is varying from −15 MPa (compression) to 50 MPa (tension). For each sample cut in a certain direction, the magnetization is applied along the direction of the applied stress, Fig. 1.

Table 1
Magnetic properties of NO 3% Si-Fe

Material grade M235-35A

Specific total loss at 50 Hz (W/kg) 2.25

Magnetic polarization at 50 Hz for H = 2500 A/m (T) 1.53

Anisotropy of loss (%) 10

Coercivity (DC) (A/m) 35

Relative permeability At 1.5 T 610

Anisotropy constant K1 (kJ/m3) 35

Magnetostriction constants: 𝜆₁₀₀ and 𝜆₁₁₁ (μm/m) 23 and 5

Material grade	M235-35A
Specific total loss at 50 Hz (W/kg)	2.25
Magnetic polarization at 50 Hz for H = 2500 A/m (T)	1.53
Anisotropy of loss (%)	10
Coercivity (DC) (A/m)	35
Relative permeability At 1.5 T	610
Anisotropy constant K1 (kJ/m3)	35
Magnetostriction constants: 𝜆₁₀₀ and 𝜆₁₁₁ (μm/m)	23 and 5

Fig. 1.

Applied stress and magnetic field direction for samples cut at θ = (0°,10° … 90°) with respect to the rolling direction.

Table 2

H-coil, B-coil and strain gauge characteristics

	H-coil	B-coil	Strain gauge
Length × width (mm)	26 × 12	38 × 33	2 × 3
Number of turns	100	130	-

Fig. 2.

Experimental setup of magnetostriction and magnetic measurements under applied stress.

To avoid buckling during the measurements at compression, a retention plates were placed on the surface of the sample on both sides (Fig. 2). Besides, to minimize the damping effect on magnetostrictive deformation, the retention plates were lubricated.

Figure 3 shows the mechanism used for applying the uniaxial stress in the plane of the SST samples. It offers the possibility to exert both tensile and compressive stress up to ±50 MPa for a 30 × 0.35 mm cross-sectioned SST samples. To apply the required force, a manual locking screw system is used. For a fine control of the stress level, a compression spring is considered. Thus, a stress resolution of 0.1 MPa can be achieved. Furthermore, clamps with a grinded surface are used to ensure proper gripping of the SST samples. Guide rails passing through the lower part of the clamps and fixed to the rigid back wall, ensure the in-plane application of the force. Finally, all the components of the stressing mechanism are made of non-magnetic stainless steel to avoid any leakage path.

Fig. 3.

Description of the stressing device [23].

3. Results and discussion

To present the results of magnetization under stress, we have considered the median curve between the branches of the hysteresis cycle (averaged over several periods) as the anhysteretic curve. After removing the strain corresponding to the elastic deformation, the magnetostriction curves have been extracted following the same process, by calculating the median curve of the butterfly loops. This procedure of calculating the median curve can be used for low-frequency (quasi-static) measurements as it is the case in this experiment [24].

3.1. Effect of stress on magnetic properties: Permeability

3.1.1. Samples cut at 0°, 90° and 50° with respect to the rolling direction

Magnetic measurements were carried out under various mechanical loading from −15 MPa (compression) to 50 MPa (tension), with a sinusoidal flux density of 1.4 T and a frequency of 6 Hz. Only certain directions are chosen to illustrate the magnetic behavior of the material under stress. Figure 4 shows the B (H) curves of the samples under tensile and compressive stresses at 0°, 50° and 90° with respect to the rolling direction. As general trends, the magnetization curves reveal that a tensile stress improves the permeability and compressive stress decreases it. Previous works have observed the same behavior but just for the rolling direction [3,9,25,26]. However, the measurements carried out hereafter shows a different behavior for the other directions particularly under tensile stress (Figs 4 and 5). In fact, the sample is more sensitive to the effect of tensile stress as the direction passes from 0° to 90° direction. For 0° direction, the curves at 0 MPa and 10 MPa are superimposed, which proves that the permeability is improved in this interval; beyond 10 MPa the permeability decreases. For 50° direction, a slight amelioration is noticed at 10 MPa. Whereas for 90° direction the permeability improves up to 30 MPa (tensile stress). By contrast, whatever the level of compressive stress and the direction of cut, the permeability decreases even at low strength (-5 MPa). In addition, as it can be seen from Fig. 4, some curves cross each other at particular field magnitudes, this crossing correspond to Villari effect [27,28]. This effect can be analyzed by considering the equilibrium law based on Maxwell relations and defined by Eq. (1): $\begin{eqnarray}\displaystyle \left(\displaystyle \frac{\partial {\lambda}}{\partial H}\right)_{{\sigma}}=\left(\displaystyle \frac{\partial B}{\partial {\sigma}}\right)_{H}. & & \displaystyle\end{eqnarray}$ (1)

Where B is the flux density, 𝜆 the magnetostrictive strain, σ corresponds to the applied stress and H to the magnetic field. The subscripts σ and H mean that the derivative is made at constant values of these quantities. That is to say, that when mechanical stress is applied at particular field strength, there is an increase or a decrease in the magnetic flux density in the sample. In the case of Si-Fe samples, saturation magnetostriction 𝜆_s is positive, hence, if we assume medium tensile stress, when the product 𝜆_sσ is positive (tensile stress), the flux density B increases. At compressive stress, 𝜆_sσ is negative and the flux density B decreases. In this respect, the same behaviors are noticed in the measurements results.

Fig. 4.

Influence of uniaxial stress on B (H) curves of NO Fe-3% Si, when magnetized at 1.4 T, 6 Hz (RD, 50° and 90°).

Fig. 5.

Stress sensitivity of permeability in NO Fe-3%Si samples, when magnetized at 1 T, 6 Hz (RD, 10°, 30°, 50°, 70° and 90°).

It is known that a tensile stress favors magnetization along easy axis that is close to the stress direction. Besides, at unstressed state, the magnetic material exhibits non-monotonic magnetic anisotropy as observed in [1,5]. Regarding the rolling and transverse direction; the magnetization is higher in the rolling direction because of the fabrication process. Also, assuming that the domains are more developed along the rolling direction, explains the small improvement in the magnetization at small tensile stress. Whereas in the transverse direction the easy axis is perpendicular to the magnetization direction. Thus, when applying a tensile stress, it improves the magnetization since less energy is needed to orientate the magnetic domains.

All in all, a close connection between stress and magnetization at some directions of cut is pointed out, referred commonly to magneto-elastic effect. Similarly, the discussion will be extended to other directions of cut.

3.1.2. Overview in many directions

In this part, we extend the discussion to other directions to give a global analysis on the influence of the stress on the permeability. Figure 5 shows the relative permeability curves for NO samples cut in different directions with respect to the rolling one, under uniaxial stress, at 1T peak flux density level and a magnetizing frequency f = 6 Hz. In addition to the explanation given before for 0°, 50° and 90° directions, for other directions, taking the unstressed state as reference (σ = 0 MPa), relative permeability decreases rapidly with compressive stress as well. On one hand, it is observed that for each cutting direction, the relative permeability does not evolve in a monotonous manner with the applied stress. On the other hand, going from an easy magnetization direction (RD) to the transverse direction (TD), the relative permeability curves have a non-monotonic behavior over the whole stress range (curves crossing). In fact, for 0° and 10° direction with respect to the RD, permeability decreases between σ = 0 MPa and σ = 10 MPa , while for 30°, 50° and 70° it increases slightly before decreasing again. But for 90° direction, the permeability increases from σ = 0 MPa to σ = 20 MPa and starts decreasing after. At compressive stress the movement of domains wall is prevented, which makes it more difficult to magnetize the samples (compressive stress). Whereas at tensile stress the magnetization is easier.

Fig. 6.

Influence of uniaxial stress on magnetostrictive strain of NO Fe-3%Si, when magnetized at 1.4 T, 6 Hz (RD, 50° and 90°).

To determine the effect of stress on magnetic behavior, we assume an isotropic magnetostriction (for simplicity). Hence, in the case of uniaxial stress σ acting upon a single magnetic domain, the magnetic strain energy density E _σ can be written as follow [29]: $\begin{eqnarray}\displaystyle E_{{\sigma}}=-\displaystyle \frac{3}{2}{\lambda}_{s}{\sigma}\cos ^{2}({\theta}). & & \displaystyle\end{eqnarray}$ (2) Where 𝜆_s is the magnetostriction at saturation and θ is the angle between the saturation magnetization and the stress direction. For instance, for iron 𝜆_s is positive, which leads to a minimum energy for θ = 0 when tensile stress (σ > 0) is aligned with the saturation magnetization. Although the domain structure is complicate to describe, if we consider a small portion of the sample containing four domains, the stress-induced domain reorientation in a single crystal can be represented schematically by Fig. 7, [31]. This configuration assumes that only mechanism of magnetization variation is domain wall motion. Thus, two kinds of domain wall exist: 180° domain wall and 90° domain wall. Consequently, the volume of domains magnetized parallel to tensile stress axis increases making the magnetization improved by tension. But, when σ is negative, the process is reversed and the magnetization decreases.

Fig. 7.

Schematic representation: the stress-induced domain reorientation, 90°/180° domain wall and magnetization direction.

3.2. Effect of stress on magnetostrictive deformation

3.2.1. Samples cut at 0°, 50° and 90° with respect to the rolling direction

In the previous section, the influence of stress on magnetic behavior has been discussed. As one would expect, the stress has also an important influence on the magnetostriction strain. Figure 6 shows 2D curves of the longitudinal magnetostrictive strain as a function of the flux density B and under various stress level σ for 0°, 50° and 90° directions. Looking at the measurements, it can be seen that compressive stress increases magnetostriction strain while tensile stress tends to decrease it and even turn it negative for high tensile stress. We also observe that a tensile stress tends to saturate magnetostriction deformation rapidly. These observations were confirmed as well by authors in [26,30] for the rolling direction. However, a close look at Fig. 6 shows that the shape of the measured deformation under stress is different from a direction to another. Considering the magnetic domain structure under stress of each direction, we can assume the following: tensile stress has a small effect on magnetostriction variation because some anisotropy does exist in non-oriented steel sheets (depending on direction with respect to the rolling direction) and an infinitesimal stress or magnetic field should be sufficient to reach rapidly saturation. As a result, domains with 180° domain walls grow and the closure domains (90°) decrease (Fig. 7). To this end, the 180° domains walls remain unaffected while 90° domain walls move. But for compressive stress, the structure (iron based) is strongly affected because we favor 90° domains walls that are stress sensitive as illustrated in Fig. 7. This explains the high magnetostriction deformation for all direction when a compressive stress is exerted.

Fig. 8.

Variation of magnetostriction with angle of cut in NO Fe-3%Si for applied compressive and tensile stresses σ = [−15, −10, −5, 0, 10, 30, 50] MPa, when magnetized at 1.4 T, 6 Hz.

3.2.2. Maximum magnetostriction for samples cut at 10 directions with respect to the rolling direction θ = (0°, 10° … 90°)

A detailed description of the magnetostriction curves under stress along RD, TD and at 50° direction has been introduced and analyzed. In the following, we will be interested in the influence of stress on magnetostrictive strain in other directions with respect to RD. The variation of maximum magnetostriction with angle with respect to RD θ = (0°,10°…90°) is shown in Fig. 8. For each stress value, the sample was magnetized to a maximum flux density of 1.4 T and a frequency of 6 Hz.

It is worth mentioning that magnetostriction measurements are highly sensitive to the different disturbances that may impact the measurement results because of the small deformations involved. Due to the dispersions observed during the magnetostriction measurement, it was possible to identify some of these sources of disturbance: dispersion due to the sheets or sticking of the gauges and the measurement uncertainty. The measurement results show a difference in maximum magnetostriction of $0.27 \times 10^{-6}$ for two samples cut on the same direction (TD) and with strain gauges belonging to the same series, and a difference in maximum magnetostriction of 10⁻⁶ for the same sample but with two strain gauges from two different series. Based on these results, the same series of gauges was used to measure magnetostriction in different directions. For the measurement uncertainty, a maximum error of 5% corresponding to the sample cut according to RD was estimated. A good assessment of uncertainties would require more measurements.

The results confirm the previous findings for all direction: A compressive stress increases the magnetostriction strain, while tensile stress decreases it and makes it even negative for high value of tensile stress. Nevertheless, the appearance of negative magnetostriction is not the same and depends on the angle of cut. Furthermore, the magnitude of magnetostriction has a non-monotonous variation between RD (0°) and TD (90°) due to crystallographic anisotropy. The fact that some variations (measurements uncertainty, sample to sample variations…) may interfere with the measurements is not totally excluded, however, this variation cannot be attributed mainly to the sheet dispersion or the uncertainties because this behavior was also observed in previous work at free stress conditions (σ = 0 MPa) in [1,5]. In comparison, we notice that this remain valid under uniaxial stress conditions. Besides, we can clearly see from Fig. 8 that the non-monotonous behavior is still present for small stresses (between σ = 20 MPa and σ = −10 MPa) and starts to become less striking for high tensile stresses. This proves that the relative effect of crystallographic texture is strongly decreased at high stress amplitudes for all the directions with respect to the rolling direction. Thus, at σ = 50 MPa we start achieving the saturation state of magnetostriction deformation and all directions have small variation of magnetostriction strain between them at the peak value of flux density. At this stage, the majority of the transverse closure domains (90° domains) are extremely reduced (Fig. 7). For compressive stress, the highest magnitude of magnetostriction was found for the transverse direction and the lowest was for sample cut at 20° with respect to the rolling direction. Furthermore, at 10 MPa, magnetostriction at 90° direction is three times larger than magnetostriction at 20° direction.

As can be seen in Fig. 7, the growth of the domains either parallel to the tensile stress or perpendicular to the compressive stress induces the additional magnetostriction to the elastic strain. In general, when a sample is magnetized, magnetostriction occurs as a result of the movement of the 90° wall. When a sample is magnetized parallel to the stress direction (as in the present experiment) the maximum magnetostriction decreases with tensile stress and increases with compressive stress. Consequently, as shown in Fig. 8, the effect of compressive stress is more pronounced for sample cut in RD (0°) as we create more 90° domain walls [4]. However, for all 10 angles, saturation of magnetostrictive strain is reached rapidly when a tensile stress is applied. This phenomenon is expected as the studied material is a non-oriented one.

Fig. 9.

ΔE effect on stress-strain curve.

3.3. ΔE effect

Another consequence of stress is the dependence of Young modulus E on the magnetization state of the magnetic materials. Thereby, when a demagnetized ferromagnetic material is submitted to a tensile test, we observe a non-linear variation in the curve σ (ϵ) due to magnetostriction strain (Fig. 9). The total measured strain is a superposition of an elastic deformation ϵ^e and a magnetostrictive deformation ϵ^𝜇: $\begin{eqnarray}\displaystyle {\varepsilon}(M,{\sigma})={\varepsilon}^{e}({\sigma})+{\varepsilon}^{{\mu}}(M,{\sigma}). & & \displaystyle\end{eqnarray}$ (3)

Thus, magnetostriction leads to an apparent loss of linearity in the elastic behavior of demagnetized magnetic samples [29], so-called ΔE effect [31]. It represents the evolution of magnetostriction deformation at zero magnetization.

Fig. 10.

Schematic extraction procedure of $ϵ^\mu(0, σ)$ (ΔE effect).

Fig. 11.

ΔE effect: influence of stress on longitudinal magnetostriction at different directions with respect to RD.

The measurements of ΔE effect are obtained from magnetostrictive measurements under stress (Fig. 6). The procedure is based on an assumption of magnetic saturation of magnetostriction: Whatever the uniaxial stress level, magnetostriction at saturation is the same (same domain configuration at saturation). First, a stress value is applied resulting in an elastic strain ϵ^e(σ) and a magnetostrictive strain ϵ^𝜇(M = 0, σ) according to Eq. (4): $\begin{eqnarray}\displaystyle {\varepsilon}^{\prime }(M=0,{\sigma})={\varepsilon}^{e}(M=0,{\sigma})+{\varepsilon}^{{\mu}}(M=0,{\sigma}). & & \displaystyle\end{eqnarray}$ (4)

However, after demagnetization, the magnetostrictive strain ϵ^𝜇(M = 0, σ) is very difficult to measure as it is much lower than the elastic one. Hence, the deformation ϵ^′ is put to zero (initialization). Next, we proceed to magnetostriction measurements under quasi-static conditions corresponding to a variation of deformation due to magnetization at constant stress ϵ^′′, Eq. (5). Because the elastic strain is the same (ϵ^e(M, σ) = ϵ^e(M = 0, σ)), the measurements agree now to the following equation: $\begin{eqnarray}\displaystyle {\varepsilon}^{\prime \prime }(M,{\sigma}) & = & \displaystyle {\varepsilon}(M,{\sigma})-{\varepsilon}^{\prime }(M=0,{\sigma})\nonumber\\ \displaystyle & = & \displaystyle {\varepsilon}^{{\mu}}(M,{\sigma})-{\varepsilon}^{{\mu}}(M=0,{\sigma}).\end{eqnarray}$ (5)

From Eq. (5), we can deduce that $\varepsilon''(M=0,\sigma)$ is always zero whatever the stress level. If we assume that magnetization saturation M _s is reached at high field, then the domain configuration and hence the magnetostriction strain is the same regardless of the stress level. Which mean that ϵ^′′(M _s,0) = ϵ^𝜇(M _s,0). Consequently, ϵ^𝜇(M _s,0) is considered the reference curves that all strains ϵ^′′(M, σ) must reach (magnetic saturation of magnetostriction). By proceeding to a shift between ϵ^′′(M _s,0) and ϵ^′′(M, σ) as illustrated in Fig. 10 we obtain the magnetostriction at zero magnetic field corresponding to a point of ΔE effect curve.

Figure 11 shows the ΔE effect of samples cut in different directions with respect to the rolling direction and under applied stress varying from −10 MPa to 50 MPa. We observe a positive magnetostriction deformation for tensile stress and negative for compressive stress. For tensile stress, magnetostriction deformation tends to saturate and maintain the same amplitude at around σ = 30 MPa. For compressive stress, it seems that the saturation state have not been reached yet at σ = −10 MPa (buckling beyond σ = −15 MPa). However, we expect a saturation state beyond −10 MPa as illustrated in [3,32] for the rolling direction. At compression, a higher magnitude of ΔE effect than tension is to be observed at saturation for all directions, because at σ = −10 MPa we have already exceeded magnitude at saturation state of tension (50 MPa).

The magnitude of ΔE effect at saturation state is not the same for all directions. The lowest value is obtained for 20° and 30° samples and the highest for 90° sample. As explained before, this non-monotonous behavior can be related to domain reorientation under stress.

4. Conclusion

Stress dependence of magnetic properties and of magnetostriction were studied for non-oriented 3% Si-Fe samples cut in different directions with respect to RD (0°, 10° … 90°). The main findings can be summarized as follow:

–

A tensile stress increases magnetization and compressive stress decreases it for all directions with respect to RD. The increase of magnetization under tensile stress depends on the angle between magnetization and the rolling direction. Besides, non-monotonic behavior was observed and confirms that this magnetization variation depends on the direction of magnetization with respect to the RD.

–

Longitudinal magnetostriction increases when compressive stress is applied, while it decreases with tensile stress for all direction of cut. This behavior is related to the domain reorientation under mechanical stress. Also, anisotropic dependence under stress was observed as in the unstressed state. However, the anisotropy tends to disappear at high values of tensile stress.

–

ΔE effect has been identified for tensile and compressive stress for different directions. This effect is greater under compressive than tensile stress. In addition, anisotropic behavior with respect to the direction has been highlighted.

In future work, these experimental results will be used for identification of the model parameters for magnetostriction prediction under stressed conditions. Another interesting approach will be to compare these results obtained for samples cut in different directions with sample under rotational field.

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