Magnetization Changes Induced by Stress Noncoaxial with the Magnetic Field in a Low-Carbon Steel

Abstract

Ferromagnetic materials are widely used in the manufacturing of key parts of energy equipment, due to their good mechanical properties, such as in nuclear power and pipes. Mechanical stress exists inside of these key parts during operation. Stress can be estimated indirectly by nondestructive testing methods that measure the magnetic flux leakage signals on the surface of the structure, which is of great importance for ensuring the safety of the equipment. However, the physical mechanism of the stress and magnetic field in the magnetization of ferromagnetic materials is still unclear, leading to limited applications of the technique in practice. In this paper, magnetization tests were carried out to investigate magnetization changes under the coupling effect of stress and a noncoaxial magnetic field. Two identical Q195 low-carbon steel specimens were tested. Specimen 1 was subjected to magnetic field values successively increasing from 0 A/m to 6000 A/m under constant uniaxial tension at different angles θ between the field and stress axis. Specimen 2 was subjected to the same magnetic field under different levels of stress at an angle of 0°. The surface magnetic induction B of the specimens was measured and analyzed at each angle of stress–field orientation and at different levels of stress. It was found that there was a difference in the direction between the B and the magnetic field H at different angles θ. The magnetization curves correlated to the angle θ and the stress levels. The behavior of the derived maximum differential permeability and maximum magnetic induction could be used for the nondestructive evaluation of stress magnitude and direction in materials already in service.

1. Introduction

The magneto-mechanical effect, which is the change in magnetic properties of a magnetic material resulting from applying a changing stress under a constant applied field, is an old problem that has never been adequately explained because of its scientific complexity. Nevertheless, it has attracted significant attention because of its application value in the field of nondestructive stress evaluation. As is well known, there is a close correlation between the leakage magnetic field signals and the stress or defects of ferromagnetic materials [1]. Stress detection is crucial for evaluating the lifetime of metal components and the safety of energy equipment [2,3]. However, the physical mechanism of stress and an external magnetic field in the magnetization of ferromagnetic materials remains unclear, leading to limited applications of the technique in practice.

Widespread efforts have been made to study the magnetization changes induced by stress and magnetic fields. A theory of the magnetization process in ferromagnets, based on domain rotation and domain wall motion, was presented by Jiles and Atherton [4]. The authors proposed a model considering the effect of the angle between the magnetic field and the stress on the effective field H. Nevertheless, there was no specific discussion of the change in magnetic properties caused by the angle. Sablik [5] advanced a model as a function of stress for various angular orientations between the field and stress axis and analyzed the effects of noncoaxial stress and magnetic field on the magnetization properties of ferromagnetic materials. However, there was a lack of systematic experimental results to compare with the proposed model. Kaminski [6,7] investigated the angular dependence of the change in magnetic properties under various stress levels, but the issue was not studied in depth, and the change in magnetic properties was not studied with the magnetic field changed under a constant stress. Atherton [8] observed the magnetization changes induced by a stress applied coaxially with a constant field for pipeline steel and found that the irreversible and reversible magnetization components varied symmetrically and asymmetrically with the applied stress, respectively. However, stress noncoaxial with the magnetic field was not considered. Pengju Guo [9,10] studied the effect of tensile stress on the variation of the normal component of surface magnetic field signals of Q345R steel after tensile testing and unloading under a geomagnetic field. They found that the initial magnetic signals greatly affected the normal component of the surface magnetic field signal variation, especially in the elastic deformation stage.

In conclusion, much attention has been paid to the magnetization changes induced by stress under a co-applied magnetic field [11,12,13,14,15,16,17,18,19]. However, attention has mostly been given to mathematical models of an uniaxial stress applied noncoaxially with the field [20,21,22,23]. Few experiments have been conducted for the case where a magnetic field H is not aligned with the stress axis [24,25,26,27,28,29,30]. Clearly, many of a magnetic material’s magnetic properties depend on the angle between the field and stress axis. Therefore, it is necessary to take measurements for the case in which H is in the general direction with respect to the stress axis.

In this article, we performed an investigation of the magnetization changes induced by stress noncoaxial with external magnetic field, which has not been systematically researched in previous works. Specifically, two specimens were tested. First, tests for specimen 1 included the variation of the induced magnetization with a noncoaxial magnetic field at a constant applied stress. Second, tests for specimen 2 included variation of the induced magnetization with different stress levels when the angle between the stress and magnetic field was 0°. Finally, possible reasons for the different characteristics of the magnetization variation were considered.

2. Materials and Methods

Two identical specimens, made of Q195 low-carbon steel, were tested. Neither of the specimens were demagnetized in the initial state. Q195 is widely used as a structural steel in China. The chemical composition and mechanical properties of the steel are listed in

Table 1. Chemical composition (wt.%) and mechanical properties of Q195 steel.

Material	C	Mn	Si	S	P
Q195	0.06–0.12	0.25–0.50	≤0.30	≤0.05	≤0.045

and

Table 2. Mechanical properties of Q195 steel.

Material	Elastic Modulus, E (GPa)	Yield Strength, σs (MPa)	Ultimate Tensile Strength, σb (MPa)
Q195	0.06–0.12	195	315–430

. Figure 1 presents the initial magnetization curve of Q195 steel using a soft magnetic material DC measurement device FE-2100SD.

The specimens were cut from a 3 mm plate of ferromagnetic Q195 low-carbon steel and annealed to reduce the residual stress by heating them at 650 °C for 2 h and then allowing them to cool naturally in the furnace. The dimensions of the specimens are shown in Figure 2. The surface magnetic signals were detected using an array probe in the middle of the specimen, occupying an area of 30 mm × 30 mm. The X-axis is along the long axis of the specimen, and the Y-axis is perpendicular to the X-axis.

Figure 3 shows a block diagram of the measurement system. A DC external magnetic field and stress were applied to the specimen. The external magnetic field was provided by a U-shaped electromagnet (the core was formed by U-shaped Mumental laminations with magnetizing coils wound on the two poles; the number of turns of each coil was 500), the direction of the applied magnetic field could be changed by rotating the poles of the electromagnet in different directions to provide noncoaxial magnetic fields. The value of the external magnetic field was controlled by the current of the DC power supply. A material testing machine MTS with a peak capacity of 100 kN was used to load uniaxial tension. The change in the magnetization caused by the stress and magnetic field was detected using a magnetic array probe. The key parts of the array probe were 25 magnetic probes based on TMR2505 sensors (working voltage VDD = 5 V; magnetic field measurement ranges from plus to minus 200 Oe; sensitivity Sen = 2.2 mv/V/Gs within the range of ±30 Oe; 1 Oe = 1 Gs in air = 0.1 mT = 79.8 A/m). The data were collected using a 16-bit resolution multi-channel magnetic field measurement system HB-1000 and processed by MATLAB software.

The detailed process of the experiment for specimen 1 was as follows:

(1)

The specimen was loaded to a predetermined stress level of 80 MPa and held. A tensile force was applied parallel to the longitudinal axis of the specimen using the material testing machine MTS.

(2)

Magnetic field values, controlled by the current supplied to the coils of the U-shaped electromagnet from the DC power supply, successively increasing from 0 A/m to a maximum of 6000 A/m were applied to the specimen. Notably, the air gap between the poles of the core and the sample should be as small as possible, to reduce the variation in reluctance.

(3)

During the magnetization process, the magnetic field and the normal component of surface magnetization of the plate specimen was measured online, by means of an array probe arranged on other side of the specimen and rotated around the poles of the U-shaped electro-magnet, as shown in Figure 4. The experimental setup is shown in Figure 5. Although the measured magnetization was not from inside of the specimen, it was proportional to the real magnetization value and could reflect the change of the real magnetization of the specimen [25].

(4)

The specimen was demagnetized after the surface magnetization measurement was conducted and removed from the testing machine. Then, the specimen was reinstalled onto the testing machine, and the poles of the electromagnet were rotated 22.5°. The testing procedure was repeated. As shown in Figure 6, the angles between the poles of the electromagnet and the stress axis θ were 0°, 22.5°, 45°, 67.5°, and 90°.

For the magnetization of specimen 2, a measurement was only conducted at θ = 0°, but the preset maximum stress was varied. At this angle, measurements were taken under applied stresses of 0, 30, 60, 90, and 120 MPa, which are below the elastic limit. The operation at each stress level was the same as that in specimen 1 under a constant angle between the magnetic field and stress.

Finally, the effects of the magnetic field at different angles on the magnetization of specimen 1 under a constant stress, and the effects of the magnetic field at the same angle on the magnetization of specimen 2 under different stress levels, were analyzed. The mechanisms underlying the experimental characteristics were also considered.

3. Results

X-ray diffraction (XRD) was used to investigate the phase structures and purity of the prepared specimens. Figure 7 shows the XRD pattern of the prepared Q195 steel sheets. The XRD pattern confirmed the existence of α-Fe and C phases. Diffraction peaks can be observed at 44.58° and 64.88°, corresponding to the (110) and (200) planes of the α-Fe phase (PDF# 006-4192), with the diffraction peak at 26.75° corresponding to the (002) plane of the C phase (PDF# 014-0337). No other detectable peaks were observed in the, which indicates a low content of Mn, Si, S, and P in the specimen.

Figure 8 shows the distribution of surface magnetic induction B when the electromagnet poles were placed at θ = 0°, 22.5°, 45°, 67.5°, and 90° to the direction of stress for specimen 1 magnetized with a magnetic field of 3000 A/m. Data from the probes in the middle area of 20 mm × 20 mm were extracted because the field strength in this region is more uniform. Please note that the positive direction of the Y-axis is the direction of the external magnetic field H. The direction perpendicular to the zero contour is the direction of the surface magnetic induction B. Clearly, there was a difference in the directions between B and the magnetic field H at different angles. The direction of B was rotated with the increase in θ. Moreover, the amplitude of B reached a maximum of 0.6 mT at 45 °.

Figure 9 shows the magnetization curves for specimen 1 at different angles θ under a stress of 80 MPa. These results were taken from the point of probe 8 (numbered in Figure 1). One can see that the magnitude of magnetic induction B varied with the magnetic field at different angles. The behavior at small angles showed an increase in the magnetic induction B with the increase in magnetic field H. It is also apparent from Figure 8 that the magnetic induction B reached a peak value of 2.62 mT at 45°. Further increase of the angle from 67.5° to 90° resulted in a decrease in the value of magnetic induction B. It is interesting to note that the magnetic induction B first increased and then decreased to a small negative B at 90°. It can also be noted that with the increasing magnetic field H, the changes in magnetic induction B become greater at the different magnetization angles.

Figure 10 and Figure 11 show the effect of angle on the maximum differential permeability ${\mu }^{\prime }{}_{\max }$ and the maximum magnetic induction $B_{\max }$ for specimen 1. The behavior at small angles showed an increase in ${\mu }^{\prime }{}_{\max }$ and $B_{\max }$, reaching a peak value at 45°, and then decreasing at higher angles. In addition, the values of ${\mu }^{\prime }{}_{\max }$ and $B_{\max }$ were smallest at 90°.

Figure 12 shows the magnetization curves for specimen 2 under different levels of stress at an angle between stress and magnetic field of 0°. Its behavior showed an increase in the slope of the magnetization curve with the increase in magnetic field H under stress, from 0 MPa to 60 MPa, and then a decrease at higher tensions. Thus, the derived magnetic induction B indicated a peak value of 3.74 mT at 60 MPa.

Figure 13 and Figure 14 show the effect of stress on the maximum differential permeability and the maximum magnetic induction for specimen 2, respectively. The behavior at low tensions showed an increase in ${\mu }^{\prime }{}_{\max }$ and $B_{\max }$, reaching a peak value at 60 MPa, and then decreasing at higher tensions. Interestingly, a similar phenomenon occurred with other angles of θ.

To evaluate the accuracy of the measurements, Figure 15 shows the error bars of magnetization measurements for specimens at different angles and at different levels of stress, respectively. The error bars represent the standard deviation of the measured data of three specimens under the same experimental conditions. One can see that the measurement data were less discrete and the error was not large. The maximum standard deviation of the measured data was 0.1 mT. The reasons for this measurement error were related to the offset voltage of the probe, structure of specimens, and measuring environment.

4. Discussion

First, as shown in the experiment results in Figure 8, the resulting magnetic induction B was not parallel to the magnetic field H at different angles, it rotated slightly with the increase in θ. This phenomenon could be attributed to the stress making the steel anisotropic. It is well known that, for isotropic steel, B is parallel to H. Magnetic anisotropy in the sample would cause a shift in the direction of the surface magnetization. According to Jiles’ model [26], the effects of uniaxial stress on magnetization can be described in terms of an effective field due to the stress, that is

$$\mathrm{H}\left(\mathsf{\theta }\right)=\frac{3}{2}\frac{\mathsf{\sigma }}{{\mathsf{\mu }}_0}\left(\frac{\partial \mathsf{\lambda }}{\partial \mathrm{M}}\right)\left({\cos }^2{\mathsf{\theta } - \mathsf{\nu }\sin }^2\mathsf{\theta }\right)$$

(1)

where $\mathsf{\theta }$ is the angle between the axis of the applied stress $\mathsf{\sigma }$ and the axis of the magnetic field H. This means that the magnetization of an isotropic ferromagnetic material will change as a function of the angle between the stress and magnetic field as a direct result of the angular dependence of the stress equivalent field. Therefore, the stress introduces an anisotropy field, whose macroscopic angular dependence is given by Equation (1). The surface magnetic induction B at field H and stress $\mathsf{\sigma }$ is identical to the surface magnetic induction at field H + H($\mathsf{\theta }$) and zero stress. Therefore, for different values of $\mathsf{\theta }$, B and H are not in the same direction. The amplitude of B reaches a maximum at 45°, which is attributed to the Villari reversal.

Second, there was an obvious relationship between the magnetization curve and the angle, as shown in Figure 9. The possible reasons for such a phenomenon may be explained as follows: (1) stress-induced magnetic anisotropy; (2) the easy magnetization axis of the specimen was 45°; (3) reorganization of the domain structure by domain wall movement and magnetic moment rotation under the application of stress and a magnetic field. Stress and the increase in the amplitude of magnetic field promoted the motion of magnetic domain walls and the rotation of the magnetic moments. As a result, the magnetic induction increases with the increase of magnetic field under a constant stress at small angles. Some of the domains in the specimen could be forced to line up along the stress direction when a stress was applied at 67.5° or 90° to the direction of the magnetic field. Thus, the intensity of the magnetic induction weakened in the magnetic field direction. Previous studies showed that discontinuous changes of domain structure occur in specimens under a tension applied perpendicular to a magnetic field [31]. No doubt, there is nucleation and growth of new domains in this process, so that the magnetic induction B at first increases slowly, and then falls.

Third, it is clear that the magnetization curves proved to be sensitive to the levels of stress, as shown in Figure 12. This finding could be explained that, for a magnetic material with positive magnetostrictive coefficient, such as Q195 mild steel, the minimum energy of a domain under stress occurs when the domain magnetization direction is parallel to the direction of the stress. The magnetization of the specimen will increase with the increase of field strength when a mechanical stress is applied because of the increase of anisotropic energy [8]. When the stress is beyond 60 MPa, the magnetostriction constant changes its polarity at high levels of magnetization, which induces a decrease in the slope of the magnetization curve.

Fourth, the peak exhibited by the maximum differential permeability and the maximum magnetic induction in Figure 10 and Figure 11 show that it was possible to measure the direction of stress by measuring the maximum differential permeability and the maximum magnetic induction under different angles. The derived maximum differential permeability and maximum magnetic induction are a function of the angle between the stress and the external magnetic field. In practice, the direction of the stress in materials can be measured by rotating the poles of the electromagnet to obtain the maximum differential permeability or the maximum magnetic induction. Similarly, the behavior in Figure 13 and 14 show that it is possible to detect the magnitude of the stress by measuring the maximum differential permeability and the maximum magnetic induction under different levels of stress.

Kaminski [6] published data showing the variation of magnetic properties with stress for angles of 0°, 22.5°, 45°, 67.5°, and 90°. Figure 16 shows plots of the effect of stress and angle on the maximum differential permeability in his article. The results provided by Kaminski in Figure 16 were similar to those seen in Figure 10 and Figure 13. Under a stress of 80 MPa, the maximum differential permeability reached a peak value at 45°. Similarly, under an angle of 0°, the maximum differential permeability first increased with the increasing stress and then decreased with increasing stress, reaching a peak value at 70 MPa, which is consistent with the test results. However, the maximum differential permeability value at 120 MPa was greater than 0 MPa, which is inconsistent with the test results.

Sablik [5] advanced a model to describe the effect of uniaxial stress applied noncoaxially with the field. In Figure 1 of his article, numerical results are displayed from a model for the maximum induction as a function of stress for different angles θ, also displaying the maximum induction as a function of angle for different stress values. The pattern seen by Sablik was that the maximum magnetic induction increased monotonically with the increase of stress at 0° and did not show any peaks, which is inconsistent with the test results in Figure 14. This is due to the model ignoring the Villari effect, which is a result of variations in the magnetoelastic coupling constant with stress. The trend of the maximum magnetic induction relative to the angles predicted by the model cannot be compared due to the applied stress being inconsistent with that in this paper.

5. Conclusions

In this research, surface magnetization changes induced by a stress noncoaxial with the magnetic field for Q195 steel were measured and analyzed. The results indicated the following:

(1)

The angle θ between the stress and the external magnetic field appeared to be closely related to the distribution of the surface magnetization. When the specimen was magnetized at different angles θ under a constant stress, there was a difference in the direction between the magnetic induction B and the magnetic field H at different angles.

(2)

The magnitude of the magnetization curves varied with the magnetic field at different angles. The behavior at small angles showed an increase in magnetic induction B with the increase in magnetic field H, reaching a peak value of 2.62 mT at 45° and then a decreasing when the angle was increased from 67.5° to 90°.

(3)

The changes in magnetization curves proved to be sensitive to the level of stress. The slope of the magnetization curve showed an increase in the magnetic field under stress from 0 MPa to 60 MPa and then a decrease at higher tensions.

(4)

The derived maximum differential permeability and maximum magnetic induction, as a function of the angle between the stress and the magnetic field and as a function of the stress level, show the capability for measuring the direction and magnitude, respectively, of the stress in materials that are in service.

(5)

The results of the experimental data were compared with experimental results published by Kaminski and the numerical results from a model advanced by Sablik. In some cases the agreement is excellent. The results of Kaminski, seen in Figure 16, were similar to those seen in Figure 10 and Figure 13. The pattern presented by Sablik was inconsistent with the test result in Figure 14, mainly due to the Villiari effect not being incorporated into the model. In addition, phase structures using XRD and measurement errors for the specimen were also studied. The XRD pattern of the Q195 confirmed the existence of α-Fe and C phases in the specimen. The error bars show that the experimental data were stable, with little dispersion and high reliability.

Further research will be focused on the influences of a stable magnetic field and varying stress on the magnetic properties of ferromagnetic materials at different angles between the magnetic field and stress axis, such as 0°, 22.5°, 45°, 67.5°, and 90°. Moreover, it is necessary to improve the measurement process, together with a more detailed analysis of the effects of stress and magnetic field on the magnetic properties of ferromagnetic materials, such as the hysteresis loop, coercivity, and remanence.