Leakage magnetic field variation induced by inner surface grooves during loading in geomagnetic environment

Abstract

The leakage magnetic field which induced by the inner surface groove during loading had been measured from the outer surface in geomagnetic environment. Compared the variation of the leakage magnetic field along the load with the location and development of the groove, it was found that two phenomena are relate to the magnetic field aberration. The relation can be described by the pink-pink value and the gradient of the magnetic field aberration. This result can be used to evaluate and monitor the inner defect by the magnetic field aberration characters.

Keywords

Leakage magnetic field variation inner surface groove loading geomagnetic environment

1. Introduction

The leakage magnetic field variation of the piece surface can be used to inspect the surface crack and evaluate the stress concentrate status [1]. This method is called Magnetic Memory Method (MMM) by Doubov [2,3]. The phenomenon is that the stress induces to magnetization of ferromagnetic materials and the induced magnetic field by the stress concentration is varied greatly. But it is difficult to inspect the real flaw because the signal is weak. In order to get the characteristics of leakage magnetic field induced by stress, many scholars have carried out research work. Magnetic field aberration of stress concentration zone induced by cycle stress [4] and magnetic field signal characters of surface crack during loading [5] had been given. Singh [6] revealed that the stress-induced geometry effect has a great influence on the self-magnetic leakage field (SMLF) signals, especially in the plastic deformation stage. Huang [7] found that the final fracture locations of tensile testing specimen were inconsistent with the locations predicted by metal magnetic memory testing theory and there is no perfect correlation between the two areas existed. Huang [8] had discussed the effect of the applied magnetic field on SMLF. A linear magnetic-charge model [9] is employed to analyze the SMFL distribution in the local stress-concentration zone, and the model provides some quantitative results about the effects of defect depth and location (surface- or inner-defects) on SMFL signals. But there is no report about the magnetic field aberration induced by the inner crack during loading.

2. The experiment

In order to get the magnetic field aberration induced by the inner crack without marginal effect and the other influencing factors [10], a closed vessel with inner surface groove was chosen and loaded by hydraulic pressure. The magnetic field of outer surface was measured from the line according to the groove location and the groove size was monitored by TOFD (Time of Flight Diffraction).

2.1. The specimen

The specimen is a welding vessel (Fig. 1). The material of the vessel is HP345, the thickness of the vessel wall is 10 mm, and the design pressure is 2.5 Mpa. The groove was machined from the inner surface of the vessel. The length of the groove is 40 mm, the width is 0.5 mm (bottom) and 0.1 mm (tip), and the depth from the inner surface is 5 mm. The heat treatment had been done to release the residual stress after the groove machined and the vessel welded.

2.2. Measuring equipment

The magnetic field measuring equipment is TSC-1M-4 with 4 channels. The measurement step is 1 mm, the range is ± 2000 A/m (± 25 Gauss) and the resolution is 1 A/m (1.25%Gauss). Three sensors are used to measure the magnetic field of the surface of the specimen and one is used to measure the environmental magnetic field. The measured surface magnetic field (Hp) is perpendicular to the surface of the specimen.

2.3. Experimental procedure

First, the groove details wer measured by TOFD and the position was marked on the surfac of the vessel. Then, the scanning line was drawn by the TOFD data which cros and perpendicular to the groove (Fig. 2). The length of the line is about 400 mm.

The pressure was gradually increased by pump from 0 MPa to the specimen failure. When the pressure reached on each step, kept the pressure and measured the magnetic field along the scanning line, then unloaded the pressure and measured the magnetic field in the same way.

Fig. 1.

The specimen and the inner groove.

Fig. 2.

The inner groove and the scanning line.

2.4. Experimental results

The typical magnetic field curves and gratitude curves are shown in Figs 3 and 4 at different load. The focus of H_p signals is the peak-to-peak magnetic fields (H_P−P) and the gradient k (dH∕dx) of the groove zone. The value of the magnetic field (H_p) of the groove zone is varied from the other zone and the gradient (k) is more than 10. But the H_p and k have great different change with the increasing load. The curve is flat and varied slowly when the load is small, and the peak-to-peak magnetic field (H_P−P) is increasing rapidly during loading.

Fig. 3.

The H_p signals on 3 MPa.

Fig. 4.

The H_p signals on 8 MPa.

3. Data analyzed and discussion

3.1. The varied regulation of H_p curve

Figure 5 shows the H_p curve at different load. Compared the amplitude and shape of these curves at different load, it can be found that the variety of the amplitude and gratitude of H_p signals in the groove area are far more drastic than the signals of the other zone when the load is increasing. According to the curve feature, the variation can be divided into three steps.

When the load is 0, the abnormality of H_p signals can be found in the groove area. This abnormality is very small and difficult to distinguish. But it is enough to be used to find the location of the inner defect. The aberration value is small because the magnetic field caused by the stress concentration at the tip of the groove is small at 0 loads.

The second phase is the load from 0 to 5 MPa. In this phase, the whole curve is smoother with the load increasing and the aberration value of the groove located zone was growing. In this phase, the values of H_p signals are from −55 A/m∼–25 A/m, but the H_P−P values increased and the shape of the curves of the H_p signals changed to sharp.

The third phase is the load from 5 MPa to 9.7 MPa. The groove depth is from the 5 mm to 7.5 mm. In this phase, the load increasing continually aroused the stress level going up and the groove resulted in the H_p signals enhancing. The rising of stress level and the crack emerging leaded the rapidly increasing of the H_P−P values. The maximum of the H_P−P values is 97 A/m. There is a sharp peak at the place of the groove.

From the curve of H_p signals, it is easy to find the location of the inner groove. According to the theoretical model of magneto-mechanical effect and the simulation method [11] of magnetic field changes caused by stress concentrations, the SMLF induced by the stress distribution and the discontinuity of structure can be separated.

Fig. 5.

The magnetic field variation curve during loading.

3.2. The varied regulation of Hp curve

In order to investigate the change of the surface leakage magnetic field caused by the internal macro discontinuity in the geomagnetic environment, the variation law of the surface leakage magnetic field caused by the uneven stress magnetization is further determined. Assume that there is a permanent magnet source inside the cylindrical work piece. Calculate the surface leakage magnetic field strength at the corresponding position of the work piece.

As shown in Fig. 6, the green area is air, the purple area is steel, and the red is permanent magnet source.

Fig. 6.

Schematic diagram of the simulation model.

The specific size parameters are shown in Fig. 7.

Fig. 7.

Grid and size parameters.

The calculation results are shown in Fig. 8.

Fig. 8.

The simulation results.

By measuring the leakage magnetic field strength at a distance of 0.5 mm from the corresponding surface of the magnetic source, it is found that the strength of the leakage magnetic field changes linearly with the intensity of the magnetic source, as shown in Fig. 9, which means that the internal magnetic field strength can be obtained by the change of the surface magnetic field strength variation.

Therefore, it can be concluded that the surface leakage magnetic field caused by the existence of macroscopic discontinuity gradually decreases with the macroscopic discontinuity away from the surface under the action of a uniform magnetic field. Under the action of the earth magnetic field, the surface leakage magnetic field strength caused by the macroscopic discontinuity is less than the earth’s magnetic field. Assuming that the macroscopic discontinuity is a magnetic source, the surface leakage magnetic field corresponding to the macroscopic discontinuous position is approximately linear with the magnetic source strength.

Fig. 9.

The leakage magnetic field varies with magnetic source strength.

Comparing the calculation results of the leakage magnetic field caused by the internal magnetic source and the variation of the leakage magnetic field intensity caused by the macro discontinuity during the loading process, it can be drawn that the stress magnetization is much larger than the intensity of the magnetic field caused by the macro discontinuity under the geomagnetic field environment. It can be ignored that the magnetic field change caused by macro discontinuity.

3.3. The varied regulation of the H_P−P and k of H_p abnormality signals

H_P−P and k are the major parameters to analyse the H_p abnormality signals. Figure 10 shows the H_P−P and k curve during loading. It is easily to found that the magnetic field variation is nonlinear ascension. The curve can be divided into three stages. The critical stress value is the region which leads to the groove propagation. The first stage is the flat stage. In this stage, the values of the H_P−P and k of the H_p abnormality signals are small. That means the groove is growing along the depth during loading which is confirmed by TOFD. The second stage is the transition stage. In this stage the groove is growing slowly and the stress concentration is enhancing with load increasing. The third stage is steep rise stage and the stress is higher and the groove remains unchanged. But this stage is more dangerous than the other two stages because the groove may penetrate quickly. These stages can be used to evaluate the groove status.

Fig. 10.

The H_P−P and k curve during loading.

According to the stress magnetization equivalent equation, it can be further discussed that the relationship between the stress distribution and the leakage magnetic field. $\begin{eqnarray}\displaystyle \begin{array}{@{}c@{}}H_{{\sigma}}={\displaystyle \frac{3}{2}}{\displaystyle \frac{{\sigma}}{{\mu}_{0}}}\left({\displaystyle \frac{d{\lambda}}{dM}}\right)_{{\sigma}}(\cos ^{2}{\theta}-{\nu}\sin ^{2}{\theta})\\ {\sigma}={\sigma}_{0}(\cos ^{2}{\theta}-{\nu}\sin ^{2}{\theta})\end{array} & & \displaystyle\end{eqnarray}$ (1)

H_σ - Stress magnetization, σ₀ - the principal stress, 𝜈 - the Poisson’s ratio.

𝜆 - magnetostrictive coefficient, M - magnetization

The vertical magnetic field on the surface of the stress concentration area changes significantly. The vertical magnetic field on the surface is the leakage magnetic field in the vertical direction of the material surface, which originates from the inconsistency of the local magnetization of the material. When the magnetization of the material is evenly distributed, the intensity of the vertical magnetic field on the surface is close to zero. When the magnetic strength of the material is not evenly distributed, the magnetic field intensity difference appears in the local area, and the leakage of the magnetic field line appears in this area, and the vertical magnetic field on the surface increases. Therefore, when there is no discontinuity in the structure, the change of vertical magnetic field (H_p) is the leakage caused by the difference of magnetization caused by the change of local regional stress. $\begin{eqnarray}\displaystyle H_{p}\propto {\displaystyle \frac{dM}{dx}}=\frac{dM}{d{\sigma}}\frac{d{\sigma}}{dx}. & & \displaystyle\end{eqnarray}$ (2)

It shows that the transformation of the leakage magnetic field can reflect the stress distribution, and the leakage magnetic field can identify the location of the stress concentration. The direct relationship between the change of the leakage magnetic field and the stress change is established, which provides a theoretical basis for the evaluation of the stress state by using the leakage magnetic field signal in the magnetic memory testing method.

4. Conclusion

(1) The variety of the surface magnetic field can be used to inspect the inner crack and stress concentration zone which is induced by stress concentration.

(2) The amplitude and gratitude of the H_p abnormality signals with load are higher than without load but only if the stress is not released.

(3) The inner groove emerged result in the values of the H_P−P and k of H_p abnormality signals rapidly increasing and the curve of H_p abnormality signals change to sharp. The stress released results in decreasing of the H_P−P and k. These different stages can be distinguished by the trend of the σ − H_P−P and the σ − k curve. So the surface H_p abnormality signals can be used to evaluate the status of inner stress concentration and crack.

Footnotes

Acknowledgements

This study is financially supported by National Key Research and Development Project (2017YFF209701).

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Leakage magnetic field variation induced by inner surface grooves during loading in geomagnetic environment

Abstract

Keywords

1. Introduction

2. The experiment

2.1. The specimen

2.2. Measuring equipment

2.3. Experimental procedure

3.1. The varied regulation of H p curve

Footnotes

Acknowledgements

References

3.1. The varied regulation of H_p curve