Experimental investigation of the magnetic field variation induced in ferromagne

Abstract. The fatigue tests on 15CrMo steel specimen were carried out and the metal magnetic memory （MMM） signals were detected. The experiment shows that the magnetic signals of specimen contain the information of stress distribution in the material inside. Furthermore， the experimental results show that the magnetic signals increase initial while then decrease slightly with the stress increase from 0kN to 200kN. Though analysis the MMM signals induced by different tensile stress within the plastic region of the specimen， a simple model was derived. The experimental results are consistent with the calculated results based on the Jiles-Atherton model.

Key words： metal magnetic memory， stress-induced magnetic field， stress concentration zone， Jiles-Atherton （J-A） model

1. Introduction

The high-pressure steam pipeline is one of the important equipments used in the Shengli oilfield. Because the pipeline bear high pressure and high temperature， the stress concentration occurs will result in failure and catastrophic accidents. However， the traditional non-destructive testing （NDT） methods could be only used to find out existing defects[1]. Thus， it is a very important to find a new method to detect the early fatigue damage or stress concentration zone within the ferromagnetic materials.

Metal magnetic memory （MMM）， which is proposed in 1990s by Doubov， is a new non-destructive testing technology[2，3]. The method is based on the magnetomechanical effect in the ferromagnetic materials. It has been widely applied in many fields for its advantage to detect the early fatigue damage. Through magneto-elastic effect has drawn much attention due to their widely application[4，5]. However， the effect has been adequately explained. Therefore， experiments on ferromagnetic materials have been carried out in order to find the relationship between the residual stress and the variation of magnetic signals inside materials.

To investigate the mechanism of the MMM， a fatigue experiment is carried out. In this paper， the test material is 15CrMo steel and uniaxial tensile stress testing was applied. The distribution of the leakage magnetic signals was measured. Combined with the J-A model， the results were discussed.

2. Experimental details

The material investigated is 15CrMo steel， which was widely used in under pipeline. Table 1 shows the mechanical properties of 15CrMo steel. And， σy represents the yield strength and σt represents the maximum tensile strength， respectively.

Table 1. Composition and mechanical properties of 15CrMo steel

Figure 1 represents the schematic diagram of the specimen and the specimen is in shape of strip. The length of the specimen is 600mm， width is 35mm and thickness is 12mm. there are six pre-cut round holes， whose diameter were 3， 5， 7， 9， 12， 15 mm respectively. Moreover， the distance between each defect is 50mm， and the depth of each defect is 2mm. The magnetic signals were taken along four red lines as shown in Fig. 1. The signals obtained along each line contain two components， which represent Hx and Hy respectively.

At first， the measurement of the magnetic field signals of specimen surface was taken with the tensile stress 0kN. Then， the stress was increased and 150kN stress application test was made. Finally， the tension force in the test is 200kN. After remove the tension， the measurement was done.

3. Results and discussion

Figure 2， figure 4 and figure 5 are the measured magnetic signals with tensile force 0， 150kN （358MPa） and 200kN （476MPa） respectively.

In order to confirm the ability to detect the stress concentration zone within in materials， the surface magnetic signals along lines without stress have been shown in figure 2. From fig.1， it can be seen that the signals were very complex caused by the defects manufacture process under the geomagnetic field. The obtained magnetic field values without stress are in the range of -150A/m to 90A/m， which is attributed to the defects manufacture process. There are some zero-crossing points， which could not distinguish easily from the signals. In order to detect the stress concentration zone， the gradient of magnetic field has been proposed. Figure 3 show the absolute value of the gradient of the Hy_A curves， |K|， which could be described by Eq. （1） as following.

（1）

Where is the differential value of vertical component of magnetic field along line A； the distance between the two measurement points. As shown in Fig. 3， there are seven obviously peak value located at 50， 100， 300， 400， 450， 475 and 500mm. The peak points of 300， 400 and 450mm are three locations of the pre-cut defects， while other defects could not be distinguished out because of the defects influence each other.

As shown in Fig. 4 and Fig. 5， the magnetic signals present the specimen in the plastic regime because the yield strength of 15CrMo steel is 295MPa （the yield strength of this specimen is 123kN in this case）. It can be seen that the magnetic signal curve is almost linear， and the zero-crossing points are near the zone range from 375mm～400mm， which is exactly the zone of crack. Moreover， the results show that the magnetic field decreases slightly when the tensile stress from 150kN to 200kN except the measurement data obtained from fixture position. The magnetic values are in the range of -200A/m to 250A/m with the stress 150kN while the range of -200A/m to 200A/m with the stress 200kN.

According to the ‘law of approach’[6]， application tensile stress will lead to unpinning of domain walls， thereby causing magnetization to approach the anhysteretic. That is why the initial magnetization at 0kN increased after application the stress to 150kN （from ±150A/m to ±200A/m）. In order to explain the phenomenon of magnetic signals decreased slightly with stress increased， a model developed by Jiles and Atherton has been applied. Based on the Jiles-Atherton model， a equation was proposed to describe the change in magnetization with applied stress under a constant magnetic field as following[7]：

where is the angle between the axis of the applied stress and the axis of the magnetic field， is the Possion’s ratio of the material and is the magnetostriction.

The effective magnetic field could be given by

Using the magnetostriction data of Cullity[8]， the effective magnetic field values will be obtained. Figure 6 show the relationship between stress and additional magnetic field. As shown in Fig.6， the magnetic field decrease slightly， about less than 10A/m， when the stress increase from 150kN （358MPa） to 200kN （476MPa）. The calculated is consistent with the experimental results.

4. Conclusions

In conclusion， we have investigated the variation of spontaneous magnetic field associate with different stresses in 15CrMo steel. The experimental results show that Magnetic signals of the 15CrMo specimen contain the information of stress distribution in the material inside. MMM method could effectively locate the stress concentration zone. Furthermore， experimental results also show that the magnetic field decrease from 250A/m to 200A/m while the stress increase from 150kN to 200kN. This phenomenon could be described by Jiles-Atherton model， i.e. the residual magnetic field of specimen could be described as a function of geomagnetic field and stress. The model works well on explaining the experimental results.

References

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