## Abstract

Pipelines are the primary means of land transportation of oil and gas globally, and pipeline integrity is, therefore, of high importance. Failures in pipelines may occur due to internal and external stresses that produce stress concentration zones, which may cause failure by stress corrosion cracking. Early detection of stress concentration zones could facilitate the identification of potential failure sites. Conventional non-destructive testing (NDT) methods, such as magnetic flux leakage, have been used to detect defects in pipelines; however, these methods cannot be effectively used to detect zones of stress concentration. In addition, these methods require direct contact, with access to the buried pipe. Metal magnetic memory (MMM) is an emerging technology, which has the potential to characterize the stress state of underground pipelines from above ground. The present paper describes magnetic measurements performed on steel components, such as bars and tubes, which have undergone changing stress conditions. It was observed that plastic deformation resulted in the modification of measured residual magnetization in steels. In addition, an exponential decrease in signal with the distance of the sensor from the sample was observed. Results are attributed to changes in the local magnetic domain structure in the presence of stress but in the absence of an applied field.

## 1 Introduction

The metal magnetic memory (MMM) method is a passive magnetic non-destructive testing (NDT) method that does not require the application of an external field. It is based on the principle of the magnetomechanical effect (Villari effect or piezomagnetic effect) for which magnetization of ferromagnetic material occurs in areas of large strains due to exposure to working loads [1]. It is defined as the change in the internal magnetic field in response to the stress applied to the material [1,2]. Magnetic domains within ferromagnetic materials are oriented in a manner that minimizes their total energy by optimizing flux closure of domain configurations [3].

When stress is applied to a steel material, the magnetic domain configuration energy is modified and a reconfiguration of the domain structure results in a magnetization of the material. Therefore, the effect of stress is similar to the effect of an applied magnetic field. The magnetoelastic energy of a material under stress can be written as [2,3]:
$Eσ=32λsσcos2θ$
(1)
where θ is the angle between σ and the saturation magnetization direction of the domain. In order to minimize this energy, domains most closely aligned with the stress direction will shrink or grow depending on the sign of λsσ. This implies that stress can cause a change in magnetization. This effect can be amplified by a stress concentration due to a defect. This change in magnetoelastic energy under stress modifies the balanced energy state of the material. To compensate, the magnetoelastic energy is converted to magnetostatic energy by the formation of dipole moments. The change in energy generates an effective force, which results in the movement of domain walls over pinning barriers. This is explained in detail in Ref. [4], where a relationship is developed between stress and width of the excess domain created due to stress.

Pipelines are self-magnetizing due to magnetoelastic effect in stress concentration regions due to working loads. For example, an underground steel pipe that carries a high pressure fluid or gas will be subjected to stress from its internal pressure, together with any stress due to other sources, such as ground movement. This will generate residual magnetization in the pipe [57]. The manufacturing process of the pipe may also cause additional magnetization. In addition, stress concentration zones and anomalies cause a local change in magnetic permeability, which allows magnetic flux leakage at that point [2,8,9]. This implies that magnetic variations are maximum near anomalies and stress concentration zones. Thus, it should be possible to detect these regions by a measurement that is above the ground and non-invasive. However, the range over which this phenomenon may extend and the influence of other neighboring magnetization sources, including the presence of the Earth's magnetic field, needs to be accounted for. In the present study, the effect of bending on the residual magnetization of a steel bar and a tube is investigated. In addition, the liftoff distance up to which these stresses can be detected by the sensor has been identified.

## 2 Materials and Methods

Measurements were performed on structural steel samples with different shapes, dimensions, and degree of deformation. The dimensions of the samples are listed in Table 1.

Measurements were performed in the laboratory on stressed and unstressed steel samples using a Honeywell 3-Axis (HMC 5883L) anisotropic magnetoresistive (AMR) sensor with 4.5 milliGauss (mG) resolution and ±8 Gauss maximum field range. This sensor was used to detect three components of magnetic flux signals over a sample's surface, simultaneously. Scans were performed from one point to another along the length of the sample (Fig. 1) with a step size of 10 mm and liftoff distance that varied from zero (contact) to 160 mm.

## 3 Results and Discussion

The normal magnetic field component (Bz) obtained from magnetic scans (at different liftoffs) on Sample 1 before bending is shown in Fig. 2. The maximum value of the field was observed near the two ends of the sample and flux density changed from positive to negative. This is attributed to some residual magnetization in the bar allowing it to act as a bar magnet, where magnetic field lines emerge from one end and enter into the other end, with a transition from positive to negative field occurring at the center of the sample. Also, the magnitude of the field was maximum close to the sample and decreased with distance away from the sample (liftoff distance).

After performing magnetic measurements on the sample, it was bent beyond its elastic limit, allowed to relax, and measurements were performed again. The normal component of the magnetic field as a function of the position of the sensor along the length of the bent sample is shown in Fig. 3(a). The normal field component exhibited two peaks, near each end of the sample, and the flux density changed from positive to negative from one end to the other. The transition from the positive to the negative field was observed near the 75 mm position along the x-axis. This indicates that the magnetic signature of the sample changed with plastic deformation and the resulting induced residual stresses.

Models of residual stress formation in bars under bending provide the anticipated residual stress patterns [10,11]. Outer layers undergo plastic deformation first. As bending continues, layers closer to the center of the bar deform, leaving only a small cross section of the bar in the elastic regime. When unloaded, strain energy from both elastic and plastic regimes is released, allowing the bar to straighten somewhat, but not to its original state, as shown in Fig. 3(b). As the bar is unloaded, the plastically loaded regions relax causing spring back. This causes internal regions that were only elastically loaded to be stressed elastically in the opposite sense. These remaining residual elastic stresses modify the magnetic signal from the original unbent bar shape, as qualitatively expressed by Eq. (1) (compare Figs. 2 and 3(a)).

Similar measurements were performed on a longer bar, Sample 2 and tube, Sample 3, and magnetic field component values were taken at different positions along the length of the samples. Magnetic field as a function of position along the length of the longer bar, Sample 2, is shown in Fig. 4. Field intensity was maximum near the end, and the transition from the positive to the negative field was observed at the center, similar to that of short bar sample (Fig. 2).

Magnetic field component in the radial direction (Bz) along the length of the tube, Sample 3, before and after bending, is shown in Figs. 5 and 6, respectively. Measurements were performed on a small section along the tube length (Sample 3). It was observed that the magnetic signature of the tube is different from that of the bar. This is attributed to different stress distributions after bending of the tube compared to the bar resulting in a different magnetic domain configuration. The top and bottom portions of the tube deform under bending, similarly to that of the bar (top and bottom of the tube become plastically deformed before other portions of the tube) [12,13]. However, in the case of the tube, the sidewalls carry the remaining deformation [12,13]. Similar to the bar, upon unloading, plastically deformed regions and elastic strain energy force other sections of the tube into residually stressed states. The difference that arises is that instead of being transferred through the thickness of the specimen, the strain is taken up around the circumference of the tube.

Peak magnetic flux density as a function of liftoff for each sample before and after bending is shown in Figs. 7 and 8, respectively. It was observed that the signal decreases exponentially with an increase in the liftoff. Best fit for exponential decay of the normal field with liftoff is given as
$y=C+Aexp(−xd)$
(2)
where y is the normal flux density, C and A are constants, x is the liftoff, and d is the decay constant. The value of these variables obtained for each sample is given in Table 2.

As shown in Figs. 7 and 8, there is still a significant field far from the sample, even at higher liftoffs. From Table 2, the exponential decrease in the field with liftoff for the bar sample (Sample 1) had a decay constant of 22 mm before bending and increased to 30 mm after bending on the concave side, which contained the residual tensile stress. Similarly, for the tube sample (Sample 3), the decay constant changed from 21 mm to 31 mm (concave side) after bending. There was a negligible change in the decay constant on the convex side of the tube. This again is attributed to the different types of residual stress (tensile/compressive) accumulated on the concave and convex sides of the tube. Assuming that the liftoff decay constant scales with the magnetic material present, this implies that the MMM method could be used to detect tensile stress concentration zones in pipe even without surface contact. However, a challenge is still dealing with the unknown initial magnetic state of the pipe.

## 4 Conclusion

The magnetic metal memory method is an NDT method with significant potential for pipeline inspection applications. Critical challenges include establishing a quantitative relationship between stress and residual magnetization in the sample, the lack of a complete physical model of the phenomena, and dealing with the unknown initial magnetic state of the pipe. The current study was performed to explore the contact/non-contact MMM inspection technology. Bending, which introduced plastic deformation and residual stress, affected the magnetization of various steel samples. An exponential decrease in signal with an increase in the liftoff was observed with a larger change arising under conditions of residual tensile stress.

## Acknowledgment

This work was sponsored by an Ontario Centres of Excellence (OCE) grant and the Natural Sciences and Engineering Research Council of Canada (NSERC) through the NSERC Engage program.

## Nomenclature

• B=

magnetic flux density

•
• $Eσ$=

magnetoelastic energy

•
• λs=

saturation magnetostrictive constant

•
• θ=

angle between saturation magnetization of domain and applied stress

•
• σ=

applied stress

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