Investigation of the role of a nonmagnetic spacer in local wall thinning inspection

Abstract

Detectability of an artificial slot, placed at the bottom of a steel plate was investigated by the method of Magnetic adaptive testing (MAT), when the measurement was performed through another steel plate. Influence of an air gap (or of a nonmagnetic spacer) located either between the magnetizing yoke and the top plate surface or between the two plates was explored. It was found that if the thickness of the nonmagnetic spacer was not larger than 0.15 mm, it had no influence on the detectability of the slot in the given geometry. This result shows an excellent applicability of MAT, and it is encouraging for possible future practical applications. The empirical data were compared with results of an electromagnetic simulation, and the outcome was interpreted and explained.

Keywords

Local wall thinning magnetic NDT magnetic adaptive testing nonmagnetic spacer

1. Introduction

Local wall thinning is a very serious and frequent defect type in pipes used in industry [1, 2]. To avoid severe accidents, inspection of the thickness reduction of pipes is a very important task. Several nondestructive testing techniques, such as X-ray [3], microwave [4] ultrasonic [5, 6, 7], acoustic emission [8, 9, 10], eddy current [11], thermal infrared measurements [12] and others are used for the evaluation of the pipe wall thinning. The magnetic flux leakage (MFL) method is also a frequently used pipeline testing technique [13, 14, 15, 16, 17, 18].

In most cases the wall thinning inspection should be done from the outer side of the pipe, because – even though this phenomenon frequently occurs inside the tube due to the stream of coolant flowing inside the pipe – long length of the pipe usually prevents any testing from inside. A more difficult problem is to detect the local wall thinning at locations under an enforcement shield that covers the pipe outside where a branch pipe is connected to the main one. Because the enforcement shield and the pipe wall form two layers of metal, it is difficult to inspect the inner side of the pipe under the enforcement shield by any ultrasonic method. Pulsed eddy current testing technology was developed in recent years to challenge this problem [19, 20, 21]. In this case the targets are non-ferromagnetic materials, and due to the rich frequency spectrum and the applicability of large electric current, pulsed eddy current method shows promising capability in the detection and evaluation of defects in deep regions of the material.

If pipes are made of ferromagnetic materials (e.g. steel), magnetic methods are also suitable electromagnetic nondestructive testing methods for the inspection of local wall thinning even at locations under enforcement shields. The feasibility of the application of the magnetic flux leakage (MFL) method for the investigation of wall thinning of pipes under reinforcing plates was discussed. Assessment of size of a slot fabricated on the under-layer of a layered specimen was shown to be possible from the flux leakage profile. It was also shown that conditions of wall thinning under reinforcing plates can be monitored by the MFL method [22, 23]. Another example, a recently developed nondestructive method, called Magnetic adaptive testing (MAT), which is based on systematic measurement of minor magnetic hysteresis loops, was applied for the detection of local wall thinning in ferromagnetic plates. It was shown that even a relatively small, local modification of the sample thickness could be detected with adequate signal/noise ratio from the other side of the specimen. The measurements gave good results also, if the investigated plate was covered by other plate(s) [24, 25].

In spite of a great number of publications in this area, the influence of an air gap/nonmagnetic spacer between the magnetizing yoke and the sample surface is discussed in a very limited way. In practical cases some air gaps always necessarily exist, even between polished surfaces, the question is only the thickness of the air gap. The surfaces of tubes, and other objects to be inspected are frequently painted, which by itself produces a nonmagnetic spacer, not to speak about the frequent case, where the surfaces are rough, dirty or corroded. The problem becomes even more pronounced if the wall thinning to be detected is under an enforcement shield, because in this case also some air gap – due to the surface roughness of the plates – always exists between the two ferromagnetic plates. In an earlier work [26] with MAT measurements we intentionally applied non-magnetic spacers (with thicknesses of 0.08 mm and 0.23 mm) for relative indication of the samples’ micro-structural conditions. It was shown that the spacers modify shapes and size of the measured signals, and they substantially reduce scatter of experimental points. Sometimes, with thick spacers in particular, they are able to modify shapes of the measured signals qualitatively and even to bring about considerable increase of sensitivity, especially if the degradation functions are computed from the signal derivatives.

The purpose of the present work is to investigate and to analyze the influence of the air gaps – which is nothing else but a nonmagnetic spacer between the plate surfaces – in local wall thinning experiments performed by MAT. We investigate how the artificially applied nonmagnetic spacer between a magnetizing yoke and a sample surface, and also between the two plates, influences the measured signal, and the detectability of the artificially made slot in the bottom plate. Especially we investigate what is the thickest nonmagnetic spacer, which still makes possible (in the case of the given configuration) the detection of local wall thinning. Some experimental results are compared with a numerical simulation.

2. Samples

Two low carbon commercial steel plates of size 500 m $\times$ 300 mm $\times$ 6 mm were used for the measurement. One of them contained a 3 mm deep artificial rectangular slot, the other plate was without any slot. The length of the slot was equal to one of the dimensions of the plate (300 mm), while the width of the slot was 10 mm.

3. Simulation of the magnetic flux change

The variation of the magnetic flux density in the cross section of the magnetizing yoke due to the presence of the artificial slot was calculated by the AC/DC Module of the Comsol Multiphysics ${}^{\@setsize{\scriptsize}{9.5pt}{\viiipt}{\@viiipt}\textregistered}$ finite element software [27]. In this simulation several parameters (size of the magnetizing yoke, size of the slot, air gap between the yoke and the plate surface, air gap between the plates) were taken into account. The magnetic flux values in the yoke, $\Phi_{1}$ (if there is no slot) and $\Phi_{2}$ (with the slot), were calculated. As an illustration of the results presented in [27], Fig. 1 shows how in the investigated double layer configuration the magnetic flux is modified due to the presence of a 10 mm wide slot as a function of the distance between yoke legs for three different thicknesses of air gaps (0 mm, 0.005 mm and 0.01 mm) applied between the magnetizing yoke and sample surface. The slot is located in the middle of the yoke in the bottom of the bottom layer, while magnetizing yoke is placed on the top of the top layer. The relative flux change: $\eta=|\Phi_{1}|$ / $|\Phi_{2}|$ shown at vertical axis means, that this is the ratio of the magnetic flux densities, calculated for the case without slot ( $\Phi_{1}$ ), and for the case when slot exists ( $\Phi_{2}$ ). In other words, this is the influence of the slot on the flux density.

Figure 1.

Relative change of the magnetic flux ( $\eta)$ in a double layer configuration due to the presence of a 10 mm wide slot as a function of the distance between yoke legs for three different air gaps (no air gap , 0.005 mm, and 0.01 mm thick air gap between the magnetizing yoke and sample surface).

It is seen in Fig. 1 very well, how significantly the relative magnetic change due to the presence of the slot is decreased with the increased air gap. For even better illustration of the influence of the air gap, Fig. 2 shows how the maximum of the relative flux change (peak values of the curves in Fig. 1) depends on the thickness of the air gap in the double layer configuration with a 10 mm wide slot. In this case the relative change of the magnetic flux is shown for a significantly wider range of air gaps.

Figure 2.

Sketch of the measurement configuration, when a nonmagnetic spacer is applied between the surface of the plate and the magnetizing yoke.

4. Magnetic adaptive testing (MAT)

Magnetic adaptive testing was used for the magnetic measurements. This method is described in detail in [28]. Series of minor magnetic hysteresis loops were measured using a yoke for magnetization of the samples. The yoke was a C-shaped laminated Fe-Si transformer core, placed directly on the plate to be measured. When equipped with a magnetizing coil and a pick-up coil, the yoke is called the “measuring head”. Lateral dimensions of the measuring head are characterized by its cross-section: $S=$ 16 $\times$ 19 mm ${}^{2}$ , the distance between the legs is 30 mm. The magnetizing coil was wound on the bow of the yoke with $N=$ 150 turns and the pick-up coil was wound on one of the yoke legs with $n=$ 100 turns.

The magnetizing coil gets a triangular waveform current with step-wise increasing amplitudes and with a fixed slope magnitude in all the triangles. This produces a triangular time-variation of the effective field in the magnetizing circuit and a signal is induced in the pick-up coil. As long as the field sweeps linearly with time, the voltage signal in the pick-up coil is proportional to the differential permeability of the magnetic circuit. The Permeameter works under full control of a PC computer, which registers data-files for each measured family of the minor “permeability loops”.

The experimental raw data are processed by an evaluation program, which divides the originally continuous signal of each measured sample into a family of individual permeability half-loops. The program filters experimental noise and interpolates the experimental data into a regular square grid of elements, $\mu_{ij}\equiv\mu$ ( $h_{ai}$ , $h_{bj}$ ), of a $\mu$ -matrix with a pre-selected field-step. The coordinates $h_{ai}$ , $h_{bj}$ of the elements represent the actual magnetic field value, $h_{ai}$ , on the actual minor loop with amplitude $h_{bj}$ . Each $\mu_{ij}$ -element represents one “MAT-descriptor” of the investigated material structure variation.

The matrices are processed by another evaluation program, which divides values of their elements by corresponding element values of a chosen reference matrix (i.e. matrices standardization), and arranges each set of the mutually corresponding elements $\mu_{ij}$ of all the evaluated $\mu$ -matrices into a $\mu_{ij}(x)$ -degradation function. In this way the normalized $\mu_{ij}$ -descriptors hold information about the relative changes, which occur in the deformed/degraded/processed samples. Here $x$ can be any independently measured parameter. In our case this independent parameter is the distance $t$ , which determines the position of the magnetizing yoke if it is moved over the surface of the sample. The reference “sample“ was the corresponding MAT descriptor, measured at the farthest distance ( $t=$ 80 mm) from the axis of the slot, where no influence from the slot and no influence from the ends of the plate were felt. All other descriptors were normalized by this descriptor.

The matrix-evaluation program calculates also sensitivity of each degradation function and draws their “sensitivity map” in the plane of the field coordinates ( $h_{ai}$ , $h_{bj}$ ) $\equiv$ $(i,j)$ . This map shows relative sensitivity of each $\mu_{ij}(t)$ -degradation function with respect to the position of the yoke over the investigated sample. Sensitivity of each degradation function is computed as the slope of its linear regression and it is expressed by a color and/or shade in the sensitivity map figure. The sensitivity map gives useful information about the relative change of the investigated magnetic descriptor with respect to the independent variable (the top of the “hills” are those area(s) from where the most sensitive MAT-degradation functions can be taken). On the other side it also indicates, how reliably the parameter can be determined if the measurement is repeated (large plateaus are favourable from this point of view, where parameters depend only very slightly from the actual choice of the exact field coordinates values $h_{ai}$ and $h_{bj}$ ).

In this measurement it is difficult to determine exact values of the magnetic field, h, inside the sample, due to the open magnetic circuit. Because of this the magnetizing current, $I$ , (given in mA) is used to characterize the samples’ magnetization when MAT descriptors $\mu_{ij}=\mu(I_{ai},I_{bj}$ ) are calculated. Real value of the magnetic field inside the sample is always proportional to the magnetizing current at a given arrangement, so this simplification does not cause any problem in the calculated (normalized) MAT descriptors. The surface qualities of the investigated plates are exactly the same. It means that the correlation between the magnetizing current and the internal field is for all the samples really comparable. Because of this, to simplify the description, in the following part of the paper we will use simple ${\bm{\mu}}$ instead of $\mu_{ij}=\mu(I_{ai},I_{bj}$ ).

Analyzing the measured MAT parameters, taking into account accuracy of the measurement and repeatability of the measured values, error of the MAT descriptors is estimated about 5%.

When any magnetic $\mu$ -descriptor is plotted as a function of the distance, $t$ , from the axis of the slot, it is called the $\mu$ -degradation function. The degradation functions, which were created straight from the induced signal (which is proportional to the average permeability measured in the magnetic circuit “measuring head – measured plate”), are labeled as the $\mu$ -degradation functions. However, degradation functions based on the derivative of permeability $\mu=d\mu/dI$ are usually more sensitive. They are referred to as the $\mu$ -degradation functions, and used throughout this paper and in all the next figures.

Figure 3.

Sketch of the measurement configuration, when a nonmagnetic spacer is applied between the surface of the plate and the magnetizing yoke.

5. Results

5.1 Drop of the signal due to spacers

To illustrate how the existence of a nonmagnetic spacer modifies the measured signal (i.e. the permeability minor loops), we compared signals of the pick-up coil for the cases with and without the spacer. For the comparison only one plate without the slot was measured as shown in Fig. 3. Thickness of the used spacer is 0.075 mm. The large difference between the signals is clearly seen in Fig. 4: permeability drops down as a consequence of the nonmagnetic gap between the surface of ferromagnetic plate and the magnetizing yoke. The thicker is the gap, the more the signal drops down.

Figure 4.

Signal of the pick-up coil measured on the plate without the slot. Measured signal with and without application of the spacer between the sample surface and the magnetizing yoke.

5.2 Double plate system

The main measurements were performed on two steel plates with the magnetizing yoke attached to the top surface of the top plate, which did not have any slot. The artificial slot was always located at the bottom of the bottom plate. Figure 5 shows the sketch of the measurement, when a spacer was applied. During measurement of the degradation functions the magnetizing yoke was moved step by step over the surface along a line, which was perpendicular to the length of the slot. The vertical distance, $t$ , between middle of the slot and middle of the yoke was used as the independent variable of the degradation functions. Direction of the movement of the yoke is indicated by an arrow in Fig. 5.

Figure 5.

Sketch of the measurement. The arrow indicates the direction of the movement of the magnetizing yoke.

Figure 6.

Optimally chosen $\mu^{\prime}$ -degradation functions for three non-magnetic spacers with different thicknesses (0.075, 0.150 and 0.210 mm) placed between the yoke and the plate surface, and for the reference case (without spacer).

Figure 7.

Map of relative sensitivity of the $\mu^{\prime}(t)$ -degradation functions.

MAT measurements were performed for two arrangements: in one of them nonmagnetic spacer or spacers were placed between the top plate and the magnetizing yoke, in the other one the spacer or spacers were placed between the two plates. (In this latter case there was no spacer between the yoke and top plate.) Results of the MAT measurements are shown in Fig. 6 for the case where spacers were placed between the yoke and the top plate. Figure 6 contains the results of four independent measurements: 0 mm, 0.075 mm, 0.15 mm and 0.21 mm thick spacers were applied. The optimally chosen MAT degradation functions are shown for the three spacer thicknesses and for the reference case (no spacer). At position “ $t=$ 0 mm” the magnetizing yoke is exactly above the slot, as indicated in Fig. 5. All the MAT degradation functions are normalized with the corresponding reference value, measured at the 80 mm distance from the center.

During evaluation of the great number of possible MAT parameters always those degradation functions are chosen for the presentation, which are the most sensitive for the given material deformation/ degradation. In the present case the derivative $d\mu/dI=\mu^{\prime}$ was found as the most sensitive descriptor and therefore in the whole work the $\mu$ -degradation functions are used.

Figure 8.

Sketch of the measurement. A nonmagnetic spacer is applied between the two plates.

Figure 9.

Optimally chosen $\mu^{\prime}$ -degradation functions for three non-magnetic spacers with different thicknesses (0.075, 0.150 and 0.210 mm) placed between the two plates, and for the reference case (without spacer).

It is well known that in general derivatives can be notoriously noisy and usually associated with low signal to noise ratio (SNR). However, based on the sensitivity map (mentioned above) it is possible to determine, how robust is our $d\mu/dI$ MAT descriptor. The sensitivity map, correlated to the measurement, presented in Fig. 6, are shown in Fig. 7. The area, marked by a blue rectangular is the most sensitive and at the same time the most trusty area. All $\mu^{\prime}$ descriptors, taken from this area are practically the same: they are robust and do not scatter. The “optimally chosen” MAT descriptor, $\mu^{\prime}$ ( $I_{ai}=$ 8 mA, $I_{bj}=$ 44 mA), was taken from the middle of the rectangular, and it is illustrated by crossing lines in Fig. 7. It means that the optimal chosen $\mu^{\prime}$ -degradation function is one single element in the previously defined matrix $\mu^{\prime}$ with the above defined coordinate $I_{ai}$ and $I_{bi}$ , and this element is the most sensitive to the artificial slot. The same parameter was used in Fig. 9 as well.

In another arrangement the nonmagnetic spacer/spacers were placed between the two plates, as indicated in Fig. 8. Again, spacers with three different thicknesses (0.075 mm, 0.150 mm and 0.210 mm) and the reference case, without spacer were applied. The results are given in Fig. 9.

For the sake of the complete investigation, an arrangement was also investigated, where one spacer was placed between the yoke and the top plate surface, and another one between the two plates. Very similar results to those shown in Figs 6 and 9, were obtained (not presented here), where the total sum of thicknesses of the two spacers was considered.

All other possible configurations of the three spacer applications were also studied, but in all cases when the total thickness of the nonmagnetic spacers was increased to 0.21 mm, the result was not satisfactory, similarly to the case, shown in Figs 6 and 9 for 0.21 mm spacer: no reliable detection of the artificial slot in the bottom plate was possible. Some indication of the slot is seen, the $\mu^{\prime}$ -degradation functions in their central region increase a bit, but the scattering of the measured points in such a case became comparable with the expected local maximum of MAT descriptors.

6. Discussion

It is evident from the measurements that the slot was clearly detectable in the given arrangements, in accordance with our previous experience. Existence of the 10 mm wide and 3 mm deep slot generated more than 50% change in the optimally chosen MAT $\mu^{\prime}$ -degradation functions.

Purpose of the present work is to analyze the influence of the air gap (and/or of the nonmagnetic spacer) on detectability of an artificial slot existing in the tested ferromagnetic plate. It is well known that the air gap is an important factor of the measurement, and in our present work we gave an empirical, quantitative estimation for the maximal thickness of the air gap, which still makes possible the detection of the slot in the given arrangement.

It was found that even a 0.15 mm thick air gap does not cause remarkable decrease in the variation of the properly chosen MAT degradation function. In the double plate arrangement, position of the air gap between the magnetizing yoke and the top plate surface is equivalent to its position between the two plates, and in case that there are air gaps both in the former and in the later position, their influence is simply summed up. This result is rather encouraging for possible practical applications.

Simulation results revealed that the slot-dependent change of the magnetic flux density in the “yoke-plates” open magnetic circuit decreases rapidly by increasing the air gap. It can be determined from Fig. 2 that the magnetic flux change due to the presence of a slot is less than 1 percent if a 0.15 mm wide air gap is considered in the given geometry. In spite of this fact, the slot can be well detected by the Magnetic adaptive testing. This experience shows an excellent applicability of MAT even in this case.

The possible explanation of this unexpected sensitivity is that during the MAT evaluation the derivative of permeability is used. Due to any air gap the flux density in the open magnetic circuit decreases dramatically – as proved by the simulation – but the primarily measured signal (which is shown in Fig. 4) is proportional to the differential permeability, $\mu$ , of the circuit. This differentiation improves the signal to noise ratio significantly. One more reason of the very satisfactory difference between the “slot – no slot” case is that the MAT measurement results (shown in Figs 6 and 9) were evaluated from the derivative of differential permeability, so that one more derivative is applied. As it is seen in Figs 6 and 9, the $\mu^{\prime}$ -degradation functions ( $\mu^{\prime}=d\mu/dI$ ) were found to characterize the local thinning of the plates the best (The $\mu$ -degradation functions did not result in such a satisfactory signal/noise ratio).

Next factor, which supports the good results is, that the degradation functions are always normalized by a reference value (The reference value in this case is the level of the corresponding degradation function measured far from the position of the slot, i.e. the “no-slot” level). It means that even a small difference becomes large by this normalization.

It may seem surprising that the evaluated experimental curves (Figs 6 and 9) practically do not depend on thickness of the air gap in the investigated range. This fact seems to be in contradiction both to the results of simulation (Fig. 2), and to the significant decrease of the permeability curves shown in Fig. 4. However, the explanation is again the normalization: the larger air gap results in lower permeability, but these lower $\mu$ values are valid also for the reference measurement.

It is seen in Figs 6 and 9 that for larger air gaps the shape of the $\mu^{\prime}$ -degradation curves is wider. This effect is very well seen on both of the figures, but it is not significant, and it has no influence on the proper detection of the slot in the bottom plate.

7. Conclusions

Detectability of a 10 mm wide and 3 mm deep artificial slot, placed at the bottom of a 6 mm thick steel plate was investigated by Magnetic adaptive testing when the measurement was performed through another 6 mm thick steel plate. Role of an air gap between the magnetizing yoke and the top plate surface and also between the two plates was studied. It was found that if the thickness of the air gap (or sum of the thicknesses of air gaps) was not larger than 0.15 mm, it had no influence on detectability of the slot. This result shows the excellent applicability of MAT in this case, and it is encouraging for possible future practical applications.

The empirical results were modelled by electromagnetic simulation and it was shown that air gap caused a dramatic decrease of the relative change of the magnetic flux, due to the presence of a bottom slot. However, in spite of this big change, detection of the slot is possible with a good signal/noise ratio. This result was interpreted and explained.

Footnotes

Acknowledgments

This work was supported by the Hungarian Scientific Research Fund (project K 111662), by the Researcher Exchange Program between the Japan Society for Promotion of Science and Hungarian Academy of Sciences, and by the Researcher Exchange Program between the Czech Academy of Sciences and Hungarian Academy of Sciences. The co-author I.T. also appreciates financial supports by project No. 14-36566G of the Czech Science Foundation. The work was also partly supported by the JSPS Core-to-Core Program “Advanced Research Networks: International research core on smart layered materials and structures for energy saving”.

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