Efficient magnetization is the basis to realize MFL inspection for inner defects. There are three types of MFL methods using different magnetization modes, namely, pulsed MFL [29], alternating current (AC) MFL [30, 31] and direct current (DC) MFL. However, for deep-buried defects inspection, the former two magnetization methods are unsuitable due to skin effect of alternating magnetic field. In contrast, with large DC magnetizing intensity, DC MFL can magnetize thick specimens into saturation status to maximize leakage magnetic field of deep-buried defects. In this paper, a Helmholtz coil magnetizer are proposed to produce a strong and uniform magnetizing field for thick specimen. In order to validate the MFL course of inner defects, numerical simulations are conducted by Ansoft Maxwell with the magnetostatic solver. A two-dimensional finite element method (FEM) model is built as shown in Figure 2. The parameters of the Helmholtz coils are as follows: the height of the coil is 100 mm, the thickness of the coil is 100 mm, the distance between the coil inner surface and the specimen surface is 20 mm, and the distance between the two coils is 100 mm, respectively. An inner defect (width: 4.0 mm; height: 6.0 mm) is made inside a steel plate (length: 1000.0 mm; thickness: 100.0 mm; Relative permeability: μ-H curve of ASTM A29). The magnetization current density in each coil is set as 6 × 106 A/mm2 to magnetize the thick plate into saturation state.
Figure 3 shows the distorted magnetic field distribution caused by inner defects with buried depths of 0.0 mm, 2.0 mm, 5.0 mm and 8.0 mm, respectively. The rainbow lines above the specimen surface display the leakage magnetic flux distribution BMFL. It can be seen different BMFL distributions are generated by these defects with different buried depths. In addition, with the buried depth increasing, leakage magnetic flux density is decreasing.
In previous MFL distribution studies, the BMFL above the specimen surface is the main concern while the magnetic flux distribution inside the specimen has been ignored. In order to investigate the magnetic effect of near-surface wall on the MFL course, the magnetic flux distributions inside the specimen are simulated as indicated by rainbow color map. It can be seen that the magnetic flux in the near-surface wall is distorted greatly, and that the BMFL above the specimen is actually generated by the distorted magnetic flux in the near-surface wall. As displayed in Figure 3(a), along the collecting line Lc (length: 30.0 mm; lift-off distance ld: 1.0 mm) the normal component of magnetic field above the surface-breaking defect is collected and indicated by red solid line as shown in Figure 4. It can be seen that the signal manifest itself an odd function with the sharpest gradient in the center. In addition, there is a baseline-shift phenomenon of the testing signal. Specifically, the left side of the signal has a positive baseline shift while the right side is characterized by a negative one, which will result in a rough evaluation.
As schematically illustrated in Figure 5, the measured magnetic field (defined as Bm-defect) at the sensor location is actually composed of leakage magnetic field generated by the defects (defined as BMFL), magnetizing field generated by the magnetizer (defined as Bmg), and the demagnetizing field caused by the specimen (defined as Bdmg). Background magnetic field (defined as Bbk) is composed of the Bmg and the Bdmg. The relationship can be expressed by follows [33]:
$$B_{{\text{m-defect}}} = B_{{{\text{MFL}}}} + B_{{{\text{mg}}}} + B_{{{\text{dmg}}}} = B_{{{\text{MFL}}}} + B_{{{\text{bk}}}}$$
(7)
where Bmg and Bdmg are determined by the magnetizing field distribution and the specimen structure. The Bbk is normally constant under the same conditions.
When there is no defect in the specimen, the measured magnetic field Bm-defect-free contains only Bbk:
$$B_{{\text{m-defect - free}}} = B_{{{\text{bk}}.}}$$
(8)
Then, BMFL can be obtained from Eq. (7) by subtracting Eq. (8):
$$B_{{{\text{MFL}}}} = B_{{\text{m-defect}}} - B_{{{\text{m - defect - free}}.}}$$
(9)
In order to eliminate the Bbk and observe the BMFL alone, a defect-free specimen under the same condition is simulated. The normal component of the Bm-defect-free (defined as Bzm-defect-free) is calculated and indicated by black solid line in Figure 4. It can be seen that the Bzm-defect-free shows a slash with a negative slope. After subtraction, the normal component of BMFL (defined as BzMFL) is obtained as indicated by the blue solid line, and the baseline shift phenomenon disappears. In the following simulation, the Bbk will be eliminated by the same subtraction method, and the peak amplitude of BzMFL (defined as Vp) will be used to compare the sensitivity as shown in Figure 4.
Further, ten defects with different buried depths from 0.0 mm to 10.0 mm are simulated. Along the collecting line Lc at the same lift-off distance ld of 1.0 mm, the BzMFL are collected and plotted, as shown in Figure 6. It can be seen at the same lift-off distance ld of 1.0 mm, the deeper-buried defect generates a weaker signal response. Then, their peak amplitudes of BzMFL (Vp) are extracted and indicated by dotted blue line in Figure 7, which shown a descending trend with the increasing buried depth. Further, along other collecting lines Lc with the ld varying from 2.0 to 9.0 mm, the Vp of the ten defects are extracted and displayed in Figure 7. It can be seen that the deeper-buried inner defect has a lower sensitivity at the same lift-off distance ld.
The above simulation is used to illustrate different MFL course of defects D1 and D2, as shown in Figure 1(a). As we know, there are two different influencing factors, i.e., the distance between the sensor and the inner defect, and the magnetic effect of the near-surface wall, which must be analyzed separately.
In order to analyze the magnetic effect of near-surface wall, the distance between the defect and the sensor is set as a fixed value of df as illustrated by the Defects D2, D3 and D4 in Figure 1(a). Firstly, setting the fixed distance df of 10.0 mm, the BzMFL of ten inner defects are collected and plotted in Figure 8. It can be seen that when the df is set as a fixed value, the deeper-buried defect generates a stronger signal response. Then, their Vp are extracted and indicated by black solid line in Figure 9, which shown an increasing trend with the buried depth increasing. Further, other df (from 1.0 mm to 9.0 mm) are simulated, as shown in Figure 9. The results validate that the near-surface wall actually has an enhancing effect on the MFL course of inner defect. The simulation results match the theoretical model well as expressed by Eq. (5).