Proceedings of the ASME 2011 Pressure Vessels & Piping Division Conference PVP2011 July 17-21, 2011, Baltimore, Maryland, USA PVP2011-57514 NUMERICAL SIMULATION AND EXPERIMENTAL RESEARCH ON CRACK MAGNETIC FLUX LEAKAGE FIELD Fujun Liu*, Mulin Zheng, Shuai Kong, Zhangwei Ling, Yueqiang Qian (Zhejiang Provincial Special Equipment Inspection and Research Institute, Hangzhou, Zhejiang, China, 310020) ABSTRACT Magnetic flux leakage (MFL) testing is widely used to inspect and characterize defects in pipelines, storage tanks and other structures. In this paper, based on the Maxwell Equations, numerical simulation and experimental research of crack magnetic flux leakage field were carried out. The three-dimensional models of cracks were established, the influence of the generalized crack parameters to the magnetostatic MFL field, including depth, width, inclination angle and crack spacing, was discussed. The relationship between defect parameters and MFL amplitude was obtained. The amplitude is significantly affected by the inclination angle. Therefore, single direction inspection may lead to undetected in practice. While the two cracks interval is less than 5 mm, the MFL fields would overlap. Furthermore, the experimental investigations were developed, and the results agree well with that of the simulation. The conclusions could provide valuable reference for inspection. INTRODUCTION The tanks and pipelines are important carrier for transfer and storage of crude oil, natural gas, and petrochemical raw materials. However, the leakage of storage tanks and pipelines occurs frequently due to corrosion, mechanical damage and other causes. Thus, periodic inspection and safety evaluation is necessary. In comparison with other detection technologies, the magnetic flux leakage (MFL) testing is more effective, lower cost and has little influence by oil contaminant. Thus the MFL testing is widely used to inspect and characterize defects of in-service storage tanks and pipelines. Literatures [1, 2] took the MFL testing as one of the comprehensive testing and evaluation technologies applied in in-service tank floor, and pointed out the main influence factors of MFL testing such as the direction, position, depth and dimension of defects. In literature [3], the leakage field of local corrosion and surface pit defects were analyzed by experimental and theoretical models, and pointed out that the corrosion defect leakage field increased with the corrosion depth. In literature [4], based on current MFL machines, defects located on the top and those on the bottom of the tank floor were distinguished, and the experimental results showed that there was a very high similarity between signals belonging to top and bottom defects which suggested such discrimination was not viable using standard MFL. 1 Copyright 2011 by ASME
Presently, almost MFL published research take corrosion defects as the research object, but the cracks are considered as the most dangerous in all defects of tanks and pipelines. According to incomplete statistics, 80% of the fire and explosion accidents in petrochemical plants are caused by cracks in the components. Stress concentration, alternating load, vibration and other factors during production operation could cause stress corrosion cracks, fatigue cracks in the weld, heat affected zone or structural discontinuity, which greatly reduce the safety of the tanks. In this paper, based on the electromagnetic theory [5-9], the complex natural cracks were simplified. Numerical simulation and experimental research of crack MFL field were carried out. The three-dimensional models of cracks were established. The influence of the generalized crack parameters to the magnetostatic MFL field, including depth, width, inclination angle and crack spacing, was discussed. The relationship between defect parameters and MFL amplitude was obtained. Furthermore, the experimental investigations were developed, and the results agreed well with that of the simulation. with the MFL field. Therefore in this paper we extend that work further by numerical simulation software for modeling and simulation analysis. NUMERICAL SIMULATION OF CRACK MFL Analytical model The geometry of the natural cracks in engineering practice is complex and irregular, which induced the MFL field became random and fuzzy. In this paper we simplified the complexity of the natural cracks, and the crack shape is similar to the simplified upper face groove, the lower part of the V-shaped, as shown in Figure 1. NUMERICAL SIMULATION MODEL OF MFL MFL testing is dependent on the quantitative relationship between the electromagnetic energy and the components. The quantitative relationship could be expressed by the Maxwell's equations. The Maxwell's equations are the basis of macro-electromagnetism problems, the differential equations as followed: B E 0 (1) t D H 0 (2) t D (3) B 0 (4) E--Electric intensity (V/m); D--Electric flux density (C/m 2 ); H--Magnetic field intensity (A/m); B--Magnetic flux density (Wb/m 2 ); J--Current density (A/m 2 ); ρ--charge density (C/m 3 ). It is difficult to apply the Maxwell's equations to deal a crack b meshed crack Figure1 crack model In this paper, the magnetostatic MFL field of cracks was 1 keeper 2 permanent magnet 3 pole shoe 4 air gap 5 steel plate 6 crack FIGURE 2 SIMULATION MODEL OF CRACK MFL analyzed using edge element method. As shown in Figure 2, the model was consisted of two NdFeB permanent magnets 2 Copyright 2011 by ASME
which magnetized the steel plate, the ferromagnetic plate was FIGURE 3 MESHED SIMULATION MODEL OF CRACK Q235 with thickness 6mm, and the keeper and pole shoes were high magnetic conductive material electrical pure iron. The SOLID117 was selected as the unit type according the Equation (5) represents that the leakage magnetic field is a multi-dimensional function on the crack location, geometric parameters and other parameters. In this section the influence of the generalized crack parameters to the MFL field, including depth, width, inclination angle and crack spacing, was discussed. The relationship between defect parameters and MFL amplitude was obtained. Influence of the crack depth Crack depth is the most important parameter for component security. In order to determine the influence of the crack depth to MFL, the simulation model of the cracks had width 1mm, length 40mm, and depth from 1mm to 6mm with 1mm increment, and totally 6 cracks were built with 3-D simulation model. The amplitude of magnetic flux density B and crack depth was carried out as shown in Figure 5, which FIGURE 4 THE RESULT OF CRACK MFL SIMULATION edge element method and was used to map grid for crack MFL filed, as shown in Figure 3. Took the crack with depth of 4mm, width of 1mm as an example, the results were shown in Figure 4. Figure 4 showed that magnetic flux density B larger in ferromagnetic plate than in the air above the crack, and B attenuated quickly in the air, the reason for results was that the permeability of ferromagnetic material was much larger than the air permeability. Influence of crack parameters to MFL The crack leakage magnetic field is a space vector, which is a distribution function about crack coordinates (x, y, z), depth (h), width (w), length (l), angle (β), namely: B f x, y, z, h, w, l, (5) FIGURE 5 THE RELATIONSHIP CURVE OF MAGNETIC FLUX DENSITY B AMPLITUDE AND CRACK DEPTH illustrated the relationship curve between amplitude of B and crack depth, the amplitude of B increased as the crack depth, and the curve fitting as monotone increasing line. So when the other geometric parameters of cracks such as length, width, inclination angle are unchanged, the amplitude of crack MFL B increasing linearly with as crack depth as, namely: Bp abh bb (6) B p amplitude of magnetic flux density, T h crack depth, mm a B coefficient b B --constant The a B and b B are the coefficients associated the geometry parameters of the crack and detection conditions. 3 Copyright 2011 by ASME
Due to B H, similarly, the relationship between amplitude of crack MFL field intensity H and crack depth is increasing linearly, namely: Influence of crack width H p ahh bh (7) The width is an important parameter of the crack [9]. However there is little work had been reported on the crack width influence. In this section the crack MFL simulation models were established with depth 3mm, length 40mm, width from 0.5mm to 5mm, with 0.5mm increment, totally 10 cracks, to analyze the influence of width on crack MFL. The relationship fitting curve between amplitude of crack magnetic field intensity H and the crack width was shown in Figure 6. depth 4mm, were established. Then the inclination angle β thaws changed in order to analyze the influence of β to the crack MFL. Figure 8 shows the results of B and H when the β changing. It is shown that with the crack angle increasing, B and H are increasing as well, and the relationships between the crack inclination angle and the B and H are monotone increasing. FIGURE 7 THE CRACK INCLINATIONβ FIGURE 6 THE RELATIONSHIP CURVE OF MAGNETIC FIELD INTENSITY H AMPLITUDE AND CRACK DEPTH Figure 6 shows that the amplitude of H has the maximum when the width is 0.5mm, and as the crack width increased from 0.5mm to 5mm, H decreases quickly. It is shown that the relation between the amplitude of H and crack widths is monotone decreasing linearly. Influence of crack inclination angle The acute angle between the direction of magnetic field and crack axial was defined as the inclination angle of crack, indicated as β, showed in Figure 7. The crack inclination angle played an important role in crack MFL analysis [10], and had greater impact on crack MFL, especially in the engineering practical inspection. According to practical inspection, the crack simulation models with length 40mm, width 1mm, and FIGURE 8 THE RELATIONSHIP CURVE OF MAGNETIC FIELD AND CRACK INCLINATION Influence of two parallel cracks spacing In practical, there could be two or even more cracks existing in the same area [7], and the MFL of cracks could be superimposed. In order to analyze the influence of multiple cracks to the MFL, 10 crack models were established with length 40mm, width 1mm and depth 4mm, and the spacing were 0.5mm, 1.0mm, 2.0mm, 3.0mm, 4.0mm, 5.0mm, 8.0mm, 10.0mm, 12.0mm and 15.0mm, respectively. The distribution curves of crack MFL B for each spacing are shown in Figure 9. From Figure 9, it is shown that when the two cracks parallel spacing are 0.5mm and 1mm, the crack MFL B has only one peak, thus we know that when crack spacing is less than or equal to 1mm, the crack MFL could be superimposed seriously. The curves of B gradually appeared two peaks when 4 Copyright 2011 by ASME
the spacing increasing. It means that the influence of two cracks becomes weak gradually. From Figure 10, it is shown that when the spacing is larger than 5mm, two obvious peaks appear in distribution curve. When the spacing increasing to 10mm, the leakage field has little influence to each other, and when the spacing increasing to 15mm, there was no influence between each other at all. with length 40mm, depth 3mm, width from 0.5mm to 5.0mm, totally 10 cracks. (3) Experimental plate of crack inclination angle The inclination angle experimental plate had crack length 40mm, width 1mm, depth 4mm, and the inclination angles from 0 to 90, with increment 15, totally 7 cracks, as shown in Figure 12. (4) Experimental plate with parallel cracks The experimental plate for parallel crack experiment was shown in Figure 13. The spacings between parallel cracks were 10mm, 8mm, 5mm, 3mm. A single crack was also made in the plate. All the cracks had same length 40mm, width 1mm, and depth 4mm. FIGURE 9 THE CURVE OF MAGNETIC FLUX DENSITY B OF DIFFERENT CRACK SPACE From the simulation results above, when two crack spacing was greater than 10mm, little influence between each other, and the two cracks could be distinguished clearly. FIGURE 10 THE EXPERIMENTAL PLATE OF CRACK DEPTH EXPERIMENTAL RESULTS To further verify the accuracy of numerical simulation, a MFL inspection experimental system was established, using artificial prefabricated cracks to simulate the natural cracks [11, 12]. Analysis of the relationship between crack signal amplitude and crack parameters such as crack depth, width, inclination angle and spacing of parallel cracks, was proposed. The experimental plate material was Q235 with thickness 6mm. FIGURE 11 THE EXPERIMENTAL PLATE OF CRACK WIDTH FIGURE 12 THE EXPERIMENTAL PLATE OF CRACK INCLINATION ANGLE Experimental plates for crack MFL detection (1) Experimental plate of crack depth The schematic diagram of experimental plate for crack depth experiment was shown in Figure 10. The crack length was 40mm, width was 1mm, and depth from 1mm to 6mm, totally 6 cracks. (2) Experimental plate of crack width The width experimental plate was shown in Figure 11, FIGURE 13 THE EXPERIMENTAL PLATE WITH PARALLEL CRACK 5 Copyright 2011 by ASME
Crack MFL detection experiment results (1). The amplitude values of MFL testing signal increased linearly with the crack depths, as shown in Figure 14. the MFL signals could not be detected effectively, thus there was no value in Figure 15 for angles 15 and 0. This result indicated that in practice, MFL testing should be scan from different directions to prevent crack detection missing. FIGURE 14 THE RELATIONSHIP CURVE OF AMPLITUDE OF MFL TESTING SIGNAL AND CRACK DEPTH (2). When the crack length and depth is constant, the amplitude values of MFL testing signal decreased linearly with the crack width increases, as shown in Figure 15. The results of depth and width experiments supported the numerical simulation analysis. It was confirmed that the conclusion of numerical simulation analysis. FIGURE 16 THE RELATIONSHIP CURVE OF AMPLITUDE OF MFL TESTING SIGNAL AND CRACK INCLINATION ANGLE FIGURE 15 THE RELATIONSHIP CURVE OF AMPLITUDE OF MFL TESTING SIGNAL AND CRACK WIDTH (3). The relationship between the amplitude values of MFL testing signal and the inclination angle was show in Figure 16. From Figure 16, we could get: (a) When the angle was 90, which meant the crack and external magnetic field was vertical, the amplitude value of testing signal was up to maximum. (b) The amplitude values of the MFL signals was obviously decreasing with the decrease of the inclination angle, as shown in Figure 15. When the angles are 15 and 0, FIGURE 17 THE RELATIONSHIP CURVE OF AMPLITUDE OF MFL TESTING SIGNAL AND CRACK PARALLEL CRACKS (4). Figure 17 showed the part of signals of MFL when MFL testing equipment moved on the parallel cracks plate from left to right which was shown in Figure 13. The signals showed that when the spacing less than or equal to 3mm, the signals was almost invariant, only the width of the signal increased, as shown the NO.4 and 5 in Figure 17. The experiments also proposed when the crack spacing was 5mm, the detection signal waveform appeared a little peak and valley value as shown the NO.3 in Figure17, and the small peak and valley of MFL signal increased gradually along with the crack spacing increased, when the crack spacing was 10mm, two obvious crack MFL detection signal waveforms occurred, the MFL detection signal had been no mutual 6 Copyright 2011 by ASME
influence, then the two cracks can be distinguished clearly, as shown the NO.1 in Figure 17. CONCLUSIONS In order to study the magnetic flux leakage (MFL), numerical simulation method had been used to simulate and analyze crack defects. Then, experiments were carried out to verify the calculated results. (1). The magnetic flux density B and magnetic field intensity H are increased linearly with crack depths. Additionally, the B and H are decreased linearly with crack width. (2). When the inclination angle β increasing, the B and H increase. Especially, when β is equal to 90, the B and H have the maximum values. In practice, MFL need be scan from different directions to prevent crack detection missing. (3). When the spacing between two parallel cracks is less than 5mm, the signals are superimposed seriously which leads to distinguish the cracks unreliable. When the spacing of two cracks amounts to 10mm, the MFL signals have no interference, thus these cracks could be identified easily. REFERENCE: [1] Liu, F. J., Guo, X. L., Hu, D. M., et al., 2010, Comprehensive inspection and evaluation technique for atmospheric storage tanks, Nondestructive Testing and Evaluation, 25(1), pp. 45-59. [2] Liu, Z. P., Kang, Y. H., Wu, X. J., et al., 2003, Recent development in magnetic flux leakage technology for petrochemical tank floor inspections, Materials Performance, 42(12), pp.24-27. [3] Kasai, N., Sekine, K., and Maruyama, H., 2003, Non-destructive evaluation method for far-side corrosion type flaws in oil storage tank bottom floors using the magnetic flux leakage technique, Journal of the Japan Petroleum Institute, 46(2), pp.126-132. [4] Ramirez, A. R., Mason, J. S. D., Pearson, N., 2009, Experimental study to differentiate between top and bottom defects for MFL tank floor inspections, NDT&E International, 42(1), pp. 16-21. [5] Khodayari-Rostamabad, A., Reilly, J. P., Nikolova, N. K., et al., 2009, Machine learning techniques for the analysis of magnetic flux leakage images in pipeline inspection, IEEE Transactions on magnetics, 45(8), pp. 3073-3084. [6] Minkov, D., Takeda, Y., Shoji, T., et al., 2002, Estimating the sizes of surface cracks based on Hall element measurements of the leakage magnetic field and a dipole model of a crack, Applied Physics A: Materials Science & Processing, 74(2), pp. 169-176. [7] Ravan, M., Amineh, R. K., Koziel, S., et al., 2009, Sizing of multiple cracks using magnetic flux leakage measurements, Science, Measurement & Technology, IET, 4(1), pp. 1-11. [8] Minkov, D., Lee, J., and Shoji, T., 2000, Study of crack inversions utilizing dipole model of a crack and Hall element measurements, Journal of Magnetism and Magnetic Materials, 217(1-3), pp. 207-215. [9] Li, L.M., Zheng, P., Huang, S. L., et al., 1999, Effects of surface crack width on Y component of magnetic flux leakage field, J. Tsinghua Univ (Sci &Tech), 39(2), pp. 43-45. [10] Kovacs, G., Kuczmann, M., 2009, Simulation and measurement of magnetic based nondestructive tester, Przeglad Elektrotechniczny, 85(12), pp. 76-79. [11] Zhang, Y., Ye, Z. F., Wang, C., 2009, A fast method for rectangular crack sizes reconstruction in magnetic flux leakage testing, NDT & E International, 42(5), pp. 369-375. [12] Christen, R., Bergamini, A., and Motavalli, M., 2009, Influence of steel wrapping on magneto-inductive testing of the main cables of suspension bridges, NDT & E International, 42(1), pp. 22-27. 7 Copyright 2011 by ASME