3D modeling and experimental validation of flaw responses provided by Magnetic Flux Leakage NDT system inspecting ferromagnetic pipes

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1 19 th World Conference on Non-Destructive Testing D modeling and experimental validation of flaw responses provided by Magnetic Flux Leakage NDT system inspecting ferromagnetic pipes Guillaume WOLF 1, Edouard DEMALDENT 2, Christophe REBOUD 2, Stéphane BARREZ 1, Adrien TRILLON 1, Francois DENEUVILLE 1 1 Vallourec Research Center France, 60 Route de Leval - BP20149, Aulnoye-Aymeries, France 2 CEA LIST, Saclay, Gif sur YvetteGif-sur-Yvette, France Contact guillaume.wolf@vallourec.com Abstract. Magnetic flux leakage is a well-known non-destructive testing for ferromagnetic pipes during production at Vallourec. A testing bench is composed of an inductive circuit to create very high magnetic field within the piece under test and one or several sensors on the outer side of the pipe to detect flux leakages due to flaws. As opposed to other non-destructive techniques (like UT, ECT, RT, etc.), there is no available dedicated modeling tool on the market for this technology permitting to ease the development of new innovative sensors or optimize the testing. Vallourec Research Center France (VRCF) and CEA LIST are collaborating to develop a tool to fulfil this lack. Concerning modeling, this problem is difficult to solve due to high differences between flaw and magnetic circuit in terms of size and magnetic nonlinearity of ferromagnetic pipes. This article presents results in the magneto-static case with linear behavior based on surface integral framework by CEA LIST. The results from this modeling are compared to finite element modeling (FEM) on a set of longitudinal and oblique reference notches, and also to experimental data coming from 3D active Hall effect sensors developed by the Vallourec Research Center. Benefits of the proposed solution and perspectives of this tool are discussed. Introduction The magnetic flux leakage (MFL) testing method is one of the most widely used nondestructive testing techniques (NDT) and has been extensively used in the quality loop control for pipe production. Among all the classical NDT techniques (ultrasonic testing, eddy current testing, radiographic testing), magnetic flux leakage testing is especially efficient in the detection of volumic defects in ferromagnetic material. In particular on-line flux leakage testing is used for ensuring process reliability and is particularly well suited to detect imperfections generated by the rolling process that can create longitudinal and oblique flaws. MFL testing relies on the fact that when a magnetic field is applied to a piece of ferromagnetic material, any geometrical discontinuity in the material will cause the field to License: 1 More info about this article:

2 leak out of the material, into the air [1]. This flux leakage is measured by a magnetic field sensor such as inductive coils, Hall effect sensors or also magnetoresistive sensors (AMR, GMR). The Vallourec Research Center France (VRCF) is deeply involved in the improvement of MFL techniques within Vallourec mills: development of innovative sensors or signal processing techniques. To do so our Lab is equipped with a Rotomat Ro440 based apparatus provided by Institut Dr Foerster illustrated in Figure 1. The excitation magnetic field is performed through inductive coils with DC-current. The magnetization field is channelled to the pipe through magnetization shoes. Between the two shoes, the field is channelled by the wall thickness. In the presence of a flaw, the field leaks. To catch the leakage, the magnetic field is measured at the surface of the pipe. (a) global overview (b) Pipe, sensor and magnetization shoe Fig. 1. Description of VRCF MFL lab bench Improvement of MFL technique only by experiments would prove to be costly and time consuming. Conversely, modeling allows exploring new concepts, choosing the right direction for the development and limiting the necessary experiments. To our knowledge, there is no dedicated modeling software in the market. The only manner to model this problem is to resort to finite element modeling through commercial software able to handle electromagnetic equations. Finite element modeling is well-known to be efficient to deal with problems with complex geometries. Nevertheless, even with commercial software, the set-up of the models is not easy and the required computation time and memory can be very high. To overcome these limitations and improve the performance of flaw detection, CEA LIST and the VRCF are collaborating on MFL modeling. A first model has been proposed to simulate magnetic field for MFL testing [2], which allowed the simulation of 3D defects in a first simulation tool dedicated to longitudinal flaws inspection. This model is now integrated as a 3D MFL plug-in into the CIVA software, and offers fast and accurate simulation of 3D defects, whatever the orientation of the notch. This paper presents this 3D model, compares the results obtained on longitudinal and oblique 3D flaws to finite element model (FEM) simulation. Finally, validation experiments are conducted by using a 3D magnetic sensor developed by the VRCF. 2

3 2. 3D models for magnetic flux leakage testing 2.1 Integral model As a first approximation, the magnetic field is assumed to be static. It means that the eddy currents due to the rotation of the pipe are not taken into account. This assumption allows reducing the model to a Laplace problem. This problem is considered under the integral form of the simple layer potential [3]. In this case, the surface density to be determined on the surface of the magnetic objects is the normal component of the magnetization vector. The magnetic field is computed through the calculation of the radiation of the density solution at the observed points. For this study, the pipe and the magnetization shoes (Figure 1.b) are finely meshed and the cylindrical circuit between the poles (Figure 1.a) (with the coils) is grossly meshed. The mesh and the surface density are illustrated in Figure 2. The same magnetic permeability has been used for all the pieces (relative magnetic permeability is 420). The main difficulty is to represent a small reference notch (less than 1 mm in deep and width) in a huge system (the outer diameter of the cylinder measures around 1.3m and the pipe is 1m long). Moreover, the surface density around the defect is low regarding the density around the poles; it may lead to numerical noise in the defect area. This problem should be normally solved through the fine meshing around sharp edges of the geometry and around the defect. Furthermore, approximate functions resorted are 2nd or 4th order polynoms. Thanks to this, the mesh can be unleashed around the poles and the defect allowing a reasonable computation time and a good accuracy of the solution. Fig. 2: normalized solution of the integral probe. From left to right: global overview, zoom on pole and pipe, zoom on the notch. Coils are illustrated in yellow and the meshing is in white To avoid a different meshing at different position of the notch around the pipe, it is referred to put the notch at the top of the pipe and to observe the magnetic field around the notch. 2.2 Finite element model Simulations of magnetic flux leakage testing have also been carried out with a FEM software package (COMSOL Multiphysics). One of the advantages of FEM software is the possibility to handle a wide range of physics and geometries. In order to reduce the numerical noise and to obtain sufficiently accurate results, the notch and pipe have been finely meshed (Figure 3). The schemes discretization in space is based on second-order elements. 3

4 Fig. 3: mesh discretization. From left to right: global overview, zoom on pole and pipe. Even though it would have been possible to take the pipe rotation into account, it was decided to model a stationary pipe for this study. As in the integral model, the notch was positioned at the top of the pipe. 3. Comparison with experimental data on a longitudinal notch 3.1 Test-cases definition To validate the models, a test case has been defined as described hereunder: Carbon steel pipe: - Outer diameter: mm; - Wall thickness: mm. Rotation speed: 200 rounds/min; Linear speed of the pipe: 1000 mm/min. All the pieces have a relative magnetic permeability of 420. The rotation speed is low enough to respect the magneto-static assumptions and to limit the effects of the eddy currents in the pipe. In a first stage, modeling results and experimental data (from the VRCF bench) are compared on a longitudinal reference notch and then on oblique notches with the following characteristics: Table 1. Notches characteristics Notch Length Width Depth Obliquity (around pipe longitudinal axis) Longi 5% of the wall mm 1 mm thickness i.e mm 30 The 3D distribution is measured by employing a high sensitivity 3 axis magnetic Hall effect field sensor designed by VRCF, illustrated in Figure 4. 4

5 Fig. 4: illustration of the 3D sensor The three directions are measured: the radial one one, and the longitudinal one as illustrated in Figure 5., the tangential Fig. 5: conventions for the magnetic field The magnetic field is measured at a height of 1 mm above the pipe outer surface. 3.2 Mapping for the longitudinal reference notch Mappings represent the magnetic field measured around the pipe and in the area around the notch. For all the mappings, the x-axis represents the longitudinal position of the sensor along the length of the pipe (Z) and the y-axis the angular position around the circumference of the pipe (Ө). To compare all the results together (experimental data and simulated data), the entire dataset has been normalized according to the maximum amplitude of the signal. It must be stated that a modeling of the sensor, in particular of its active area, is integrated into the simulation to fit as much as possible to its real behavior. The comparison of mapping of the radial direction of the measured magnetic field and simulated magnetic field through the integral form and finite element model is illustrated on Figure 6 in the case of the longitudinal reference notch. (a) Magnetic field measured on the VRCF bench Fig. 6: mapping of the radial direction (c) Simulated magnetic field (finite element model) 5

6 The comparison of mapping of the tangential direction of the measured magnetic field and simulated magnetic field through the integral form and finite element model is illustrated on Figure 7 in the case of the longitudinal reference notch. (a) Magnetic field measured on the VRCF bench Fig. 7: mapping of the tangential direction (c) Simulated magnetic field (finite element model) The comparison of mapping of the longitudinal direction of the measured magnetic field and simulated magnetic field through the integral form and finite element model is illustrated on Figure 8 in the case of the longitudinal reference notch. (a) Magnetic field measured on the VRCF bench Fig. 8: mapping of the longitudinal direction (c) Simulated magnetic field (finite element model) Results appear similar, thus illustrating the efficiency of the model. Slight differences could be explained by a lower resolution along the z axis of measured data compared to simulated ones. Another explanation is relative to the resolution of the sensor itself. In the case of simulated data, the mapping is the magnetic field picked-up on points whereas in the case of experimental data, the measurements cannot be point-wise due to the size of the active area of the magnetic sensor. 3.3 Comparisons between experimental data and simulated data on a longitudinal reference notch In order to compare the models with the experimental data, the three components of the magnetic field are plotted together. and have been validated and presented in [2]. Thanks to the 3D sensors we are now able to compare simulation and experimental data for the longitudinal component. On Figure 9 the longitudinal field is plotted in the case of the longitudinal reference notch. On the left, the maximum value for each spire is plotted. On the right, the maximum value for each line is plotted. 6

7 z [mm] Fig. 9: longitudinal component for a longitudinal notch The correlation between simulated field and the measured field is good illustrating the efficiency of the model. 4. Cases of oblique defects Modeling results and experimental data from the VRCF bench are compared on the oblique notches described in section 3.1. First, mappings and amplitudes of the three components of the magnetic field are compared in the case of a 30 obliquity reference notch. The response of the 15 and 30 oblique notches are then compared to the longitudinal notch. 4.1 Mapping for the oblique 30 reference notch Mappings of the three components obtained by experiment and simulation through the integral form and finite element model are compared in Figure 10, Figure 11 and Figure 12 in the case of the 30 reference notch. (a) Magnetic field measured on the VRCF bench Fig. 10: mapping of the radial direction (c) Simulated magnetic field (finite element model) (a) Magnetic field measured on the VRCF bench Fig. 11: mapping of the tangential direction (c) Simulated magnetic field (finite element model) 7

8 (a) Magnetic field measured on the VRCF bench Fig. 12: mapping of the longitudinal direction (c) Simulated magnetic field (finite element model) Results appear close together illustrating the efficiency of the model. Slight differences could be explained by a lower resolution of measured data compared to simulation ones and size of the active area of the sensor. 4.2 Comparisons experimental data / simulated data on the oblique 30 reference notch In order to compare the models with the experimental data, the three components of the magnetic field are plotted together. Figure 13, the normal field is plotted in the case of the 30 notch. On the left, the maximum value for each spire is plotted. On the right, the maximum value for each line is plotted. Figure 14 and Figure 15, the same plots are illustrated for the tangential field and the longitudinal component z [mm] Fig. 13: radial component Sim integral form z [mm] Fig. 14: tangential component for a 30 notch for a 30 notch

9 Sim integral form z [mm] Fig. 15: longitudinal component for a 30 notch It appears on these figures that the simulated field and the measured field have a good matching. The asymmetry of the components along the angular position θ (figures at the right) is present in experimental data and simulated data. Nevertheless, along the longitudinal z position the step-like profiles in the simulated data (figures at the left) are not observed in the experimental data. This difference could be explained by the limited resolution along z axis and also by the fact that the modeling of the transfer function of the sensor should be still optimized. 4.3 Comparisons of longitudinal and oblique defects response The responses of the three notches described in section 3.1 are compared in the following section. In Figure 16, the maximum of the amplitude measured on each notch is compared to simulation. The notch presenting the maximum amplitude is taken as reference. response of the notch [db] Radial direction of the magnetic Field longi notch (a) radial direction Sim Integral form sim FEM response of the notch [db] Tangential direction of the magnetic Field longi notch (b) tangential direction Longitudinal direction of the magnetic Field longi response of the notch [db] notch (c) longitudinal direction Fig. 16: Comparison of response of oblique notches compared to longitudinal defect The two models give satisfactory results close to the experimental data, in particular for the radial and tangential direction. 9

10 Nevertheless, we observe some minor differences in maximal amplitude (around 4 to 5 db) between experimental data and models on the longitudinal component of the magnetic field. This could be explained by the difficulty to catch the edge of the notch, where the signal is maximal, with the axial resolution used for the experiment. It must be also stated that the longitudinal direction shows a better detection in the case of oblique defects compared to longitudinal ones. An improvement of 4 db in the case of 15 obliquity flaw is achieved. In addition to the way to handle the sensor and the manufacturing tolerances of the notches used in experiments, the differences between experimental data and simulated data could be explained by: Magneto-static assumption: the eddy currents are not taken into account with these models. This can influence the results even if the experimental data are acquired with a low rotation speed; Nonlinear material: the B-H curve is not taken into account in this model. The magnetic permeability is the same in all the elements. This also could influence the results. These points represent potential ways of evolution of the models which could be studied in the future to raise the models as close as possible to the experiments. 5. Conclusion Through a partnership between Vallourec Research Center France and CEA LIST, two modeling methods of magnetic flux leakage inspection of ferromagnetic steel pipes has been developed using respectively integral forms and finite elements. Results of the modeling show a good matching with experimental data for the three directions both on longitudinal and oblique flaws. In conclusion, models appear as promising for supporting future developments in Magnetic Flux leakage inspection. This work has permitted also to underline some potential ways of evolution in order to get more realistic models. For examples, the transfer function of the sensors should be optimized into the models to take more precisely in account the active area size of the sensor. The resolution along the axis of the pipe could also be improved. The authors would like to thank Alexandre Mallart and David Louboutin for the simulations, Samuel Poulain and Antoine Marion for the experimental measurements. References [1] Y. Sun, Y. Kang, A new MFL principle and method based on near-zero background magnetic field, NDT & E International, 43, Issue 4, (2010). [2] A.Trillon, E. Demaldent, C. Reboud, S. Barrez, F. Deneuville, "Modeling of magnetic flux leakage testing through surface integral formulation", ECNDT2014 Conference Proceedings, 2014 [3]. U. Langer, M. Schanz, O. Steinbach, W. L. Wendland, Fast Boundary Element Methods in Engineering and Industrial Applications, Springer, Lectures Notes in Applied and Computational Mechanics, Volume 63 (2012). 10