Detection of localized damage by eddy currents technique

. Non destructive evaluation techniques based on eddy currents (EC) are largely used for quality control of the castings in a lot of industries. The principle of detection by EC consists in using an adequate inductive coil to generate them by a variable magnetic field, and measuring their effects by using one or several sensors. These effects result from the interaction between the induced magnetic field and the excited conductive material. A local variation of the physical properties or geometry of the tested sample, due to a singularity or a flaw, causes a modification of the EC distribution, enabling thus detection. In order to optimize the capacity of defect revealing by means of EC based probes, an accurate modelling of the problem is essential. This can be used to perform simulation of the EC distribution under different circumstances and to analyze the EC sensitivity to the various implicated parameters. In this work, the modelling of EC is made by using the finite element method. Using a B-scan strategy was used, detection of a small defect having the shape of an open cavity is shown to be correctly indicated via monitoring variations of the induced voltage in the receiver coil.


Introduction
Non destructive evaluation (NDE) techniques based on electromagnetic methods are frequently used for damage detection in conducting metallic parts. These types of inspection methods are largely employed for quality control of for example the castings in car and oil industries, with the aim to detect surface and subsurface discontinuities in the tested parts. The electromagnetic based methods incorporate mainly two categories: magnetic particle inspection (MPI) [1] and eddy currents (EC) [2]. In the MPI based method, the process consists of putting a magnetic field into a ferromagnetic part such as iron, nickel, cobalt, and some of their alloys. The piece can like this be magnetized by direct or indirect magnetization. Direct magnetization occurs when the electric current is passed through the test object and a magnetic field is created in the material. Indirect magnetization occurs when no electric current is passed through the test object, but a magnetic field is applied from an outside source. The magnetic lines of force are perpendicular to the direction of the electric current which may take the form of either alternating current or direct current. The presence of a surface or subsurface discontinuity in the material allows the magnetic flux to leak. If ferrous iron particles are applied to a part with an area experiencing flux leakage, the particles will build up at this area and form what is called an indication. The indication can then be handled to determine what may have caused it.
The need to use ferrous particles makes the MPI less attractive than EC based methods. Moreover, EC testing uses electromagnetic induction to detect flaws in conductive materials that are not made necessary from ferromagnetic materials. The surface of the conductive material should however be accessible and the finish of the material should be enough smooth to not disturb the readings. In this technique, the depth of penetration into the material is controlled by the conductivity of the tested material and the frequency used. Flaws that lie parallel to the probe may not be detectable, so proper orientation of the probes should be arranged.
In a standard EC testing a coil carrying current is placed in proximity to the test specimen. The alternating current in the coil generates variable magnetic field which interacts with test specimen and generates EC. Variations in the phase and magnitude of these EC can be monitored using a second receiver coil or by measuring changes appearing in the current flowing in the primary excitation coil [3,4]. Variations in the electrical conductivity or magnetic permeability of the test object, or the presence of any flaws, will cause a change in these EC and as a consequence changes in the phase and amplitude of the measured current will be observed [5]. This constitutes the basis of standard EC inspection which is the most widely used EC technique in practice. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 3.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The main advantage of EC testing is that they can detect very small cracks in or near the surface of the conductive material. Use of the eddy currents as an inspection technique is expected to go forward because of its ability to be easily implemented, its cost which is not very expensive and the unnecessary contact with the part to be controlled. The increasing complexity of the structures to be controlled and the augmented requests in terms of capacity of detection, particularly in terms of reachable depth and orientation of flaws as well as on the dynamics of measurement and space resolution, have shown the limits of most of the actual EC sensors.
To extend the performance of detection in terms of accessible depth, signal ratio to noise and space resolution, it is useful to have a close understanding of measurement problems involved in the EC testing systems. Indeed the simplicity of implementing NDE by EC, because of the simplicity to create these currents by means of an inductor and to detect the induced field by a sensor should not cover up the very complex task associated to optimizing the configuration of a highly effective EC based probe. The challenge is about in fact, for a given control to be carried out, how to determine the optimal distribution of the EC probe making it possible to get the best signal indication of the defect. Many parameters enter in fact in the problem and it is suitable to carry out simulations which make enable to resolve the influence of each factor on the quality of the obtained indication.
In this work, modelling is performed for the EC generated in a homogeneous and isotropic perfect conductive mass, when subjected to the action of a stationary induction field created by a feed circuit. The modelling is conducted by means of the finite element method under Comsol software package [6]. Key parameters that include, the frequency of work, the distance separating the coil sensor form the tested sample are taken into account. Using a B-scan sweeping, the presence of a small defect having the shape of an open cavity is shown to be well indicated via monitoring the variations affecting the distribution of the EC. This opens the way to perform a parametric study in order to achieve optimization of the probe and to improve further the capacity of this system in detecting small flaws having various orientations.

Modelling eddy-current field in a perfect conductive material
Maxwell equations for a perfect conductive material are of the form where B is the inductive magnetic field, D the electric displacement, H the magnetic excitation vector, E the electric field, ρ the density of charges and J the current density.
In a perfect Ohmic homogeneous and isotropic conductive medium, the constitutive equations take the following form where σ is the electric conductivity of the medium, ε the permittivity and μ the permeability.
In case of a metallic material, the distribution of charges vanishes quickly due to the high conductivity and it is quite admissible to assume the hypothesis that 0 ρ = .
A decoupling can then be operated in the Maxwell system of equations (1), to obtain the following propagation-diffusion equations Let's consider a stationary and harmonic regime which is occurring at the radial frequency ω for which ( ) 0 Equations (2) and (4) yield the existence of a permanent density of currents that are permanently circulating in the conductive material and having the form These are called eddy-currents (EC).
For a given sample geometry, the field J can be computed by integrating equations (4) under some specified boundary conditions. In the presence of a singularity or a flaw in the medium, the conductivity varies and the EC distribution will manifest changes as compared to that one associated to the intact geometry. This gives hence the possibility of using these EC to monitor flaw detection in metallic parts. circuit that is influenced by the variable magnetic field created by the EC. This can provide thus the defect indication as a perturbation endured by the electric tension while the sensor is crossing a zone with variable local conductivity.
The material is excited by a circulating current in the inductive coil and an induced voltage in the receiver coil which defines the sensor. This voltage is proportional to the intensity of EC field developing in the skin of the material. If the induction field depends only on the z coordinate (counted starting from the material surface), assuming that the material can be viewed to be a semiinfinite medium, solution of equations (4) can be conducted analytically and one finds in real notations the following distribution of the EC [7] 0 ( , ) exp cos f ω π = is the work frequency. In practice, the excitation frequency can be monitored to reach deep points of the material, but also the magnitude of the inductive magnetic field 0 B can be increased by using a coil containing a high number of whorls. This shows the advantage to work with low frequencies for which the condition c ω ω is easily satisfied. Validity of equations (4) to model the EC phenomenon is then stated.
For a material whose geometry can not be assimilated to a semi-infinite medium, or presenting irregularities at its surface solution of equations (4) can be achieved by means of the finite element method. In the following Comsol software packages is used to model a testing setup having the form of system shown in figure 1, [8].  A finite element model was derived under the code Comsol Multiphysics [7]. Figure 4 gives the considered mesh corresponding to the finite element convergence. The mesh was generated automatically by using free tetrahedral elements; its maximum size was 0.02m for the plate and 0.01m for the coils. The tree elements constituting the probe-coil set-up are meshed using the same element type. As the excitation coil radiates electromagnetic waves through air according to equations (3) before these can reach the plate material, the environmental air should also be modelled.

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Because meshing an infinite volume is necessary to specify a finite volume t for it. In the present case, the whole pro placed at the centre of a cube as shown avoid reflection that is susceptible to tak volume, the default boundary con Insulation is used. This condition force tangential to the exterior boundaries. Th is sufficiently large its edge is chosen equal to 2m . Figure 5(b) shows the under Comsol for this cube. To comp properties, the air electric conductiv Considering a cut-line that crosses centre (as shown in red colour in figure of the coils were considered along th performing a basic B-scan. The idea is results to the defect will vary accordin separating the coils from the defect lo presents the selected sequence of thes first position corresponds to the cent distance 0.22m from the defect position positions correspond to successi translations of 0.1m magnitude. The intensity of the EC as generated coil while working consecutively with 1 50 f Hz = and 2 100 f Hz = was calcula the finite element model. Internal bo corresponding to electric and magnetic applied, and the density of charge was fi is not possible, it to mesh and solve obe-coil setup was in figure 5(a). To ke place in a finite ndition Magnetic es the field to be he cube used here to have a length mesh developed plete the material vity is fixed at probe set-up; nside the cube; the defect at its 6), four positions his line to enable that sensitivity of ng to the distance ocation.   Figure 8 presents the ob current density for the four po in figure 6. One can see th intensity appears at the defec indicates the presence of a however that, when the coils on the defect, the perturbation small and cannot be easily instance current probes pros along the cut-line. The ideal po effect corresponds in the p between positions 2 and 3 or p Figure 8 shows also that increase the EC magnitude. between the two frequencies v defect zone as the two work f same result. One can conclude is quite sufficient. Moreov associated to this frequency wi Scanning the plate along a the best practical solution be that will arise and the irregul surface which will perturb m single cut-line would not be strategy would be required. Th generally used to get more eas the presence of a flaw defect in The receiver coil shown in and the blades will show an e the magnetic field created by tained cut-line of induced ositions of the coils as given hat a sudden decrease of ct zone. This discontinuity a defect. One can notice are too far or centred right n associated to the defect is detected when using for specting the plate surface ositions to obtain maximum present case to positions positions 3 and 4.
increasing frequency will . However the difference vanishes when crossing the frequencies give almost the e then that using 1 50 f Hz = ver depth of penetration ill be higher. a cut line with probes is not ecause of contact problems larities present on the plate measurement. Moreover a e sufficient and a C-scan his is way a receiver coil is sily the effect resulting from n the inspected plate. n figure 3 is an open circuit lectric volage as a result of y the EC in the plate. This 07001-p.4 voltage varies with the position of the point on the blade. The corner points of these blades were chosen as measurement points. Figure 9 shows the labelling used for these points. Connecting these points with a voltage measuring instrument can be used to monitor the information about the existence of a defect. This can be performed in comparison with a defect free state of the plate. The obtained voltages in the eight points for both defect free and defected plate were processed to give the maximum variation of voltage when the coils are displaced according to the three transitions:

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From figure 10, one can see that by monitoring voltage variations on the surface of the blades, it is quite possible to get information about the presence of a defect. From table 1, one can observe that the highest variations associated to the plate configuration with a defect are at least from 5 to 58 times greater than those of a plate without defect. These variations admit peaks when the coils are in the vicinity of the zone where the defect is located.
Optimisation of the system and reliability of results has still to be performed. One of the important problems that could limit reliability of the system is its sensitivity to the distance separating the coils from the plate which can vary because of roughness of the plate surface.

Conclusions
Non destructive evaluation based on eddy currents has been investigated in this work in the particular case of surface like defect located on a plate. Finite element modelling of the problem was performed under Comsol software package where the electromagnetic stationary solution was calculated. Post-processing of the obtained results has shown that detection of defects can be performed by rather using the information collected on voltage variation as experienced in different points of the receiver coil. The present finite element model can be used to further investigate detectability of small defects and to assess reliability of detection as it could be affected by uncertainties due to the part profile and voltage measurement on the receiver coil.