The paper contains an original comprehensive review of finite element analysis (FEA) applied by researchers to calibrate and improve existing and developing electromagnetic non-destructive testing and evaluation techniques, including but not limited to magnetic flux leakage (MFL), eddy current testing, electromagnetic-acoustic transducers (EMATs). Premium is put on the detection and modelling of magnetic field, as the vast majority of ENDT involves magnetic induction, either as a primary variable MFL or a complementary phenomenon (EC, EMATs). FEA is shown as a fit-for-purpose tool to design, understand and optimise ENDT systems, or a Reference for other modelling algorithms. The review intentionally omits the fundamentals of FEA and detailed principles of NDT. Strain-stress FEA applications in NDT, especially in ultrasonography and hole-drilling methodology, deserve as well a separate study.

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Finite Element Method Applied in Electromagnetic NDTE: A Review

In this paper, a new method of contactless electric conductivity measurement is developed. This method is essentially based on the association of the coupled electric field forward model, which we have recently developed, with a simple and efficient research algorithm. The proposed method is very fast because 1.3 s are sufficient to calculate electric conductivity, in a CPU of 2 GHz and RAM of 3 GB, for a starting research interval of 1.72–17.2 %IACS and tolerance of 1.72 × 10− 5 %IACS. The study of the calculation time according to mesh density and starting interval width has showed that an optimal choice has to be made in order to improve the rapidity while preserving its precision. Considering its rapidity and its simplicity of implementation, this method is more adapted, in comparison to direct current techniques using Van der Pauw geometry, for automated applications.

New contactless eddy current non-destructive methodology for electric conductivity measurement

The study of 3D eddy current non destructive testing system for cracks characterization using finite element method requires a great amount of computing time and memory space. In this article, we have validated the developed model and then determined directly the crack length by analyzing the complete signal. Afterwards, we have extracted from the complete sensor sweep signal the maximal amplitude that we have exploited to estimate the crack depth.

Eddy Current Characterization of 3D Crack by Analyzing Probe Signal and Using a Fast Algorithm Search

A computationally efficient gradient-based optimization approach for inverse material characterization from incomplete system response measurements that can utilize a generally applicable parameterization (e.g., finite element-type parameterization) is presented and evaluated. The key to this inverse characterization algorithm is the use of a direct inversion strategy with Gappy proper orthogonal decomposition (POD) response field estimation to initialize the inverse solution estimate prior to gradient-based optimization. Gappy POD is used to estimate the complete (i.e., all components over the entire spatial domain) system response field from incomplete (e.g., partial spatial distribution) measurements obtained from some type of system testing along with some amount of a priori information regarding the potential distribution of the unknown material property. The estimated complete system response is used within a physics-based direct inversion procedure with a finite element-type parameterization to estimate the spatial distribution of the desired unknown material property with minimal computational expense. Then, this estimated spatial distribution of the unknown material property is used to initialize a gradient-based optimization approach, which uses the adjoint method for computationally efficient gradient calculations, to produce the final estimate of the material property distribution. The three-step [(1) Gappy POD, (2) direct inversion, and (3) gradient-based optimization] inverse characterization approach is evaluated through simulated test problems based on the characterization of elastic modulus distributions with localized variations (e.g., inclusions) within simple structures. Overall, this inverse characterization approach is shown to efficiently and consistently provide accurate inverse characterization estimates for material property distributions from incomplete response field measurements. Moreover, the solution procedure is shown to be capable of extrapolating significantly beyond the initial assumptions regarding the potential nature of the unknown material property distribution.

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A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

This article presents an innovative technique for detecting flaws in conductive materials by using an ideal filamentary coil. To characterize such a coil accurately and explicitly, it is sufficient to be in possession of merely two parameters: the radius of the circle within which all the turns are located and the distance of the coil from the tested surface. The mathematical model derived using the truncated region eigenfunction expansion method enables the calculation of the changes in the components of the filamentary coil impedance that are the result of positioning the coil close to the conductive material with a hole. Because of this, the air-cored coil model can be replaced with a much simpler filamentary coil model. This solution makes it is possible to detect various types of holes (internal, surface, subsurface or through) occurring in both multilayer magnetic and non-magnetic materials. The derived results were verified by means of measurements and numerical calculations based on the finite element method. Very good agreement was observed in both cases. The paper contains the source code implemented in Matlab, which is used to for calculations.

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Locating Defects in Conductive Materials Using the Eddy Current Model of the Filamentary Coil

This article presents a defect modeling in eddy current non-destructive testing systems by using a new developed method called coupled electric field. It permits to improve qualitatively several models developed so far by many authors using coupled circuit methods that consider the defect only as loss of material. However, a defect can occur with a finite conductivity such as impurity, small burns and micro-solder. For this reason, this investigation consists of extending the coupled circuit method to the modeling of this kind of defects. The proposed approach consists of firstly considering the defect as an electric conductive volume and secondly changing the state variable presenting the electric current by the electric field one. This procedure permits expressing explicitly the impedance variation caused by the presence of an axi-symmetrical defect according to its characteristics. The comparison between the impedance variations calculated using finite elements method and the proposed one demonstrates a very good concordance. After this validation, the study covers also the influence of the defect shape and position on encircling probe impedance. This method is interesting since it permits a fully characterization of this kind of defects and facilitates the inversion process. Moreover, using a 3D finite element observation, this fast tool of simulation can be adapted for a fast phenomenological modeling of asymmetrical configurations.

Novel Coupled Electric Field Method for Defect Characterization in Eddy Current Non-destructive Testing Systems

This article presents the modeling of non-destructive testing systems containing magnetic materials using a fast numerical method. Its main aim consists of correcting the half analytical expression of the impedance variation, formulated by some authors, caused by the presence of a conducting plate below of an absolute ferrite core probe. The obtained results of this correction are found to be consistent and satisfactory comparatively to those of finite element method. It also deals with the study the method rapidity by comparing its simulation time to that of the finite element method. As result, the proposed method is found to be very fast and a very short simulation time is required to calculate the sensor impedance. Indeed, for the studied system the coupled circuit simulation time is lower than 1.09 s. This study is appreciable, since it permits to solve quickly the inverse problem by expressing the physical and geometrical features of the material or defect according to the measured parameters. More importantly, this method is applicable to any axi-symmetric systems and can be adapted for the simulation of three-dimensional configurations.

T. Bouchala

Papers

Novel Coupled Electric Field Method for Defect Characterization in Eddy Current Non-destructive Testing Systems

Fast Analytical Modeling of Eddy Current Non-Destructive Testing of Magnetic Material