In this paper, an iterative technique, employing the T formulation associated with the finite element method, based on Maxwell's equations and the Biot-savart law, is used for analyzing the density of eddy currents in composite carbon fiber reinforced polymer (CFRP) materials. For this purpose, a code has been developed for solving an electromagnetic 3D non-destructive evaluation problem. This latter permits the characterization of this CFRP and determinate of fibers orientation using the impedance variation which is implanted in polar diagram. Firstly, the obtained results are compared with those of the analytical model. This comparison reveals a high concordance which proves the validity of the proposed method. Secondly, three different applications are shown for illustrating the characterization of unidirectional, bidirectional and multidirectional piece using a rectangular coil plotted in normalized impedance diagram.

This paper presents a new modeling approach of eddy current nondestructive evaluation systems containing magnetic materials. Originally, the proposed model is based on coupled circuits principle and the notion of equivalent current density. In order to make the model homogenous, we consider the current density as a state variable since this density is compatible with the representation of the magnetisation by equivalent currents. By introducing the fictitious electric conductivity approach, the sensor impedance is expressed according to magnetic tube or plate characteristics such as electric conductivity and magnetic permeability. An excellent concordance is achieved by comparing the calculated results to those of analytical ones. Regarding the mesh simplicity and the fast calculation, this method is very adapted for the resolution of the inverse problems for real time evaluation of the properties of magnetic materials.

This article presents a study of a Multi-coils circular eddy current non-destructive testing sensor for determining the fibers orientation as well as the detection of defect in multidirectional carbon fibers reinforced polymer (CFRP). The developed sensor contains 16 rectangular coils connected in series and supplied by a single-phase sinusoidal source. This sensor allows the annulations of the mechanical rotation of the conventional sensors and it permits to reduce the inspection procedure duration. The electromagnetic phenomena are calculated by using 3D finite element method (FEM) based on the electromagnetic AV-A formulation. Finally, the Multi-coils circular sensor responses are analyzed through polar diagrams of the impedance variation, where the defect is taken into consideration. A great concordance between the obtained results and those of literatures has been noticed. The provided results show that the proposed sensor allows an efficient characterization of multidirectional CFRP and detection of defects in different layers.

This paper presents a study of a surface crack detection in which the volume is filled by conductive substances due to the polluting environment. Hence, this investigation demonstrates by numerical simulation that electric conductivity is a crucial property that has to be added to the other defect geometrical characteristics in order to complete the developed models. Consequently, introducing the tolerance in percent in the measured impedance is necessary in some conditions. So, the obtained results demonstrate that the signal amplitude passes from 0 to 78% of the maximal amplitude when the defect conductivity rises from 0 to 0.5 Ms/m. On the other hand, the relative difference of the resistance partincreases according to defect volume. For example, for a defect of 0.3 MS/m, the relative difference of the resistance varies from 52 to 62% of the maximal amplitude when the defect depth varies from 0.5 to 2.25 mm. These results can be exploited to show the effect of the conductive substances occupying the crack volume. In fact, the controller using EC-NDT technique must take into consideration the presence of conductive polluting elements in the crack volume. So, this condition becomes primordial and necessary according to the degree and nature of pollution.

This paper presents a study of a surface crack detection in which the volume is filled by conductive substances due to the polluting environment. Hence, this investigation demonstrates by numerical simulation that electric conductivity is a crucial property that has to be added to the other defect geometrical characteristics in order to complete the developed models. Consequently, introducing the tolerance in percent in the measured impedance is necessary in some conditions. So, the obtained results demonstrate that the signal amplitude passes from 0 to 78% of the maximal amplitude when the defect conductivity rises from 0 to 0.5 Ms/m. On the other hand, the relative difference of the resistance partincreases according to defect volume. For example, for a defect of 0.3 MS/m, the relative difference of the resistance varies from 52 to 62% of the maximal amplitude when the defect depth varies from 0.5 to 2.25 mm. These results can be exploited to show the effect of the conductive substances occupying the crack volume. In fact, the controller using EC-NDT technique must take into consideration the presence of conductive polluting elements in the crack volume. So, this condition becomes primordial and necessary according to the degree and nature of pollution.

The aim of this paper consists of presenting optimization criteria of coil dimensions and the exciting field frequency in order to improving eddy current probe sensitivity for small and deep cracks under fasteners. To accomplish this task, we have studied the influence of coil inner radius, coil height and exciting frequency on probe sensitivity. Then, an algorithmic searching technique is applied to determine the optimal values of the previous parameters. Hence, the obtained results have revealed that the optimum inner radius corresponds exactly to the fastener head outer radius. Furthermore, it has been noticed that as well as the coil height is reduced while keeping the same number of turns, the probes sensitivity increases. Indeed, the use of stacking flat micro-coils is well adapted. In addition, the calculation of the optimum values of the frequency demonstrate that this parameter depend relatively on the defect position, its radial and vertical depth.

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.

The development of fast and accurate method describing the electromagnetic phenomena intervening in eddy current non-destructive systems is very interesting, since it permits the design of reliable systems permitting the detection and the characterisation of defect in conductive materials. The coupled electric field method presented in this article can assume a large part of these objectives, because it is fast in comparison to the finite element method and easily invertible since the sensor impedance variation is an explicit function of target physical and geometrical characteristics. These advantages have motivated us to extend this method for multilayered structures, very interesting in aeronautic industry, by superposing the inductive effects in different layers. The impedance of an absolute sensor operating above three conducting layers will be calculated and compared to those obtained with finite element method. Afterwards, we shall exploit the model to study the effect of defect characteristics on the sensor impedance. Furthermore, regarding to the depth penetration effect, we shall make into evidence the necessity of accomplishing an optimal choice of the exciting field frequency during the inspection of multilayered materials. The essential importance of this method, besides of its rapidity, resides in its possibility to be extended to 2D irregular and 3D asymmetric configurations.

Nowadays, numerical modelling has become an interesting tool for determining impedance variations due to various conductive flaws in eddy current nondestructive evaluation systems. These kinds of defects, rarely treated in the published works, are taken into consideration in the modelling while introducing them as electrically conductive volumes with a finite electric resistivity. This step is very important since it permits to improve qualitatively several models developed so far by many authors whose consider the defect as loss of material only. However, in several applications, the defect can occur with a finite resistivity such as impurity, small burns and micro-solder. On the other hand, even though the defect appears with a loss of materials, som e polluting materials can fill the affected region. Indeed, the volume of the initial defect will be completely or partially occupied by these conducting pollutant materials. This paper deals with the effect of physical and geometrical characteristics of such kind of defects on the differential sensor response. Furthermore, the necessity of taking the defect electric conductivity (as an important parameter) into account will be explained, in order to develop a reliable and accurate inverse method allowing a full characterization of conductive defects.

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.