Eddy Current Nondestructive Evaluation Research Articles

Eddy current nondestructive evaluation of metallic plates electrical conductivity using artificial neural networks based inverse problem

The most used method and extensively studied in the literature for conductors’ characterization is Eddy Current Nondestructive Evaluation (ECNDE) due to its significant advantages, such as its ability to preserve the integrity of the structures or materials to be examined during manufacturing or a regular in-service nondestructive testing. Various approaches are developed for the Eddy Current measurement of the electrical conductivity. In the present work, the evaluation of the electrical conductivity is treated as an inverse problem. In pursuit of this aim, a combination is established between Eddy currents evaluation and artificial neural networks (ANN) to evaluate the electrical conductivity of homogeneous metallic plates from eddy-current probe impedance measurements. For this purpose, an experimental setup is developed, including a bobbin-coil probe, metallic plates (target), data acquisition and signal processing systems. Finally, experimental conductivity values of various metallic plates using ANN are compared with those obtained using four-point measurements of direct current potential drop (DCPD) made on the same plates and very good agreement is obtained.

Investigation of Flux Transfer along Ferrite Core of Probe Coil for Eddy Current Nondestructive Evaluation

Abstract A probe coil with a T-core above a layered conductor with surface hole is investigated for magnetic flux transfer along the ferrite core and enhancement of eddy currents in conductor. The cylindrical coordinate system is adopted and an artificial boundary is added to the solution domain with radius b, and the general formula for calculating the impedance of the T-core coil is derived using the truncated region eigenfunction expansion (TREE) method. For four special cases with different probe configurations, coil impedance changes due to the layered conductor and defect are calculated with Mathematica software over a frequency change ranging from 100 Hz to 20 kHz. The analytical results are in good agreement with those obtained by the finite element method and experimental measurements. The results show that under the same lift-off height and excitation frequency, the impedance change caused by the conductor or defect in the coil of long core column is greater than that of the short core column coil. It indicates that the probe coil with a long core column can transfer magnetic flux to the conductor, thereby enhancing eddy currents in the conductor.

Model of Ferrite-cored Driver-pickup Coil Probe Application of TREE Method for Eddy Current Nondestructive Evaluation

An analytical model of a driver-pickup coil probe, consists of a cylindrical ferrite core, located above a layered conductor is presented. The truncated region eigenfunction expansion (TREE) method is used and the solution region is truncated with a certain radius around markedasmathitalicz axis. First, the magnetic vector potential of each region of filamentary coil problem is derived and solved with variables separation method using boundary and interface conditions, and then the rectangular cross-section coil problem is solved with superposition method. The expression of induced voltage in pickup coil is obtained and can be calculated with software such as Matlab or Mathematica. Using the proposed analytical model, the influence of the excitation frequency and excitation current in the driver coil on the responses of the pickup coil is examined. Experiments are performed, and the changes of voltage induced in the pickup coil due to the conductor are measured at different excitation frequencies and excitation currents. The analytical calculation results agree with the experimental results very well, verifying the correctness of the proposed analyticalmodel.

Efficient Model Assisted Probability of Detection Estimations in Eddy Current NDT with ACA-SVD Based Forward Solver.

Model assisted probability of detection (MAPoD) is crucial for quantifying the inspection capability of a nondestructive testing (NDT) system which uses the coil or probe to sense the size and location of the cracks. Unfortunately, it may be computationally intensive for the simulation models. To improve the efficiency of the MAPoD, in this article, an efficient 3D eddy current nondestructive evaluation (ECNDE) forward solver is proposed to make estimations for PoD study. It is the first time that singular value decomposition (SVD) is used as the recompression technique to improve the overall performance of the adaptive cross approximation (ACA) algorithm-based boundary element method (BEM) ECNDE forward solver for implementation of PoD. Both the robustness and efficiency of the proposed solver are demonstrated and testified by comparing the predicted impedance variations of the coil with analytical, semi-analytical and experimental benchmarks. Calculation of PoD curves assisted by the proposed simulation model is performed on a finite thickness plate with a rectangular surface flaw. The features, which are the maximum impedance variations of the coil for various flaw lengths, are obtained entirely by the proposed model with selection of the liftoff distance as the uncertain parameter in a Gaussian distribution. The results show that the proposed ACA-SVD based BEM fast ECNDE forward solver is an excellent simulation model to make estimations for MAPoD study.

Microstructural Evolution of Inconel 718 during Aging and Its Correlation with Electric Conductivity Measurements

Abstract The microstructural evolution of the nickel-base superalloy Inconel 718 after exposition at 750°C for different holding times (10 min–1,000 h) was characterized and correlated with the Eddy current (EC) technique. The results showed that electrical conductivity increases with aging time. This behavior was associated with the precipitation and coarsening of the metastable γ″ phase and its transformation into the detrimental δ phase after 100 h. EC nondestructive evaluation was correlated with X-ray diffraction patterns in terms of the precipitation and growth of secondary carbides that were observed in the scanning electron microscope. Vickers microhardness values were also in agreement with microstructural changes and EC measurements, as the maximum hardened condition can be associated with the precipitation of secondary phases before the transformation of the γ″ phase into the δ phase.

Electromagnetic Sensing of the Corrosion at Different Microstructural Phases in a Medical Ti-6Al-4V ELI Alloy

Titanium alloys have become increasingly important for biomedical materials due to their high specific strength, good corrosion resistance, and excellent biocompatibility. In this research work, different heat treatments were performed for obtaining equiaxed and Widmanstätten microstructures of Ti-Al-4V extra low interstitials (ELI) alloy. To promote nucleation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha _{2}$ </tex-math></inline-formula> precipitates (Ti <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al), an aging process was carried out at 515 °C and 575 °C for 2, 288, and 576 h. The corrosion behavior was analyzed by double-cycle potentiodynamic corrosion tests. Hank’s balanced salt solution (HBSS) was used as the electrolyte, and the tests were maintained at 37 °C. This study uses the eddy current (EC) nondestructive evaluation technique, based on the principle of electromagnetic induction, in an effort to monitor corrosion damage in the medical Ti-6Al-4V alloy. The experimental results show significative electrical conductivity variations in EC data of different Ti-6Al-4V ELI alloy microstructures mainly on equiaxed and Widmanstätten conditions before and after corrosion performance.

Nested kernel degeneration-based boundary element method solver for rapid computation of eddy current signals

In this article, the nested kernel degeneration (NKD) based integral equation fast solver is proposed to compress the dense system matrix generated by boundary element method (BEM) for calculating eddy current signals in 3D nondestructive evaluation (NDE) problems. The near and diagonal block interactions are computed and stored by full matrices. However, for the far block interactions, not like in the single level kernel degeneration-based method that all the interaction matrices are compressed by the interpolations, the nested approximation framework makes the expression of the higher-level matrices by the ones at leaf levels and the transfer matrices between neighboring levels. Different integral kernels are degenerated and nested to ensure the performance of NKD based method. The robustness and efficiency of the proposed solver are validated and verified by making numerical predictions and comparing them with the ones achieved by analytical method, numerical methods and experiments. Our numerical experiments show that the NKD solver is more efficient than the butterfly solver (multilevel adaptive cross approximation algorithm (MLACA)) for electrically small eddy current NDE problem. With the NKD based method, O(N) computational complexity is achieved for multiscale low frequency eddy current simulations without sacrificing accuracy, where N is the number of unknowns. So far, to our best knowledge, the proposed method with linear complexity is the most efficient integral equation-based BEM forward solver to predict the eddy current signals from cracks and flaws.

A Study on the Scan Plans for Rapid Flaw Detection by Eddy Current Non-Destructive Evaluation

Raster, diagonal-raster, spiral, Lissajous, and billiard type scan plans have been analysed, for the first time, in eddy current testing for detection and imaging of flaws. The performance of these scan plans has been studied by using metrics like rapidness, complete coverage, and step size. Numerical investigations have been carried out to evaluate the performance of the five scan plans for the detection of 1000 randomly located notches in a stainless steel plate. Studies indicate that the billiard scan plan results in 98.5% detection as compared to the other scan plans, and this has been verified experimentally. Results clearly show that the billiard scan plan ensures the rapid detection of flaws in large surfaces of electrically conducting materials by eddy current testing.

Interpretation of Impedance in the Light of Energy Dissipation and Eddy Current Nondestructive Evaluation of Pipe Wall Thickness

This study analyzed the energy flow of eddy current testing and interpreted impedance signals in the light of energy dissipation and storage. The ac resistance, which is attributed to energy dissipation, was factorized into intrinsic ac resistance and frequency squared, whereas the reactance, as a measure of energy storage, was factorized into inductance and frequency. The intrinsic ac resistance and inductance reveal the interaction between electromagnetic field and material. It was found that when the skin depth is much larger than a specimen’s thickness that the magnetic field distributes nearly uniform over the thickness, the eddy current-related quantities, i.e., intrinsic ac resistance and the reduction of inductance, barely change with magnetic property but approximately proportional to the volume of the test object, e.g., cross-sectional area of a unit length pipe, which enabled us to measure a ferromagnetic pipe and estimate wall thickness at the thick-skin regime, regardless of variation of magnetic property. The experimental study showed that, by taking difference of signals measured with two serially connected identical coils, coupled cumulatively and differentially, the coils’ ohmic resistance can be eliminated. Moreover, the reduction of inductance due to the eddy current effect could be obtained by referring to signals measured at an extremely low frequency. The proposed method was numerically and experimentally validated. This study demonstrated the possibility and feasibility of measuring a ferromagnetic pipe’s thickness at tens of hertz, regardless of variation of magnetic property.

Hybrid Method of ACA and Interpolation-based Algorithms for Analysis of Eddy Current Nondestructive Evaluations

ABSTRACT In this article, the hybridization of adaptive cross approximation (ACA) algorithm and interpolation-based separation of the kernel function is proposed to accelerate solving the matrix equations resulted in the boundary element method (BEM) for 3D arbitrary-shaped eddy current nondestructive evaluation problems. The hybrid method combines the advantages of both the ACA algorithm and the interpolation-based methods, and resolves the shortcoming of pure ACA method, when modeling the planar eddy current nondestructive evaluation problems, that it cannot compress the null entries the BEM generated when the testing and basis patches are co-planar. In the proposed method, the submatrices associated with the null entries are compressed by the interpolation-based method, while the others are compressed by the ACA algorithm. Several benchmarks are shown to demonstrate both the robustness and efficiency of the proposed fast and general solver.

Integral equation fast solver with truncated and degenerated kernel for computing flaw signals in eddy current non-destructive testing

In this article, the kernel independent H-matrix method is applied as the mathematical framework. The dense matrix generated by the selected integral equation, without low frequency breakdown problem for solving 3D arbitrary shaped eddy current nondestructive evaluation (NDE) forward problems, is compressed by the truncated and degenerated (TD) kernel function method. It results in a significant reduction in computational burden with nearly linear complexity. The kernel functions (Green's function) are degenerated by Lagrange polynomials which leads to two advantages: firstly, the double integrals are separated in two single integrals, and secondly, they are represented in a factorized form with good accuracy control. Meanwhile, due to the nature of the kernel function with exponential decay in the lossy medium, it is truncated to improve the overall performance. The TD kernel function-based boundary element method (BEM) fits well for solving eddy current NDE problems over the adaptive cross approximation based BEM, especially for detections of flaws or slots in planar objects. Several numerical predictions calculated by the proposed method are compared with those achieved by others such as the experiment, analytical and semi-analytical methods from benchmarks. The robustness and efficiency are demonstrated with excellent agreements and reduced complexity.

A model of eddy current nondestructive evaluation for a current leaking crack

This paper presents a model-based study of undesirable signal loss problems, often encountered by eddy current inspections of tight cracks. Possible current leakage through a portion of the crack face is the focus here as the principal mechanism of signal reduction. Two problematic types of cracking conditions are studied particularly, i.e., a surface-smeared crack and a crack under compressive stress. With a newly developed model and its numerical results, the paper shows quantitative analyses of the signal loss for the above two cases, compared to the response of a pristine surface-breaking crack in the similar geometrical configuration.

An Overlapping Array Coil for Eddy Current Non-destructive Evaluation

An overlapping array coil for eddy current nondestructive evaluation (NDE) is proposed in this paper. Compared with the traditional NDE probe, our proposed structure works at 6.78 MHz, and generates a more stable and uniform magnetic field by interlacing and stacking coil units. Based on the propagation characteristics of a time-varying magnetic field, when a metal plate is placed in such a magnetic field, eddy currents are induced on the surface. If a scratched metal plate is placed in the same magnetic field, different eddy currents will be generated and the port impedance of the structure will be changed. Therefore, defects in the metal can be non-destructively detected.

A Novel Method for Thickness Measurement in Conducting Materials by Apparent Conductivity Calculation Through Transient Eddy Current NDE

This paper describes a novel method for thickness measurement in conducting material by combining the measurement of the decaying induced eddy current and its associated apparent conductivity calculation. In conventional frequency domain NDE (Non-destructive Evaluation), the skin depth is the limiting factor due to the single frequency excitation. In contrast, with a pulsed excitation, the induced eddy currents decay with time and the decay of the eddy current consists of continuum of frequencies and hence the entire thickness of the conducting material could be investigated in a single shot. The time at which the decay of the eddy current is maximum is called diffusion time “tm” and the corresponding calculated value of apparent electrical conductivity “σmapp” both of which can be directly correlated to the thickness of the material. Since the induction of the eddy current and its associated secondary magnetic field measured by using suitable magnetic sensors [hz α (σ/t)3/2 for B-field and Vz α (σ3/2/t5/2) for an induction coil] is directly related to the conductivity of the materials, one can calculate the apparent conductivity σapp(t) as a function of decay time. Apparent conductivity calculations have been made for aluminum plates based on the thin conducting sheet model in which the applied magnetic field is uniform throughout the thickness. Subsequently, transient measurements have been performed with stacks of aluminum plates by using pickup coils in the form of an absolute as well as differential configuration. From this, it has been shown that the square root of the ratio of the maximum diffusion time, tm and the corresponding apparent conductivity, σmapp called as maximum diffusion depth, δm which is proportional to the plate thickness. The diffusion depth is a parameter derived from standard electromagnetic equations which is analogous to the skin depth in the frequency domain. In this work, induction coil sensors of both types have been used to measure the transients, and the other instruments such as transmitter, transmitter controller and data acquisition system used for this work are the same ones used for TDEM (time domain electro-magnetic) based geophysical applications.

RECONSTRUCTION OF DEFECT SIZE AND SHAPE IN EDDY-CURRENT TESTING USING BENCHMARK PROBLEMS VALIDATION AND NEURAL NETWORK APPROACH

The benchmark problems in eddy-current nondestructive evaluation (EC-NDE) are based on careful measures of the change in coil impedance as a function of circular air cored coil position which is scanned along the axis of machined slot by electrodischarge in aluminum plate. Tow benchmark problems (TEAM workshop n° 15-1, and JSAEM n° 2-5) are presented to validate and verify ANSYS Maxwell 3D-resolution of defect size and shape using electromagnetic formulation. In order to provide a challenge for current theoretical models, slots of rectangular, elliptical, slope and triangular profiles are considered. The final impedance data can be directly used to verify theoretical inversion algorithms.

An Analytical Model of a New T-cored Coil Used for Eddy Current Nondestructive Evaluation

A model of an axisymmetric probe with a new T-core coil that can be used in eddy current testing is developed. The truncated region eigenfunction expansion (TREE) method is used to analyze the coil impedance problem of the T-core coil located above a multi-layer conductive material. First, the magnetic vector potential expressions of each region are formulated, then the coefficients of the magnetic vector potential are derived by using the boundary conditions, finally, the closed form expression of the coil impedance is obtained. The normalized impedance changes of the T-core coil caused by the presence or absence of the multi-layer conductor are calculated using Mathematica. The presented T-core coil is compared with I-core coil and air-core coil. The effects of the T-core parameter a2, relative permeability μf and the thickness of the top section on the change in the coil impedance are discussed respectively. The analytical calculation results are compared with the results of finite element method, and the two agree very well, which verifies the correctness of the proposed T-core coil model.

Analysis of electromagnetic non-destructive evaluation modelling using Stratton-Chu formulation-based fast algorithm.

The eddy current non-destructive evaluation (NDE) modelling using Stratton-Chu formulation-based fast algorithm is analysed. Stratton-Chu formulations, which have no low frequency breakdown issue, are selected for modelling electromagnetic NDE problems with low frequency and high conductivity approximations. As the main contribution of this article, the robustness and efficiency of the approximations, which result in big savings in both memory and CPU time, are validated and analysed using examples from practical EC testing. The boundary element method (BEM) is used to discretize the integral equations into a linear system of equations: the first order Rao-Wilton-Glisson (RWG) vector basis functions with the flat triangle meshes of the object and pulse basis functions are selected to expand the equivalent surface currents and the normal component of magnetic fields, respectively. Then the multilevel adaptive cross approximation (MLACA) algorithm is applied to accelerate the iterative solution process. The performance and efficiency of adaptively applying a multi-stage (level) algorithm based on the criteria concluded for the operators are shown. This article is part of the theme issue 'Advanced electromagnetic non-destructive evaluation and smart monitoring'.

A Simulative and Experimental Approach Toward Eddy Current Nondestructive Evaluation of Manufacturing Flaws and Operational Damage in CFRP Composites

Abstract The manufacturing process of carbon fiber reinforced polymer (CFRP) composite structures can introduce many characteristic defects and flaws such as fiber misorientation, fiber waviness, and wrinkling. Therefore, it becomes increasingly important to detect the presence of these defects at the earliest stages of development. Eddy current testing (ECT) is a nondestructive inspection (NDI) technique that has been proven quite effective in detection of damage in metallic structures. However, NDI of composite structures has mainly relied on other methods such as ultrasonic testing (UT) and X-ray to name a few and not much on ECT. In this paper, the authors explore the possibility of using ECT in NDI of CFRP composites by conducting simulations and experiments thereafter. This research is based on the fact that the CFRP displays some low-level electrical conductivity due to the inherent conductivity of the carbon fibers. This low-level conductivity may permit eddy current pathways to cause the flow of eddy currents in the CFRP composites that can be exploited for nondestructive damage detection. An invention disclosure describing our high-frequency ECT method has also been processed. First, the multiphysics finite element method (FEM) simulation was used to simulate the detection of various types of manufacturing flaws and operational damage in CFRP composites such as fiber misorientation, waviness, wrinkling, and so on. Thereafter, ECT experiments were conducted on CFRP specimens with various manufacturing flaws using the Eddyfi Reddy eddy current array (ECA) system.

Nondestructive Evaluation for Detection of Voids in Sodium-Bonded Metallic Fuel Pins

Nondestructive detection of sodium-free regions (voids) in metallic fuel pins is necessary for their safe and reliable operation. Eddy current and X-radiography nondestructive evaluation techniques were employed for detection of voids in experimental fuel pins. Detailed finite element model-based investigations and radiography intensity profile analysis were carried out to understand the signatures to ensure that the signals are due to voids. In addition to enabling the detection of sodium voids in metallic fuel pins, NDE studies aided in optimizing the sodium filling process and were helpful in finding out the adequacy of the heat treatment during filling process.

Fictitious electric conductivity modelling of eddy current evaluation of magnetic materials

ABSTRACTThis 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.