Finite-Element Calculations of Remote Field Eddy Current Interactions with Slit Defects

Abstract

Remote field eddy current (RFEC) excitation is a promising approach for detection of the very fine axial cracks typical of stress corrosion cracking (SCC) in pipelines. Interactions between adjacent cracks or slits can enhance responses in some cases. Detailed finite-element modeling was undertaken to establish the behavior and interactions of multiple slits such as those occurring in SCC. Three different field/slit configurations are considered, with anomalous source models used to aid interpretation of the results. The study noted that magnetic perturbations generated by ferromagnetic material tend to be vanishingly small, and that the interactions between multiple cracks give minimal enhancement, indicating that eddy current rather than magnetic field excitation is best for the detection of SCC. With eddy current excitation, field perturbations are generated by even very fine slits, and are larger in non-ferromagnetic material. For non-ferromagnetic pipes, the perturbations tend to merge as a circumferential separation between parallel axial cracks decreases, resulting in significant interaction and signal enhancement.     

Finite-Element Analysis for Remote Field Eddy Current Responses from Near- and Farside Cracks

Results of three-dimensional finite-element analysis investigations of remote field eddy current (RFEC) signal responses from internal and external stress corrosion cracking (SCC) in steel pipes are presented. The fine shallow SCC cracks were simulated by double axial slits located on the near- and farside pipe surfaces under simulated RFEC excitation. Although it is normally a characteristic of RFEC testing that responses to interior or exterior defects are approximately equal, there is a considerable difference between the farside and nearside responses from very fine defects such as SCC cracks.     

Longitudinal AC interactions with axial slits in steel pipes

The Remote Field Eddy Current (RFEC) nondestructive inspection technique uses low frequency AC and through wall transmission to inspect pipes and tubes from the inside. In steel pipes, it has generally greater sensitivity to circumferential rather than axial slits because the perturbation of magnetic fields orthogonal to slits dominates. Circumferential AC magnetic fields, generated by passing AC axially along a steel pipe from an external supply, have therefore been tested in order to give greater sensitivity to axially aligned cracks characteristic of stress corrosion cracking in pipe-lines. Anomalous source missing magnetization defect models suggest that, as slit widths are reduced, the importance of magnetic interactions is reduced until eddy current interactions predominate. This suggests that, for very fine axial cracks, true RFEC geometry, which gives circumferential eddy currents, will give stronger signals than circumferential AC magnetic fields.Research supported by Natural Sciences and Engineering Research Council of Canada, Pipetronix Ltd., and Gas Research Institute.     

Remote Field Eddy Current Technique: Phantom Exciter Model Calculations

Abstract

High resolution results of finite element calculations for remote field eddy current “phantom exciter” simulations of slit defect interactions using single through wall transit are presented. These show that fine circumferential slits cause almost no field perturbations in the case of nonferromagnetic tubes but big perturbations in ferromagnetic tubes where high magnetic H fields occur in the slits. Defect-induced magnetic field perturbations must therefore be considered in addition to eddy current perturbations when ferromagnetic materials are inspected, particularly in the case of fine slits orthogonal to the magnetic field direction. Additional details seen are the funnelling of energy into slits in ferromagnetic pipes and precursor disturbances of fields approaching defects. It is suggested that these are due to the reflection of the electromagnetic waves dictates by boundary conditions at the near side defect boundary.     

Remote field eddy current technique: Phantom exciter model calculations

High resolution results of finite element calculations for remote field eddy current phantom exciter simulations of slit defect interactions using single through wall transit are presented. These show that fine circumferential slits cause almost no field perturbations in the case of nonferromagnetic tubes but big perturbations in ferromagnetic tubes where high magnetic H fields occur in the slits. Defect-induced magnetic field perturbations must therefore be considered in addition to eddy current perturbations when ferromagnetic materials are inspected, particularly in the case of fine slits orthogonal to the magnetic field direction. Additional details seen are the funnelling of energy into slits in ferromagnetic pipes and precursor disturbances of fields approaching defects. It is suggested that these are due to the reflection of the electromagnetic waves dictates by boundary conditions at the near side defect boundary.     

Anomalous magnetic source defect modelling

Defect-induced field perturbations occurring during electromagnetic testing of ferromagnetic material can be modelled as combinations of anomalous eddy current and missing magnetization sources. At low frequencies, such as are used in Remote Field Eddy Current (RFEC) inspection of steel tubes, the anomalous magnetization defect sources dominate and give strong responses to circumferential slits orthogonal to the axial magnetic field. Here we present the results of finite element calculations and computer animations of the time-varying fields from a missing magnetization model of a slit defect. These are compared with the defect-induced anomalous field patterns obtained by phasor vector subtraction of calculations for slit defect and defect-free problems. It is noted that the ferromagnetic material in which the defect is located must be included in the missing magnetization model.Research supported by Natural Sciences and Engineering Research Council of Canada, Pipetronix Ltd., Province of Ontario, Gas Research Institute and Infolytica Corp.     

Transient Eddy Current NDE System Based on Fluxgate Sensor for the Detection of Defects in Multilayered Conducting Material

This paper describes a novel transient eddy current non destructive evaluation (NDE) system for the detection of defects in a multilayered conducting material by using fluxgate magnetometer as a sensor. In conventional eddy current NDE, the depth of defect detection is restricted due to the excitation frequency and its associated skin depth. Similarly, in conventional pulsed eddy current testing the time derivative of the secondary magnetic field, which decays much faster than the magnetic field itself, is measured by the induction coil. However, in this work we use fluxgate magnetometer which measures magnetic field directly and double “D” differential excitation coil in order to enhance the depth of investigation. In addition to this, the other instruments such as transmitter, transmitter controller and data acquisition system used for this work are the same one used for TEM based geophysical applications. The system has been used for the detection of an artificially engineered defect in an aluminum plate at a depth of 2 mm as well as 20 mm below the surface.     

Electromagnetic field formulation for eddy current calculations in nondestructive testing systems

The authors present the most practical configuration for detecting cracks in material, by applying an electromagnetic field along the largest dimension of the crack. An electromagnetic field formulation of the system equation is proposed using Maxwell's relations and separating the magnetic field into externally applied field and reaction field. The system equation is solved by using two classical methods : finite element technic for spatial problem and finite difference for time discretisation. So two dimensional eddy currents can be calculated immediately and related to the excitation characteristics for impedance calculation. Eddy currents lines in material for different cracks and sensor positions are presented. Theoretical results show important impedance changes.     

Nonlinear eddy current effects in ferromagnetic materials in the presence of DC magnetic fields

Eddy current effects in nonlinear ferromagnetic materials in the presence of a supplementary DC magnetic field are analyzed. The analysis is for a one-dimensional configuration, a semi-infinite plate magnetized homogeneously in a direction parallel to its surface. The nonlinear magnetization characteristic of the ferromagnetic plate material is assumed to be of a step-function form. Solutions of the electric field intensity on the plate surface, the penetration depth of eddy currents in the plate, the eddy current losses, and surface impedance in the presence of a DC magnetic field are obtained. A connection is found between the values obtained in simultaneous DC and AC magnetization conditions and the values obtained in the case of only AC magnetic field excitation.<>     

Techniques for depth-selective,low-frequency eddy current analysis for SQUID-based nondestructive testing

Conventional eddy current techniques are widely used for detection of surface-breaking cracks in metal structures. These techniques have limited success in the detection of deep, nonsurface-breaking flaws that require low frequency eddy currents, for which inductive pick-up probes have drastically reduced sensitivity. High resolution, Superconducting QUantum Interference Device (SQUID) magnetometers, which are very sensitive to do or low frequency magnetic fields, have been developed for detection of subsurface flaws. We have now extended SQUID NDE by utilizing a sheet inducer to produce an extended eddy current parallel to the surface in a conducting plate. The magnitude of the induced current density inside the plate reduces with the depth; however, the current component at a certain phase angle may increase with the depth. At a particular phase angle, the current density on the surface becomes zero, while the current inside the plate is large, so that the magnetic signal at that phase angle due to the surface structures can be minimized. With this method, we have detected simulated cracks in the sides of plugged holes in a thick plate, a hidden corrosion area in a specimen which consisted of two painted aluminum plates joined with sealant, as well as crack defects adjacent to fasteners in the second layer of lap joined aluminum plates. We present a theoretical model for simulation of the phase-related magnetic signal due to a flaw, which shows the relation between the phase angle and the depth of the flaw. The theoretical phase analysis is compared with the experimental results.     

电磁超声脉冲激励电路的设计

为了解决电磁超声能量转化效率较低、信号微弱的问题,设计了一种电磁超声脉冲激励电路。过零检测电路和单片机实现磁场强度与涡流激发的同步以及脉冲个数的控制;UCC3895芯片产生全桥电路的驱动信号,控制脉冲的频率和占空比;MOSFET管IRFP450构成全桥电路实现信号的功率放大。试验结果表明：该系统的稳定性好,可调节磁场强度,能有效地提高电磁超声能量转化效率。     

Effective magnetization and forces due to eddy currents

A simple method for evaluating the effective magnetization due to eddy currents excited by AC magnetic fields in finite conductive objects is presented. The values of magnetization enable the estimation of the forces exerted on the object by the effect of eddy currents. The method relies on assuming a similarity between eddy current magnetization and the magnetization due to diamagnetic effects, which is easier to evaluate. Its validity is checked by comparing results from the eddy current forces with data obtained from conventional but much more complicated methods or from experimental data. The approach may be useful for evaluating the eddy current losses in finite conductive objects excited by AC magnetic fields or the influence of small conductive objects on AC excitation coils. The method combines techniques related to the conventional evaluation of eddy currents in certain 1-D geometries with techniques that approximate behavior of the AC magnetic field in finite objects in a way similar to that followed when the magnetic forces acting on a diamagnetic object are calculated     

Inverse problem methodology and finite elements in theidentification of cracks, sources, materials, and their geometry ininaccessible locations

Inverse problem methodology is extended, through the more difficult geometric differentiation of finite-element matrices, to identify the location, material, and value of unknown sources within an inaccessible region using exterior measurements. This is done through the definition of an object function that vanishes at its minimum when the externally measured electric field matches the electric field given by an assumed configuration that is optimized to match measurements. The method is demonstrated by identifying the shape, permittivity, charge, and location of an electrostatic source through exterior measurement. The procedure is then extended to eddy current problems for the identification of the location and shape of cracks in metallic structures. An example demonstrates that when dealing with eddy current problems the least squares object function used by others has multiple local minima so that gradient methods have to be combined with search methods to identify the one absolute minimum. Procedures are also given for handling situations with no cracks and overdescribed cracks     

Defect characterisation in Austenitic stainless steel plate weld by multimulti frequency Eddy current testing technique

Multi multi frequency eddy current testing method has been a novel technique for defect characterisation and classification. In this technique any particular type of defect in a component can be detected in the presence of different type of other defects. In the present investigation attempts have been made to detect cracks in the interfaces between a weld pool and the bulk material in a thick austenitic stainless steel plate using this technique. The eddy current signals from the weld pool (having different magnetic permeability and electrical resistivity from the bulk) and the “lift off” of the eddy current sensor have been successfully suppressed by judicious choice of the experimental parameters and utilizing a software ‘mix algorithm’. This technique can be very effectively used as an NDT tool for a ‘Go/No Go’ test for any particular type of defect in components of mass production.     

用变频扫描励磁方法定量检测裂纹

目的 实现对疵病的定量检测和对材料的定性检测。方法 通过改变磁场交变频率从而引致导体中的涡流发生变化，来观测工件材料的疵病。结果 实验证明文该方法对于提高检测精度是有效的。结论 用变频扫描励磁方法进行裂纹定量检测可提高检测的可靠性。     

Off-diagonal impedance in amorphous wires and its application to linear magnetic sensors

We investigated the magnetic-field behavior of the off-diagonal impedance in Co-based amorphous wires under sinusoidal (50 MHz) and pulsed (5 ns rise time) current excitations. For comparison, we measured the field characteristics of the diagonal impedance as well. In general, when an alternating current is applied to a magnetic wire, the voltage signal is generated not only across the wire but also in a pickup coil wound on it. These voltages are related to the diagonal and off-diagonal impedances, respectively. We demonstrate that these impedances have a different behavior as functions of axial magnetic field: the diagonal impedance is symmetrical, whereas the off-diagonal one is antisymmetrical with a near-linear portion within a certain field interval. For the off-diagonal response, the dc bias current is necessary to eliminate circular domains. In the case of the sinusoidal excitation without a dc bias current, the off-diagonal response is very small and irregular. In contrast, the pulsed excitation, combining both high- and low-frequency harmonics, produces the off-diagonal voltage response without additional biasing. This behavior is ideal for a practical sensor circuit design. We discuss the principles of operation of a linear magnetic sensor based on a complementary metal-oxide-semiconductor transistor circuit.     

Pulsed Eddy Current Testing of Carbon Steel Pipes’ Wall-thinning Through Insulation and Cladding

Pulsed eddy current testing of wall-thinning through cladding and insulation was studied from both theoretical and experimental aspects. The analytical solution was derived for a simplified four-layered structure and was used to conduct simulations to ascertain the feasibility of this method. A pulsed eddy current testing probe consisting of a circular excitation coil and an AMR-sensor-embedded differential detector was fabricated to measure the time-varying magnetic field signals on the axisymmetric excitation coil??s axis. The measurement system was able to measure magnetic field down to a few hundred micro-Gausses in an unshielded environment. Simulation and test results showed that over a certain time after turning off the excitation current the magnetic field signal??s decay behavior is almost merely relevant to the pipe??s wall thickness. Future development of a carbon steel pipe??s wall-thinning can be evaluated by using decay coefficients estimated from previously obtained test data.     

Review of Advances in Quantitative Eddy Current Nondestructive Evaluation

A comprehensive review of advancements in eddy current (EC) modeling is presented. This paper contains three main sections: a general treatise of EC theory, the thin skin EC forward modeling, and the EC inverse problem. (1) The general treatise of eddy current theory begins with an exposition of the reciprocity formulas for evaluating probe impedance changes, which are derivable from first principles. Two versions of the reciprocity formulas, one with a surface integral and the other with a volume integral, are given. Any particular type of defect, as well as both one-port and two-port probes, can be treated. Second, a brief account of analytical and numerical methods for calculating the field distributions is presented. Third, theory of probe/material interactions with various defect types is described. (2) The paper then proceeds to the forward modeling section, which contains a detailed treatment of the eddy current forward problem for surface breaking cracks and EDM notches in the thin skin approximation. (3) The inverse problem section begins with a general review of commonly used inversion methods, exemplified by selected references from the literature, followed by more detailed examinations of EC inversions for surface breaking cracks and slots. The last part of this section is devoted to the inverse problem for layered structures. Although being a review in nature, the paper contains a number of new accounts for time-domain eddy current interactions. In particular, a modification is proposed to the reciprocity formula in order to take a better account of pulsed eddy current signals.     

The Influence of the Heating Rate and Thermal Energy on Crack Detection by Eddy Current Thermography

The capability of eddy current thermography in detecting cracks is investigated numerically and experimentally in relation to the crack orientation, the heating rate and the excitation period. The numerical investigation shows that, for cracks parallel to the heat flow the detection region increases with the increase of the heating rate, while for cracks perpendicular to the heat flow, it increases with the increase of the excitation period. The experimental results confirm that the detection of cracks parallel or perpendicular to the heat flow is improved by increasing the heating rate or the excitation period, respectively. The optimum time period for the detection of a crack depends on the crack orientation: For cracks parallel to the heat flow (i.e. perpendicular to the current flow), the best results are obtained at the beginning of the heating period. For cracks perpendicular to the heat flow, the optimum detection period is delayed with the distance of the crack from the heated area. If the crack is very close to the edge of the plate, both the detection period and the sharpness of the crack are reduced. The experimental results are compared to data obtained by identical experiments, where the use of a lower performance camera was combined with data processing techniques. The comparison indicates that a higher performance camera is more effective and may compensate for the improvements achieved in the detection of a crack through data processing techniques.     

Detection of the Subsurface Cracks in a Stainless Steel Plate Using Pulsed Eddy Current

The nondestructive method to detect subsurface defects is limited because conventional eddy current are concentrated near to the surfaces adjacent to the excitation coil. The PEC technique enables detection of cracks buried deeper under the surface with relatively small current density. In the present study, an attempt has been made to investigate detection of subsurface cracks using a specially designed double-D differential probe. The tested sample is a SS304 with a thickness of 5 mm; small EDM notches were machined in the test sample at different depths from the surface to simulate the sub surface cracks in a pipe. The designed PEC probe has two excitation coils and two detecting Hall-sensors. The difference between two sensors is the resultant PEC signal. The cracks under the surface were detected using peak amplitude of the detected pulse; in addition, for a clear understanding of the crack depth, the Fourier transform is applied. In time domain, the peak amplitude of the detected pulse is decreased, and in the frequency domain, the magnitude of the lower frequency component has been increased with an increase in the crack depth. The experimental results have indicated that the proposed differential probe has the potential to detect the sub surface cracks in a stainless steel structure.