Cracks are the most important type of defect in eddy current testing. The use of finite element methods to study such defects requires very fine splitting and is often difficult to achieve satisfactory results. JR Bowler et al. proposed an ideal crack model, considering the crack as a non-thickness surface defect, replacing the crack with an equivalent current dipole layer, and determining the equivalent source density by solving the integral equation on the crack surface. Since the three-dimensional problem is transformed into a two-dimensional solution, the amount of calculation is greatly reduced. The key to constructing the integral equation is to obtain the dyadic Green's function. Previous work was directed at infinitely thick conductors. The authors deduced the vortex field dyadic Green's function in uniform infinitely large plate conductors. This method was generalized to solve the crack problem of finite-thickness plate conductors, and proceeded to the practical direction. A big step.
In the above integral equation, the eddy current field (referred to as the incident field) generated by the coil in the defect-free conductor appears as a known amount. Therefore, the above method is meaningful only when the solution of the incident field is relatively easy to obtain.
For infinitely thick conductors and flat conductors, the incident field is an axisymmetric field, which is easy to obtain analytical solutions. And the pipeline problem is much more complicated. The through coil produces an axisymmetric field in the pipe, but it cannot detect circumferential cracks, and the detection sensitivity depends on the crack direction. Placement coils have the same detection capabilities for cracks of various orientations and are therefore receiving increasing attention. However, there is no analytical solution for the incident field of the placed coil in the pipeline, and the calculation of the pipe dyadic Green's function is also troublesome. The China Postdoctoral Science Foundation funded the project.
Chen Denan, born in 1969, received his Ph.D. in engineering from Xi'an Jiaotong University in 1998. He is currently a postdoctoral fellow in the Department of Power Engineering at Huazhong University of Science and Technology. His research interests include electromagnetic field theory and numerical analysis, eddy current non-destructive testing, and wavelet analysis.
Shao Keran male, born in 1946, graduated from the Electrical Engineering Department of Shanghai Jiaotong University in 1968. He received his Ph.D. in engineering in 1987. He is currently a professor of electrical power at Huazhong University of Science and Technology. He is a doctoral tutor. He is engaged in teaching research in the field of electromagnetic field theory and numerical analysis. He has published more than 30 papers in the journal.
Therefore, the ideal crack model cannot be used directly.
When the pipe radius is much larger than the coil size, the pipe wall can be treated as a flat conductor. However, if the pipe radius is not much larger than the coil size, this will cause a large error. Taking into account the similarities between the two models (eg), the work in this paper shows that it is possible to obtain sufficiently accurate simulation results for the pipeline model by introducing appropriate corrections to the flat model.
The eddy current detection of the flat coil conductor and the pipe. The coil impedance increase caused by the crack in the flat plate conductor. A brief review of the calculation method of the eddy current field of the crack defect in the flat plate conductor. If the crack width is much smaller than the eddy skin depth (about 1/4), it can be regarded as an ideal crack, and its action can be replaced by an equivalent current dipole layer distributed on the crack surface So. Let the equivalent source surface density be P, and its direction is perpendicular to SQ. As shown in Figure la, the selected coordinate system is such that the crack lies on the plane, then P has only the x component, ie P = buckle. By the following integral equation, the x-component incident field of the induced current (ie, the incident field) generated by the source and the radial mode coils in the defect-free conductor is an axisymmetric field, and an analytical solution can be obtained. Is the component of the dyadic Green's function, for a uniform infinite plate conductor with a finite thickness d (i permeability test Benchmark problem Step2W has been numerically simulated. The calculated results agree well with the experimental values; calculating 11 impedance values ​​including generation The coefficient matrix only needs lmin30s. 3 Pipe cracks cause the coil impedance to increase. The calculation of the placed coil to the pipeline is shown in Figure lb. If the ratio of the pipe radius to the coil radius i/r2 is much larger than 1, then the lower end of the coil is everywhere. The distance to the surface of the tube wall is very small, which is equal to the lifting wall of the coil can be regarded as a flat conductor. Lifting is an important parameter for calculating the incident field. When J/r2 is not much larger than 1, we try to define an The effect of lifting off, so that the flat model can be used as an approximation of the pipeline model.
In the interaction of the coil with the conductor, it is the winding that is not the relative position of the center of the coil to the surface of the conductor. Let ~, /2, and Z3 be the distances from the inner edge, center, and outer edge of the winding to the tube wall in the cross section perpendicular to the axis of the coil, as shown in Figure lb. Try to define "=*1+, 2+Z3" /3 (4) As the equivalent lift of the coil, instead of using the flat mold experimental value in Figure la, we numerically simulate the vortex flow test of the steam generator tube Benchmark 3.
=1.27mm; coil inner radius n 0.5mm. ratio of pipe radius to coil size R/r26. pipe wall material Inconel =1/140A. crack along the pipe axial direction, width 0.2mm, length 10mm, depth is 100%, Internal crack ID 60%, ID 40% and outer crack OD60%, OD40% five kinds. The coil starts from the center of the crack and moves along the crack line (set to the y-axis), and the impedance change value of the coil is calculated every 1 mm. The comparison between the calculation results and the experimental results is as follows.
Calculated value f test value 箅 value resistance AJ / 0 (b> impedance trajectory calculated value is in good agreement with the experimental value, significantly better than the calculation results given by the various methods. The calculation of 100% crack split 32x 4 60% crack is 32x3, 40% crack is 32x2. Since the coefficient matrix is ​​quasi-sparse, the amount of memory used is less than 1M; the calculation time calculates the impedance value of 11 points on the P5/133 personal computer including the generation coefficient array. It only takes more than 1 min. In contrast, the Chinese boundary element and finite element method are used to calculate the Benchmark problem Step 1 (axisymmetric field, simpler than the problem in this paper) requires 140 M memory and the calculation time is h; Calculate Benchmark problem Step 2 (flat problem, less difficult than this paper) requires 42M memory, it takes 45min on P5/166 personal computer. Inner wall ID inner wall ID resistance 厶//0(b) impedance track outer wall OD resistance AK/fl (b) Impedance trajectory outer wall OD 4 Summary Steam generator pipeline smear detection Benchmark problem The model parameters in Step 3 are exactly the same as the actual eddy current detection parameters. The results of this paper show that in this case, the pipeline crack defect is in the placed coil. in
Because of the small amount of calculation and high speed, this method can play an important role in the optimization of eddy current testing.
This paper only calculates the case of axial cracks. The method of selecting the equivalent liftoff in the paper has certain empirical properties, whether it is suitable for circumferential cracks, suitable for the case where the ratio of the radius of the pipe to the coil is smaller, etc., because the lack of experimental data for comparison, further research is needed. .
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