A study has on the modeling of Non Destructive Testing using eddy currents with FLUX 8.10, 3D application has recently been performed at CEDRAT. FLUX has demonstrated its capacity to obtain high-quality results for this kind of application with reasonable computation time. To obtain these results, one needs to pay particular attention to the modeling of the mesh design, formulations, and the description of probe motion during the simulation of such problems.
A technical paper on Non Destructive Testing with FLUX 3D application has been created that allows the user to easily reproduce this computation and understand the key points of NDT modeling in FLUX.
Problem 8: A block of austenitic stainless steel (resistivity: 7.4e-7 Ω.m-1) contains a rectangular slot representing a flaw. A differential probe moves across the surface of the block. The probe is composed of one inducing solenoid (supplied by a 500 Hz sinusoidal signal) and by two receptive coils (see Figure 1).
Figure 1 :The problem 8.
Each of the two smaller solenoids are in a branch of a Wheatstone’s bridge. An amplifier and a dephasor generate signals proportional to the difference of the magnetic flux in the two receivers. The simulation aimed at fitting the measurements for two different motions of the probe :
- Longitudinal motion: motion parallel to the plane of the crack (the axes of the two coils being in the plane of the crack).
- Transversal motion: motion perpendicular to the plane of the crack ( the axes of the two coils being in the plane perpendicular to the plane of the crack).
The “ Key points � A study of sensitivity has permitted to determine the most significant parameters for the finite element model . A good modeling of NDT devices with FLUX will follow the four following advices:
* Limit the mesh noise inherent in the flux computation.
* Limit the mesh noise inherent in the description of the probe motion.
* Mesh finely the place where eddy currents will appear.
* Use of an adapted formulation in the computation of eddy currents in a cracked geometry.
Figure 2: Geometric representation.
1. Flux computation: The probe has been modeled by non meshed coils. However, in order to ensure a precise computation, the mesh must be well structured in the air space filled by these coils. Thus, the air volumes inhabited by the coils have been geometrically represented. (see Figure 2)To limit the mesh noise, an extrusive mesh generator has been applied on the entire height of the sensor. Similarly, as the computed flux is the difference between the flux seen by the two receivers, the mesh noise is drastically reduced by meshing them identically.(see Figures 3 and 4)
Figure 3: Extrusive mesh generator.
Figure 4: Linked mesh.
Finally, the calculation of the flux itself must be done with the method “FLUX_INDUCTOR” corresponding to a volume integration in the air enclosing the coils (zone modeled by a reduced formulation versus to vector potential) :
An integration of B on a surface normal to the flux or the multiplication of the mean value of the induction on this surface would lead to important approximations.
2. Probe motion: A computation parameterized by the geometrical position of the coils would mean a remeshing of the entire model for each position. Such a remeshing introduces an unacceptable amount of noise compared with the required precision. The new 3D mechanical sets available in the version 8.10 will be used to describe the motion.
It is imperative to keep a constant mesh in the zone where you compute the flux. Thus, a first mechanical set in translation will be created in the air surrounding the coils and the flux will be computed only in this zone. The plate being fixed, we have the choice to define the mechanical sets by following two strategies :
Figure 5: Division in 3 mechanical sets.
Division in 3 mechanical sets (see figure 5):
In blue: mechanical set in translation containing the coils (zone of flux computation): constant mesh
In green: compressible mechanical set
In yellow and magenta: plate and crack, fixed mechanical set : constant mesh
Figure 6: Division in 2 mechanical sets.
Division in 2 mechanical sets (figure 6) :
In blue and green: mechanical set in translation : constant mesh
In yellow, turquoise and magenta: fixed mechanical set, constant mesh
In the 1st case, the device is surrounded by air and an infinite box, the technique of compressible mechanical set is used. In the second case, two blocks are in relative motion, a sliding surface separates them. The boundary conditions are directly defined on external faces.
3. Plate mesh: A correct mesh is necessary in the plate, which is the zone where eddy currents appear. More particularly, the study has shown that the mesh can be structured efficiently by geometrically representing the volumes of the plate over which the probe passes. Then, it is possible to refine the mesh in these zones without generating too many nodes in the rest of the plate (see figure 7). The global mesh of the device represents between 120,000 and 145,000 nodes (with second order element) depending on the chosen configuration.
Figure 7: Plate mesh
4. Formulations: The study has been realized both with scalar and vector potential formulations. Thanks to recent developments, the scalar formulations give results as precise as vector ones and demand less resources (computation time, memory requirement).
The new reduced formulation versus T0 has been used in the air surrounding the coils. The plate is modeled by a TΩ formulation (Electric vector potential, Total magnetic scalar potential) with edge interpolation. The equivalent nodal formulation is not satisfactory for NDT application as the crack makes the plate concave and the concavity leads to imprecise local computations of eddy currents with nodal interpolation.
The Studied Cases:
Beyond the sensitive study, different simulations have been performed: longitudinal and transversal motion, use of compressible mechanical set or use of sliding technique. Finally, the crack being very fine, we have the choice to represent it by a volume composed by air or by a surface on which is assigned a specific surface constraint. (see Figure 8 )
Figure 8: Mesh distribution for the defect.
The Results:
The results obtained by FLUX fits very well to the measurements. Similarly, the sliding technique and the compressible have both given satisfaction .( see Figures 9 and 10)
Figure 9: Results with the compressible mechanical set.
Figure 10: Results with the sliding surface.
Finally, the representation of the crack as a surface gives equivalent results. The surface constraint assigned to the crack requires that the local direction of eddy currents is parallel to the edges of the crack (TXN=0). We can conclude that it is not necessary to physically represent the crack itself but only the consequence of its presence on the eddy currents distribution. (see Figure 11)
Figure 11: Results with a surface crack.
The result of the computation being the difference of two close quantities, the quality of the results is very sensitive to the respect of the “key points� presented above. Without taking care when constructing the model, the results could look like the following. (see Figure 12)
Figure 12: Results using a global remeshing.
Costs:
Concerning the computation time, the scalar formulations and a fine but controlled mesh allow a reasonable computation time. Results for the 30 positions of the probe are obtained in half a working day. This makes FLUX a powerful and efficient tool for NDT applications.
This study is based on the benchmark Problem No. 8 of TEAM WORKSHOP: “A Coil over a crack” realized by Jean-Claude VERITE (EdF, Direction Etudes et Recherches). This problem has been presented in COMPEL.
HO in X direction, Z=250mm, Bz.
HO in Y direction Z=250mm, Bz.
2 degaussing coils, Z=250mm, Bz.
Mesh discontinuities of the top of an ellipsoid and connection with surrounding mesh of the air.
