2013 EDDY CURRENT BENCHMARK PROBLEM: SOLUTION VIA A COUPLED INTEGRAL APPROACH

Transcription

1 2013 EDDY CURRENT BENCHMARK PROBLEM: SOLUTION VIA A COUPLED INTEGRAL APPROACH R. MIORELLI 1, C. REBOUD 1 AND T. THEODOULIDIS 2 1 CEA, LIST, Centre de Saclay, Gif-sur-Yvette, France 2 Department of Mechanical Engineering, University of Western Macedonia, Greece

2 OUTLINE Presentation of the benchmark configurations Semi-analytical integral methods dedicated to EC modeling Coupled approach proposed and benchmark results Conclusions and perspectives

3 BENCHMARK CONFIGURATIONS EC inspection of stratified planar structures Detection of small flaws at the vicinity of larger holes Targeted application : rivet inspection Measurements carried out at

4 BENCHMARK CONFIGURATIONS Four arrangements of two plates with a hole, one also containing a crack Test case #1 Test case #2 Test case #3 Test case #4 EC inspection with an absolute coil using an impedance meter: no calibration needed Inspection frequencies: 1 khz and 5 khz Insulation layer

5 VOLUME INTEGRAL METHOD FOR ECT SIMULATION Subproblem 1: Field computation in the unflawed material Subproblem 2: Modeling of flaws as a set of interacting fictitious sources, solutions of a set of integral equations Primary field Total field Last step: Computation of the ECT signal using the reciprocity theorem Harmonic quasi-static regime, homogeneous pieces with planar or cylindrical geometries and no edges Analytical expressions of the Green dyads in the spectral domain, discretization of flaws only Invariance in translation in the transverse directions NDE 2012, New Delhi December 10-12, 2012 PAGE 5

6 BOUNDARY ELEMENT METHOD FOR ECT SIMULATION Assumptions of the BEM model: [Bow94] 1. No current passing through the crack 2. Crack opening d/2 [The10] and << f coil 3. Main crack faces are parallel z 1. Computation primary field n 2.a Surface (ideal) crack case (Assumption 1) n S 0, W 2.b Narrow crack case (Assumptions 1, 2 and 3) Surface dipole density p(r ) p(r ) p(r ) p(r ) p(r ) 3. Coil response Volume dipole density Generalized to layered half-space containing multiple cracks [Mio13] [Bow94] Bowler, App. Phys. (75) 1994 [The10] Theodoulidis, NdT&E (43) 2010 [Mio13] Miorelli, Reboud, Theodoulidis, and Lesselier, IEEE Trans. On Mag. (49)

7 BOUNDARY ELEMENT METHOD FOR ECT SIMULATION Example of result: benchmark QNDE 2012 (inconel tube inspection, crack with an opening of 85 µm) Computation time < 1 minute per frequency PAGE 7

8 COUPLED INTEGRAL APPROACH (BEM-VIM) Motivation: Efficient modeling approach for the simulation of configurations involving both volume flaws and narrow cracks Open issues: Narrow and very narrow cracks not easy to model with FEM and VIM (very large meshes required) Volume cracks like boreholes not handled with BEM (model assumptions no more true) Proposed solution: Joint simulation of narrow cracks with BEM and volume flaws with VIM in subproblem 2 volumetric flaw corner crack volumetric flaw small slot 8

9 COUPLED INTEGRAL APPROACH (BEM-VIM) Flaw 1 = narrow crack Flaw 2 = narrow crack Flaw 3 = volumetric flaw Flaw 4 = volumetric flaw State equation matrix system after the application of the Method of Moments Scalar values Coil response (reciprocity theorem) Vector values 9

10 BENCHMARK RESULTS: TEST CASE # 1 Medium characteristics: Plate thickness = 2 mm Conductivity = MS/m Operation frequency: 1.0 khz and 5.0 khz Skin depth (d): 3.7 mm Flaws dimension: Hole (r x d): (20.0x 2) mm Crack (l x w x d): (14.92 x x 2) mm Crack mesh [N x1 x N y1 x N z1 ]: BEM = [1 x 15 x 5] VIM = [30 x 50 x 8] Hole mesh [N x1 x N y1 x N z1 ]: VIM = [35 x 35 x 8] (@1 khz) VIM = [45 x 45 x 8] (@5 khz) 10

11 BENCHMARK RESULTS: TEST CASE KHZ Test case khz Simulated cartography: 80x80 positions CPU time: BEM-VIM 56 VIM 2h11 VIM hole only 41 11

12 BENCHMARK RESULTS: ROUGHER MESH Test case khz Simulated cartography: 80x80 positions CPU time: BEM-VIM 6 Hole mesh: 21 x 21 x 4, Crack mesh: 15 x1 x 4 A good agreement can be achieved quite quickly

13 BENCHMARK RESULTS: TEST CASE KHZ Test case khz 13

14 BENCHMARK RESULTS: TEST CASE #2 Medium characteristics: First layer thickness = 2 mm Conductivity = MS/m Second layer thickness = mm Conductivity = dielectric insulator Third layer thickness = 1 mm Conductivity = MS/m Operation frequency: 1.0 khz and 5.0 khz Skin depth (d): 3.7 mm Flaws dimension: Hole 1(r x d): (20.0 x 2) mm Hole 2(r x d): (20.0 x 2) mm Crack (l x w x d): (14.92 x x 2) mm Crack mesh [N x1 x N y1 x N z1 ]: BEM = [1 x 15 x 5] Holes mesh [N x1 x N y1 x N z1 ]: VIM = [35 x 35 x 8] (@1 khz) VIM = [45 x 45 x 8] (@5 khz) 14

15 BENCHMARK RESULTS: TEST CASE 1.0 KHZ Test case khz CPU time: BEM-VIM 4h38 VIM 2 holes only 4h05 15

16 BENCHMARK RESULTS: TEST CASE 5.0 KHZ Test case khz 16

17 BENCHMARK RESULTS: TEST CASE #3 Medium characteristics: First layer thickness = 2 mm Conductivity = MS/m Second layer thickness = mm Conductivity = dielectric insulator Third layer thickness = 1 mm Conductivity = MS/m Operation frequency: 1.0 khz and 5.0 khz Skin depth (d): 3.7 mm Flaws dimension: Hole 1(l x w x d): (29.65 x x 2) mm Hole 2(l x w x d): (29.65 x x 2) mm Crack (l x w x d): (14.92 x x 2) mm Crack mesh [N x1 x N y1 x N z1 ]: BEM = [1 x 15 x 5] Holes mesh [N x1 x N y1 x N z1 ]: VIM = [35 x 35 x 8] (@1 khz) VIM = [45 x 45 x 8] (@5 khz) 17

18 BENCHMARK RESULTS: TEST CASE 1.0 KHZ Test case khz CPU time: BEM-VIM 4h38 VIM 2 holes only 4h05 18

19 BENCHMARK RESULTS: TEST CASE 5.0 KHZ Test case khz 19

20 BENCHMARK RESULTS: TEST CASE #4 Medium characteristics: First layer thickness = 2 mm Conductivity = MS/m Operation frequency: 1.0 khz and 5.0 khz Skin depth (d): 3.7 mm Flaw dimension: Hole (l x w x d): (29.65 x x 2) mm Holes mesh [N x1 x N y1 x N z1 ] freq : VIM = [35 x 35 x 5] 1kHz 20

21 BENCHMARK RESULTS: TEST CASE 1.0 KHZ Test case khz 21

22 BENCHMARK RESULTS: TEST CASE 5.0 KHZ Test case khz 22

23 CONCLUSIONS AND PERSPECTIVES Simulation of 2013 ECT benchmark using a mixed integral method (available in CIVA 11, released in July 2013) Experimental data reproduced with good accuracy in each test case Perspective: performance improvement through the analytical description of the borehole inside the integral formulation First subproblem (field computation) treated in the case of a plate Introduction of narrow cracks in progress (second subproblem) Computation of the Green dyad of a plate with a hole Expected computation time: around 2minutes

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