Diapositive 1

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Recent advances in simulation of eddy current
testing of tubes and experimental validations
Christophe REBOUD, Denis PREMEL, CEA, Saclay,
France Dominique LESSELIER, L2S (CNRS/Supélec),
Gif-sur-Yvette, France Bernard BISIAUX, SETVAL,
Aulnoye-Aymeries, France
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Outline
I. Industrial context of the work II. Modeling
approach Volume Integral Method III. New ECT
configurations modeled and validations IV.
Improvement of the numerical convergence of the
model Conclusions and perspectives
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I. Industrial context of the work
Applications of ECT in Vallourec group

• Around 150 NDT automatic inspection units
• on production lines (ultrasonics, eddy
  current,
• flux leakage)
• Around 30 ECT units

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II. Modeling approach Volume Integral Method

• Harmonic regime
• Non-magnetic tubes (infinite)

Hypotheses
Introduction of a fictitious current source in W
Computation of ECT output signals
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2
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Probe
Reciprocity theorem
W
State equation solved numerically
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III. Modelling of new ECT configurations

• Encircling probe

• Sectorial probe

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Computation of the electric field Ep
Probe set of encircling coils centered on the
tube axis

• Symmetry about the z axis

• Dodd and Deeds formalism (2D), available in CIVA
• platform

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Computation of the electric field Ep
Probe set of encircling coils that may be
off-center and/or tilted with respect to the z
axis

• No symmetry about the z axis

Current source density
Greens dyad
Volume of the source

• Computation of non separable integrals
• along the r and j directions

C. Reboud, D. Prémel, G. Pichenot, D. Lesselier
and B. Bisiaux, Development and validation of a
3D model dedicated to eddy current non
destructive testing of tubes by encircling
probes, ISEM 2005 Symposium, pp. 278279,
september 2005
No information about the angular location of the
flaw
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Computation of the electric field Ep
Probe specific probe configuration used in the
Vallourec group

• General expression of the primary electric field

Emitting part
Current source density
Greens dyad
Volume of the source
Emitting part
Receiving parts
Receiving parts (differential mode)
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Modelling of specific flaws geometries
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Experimental validations centered probe

• Stainless steel tube with rough surface,
• outer diameter 32 mm,
• thickness 8 mm

• Frequency 100 kHz

• Flaws boreholes with flat bottom

Calibration (1 V, 10)
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Experimental validations off-center probe

• Stainless steel tube with rough surface,
• outer diameter 32 mm,
• thickness 8 mm

• Frequency 50 kHz

• Flaws boreholes with flat bottom

Probe used
Calibration (1 V, 10)
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Experimental validations sectorial probe

• Stainless steel tube with rough surface,
• outer diameter 50 mm,
• thickness 7 mm

• Frequency 5 kHz

• Flaws boreholes with flat bottom

f 4.5 mm, depth 7 mm
f 2.25 mm, depth 7 mm
Calibration (1 V, 10)
f 4.5 mm, depth 5 mm
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IV. Improvement of the numerical convergence of
the model
State equation solved numerically
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Numerical resolution of the state equation
Method of Moments (Galerkin variant) 2
steps

• Step 1 expansion of the unknown field on a
  basis of functions

• Step 2 scalar products with the functions Fuvw

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Existing discretisation scheme

• Definition of Fijk (r,j,z) tensor product
• of 1D pulse functions

Separation of the integral terms

• Good results are obtained for most ECT
• configurations

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Choice of the expansion functions

• Discontinuities of f(r).Et at the edge of W
• Et is approximated by a continuous or
  differentiable
• function along the j and z directions

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Case of weak perturbation of the field
Longitudinal notch
Transversal notch
2 identical bobbins in differential mode
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Case of strong perturbation of the field
Longitudinal notch
Magnitude max.
Transversal notch
Phase
Imag (dZ)
Real(dZ)
2 identical bobbins in differential mode
Longitudinal notch

• Depth 0.69 mm
• (54 of the tube thickness)
• Width 0.1 mm
• Length along the z direction 10 mm

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Comparisons with experimental data
Calibration
(1 V, 10)
Transversal notch
Longitudinal notch
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Conclusions and perspectives

• New functionalities available in the CIVA 8
  platform
• Probe Any combination of encircling coils that
  may be off-centre,
• Flaw shapes Boreholes with flat bottom

• Development of a new numerical scheme using
  non-uniform B-splines
• along the j and z directions