Quantitative Analysis of Eddy Current NDE Data

8/12/2019 Quantitative Analysis of Eddy Current NDE Data

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IV Conferencia Panamericana de ENDBuenos Aires Octubre 2007

Quantitative Analysis of Eddy Current NDE Data

Y. M. Kim, E. C. Johnson, O. EsquivelThe Aerospace Corporation, M2-248

P. O. Box 92957Los Angeles, CA 90275, USA

[email protected]

Abstract

A new method for analyzing eddy current inspection data is presented. The key concept behind this method is extraction and isolation of the sample response from the measuredsignal. The measured signal depends on many factors including, not only thecharacteristics of the probe itself, the sample material, the operation frequency, and the

probe/sample geometry, but also the measurement instrumentation and cabling. Tostart, complex impedance measurements of the (1) isolated probe and (2) probe withsample as a function of frequency were conducted. The data frequency dependence wasfound to exhibit resonance behavior that could be fit to a model RLC circuit. Thevalidity of this model circuit was confirmed by the predictable resonance change uponintroduction of additional capacitors into the measurement configuration. Withoutexternal capacitance, the value for C generally reflects the stray capacitances of theinstruments and cables and, hence, is unaffected by presence of a sample. Furthermore,

data at a fixed-frequency can be easily related to those of swept frequencymeasurements via a conformal mapping deduced from analysis of the model circuit.Using this approach, data from fixed-frequency measurements can be effectivelymapped to a corrected R and ! L plane. Data for a variety of materials reveals sampleresponses that can be easily explained in terms of surface impedance variations. Inaddition, for this corrected R and ! L plane, lift-off behavior scales in a simple

predictable fashion and data at different lift-off conditions can be analyzed to furtherreduce the properties of the sample. Furthermore, defects characteristics, such as crackwidth and depth, can be quantified with simple physical reasoning and the condition ofmultiple conductive layers can be evaluated. This improved understanding of the defectsignals can be exploited for the design of more efficient probes that are matched to thematerials under test. Moreover, this quantitative method allows one to present datataken with different probe and instrument settings in an invariant form representative ofthe fundamental surface impedance for the specimen.

1. Introduction

Conventional eddy current NDE methods generally involve measurement of the real andimaginary components of the electrical AC impedance of a probe coil at a fixedfrequency, with the results plotted in a complex plane. In this representation of signals,the signal point varies in its position depending on the electromagnetic properties of thetest sample and the degree of the proximity between the probe and the sample. The

presence of localized defects (such as cracks), and potentially detrimental material

variations (i.e., stress induced deformation, grind-burn, variation in grain texture, etc.)Support for this work under The Aerospace Corporation Independent Research and Development Program isgratefully acknowledged.

2007 The Aerospace Corporation


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IV Conferencia Panamericana de END Buenos Aires Octubre 2007 2

are detected as a relative displacement vector measured from the signal positionobtained from a standard or unaffected area of the sample. These vectoral signaldisplacements, however, are highly dependent on the probe and sample configuration,they trace nonlinear paths, and are hard to predict or relate to corresponding physicalchanges. To insure the reliability of an inspection, the measured signal is oftenmonitored and analyzed with the signal from a known defect standard exhibiting thesame geometry and made from the same material. Furthermore, upon a change of theoperational frequency, all the meanings ascribed to signal displacements with respect tomaterial variations must be redefined empirically because no simple predictive rulesapply. A model circuit for conventional eddy current inspection 1 is shownschematically in Fig. 1 with typical impedance vector displays for both an isolated

probe and probe on a sample surface.

The model of Fig. 1 is based on simple intuition regarding the presence of a coil and theinfluence of electromagnetic materials through mutual inductive interaction, whichmodifies L and R. Upon the application of a magnetic intensity ( H ) generated by ACcurrent through a coil in a probe (and consequent magnetic field, BP, resulting from theferrite in the probe), an induced current (eddy current) is generated on the surface of thetest material, which gives rise to the induced magnetic field, BI. The resulting totalmagnetic field, B, is comprised of BP and BI. For non-magnetic materials, a current isalways induced to generate an opposing magnetic field (e.g., free electrondiamagnetism). This will result in a diminishing of the total magnetic flux (decreasinginductance of the probe coil). Also, any induced current in a material with finiteconductivity produces ohmic losses, where the lost energy is re-supplied by the drivingcurrent in the probe coil, resulting in an apparent increase in coil resistance. Forferromagnetic (or paramagnetic) materials, the resulting field, BI, is predominantly inthe same direction as the field BP due to para-magnetization (e.g., real part of thesusceptibility) that presides over the weaker free electron diamagnetism, resulting in anapparent increase in the coil inductance. Since the coil is AC stimulated, further energydissipation occurs, in addition to the energy loss due to the ohmic electron current, asmagnetic loss (i.e. imaginary part of the susceptibility) resulting in further increase inthe apparent resistance. Even though this description is acceptable and sufficient fordescribing the physical interaction between the probe and sample, a fundamentalquestion still remains: Is the measured complex impedance at a fixed frequency

properly represented by R + i ! L in the conventional model circuit?

Z i

Z r

Z without sample

Z with sample

Figure 1. Model circuit and typical impedance vector display employed inconventional eddy current inspection.

R

L Z


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2. New Model Circuit

Fig. 2 depicts a typical frequency dependent complex impedance curve measured acrossa probe both with, and without a conductive sample. While the overall behavior exhibits

a resonance phenomena, the resonant frequency and the width of the resonance ismodified by the introduction of the sample. The conventional circuit model of Fig. 1does not account for this fact. In conventional eddy current methods, the operationalfrequency is chosen rather arbitrarily, and it is not too difficult to understand why themovement of the signal on the complex impedance plane cannot be easily interpretedwith the corresponding physical change of the probe-sample system. It is also clear thata change of operation frequency requires a new calibration process. The shortcoming ofthe conventional model circuit in Fig 1 clearly originates from the fact that the measuredcomplex impedance at a fixed frequency is not completely represented by R + i ! L inthe conventional model circuit.

The observed frequency dependence of the complex impedance can be explainedthrough use of a new model circuit as depicted on the right of Fig. 2. Here a capacitiveelement is simply added in parallel to the conventional model circuit to account for theinevitable capacitance contributions arising from the cable, wires, and instrumentation.In this circuit, the electrical impedance ( Z ) across two ends of the probe becomes,

1

Z =

1

R + i " L+ i " C . (1)

This impedance expression allows for excellent agreement with the observed frequencydependence of a probe with and without sample; the difference between the two cases

being accounted for by changes in the R and L values. Furthermore, empiricalintroduction of additional capacitance, parallel to the probe, results in modification to

the resonance that acts in accordance with Eq. 1. The capacitance value is correlatedwith the resonance frequency change, and even a minute dielectric loss differenceamong capacitors can be detected by the change in the width of the resonance.

L

Figure 2. Frequency dependent complex impedance curves measured across a probe bothwith, and without a conductive sample (left). New model circuit includes the addition ofa capacitive element (right).

(Without Sample)

rea l

real

imaginary

(With Sample)

imaginary

C

R

Z

I m p e d a n c e

( o h m

)

I m p e d a n c e

( o h m

)

Frequency, Hz


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To express the frequency dependence of Z (! ) and to make it simpler for deducing itscharacteristics in terms of R, L and C , Eq. 1 can be scaled with the followingcharacteristic impedance, Z 0, and frequency, f 0, defined as

Z 0 " L

C (2)

" 0

= 2 # f 0 $ 1

LC . (3)

With these definitions, the resistance, R, and the frequency f ! " 2= can be translatedinto dimensionless quantities by the following definitions:

" # R

Z 0

, (4)

" # $

$ 0

=

f f 0

. (5)

In terms of the parameters above, Eq. 1 becomes

Z (" ) = Z 0# + i "

(1 $ " 2 ) + i #" . (6)

The real and imaginary parts of this complex impedance can be written in as

2222

22022220 )1(

)1()( and )1(

)(! " !

" ! ! !

! " !

" !

+###=

+#= Z Z Z Z

ir . (7)

Assuming "


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At " = 1 , the components of Z become

" r (# = 1 ) = Z m and " i (# = 1 ) = $ " 0 . (10)

Furthermore at two well defined frequencies, " = 1 12

# , the following can be shown

in first order of " :

" r (# = 1 1

2$ ) %

1

2 Z m 1

1

2$

& ' (

) * + %

1

2 Z m and " i (# = 1

1

2$ ) %

1

2 Z m (11)

Note that the absolute values of the real and imaginary parts of the complex impedanceat these two frequencies become equal to the half value of the resonance peak, Z m. Theinterval of these two frequencies can be used as a definition of the resonance width, W .

W " f 0 # . (12)

In typical frequency dependant impedance measurement data, this resonance width can be identified by measuring the full half maximum width of Z r ( f ) or a full width at the70.71% level %).%.( 717010050 =! in the impedance magnitude Z( f ) .

The quality factor of the resonance, Q, is defined as the ratio of the resonant frequencyand the width of resonance, and becomes simply

Q " f 0W

=

1

# . (13)

The above definitions of Z m, f 0 and W provide the measurable parameters from whichthe values of RLC in the model circuit can be uniquely identified. The swept frequencyand fixed frequency conformal mapping methods described below are naturalextensions of existing eddy current methodology to which this new circuit model can beapplied for data analysis.

3. Swept Frequency Method

For an AC current where the frequency is swept (using an AC voltage source and a

large, serially connected load resistance), the amplitude of the AC voltage drop acrossthe probe can be measured for Z( f ) . The measured, frequency dependant, impedancemagnitude reveals that the influence of the sample is manifested in a convolution ofshifts in the resonance frequency and changes in the width of resonance. Alternatively,

by fitting the data, one can calculate the corresponding sample influence in R and X # ! 0 L. Two-dimensional representation of the data in either ( W , f 0) or ( R, X )coordinates are equivalently useful for understanding the physical meaning of theresults. In Fig. 3, the resonance frequencies ( f 0), and widths of the resonance ( W ) at the70.71% level of the peak value of Z( f ) are plotted for specimens of variousconductivities.

The relationship between the variation in conductivity and the resultant variation between resonance frequency and width is a well-known phenomenon in the field ofmicrowaves. Sample variations can be explained in the free electron theory by the


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equality of the surface resistance and surface reactance in the diffusion transportfrequency range. 2 The variations of the data induced by changes in the spacing betweenthe probe and samples (probe lift-off effect) are shown in Fig. 3 as well. Changes insample conductivity result in a reduced range of resonance widths as the liftoff distanceis increased. This pattern converges into the single point corresponding to empty space(infinite separation distance). In the conventional representation of eddy current data( Z r , Z i), all the points in Fig. 3 would be mapped into points defining paths of variouscurvatures that are strongly dependant on the operation frequency and hard to predict.

Practical Applications

This new approach for obtaining and analyzing eddy current inspection results has proven extremely useful in a number of practical applications involving a variety ofspacecraft components. One example is the assessment of critical surface anomalies inthe steel bearings and bearing raceways depicted in Fig. 4. In this instance, changes inthe metal crystal structure caused by surface overheating during machining (non-magnetic phase within a ferromagnetic structure) proved indistinguishable usingconventional eddy current methods, not only because of difficulty in ascribing physicalmeaning to signal variations, but also because of considerable data scatter caused by

probe/specimen geometry variations (high surface curvature, poor probe contactconditions). Fig. 4 reveals details of the probe, cylindrical bearing specimens, andcurved bearing raceway specimens used in this eddy current evaluation. Using theswept frequency method and plotting the results in the ( W , f 0) plane reveals a signaturethat can be associated with the degree of non-magnetic phase on the surface within theferromagnetic bearings. This is shown in Fig. 5 for four bearing specimens exhibiting

varying degrees of overheating. Also shown is the empty space (infinite liftoff) value

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

3000

0 100 200 300 400 500

Resonance Width (KHz)

R e s o n a n c e

F r e q u e n c y

( K H z

)

0.15 mm lift-off

1.22 mm lift-off

In contact

air

(Al)Pb

(Brass)Cu

304ss

1018ss

graphite

Figure 3. Measured values of the resonance frequency ( f 0) and width ofresonance ( W ) at the 70.71% level plotted for thick (>> skin depth) specimens ofvarious conductivities .

m o r e

d i a m

a g n

e t i c

m o r e

p a r a m

a g n

e t i c

more energy loss


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with convergent path lines for reference. The ferromagnetic property of the initialmaterial is apparent by the fact that the resonance frequency is less than that of the airreference point (more paramagnetic). Results obtained from raceways are shown inFig. 6. The data were taken at various locations of the raceway surface including roundedges, and the varying surface curvatures cause an apparent scattering of the data due tolift-off variations. However, the degree of surface overheating can still be resolved for a

particular point through consideration of the phase angle of the data point vector relativeto the air reference point. In Fig. 6 arbitrary grades (A-D) have been assigned to thedegree of surface overheating.

Figure 4. Left: EC probe, cylindrical bearing specimens and curved raceway specimens usedfor detection of overheat damage produced during grinding.

Figure 5. ( W , f 0) mapping of data obtained for cylindrical bearings with varying degrees ofsurface overheat damage. Empty space (air) and convergent path lines are also shown forreference. The ferromagnetic nature of the initial material is evident by resonant frequencies thatare less than the air reference point.

7 7 0 0

7 7 5 0

7 8 0 0

7 8 5 0

7 9 0 0

7 9 5 0

8 0 0 0

7 0 0 9 0 0 1 1 0 0 1 3 0 0 1 5 0 0 1 7 0 0 1 9 0 0 R e s o n a n c e W i d t h ( K H z )

air

fast cut

heavy burn

slow cut

pristinesurface polished

cross section

Resonance Width (kHz)

R e s o n a n

t F r e q u e n c y

( k H z

)

Eddy current probe

Curved raceway

Cylindrical bearing


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tight cracks of varying depth fall approximately along the same line with increaseddisplacement relative to the surface for deeper cracks. As the crack width increases, theresponse tends toward that of a pure lift off response. If one changes the probe orinstrument settings, the behavior will be the same, but the response will be rotatedand/or stretched. However, if one maps to the ( R, X ) plane, the results remain invariantaccording to Eq. 19. This perception resolves much of the confusion associated withchanges that occur when different probes are used or instrument settings are altered.

The conformal mapping of Eq. 19 was also used to great advantage in an examination ofa number composite overwrapped pressure vessels (COPVs). These COPVs consistedof a thin aluminum liner overwrapped with hoop and helical layers of graphite fibersembedded in an epoxy matrix 5 as depicted in Fig. 9. In these vessels, subsurface plyirregularities caused by subtle impact damage can greatly jeopardize ultimate strength.While the results of conventional ( Z r , Z i) data, shown in Fig. 10, were insufficient forhealth assessment, subsequent conformal mapping into the ( R, X ) plane (shown inFig. 11) provided enhanced resolution of the effective conductivity variations produced

by ply orientation and resin density. The effect of the helical fibers is clearly visible in

the images formed from the ( R, X ) plane.

Figure 9. Cross-section of a graphite epoxy COPV.


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70 K !

40 K !

-40 K !

0

0Z

r

Zi

10K !

10K !

70 K !

40 K !

-40 K !

0

0Z

r

Zi

10K !

10K !

Figure 10. Data collected by scanning an anisotropic eddy current probe over a filament-woundCOPV at a fixed frequency and presented in a conventional ( Z r , Z i) mapping. The probe wasdesigned to induce current normal to the top hoop ply. The rectangular mark at lower edge is dueto movement of the probe due to a bump ( excess epoxy) on the COPV surface.

COPV

scan Z r

Zi

Figure 11. Same scan data as Fig. 10 after conformal mapping to ( X, R) plane. Note the enhancedhelical fiber lay-up in the R amplitude image.

R

X

46 # 34 #

1640 #

1460

air

46 # 34 #

1640 #

1460

air

46 # 34 #

1640 #

1460

R

X

46 # 34 #

1640 #

1460

air

Al

1640 #

1460 # 34 # 46 #


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5. Summary

We have developed a new method for analyzing eddy current data through an improvedmodel circuit accounting for the capacitive elements in the measurement process. This

method permits one to extract the net sample response through the change in resistiveand inductive impedance contributions. Through such representation, data variationscan be directly linked to physical property changes in the materials and geometry. Two

practical measurement and analysis methods are presented: (a) a frequency sweepmethod , and (b) a fixed frequency conformal mapping method . Furthermore, unlikeconventional eddy current data, with minimal probe calibration, the results of distincteddy current measurements on the same object can be quantitatively compared. Thecircuit model can be extended to account for the dielectric loss with potentialapplications for a capacitive sensor. This approach not only enhances eddy currentmeasurement as a nondestructive inspection tool, but also provides a new sensitive RFconductivity measurement method for general materials research.

References

1. Cartz, Louis, Nondestructive Testing Radiography, Ultrasonics, Liquid Penetrant,Magnetic Particle, Eddy Current, ASM International, Materials Park, OH (1995).

2. Jackson, J. D., Classical Electrodynamics, 2nd edition, John Wiley & Sons, NewYork, NY (1962).

3. Kreyszig, Erwin, Advanced Engineering Mathematics, John Wiley & Sons, NewYork, NY (1972).

4. Esquivel, O., and Kim, Y. M., Quantitative Evaluation of Flaw-Detection Limits ofEddy Current Techniques for Interrogation Structures Beneath Thermal ProtectionSystems on Reusable Launch Vehicles, U.S. Department of TransportationContract DTRS57-99-D-00062, Task 8.0, The Aerospace Corporation Report. No.ATR-2005(5131)-1, February 25, 2005.

5. Nokes, J. P., and Johnson, E. C., "Inspection Techniques for Composite Over-wrapped Pressure Vessels," Structural Integrity of Pressure Vessels, Piping andComponents 1995, eds: H. H. Chung and L. I. Ezekoye, The American Society ofMechanical Engineers, PVP-Vol. 318, 279 - 285 (1995).

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Quantitative Analysis of Eddy Current NDE Data