6 Eddy Current Inspection

6.1 Fundamentals

6.2 Eddy Currents

6.3 Impedance Diagrams

6.4 Inspection Techniques

6.5 Applications

6.1 Fundamentals

Electric Field and Potential

W work done by moving the charge

Fe Coulomb force

ℓ path length

E electric field

Q charge

U electric potential energy of the charge

V potential of the electric field

E

QFe

dℓ

A

BB A ABU U U WΔ = − =

edW = − F i dℓ

BAB

AW Q= − ∫ Eidℓ

U V Q=

BB A

AV V VΔ = − = − ∫ Eidℓ

e Q=F E

Current, Current Density, and Conductivity

I currentQ transferred charget timeJ current densityA cross section arean number density of electronsvd mean drift velocitye charge of protonm mass of electronτ collision timeΛ free pathv thermal velocityk Boltzmann’s constantT absolute temperatureσ conductivity

dQIdt

=

dI d= J Ai

I d= ∫ J Ai

dne= −J v

ddQ ne d dt= − v Ai

d em

= −τ

v E

vΛ

τ =

2nem

τ= = σJ E E

21 32 2

mv kT=

E

dA

Resistivity, Resistance, and Ohm’s Law

V voltage

I current

R resistance

P power

σ conductivity

ρ resistivity

L length

A cross section area

I

+_V

A

dℓ

0 0

L Ld dRA A

ρ= =∫ ∫

σ

i i

i

LRA

ρ= ∑

1ρ =

σ

LRA

ρ=

+

-

S+ -

SV V V= − = − ∫ Eidℓ

0 0

L LJ dV d IA

= =∫ ∫σ σ

VRI

=

dU dQP V V Idt dt

= = =

Maxwell's Equations

Ampère's law:

Faraday's law:

Gauss' law:

Gauss' law:

t∂

∇× = +∂DH J

t∂

∇× = −∂BE

q∇ =Di

0∇ =Bi

Field Equations:

conductivity = σJ E

permittivity = εD E

permeability = μB H

Constitutive Equations:

(ε0 ≈ 8.85 × 10-12 As/Vm)

(µ0 ≈ 4π × 10-7 Vs/Am)0 rμ = μ μ

0 rε = ε ε

Electromagnetic Wave Equation

Maxwell's equations:

( )it

∂∇× = + = σ+ ωε

∂DH J E

it

∂∇× = − = − ωμ

∂BE H

0∇⋅ =E

0∇⋅ =H

( ) ( )i i∇× ∇× = − ωμ σ + ωεH H

( ) ( )i i∇× ∇× = − ωμ σ + ωεE E

2( ) ( )∇× ∇× = ∇ ∇ ⋅ − ∇A A A

2 ( )i i∇ = ωμ σ + ωεE E

2 ( )i i∇ = ωμ σ + ωεH H

2 ( )k i i= − ωμ σ + ωε

2 2( )k∇ + =E 0

2 2( )k∇ + =H 0

( )0 i t k xy y yE E e ω −= =E e e

( )0

i t k xz z zH H e ω −= =H e e

Example plane wave solution:

Wave equations:

Wave Propagation versus Diffusion

Propagating wave in free space:

/ ( / )0 x i t x yE e e− δ ω − δ=E e

/ ( / )0

x i t xzH e e− δ − ω − δ=H e

Diffusive wave in conductors:

kcω

=

0 0

1c =μ ε

1 ik i= − ωμσ = −δ δ

1f

δ =π μ σ

( / )0 i t x c yE e ω −=E e

( / )0

i t x czH e ω −=H e

2 ( )k i i= − ωμ σ + ωε

δ standard penetration depth

c wave speed

k wave number

Propagating wave in dielectrics:

d0 0 r

1c =μ ε ε r

d

cnc

= = ε

n refractive index

6.2 Eddy Currents

Air-core Probe Coils

single turn L = a L = 3 a

center 2IHa

=

24 rI dd

r= ×

πH e e L coil length

a coil radiusencd I=∫ H si

center/lim

L a

N IHL→∞

=

Eddy Currents, Lenz’s Law

conducting specimen

eddy currents

probe coil

magnetic field

1f

δ =π μσ

s p s( )dVdt

= − Φ − Φ

p p∇× =H J

s p s( )t

∂∇× = −μ −

∂E H H

s s= σJ E

p pN IΦ ∝ μ

s sI V∝ σ

s s sIΦ ∝ μ Λs s∇× =H J

secondary(eddy) current

(excitation) currentprimarymagnetic flux

primary

magnetic fluxsecondary

Field Distributions

air-core pancake coil (ai = 0.5 mm, ao = 0.75 mm, h = 2 mm), in Ti-6Al-4V (σ = 1 %IACS)

10 Hz

10 kHz

1 MHz

10 MHz

1 mm

magnetic field2 2r zH H H= +

electric field Eθ

(eddy current density)

Eddy Current Penetration Depth0 ( ) i t yE f x e ω=E e

0 ( ) i tzH f x e ω=H e

δ standard penetration depth

/ /( ) x i xf x e e− δ − δ=

aluminum (σ = 26.7 × 106 S/m or 46 %IACS)

f = 0.05 MHzf = 0.2 MHzf = 1 MHz

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3Depth [mm]

| f

|

6.3 Impedance Diagrams

Magnetic Coupling

12 2122 11

Φ Φ= = κ

Φ Φ

2 2 21 22( )dV Ndt

= Φ + Φ

1 1 11 12( )dV Ndt

= Φ + Φ

1 11 12 1

2 21 22 2

V L L Ii

V L L I⎡ ⎤ ⎡ ⎤ ⎡ ⎤

= ω⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

12 21 11 22L L L L= = κ

221 11

1

NL LN

= κ 112 22

2

NL LN

= κ

1 1121 11

1

I LN

Φ = κΦ = κ 2 2212 22

2

I LN

Φ = κΦ = κ

1 1111

1

I LN

Φ = 2 2222

2

I LN

Φ =

I1

N1 N2 V2

Φ11

V1

I2

Φ22Φ12 Φ21,

V1 V2L , L , L11 12 22

I1 I2

Probe Coil Impedance

e 22222ne 22 e 22

R i LLZ iR i L R i L

− ωω= + κ

+ ω − ω

2 222 e 222 2n 2 2 2 2 2 2e e22 22

(1 )LL RZ i

R L R Lωω

= κ + − κ+ ω + ω

V2V1

I1 I2

L , L , L11 12 22 Re

2 2 e 12 1 22 2V I R i L I i L I= − = ω + ω

122 1

e 22

i LI IR i L

− ω=

+ ω

1 11 1 12 2V i L I i L I= ω + ω

2 212

1 11 1e 22

( )L

V i L IR i L

ω= ω +

+ ω

2 212

coil 11e 22

LZ i L

R i Lω

= ω ++ ω

222n

22e

LZ iR i L

ω= + κ

+ ω

1 11 12 1

2 12 22 2

V L L Ii

V L L I⎡ ⎤ ⎡ ⎤ ⎡ ⎤

= ω⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

1coil

1

VZI

=

coiln

11(1 )ZZ i

L= = + ξ

ω

coil ref [1 ( , , )]Z Z= + ξ ω σ

ref 11Z i L≈ ω

2 211 2212L L L= κ

( )κ = κ

Impedance Diagram22 eL Rζ = ω /

2n n 2Re 1

R Z ζ= = κ

+ ζ

22n n 2Im 1

1X Z ζ

= = − κ+ ζ

n n0 0

lim 0 and lim 1R Xω→ ω→

= =

2n nlim 0 and lim 1R Xω→∞ ω→∞

= = − κ

2 2n n( 1) and ( 1) 1

2 2R Xκ κ

ζ = = ζ = = −

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

κ = 0.6κ = 0.8κ = 0.9

Re=10 Ω

Re=5 Ω

Re=30 Ω

22 e e3 H, = 1 MHz, / 10%L f R R= μ Δ = lift-off trajectories are straight:

n n1X R= − ζ

conductivity trajectories are semi-circles

2 22 22n n 1

2 2R X

⎛ ⎞ ⎛ ⎞κ κ+ − + =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

Electric Noise versus Lift-off Variation

0.32

0.34

0.36

0.38

0.40

0.42

0.28 0.3 0.32 0.34 0.36 0.38“Horizontal” Impedance Component

“Ver

tical

”Im

peda

nce

Com

pone

nt0.32

0.34

0.36

0.38

0.40

0.42

0.28 0.3 0.32 0.34 0.36 0.38Normalized Resistance

Nor

mal

ized

Rea

ctan

ce lift-offlift-off

“physical” coordinates rotated coordinates

nZ ⊥ΔnZΔ

Conductivity Sensitivity, Gauge Factor

nnorm

e e/Z

FR R

⊥Δ=

Δn

abse e/Z

FR RΔ

=Δ

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 0.2 0.4 0.6 0.8 1Frequency [MHz]

Gau

ge F

acto

r, F

absolute

normal0.32

0.34

0.36

0.38

0.40

0.42

0.28 0.3 0.32 0.34 0.36 0.38Normalized Resistance

Nor

mal

ized

Rea

ctan

ce lift-off

nZ ⊥Δ

nZΔ

22 e e3 H, = 1 MHz, 10 , 1L f R R= μ = Ω Δ = ± Ω

6.4 Inspection Techniques

Coil Configurationsvoltmeter

testpiece

oscillator

excitationcoil

sensing coil

~

voltmeter

testpiece

oscillator

coil

Zo

~

Hall or GMR detector

voltmeter

testpiece

oscillator

excitationcoil

~

differential coils

coaxial rotatedparallel

Single-Frequency Operation

low-passfilter

low-passfilter

oscillator driveramplifier

+_

90º phaseshifter

A/Dconverter

display

probe coil(s)

driverimpedances

processorphase

balanceV-gainH-gain

Vr

Vm

Vq

m s s r o q ocos( ), cos( ), sin( )V V t V V t V V t= ω − ϕ = ω = ω

[ ]m r s s o s o s s1cos( ) cos( ) cos( ) cos(2 )2

V V V t V t V V t= ω − ϕ ω = ϕ + ω − ϕ

[ ]m q s s o s o s s1cos( ) sin( ) sin( ) sin(2 )2

V V V t V t V V t= ω − ϕ ω = ϕ + ω − ϕ

o om r s s m q s scos( ), sin( )

2 2V VV V V V V V= ϕ = ϕ

6.5 Applications

• conductivity measurement• permeability measurement• metal thickness measurement• coating thickness measurements• flaw detection

Conductivity versus Probe Impedance constant frequency

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

StainlessSteel, 304

CopperAluminum, 7075-T6

Titanium, 6Al-4V

Magnesium, A280

Lead

Copper 70%,Nickel 30%

Inconel

Nickel

Conductivity versus Alloying and Temper IACS = International Annealed Copper Standard

σIACS = 5.8×107 Ω-1m-1 at 20 °C

ρIACS = 1.7241×10-8 Ωm

20

30

40

50

60

Con

duct

ivity

[% IA

CS]

T3 T4

T6

T0

2014

T4

T6T0

6061

T6

T73T76

T0

70752024

T3 T4

T6

T72T8

T0

Various Aluminum Alloys

Apparent Eddy Current Conductivity

• high accuracy (≤ 0.1 %)

• controlled penetration depth

specimen

eddy currents

probe coil

magnetic field

0

0.2

0.4

0.6

0.8

1.0

0.10 0.2 0.3 0.4 0.5

lift-offcurves

conductivity

curve(frequency)

Normalized Resistance

Nor

mal

ized

Rea

ctan

ceσ,

σ = σ2

σ = σ1

= 0

= s

1

23

4

Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

Instrument Calibration

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.1 1 10 100Frequency [MHz]

AEC

C C

hang

e [%

] .

12A Nortec 8A Nortec 4A Nortec 12A Agilent 8A Agilent 4A Agilent 12A UniWest 8A UniWest 4A UniWest 12A Stanford 8A Stanford 4A Stanford

Nortec 2000S, Agilent 4294A, Stanford Research SR844, and UniWest US-450

conductivity spectra comparison on IN718 specimens of different peening intensities.

Magnetic Susceptibility

0

0.2

0.4

0.6

0.8

1.0

0.10 0.2 0.3 0.4 0.5

lift-off

frequency(conductivity)

Normalized ResistanceN

orm

aliz

ed R

eact

ance

permeability

Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1 1.2

2

3

1

µr = 4permeability

moderately high susceptibility low susceptibility

paramagnetic materials with small ferromagnetic phase content

increasing magnetic susceptibility decreases the apparent eddy current conductivity (AECC)

frequency(conductivity)

Magnetic Susceptibility versus Cold Work

10-4

10-3

10-2

10-1

100

101

0 10 20 30 40 50 60Cold Work [%]

Mag

netic

Sus

cept

ibili

ty

SS304L

IN276

IN718

SS305

SS304SS302

IN625

cold work (plastic deformation at room temperature) causesmartensitic (ferromagnetic) phase transformation

in austenitic stainless steels

Thickness versus Normalized Impedance

thickness loss due to corrosion, erosion, etc.

probe coil

scanning

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6

thickplate

Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

thinplate

lift-off

thinning

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3Depth [mm]

Re

f

f = 0.05 MHzf = 0.2 MHzf = 1 MHz

aluminum (σ = 46 %IACS)

/ /( ) x i xf x e e− δ − δ=

Thickness Correction

1.0

1.1

1.2

1.3

1.4

0.1 1 10Frequency [MHz]

Con

duct

ivity

[%IA

CS]

1.0 mm1.5 mm2.0 mm2.5 mm3.0 mm3.5 mm4.0 mm5.0 mm6.0 mm

thickness

Vic-3D simulation, Inconel plates (σ = 1.33 %IACS)

ao = 4.5 mm, ai = 2.25 mm, h = 2.25 mm

Non-conducting Coating

non-conductingcoating

probe coil, ao

t

d

ℓ

conducting substrate

-100

1020304050607080

0.1 1 10 100Frequency [MHz]

AEC

L [μ

m]

63.5 μm

50.8 μm

38.1 μm

25.4 μm

19.1 μm

12.7 μm

6.4 μm

0 μm

ao = 4 mmlift-off:

Impedance Diagram

Normalized Resistance

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

conductivity(frequency)

crackdepth

flawlessmaterialω1

lift-offN

orm

aliz

ed R

eact

ance

ω2

apparent eddy current conductivity (AECC) decreasesapparent eddy current lift-off (AECL) increases

Crack Contrast and Resolution

probe coil

crack

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5Flaw Length [mm]

Nor

mal

ized

AEC

C

semi-circular crack

-10% threshold

detectionthreshold

ao = 1 mm, ai = 0.75 mm, h = 1.5 mm

austenitic stainless steel, σ = 2.5 %IACS, μr = 1

Vic-3D simulation

f = 5 MHz, δ ≈ 0.19 mm

Eddy Current Images of Small Fatigue Cracks

Al2024, 0.025” crack Ti-6Al-4V, 0.026”-crack

0.5” × 0.5”, 2 MHz, 0.060”-diameter coil

probe coil

crack

Grain Noise in Ti-6Al-4V

as-received billet material solution treated and annealed heat-treated, coarse

heat-treated, very coarse heat-treated, large colonies equiaxed beta annealed

1” × 1”, 2 MHz, 0.060”-diameter coil

Eddy Current versus Acoustic Microscopy

5 MHz eddy current 40 MHz acoustic

1” × 1”, coarse grained Ti-6Al-4V sample

InhomogeneityAECC Images of Waspaloy and IN100 Specimens

homogeneous IN100

2.2” × 1.1”, 6 MHz

conductivity range ≈1.33-1.34 %IACS

±0.4 % relative variation

inhomogeneous Waspaloy

4.2” × 2.1”, 6 MHz

conductivity range ≈1.38-1.47 %IACS

±3 % relative variation

Magnetic Susceptibility Material Noise1” × 1”, stainless steel 304

f = 0.1 MHz, ΔAECC ≈ 6.4 %

f = 5 MHz, ΔAECC ≈ 0.8 %

intact

f = 0.1 MHz, ΔAECC ≈ 8.6 %

f = 5 MHz, ΔAECC ≈ 1.2 %

0.51×0.26×0.03 mm3 edm notch