Eddy Current

3 Eddy Current NDE 3.1

Inspection Techniques

3.2

Instrumentation

3.3

Typical Applications

3.4

Special Example

3.1 Inspection Techniques

Coil Configurations voltmeter

voltmeter

oscillator

oscillator

~~

~

excitation coil

excitation coil

voltmeter

oscillator

~ Zo coil

sensing coil testpiece

Hall or GMR detector testpiece

testpiece

differential coils

parallel

coaxial

rotated

Remote-Field Eddy Current Inspection ferromagnetic pipe

exciter coil

Remote Field

Near Field

sensing coil

Remote Field

ln(Hz) low frequency operation (10-100 Hz)  

1  f  r 0 

Exponentially decaying eddy currents propagating mainly on the outer surface cause a diffuse magnetic field that leaks both on the outside and the inside of the pipe.

H z  H z 0 e z /  z

Main Modes of Operation time-multiplexed multiple-frequency

Signal

Signal

single-frequency

Time

Time

frequency-multiplexed multiple-frequency Signal

Signal

pulsed

Time

Time

D   2

excited signal (current)

detected signal (voltage)

Nonlinear Harmonic Analysis single frequency, linear response

Signal

ferromagnetic phase (ferrite, martensite, etc.) B

Time nonlinear harmonic analysis

Signal

H

Time

3.2 Eddy Current Instrumentation

Single-Frequency Operation Vr

low-pass filter A/D converter

oscillator

90º phase shifter

driver amplifier driver impedances

+

Vq

low-pass filter

Vm

_

processor phase balance V-gain H-gain

probe coil(s)

Vm  Vs cos(t  s ),

Vr  Vo cos(t ),

Vq  Vo sin(t )

Vm Vr  Vs cos(t  s )Vo cos(t ) 

1 Vs Vo  cos(s )  cos(2t  s )  2

Vm Vq  Vs cos(t  s )Vo sin(t ) 

1 Vs Vo sin(s )  sin(2t  s )  2

V Vm Vr  o Vs cos(s ), 2

V Vm Vq  o Vs sin(s ) 2

display

Nonlinear Harmonic Operation Vr

oscillator

n divider

90º phase shifter

driver amplifier driver impedances

+

Vq

Vm

_

low-pass filter A/D converter low-pass filter

processor phase balance V-gain H-gain

probe coil(s)

Vm  Vs1 cos(t  s1)  Vs2 cos(2t  s2 )  Vs3 cos(3t  s3 )  ... Vr  Vo cos(nt )

V Vm Vr  o Vsn cos(sn ) 2

Vq  Vo sin(nt )

V Vm Vq  o Vsn sin(sn ) 2

display

Specialized versus General Purpose

Nortec 2000S system

Agilent 4294A system*

frequency range*

0.1 – 10 MHz

0.1-80 MHz

probe coil

three pencil probes

single spiral coil

relative accuracy

≈ 0.1-0.2%

≈ 0.05-0.1%

frequency scanning

manual

electronic

measurement time

≈ 50 minutes for 21 points

≈ 3 minutes for 81 points

*high-frequency application

Probe Considerations sensitivity

ferrite-core coil

air-core coil

high coupling

low coupling

high coupling

high coupling

flat air-core coil eddy current

high coupling eddy current

eddy current

thermal stability I2

I1

I

V  Z I V

Z  i  L*  Rwire 

V1

V2

V1   Z11 Z12   I1  V    Z    2   12 Z 22   I 2  * Z12  i  L12

11

12 , 21

22

topology

flexible, low self-capacitance, reproducible, interchangeable, economic, etc.

3.3 Eddy Current NDE Applications • conductivity measurement • permeability measurement • metal thickness measurement • coating thickness measurements • flaw detection

3.3.1 Conductivity

Conductivity versus Probe Impedance constant frequency

1 Titanium, 6Al-4V

Normalized Reactance

0.8

Inconel Stainless Steel, 304

0.6

Copper 70%, Nickel 30%

0.4 Lead

Magnesium, A280 Nickel Aluminum, 7075-T6

0.2 Copper

0 0

0.1

0.2 0.3 Normalized Resistance

0.4

0.5

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

60

Conductivity [% IACS]

2014

2024

6061

7075

50 T0

T0

T0

40

T0 T6

T73 T76

T72 T6

30

T6

T8

T4

T3 T4

T6 T3 T4

20 Various Aluminum Alloys

Apparent Eddy Current Conductivity

magnetic field probe coil specimen

Normalized Reactance

1.0 0.8 lift-off curves

0.6 0.4

conductivity (frequency) curve

0.2 0 0

0.1 0.2 0.3 0.4 Normalized Resistance

eddy currents

• high accuracy ( 0.1 %) • controlled penetration depth

Normalized Reactance

  2

l=s

4

 1

3

l=0

, l

2

1

Normalized Resistance

0.5

Lift-Off Curvature inductive (low frequency) lift-off

ℓ =0

ℓ =s

lift-off

ℓ =0

σ2

σ2 conductivity

σ σ1

“Vertical” Component.

“Vertical” Component.

ℓ =s

capacitive (high frequency)

conductivity

σ

σ1

“Horizontal” Component

“Horizontal” Component

Inductive Lift-Off Effect 4 mm diameter

8 mm diameter

2.0

2.0

1.5 %IACS

1.0 0.5 0.0 -0.5 -1.0

-0.5 -1.0

-2.0 100

0.1

80

80

70

70

60

60 AECL [μm] . .

AECL [μm] .

0.0

-2.0

50 40 30 20

63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm 0.0 μm

30 20

0

0

-10

-10

100

100

40

10

1 10 Frequency [MHz]

1 10 Frequency [MHz]

50

10

0.1

50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm 0.0 μm

0.5

-1.5 1 10 Frequency [MHz]

63.5 μm

1.0

-1.5 0.1

1.5 %IACS

1.5

Relative ΔAECC [%].

Relative ΔAECC [%] .

1.5

0.1

1 10 Frequency [MHz]

100

Instrument Calibration conductivity spectra comparison on IN718 specimens of different peening intensities. 3.0 12A Nortec 8A Nortec 4A Nortec 12A Agilent 8A Agilent 4A Agilent 12A UniWest 8A UniWest 4A UniWest 12A Stanford 8A Stanford 4A Stanford

2.5

AECC Change [%] .

2.0 1.5 1.0 0.5 0.0 -0.5 0.1

1

10

100

Frequency [MHz]

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

3.3.2 Permeability

Magnetic Susceptibility paramagnetic materials with small ferromagnetic phase content

moderately high susceptibility

low susceptibility 1.0

4 µr = 4

3

permeability

3

2

2 1

frequency (conductivity)

1

Normalized Reactance

Normalized Reactance

permeability

0.8 lift-off

0.6

frequency (conductivity)

0.4 0.2 0

0 0

0.2

0.4 0.6 0.8 1 Normalized Resistance

1.2

0

0.1 0.2 0.3 0.4 Normalized Resistance

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

0.5

Magnetic Susceptibility versus Cold Work cold work (plastic deformation at room temperature) causes martensitic (ferromagnetic) phase transformation in austenitic stainless steels

Magnetic Susceptibility

101

SS304L SS302 SS304

100 10-1 10-2

SS305

10-3

IN718 IN625 IN276

10-4 0

10

20

30 Cold Work [%]

40

50

60

3.3.3 Metal Thickness

Thickness versus Normalized Impedance scanning probe coil

thickness loss due to corrosion, erosion, etc. 1

0.8

1

thinning

0.6

0.4 thick plate

0.2

f = 0.05 MHz f = 0.2 MHz f = 1 MHz

0.8

lift-off Re { F }

Normalized Reactance

aluminum (σ = 46 %IACS)

0.6 0.4

F ( x)  e x /  ei x / 

0.2

thin plate

0 -0.2 0

0

1

2 Depth [mm]

0

0.1 0.2 0.3 0.4 0.5 Normalized Resistance

0.6

3

Thickness Correction Vic-3D simulation, Inconel plates (σ = 1.33 %IACS) ao = 4.5 mm, ai = 2.25 mm, h = 2.25 mm

Conductivity [%IACS]

1.4

1.3

thickness 1.0 mm 1.5 mm 2.0 mm 2.5 mm 3.0 mm 3.5 mm 4.0 mm 5.0 mm 6.0 mm

1.2

1.1

1.0 0.1

1 Frequency [MHz]

10

3.3.4 Coating Thickness

Non-conducting Coating probe coil, ao

non-conducting coating

ℓ t d

conducting substrate ao > t, d > δ, AECL = ℓ + t

ao = 4 mm, simulated 63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm

12.7 μm 6.4 μm 0 μm

1 10 100 Frequency [MHz]

80 70 60 50 40 30 20 10 0 -10 0.1

AECL [μm]

lift-off:

AECL [μm]

80 70 60 50 40 30 20 10 0 -10 0.1

ao = 4 mm, experimental

1 10 100 Frequency [MHz]

Conducting Coating probe coil, ao conducting coating

ℓ t

z = δe

Je

d

z conducting substrate (µs,σs)

approximate:

large transducer, weak perturbation equivalent depth: e 

s 2

 1 AECC( f )    e     2  f   s s 

  

  1 ( z )  AECC    4  z2    s s 

analytical:

Fourier decomposition (Dodd and Deeds)

numerical:

finite element, finite difference, volume integral, etc. (Vic-3D, Opera 3D, etc.)

Simplistic Inversion of AECC Spectra 0.254-mm-thick surface layer of 1% excess conductivity 1.2 uniform input profile

1

AECC Change [%]

Conductivity Change [%]

1.2

0.8 0.6 inverted from AECC

0.4 0.2

1 0.8 0.6 0.4 0.2 0

0

-0.2 0.001

-0.2 0

0.2

0.4

0.6

0.8

1

Depth [mm]

10

1000

Frequency [MHz] 1.2

1.2 Gaussian input profile

1

AECC Change [%]

Conductivity Change [%]

0.1

0.8 0.6 inverted from AECC

0.4 0.2

1 0.8 0.6 0.4 0.2 0

0 -0.2 0

0.2

0.4

0.6

Depth [mm]

0.8

1

-0.2 0.001

0.1

10

1000

Frequency [MHz]

3.3.5 Flaw Detection

Impedance Diagram 1

Normalized Reactance

0.8

conductivity (frequency)

lift-off 0.6 crack depth

ω1

flawless material

0.4 ω2 0.2

0

0

0.1

0.2 0.3 0.4 Normalized Resistance

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

0.5

Crack Contrast and Resolution Vic-3D simulation ao = 1 mm, ai = 0.75 mm, h = 1.5 mm probe coil

austenitic stainless steel, σ = 2.5 %IACS, μr = 1 f = 5 MHz, δ  0.19 mm

crack 1

-10% threshold

Normalized AECC

0.8 0.6 0.4 0.2 detection threshold

0 0 semi-circular crack

1

2 3 Flaw Length [mm]

4

5

Eddy Current Images of Small Fatigue Cracks probe coil crack

0.5”  0.5”, 2 MHz, 0.060”-diameter coil Al2024, 0.025-mil crack

Ti-6Al-4V, 0.026-mil-crack

Crystallographic Texture J  E

generally anisotropic  J1  1 0 J    0  2  2   J 3   0 0

0 0  3 

hexagonal (transversely isotropic)  J1  1 0 J    0  2  2   J 3   0 0

 E1  E   2  E3 

0 0  2 

 E1  E   2  E3 

σM

x3

cubic (isotropic)  J1  1 0 0  J    0   1 0  2   J 3   0 0 1 

 E1  E   2  E3 

x1 θ σn

σm

basal plane

x2

surface plane

1  2

σ1

conductivity normal to the basal plane

n ()  1 cos2   2 sin 2 

σ2

conductivity in the basal plane

θ

polar angle from the normal of the basal plane

σm

minimum conductivity in the surface plane

σM

maximum conductivity in the surface plane

σa

average conductivity in the surface plane

m ()  1 sin 2   2 cos2 

M  2 a ()  ½ [1 sin 2   2 (1  cos2 )]

Electric “Birefringence” Due to Texture 500 kHz, racetrack coil

equiaxed GTD-111

1.05

1.40

1.04

1.38

Conductivity [%IACS]

Conductivity [%IACS]

highly textured Ti-6Al-4V plate

1.03 1.02 1.01 1.00

1.36 1.34 1.32 1.30

0

30 60 90 120 150 180 Azimuthal Angle [deg]

0

30 60 90 120 150 180 Azimuthal Angle [deg]

Grain Noise in Ti-6Al-4V 1”  1”, 2 MHz, 0.060”-diameter coil as-received billet material

solution treated and annealed

heat-treated, coarse

heat-treated, very coarse

heat-treated, large colonies

equiaxed beta annealed

Eddy Current versus Acoustic Microscopy 1”  1”, coarse grained Ti-6Al-4V sample

5 MHz eddy current

40 MHz acoustic

Inhomogeneity AECC Images of Waspaloy and IN100 Specimens

inhomogeneous Waspaloy

homogeneous IN100

4.2”  2.1”, 6 MHz

2.2”  1.1”, 6 MHz

conductivity range 1.38-1.47 %IACS

conductivity range 1.33-1.34 %IACS

±3 % relative variation

±0.4 % relative variation

Conductivity Material Noise as-forged Waspaloy 1.50

1.48 1.46

AECC [%IACS]

1.44 1.42 1.40 1.38 1.36

Spot 1 (1.441 %IACS)

1.34

Spot 2 (1.428 %IACS) Spot 3 (1.395 %IACS)

1.32

Spot 4 (1.382% IACS)

1.30 0.1

1 Frequency [MHz] no (average) frequency dependence

10

Magnetic Susceptibility Material Noise 1”  1”, stainless steel 304 intact

0.51×0.26×0.03 mm3 edm notch

f = 0.1 MHz, ΔAECC  6.4 %

f = 0.1 MHz, ΔAECC  8.6 %

f = 5 MHz, ΔAECC  0.8 %

f = 5 MHz, ΔAECC  1.2 %

3.4 Special Example

Residual Stress Assessment Alternating Stress [MPa]

1500

1000

with opposite residual stress service load

500

intact (no residual stress)

natural life time

0 10 2

endurance limit

increased life time

10 4 10 6 Fatigue Life [cycles]

108

Residual stresses have numerous origins that are highly variable. Residual stresses relax at service temperatures.

Surface-Enhancement Techniques Laser Shock Peening (LSP)

200

50

0

40 Cold Work [%]

Residual Stress [MPa]

Shot Peening (SP)

-200 -400

Ti-6Al-4V SP Almen 4A SP Almen 12A LSP LPB

-600 -800

-1000

0

0.2

0.4 0.6 Depth [mm]

Low-Plasticity Burnishing (LPB)

Ti-6Al-4V SP Almen 4A SP Almen 12A LSP LPB

30

20 10 0

1.0

1.2

0

0.2

0.4 0.6 Depth [mm]

1.0

1.2

Piezoresistive Effect parallel, normal, circular F

Electroelastic Tensor:

12 11 12

12  12   11 

 1 / E   / E   2   3 / E 



Axial Stress [ksi]

 1 / 0   11   /       2 0   12  3 / 0   12

Isotropic Plane-Stress ( 1  2  ip and 3  0 ) :

a / 0  11  12 ip / E

Adiabatic Electroelastic Coefficients: * 11  11  th * 12  12  th

80 60 40 20 0 -20 -40 Time [1 s/div]

Conductivity [%IACS]

ip 

F

1.403 1.402 1.401 1.4 1.399 1.398 1.397

IN 718, parallel

Time [1 s/div]

Material Types Al 2024

Ti-6Al-4V

0

0

parallel normal

0

-0.002

-0.002

-0.002

-0.004 -0.002

-0.004 -0.001

-0.004 -0.001

0 0.002 0.004 ua / E

0.002

0.004

parallel normal

0.002  / 0

0.004

0

0 0.001 0.002 ua / E IN718

Waspaloy

 / 0

0.002  / 0

0.002

0.004

parallel normal

0.004

parallel normal

0

0.002

parallel normal

0

-0.002

-0.002

-0.002

-0.004 -0.002

-0.004 -0.002

-0.004 -0.001

0 0.002 0.004 ua / E

0 0.002 0.004 ua / E

0 0.001 0.002 ua / E Copper

 / 0

 / 0

0.002

0.004

parallel normal  / 0

0.004

Al 7075

0 0.001 0.002 ua / E

XRD and AECC Measurements Waspaloy 50

40

-500 Almen 4A Almen 8A Almen 12A Almen 16A

-1000 -1500

30 Almen 4A Almen 8A Almen 12A Almen 16A

20 10

-2000

0

0

0.2

0.4 0.6 Depth [mm]

0.8

0

0.2

0.4 0.6 Depth [mm]

Conductivity Change [%]

Cold Work [%]

-500 Almen 4A Almen 8A Almen 12A Almen 16A

-1000 -1500

30 Almen 4A Almen 8A Almen 12A Almen 16A

20 10 0

-2000 0

0.2

0.4 0.6 Depth [mm]

0.8

Almen 4A Almen 8A Almen 12A Almen 16A

1 0

1 Frequency [MHz]

10

3

40

0

2

-1 0.1

0.8

50

500 Residual Stress [MPa]

3 Conductivity Change [%]

0 Cold Work [%]

Residual Stress [MPa]

500

0

0.2

0.4 0.6 Depth [mm]

0.8

2

Almen 4A Almen 8A Almen 12A Almen 16A

1 0 -1 0.1

1 Frequency [MHz]

before (solid circles) and after full relaxation for 24 hrs at 900 °C (empty circles)

10

Thermal Stress Relaxation in Waspaloy Waspaloy, Almen 8A, repeated 24-hour heat treatments at increasing temperatures

Apparent Conductivity Change [% ]

0.6 intact 300 °C 350 °C 400 °C 450 °C 500 °C 550 °C 600 °C 650 °C 700 °C 750 °C 800 °C 850 °C 900 °C

0.5 0.4

0.3 0.2

0.1 0 0.1

0.16

0.25

0.4

0.63

1

1.6

2.5

4

6.3

Frequency [MHz] The excess apparent conductivity gradually vanishes during thermal relaxation!

10

XRD versus Eddy Current inversion of measured AECC in low-plasticity burnished Waspaloy

20

1.2

200

eddy current

XRD

0

.

. Residual Stress [MPa]

15

0.8

Cold Work [%]

AECC Change [%]

1.0

0.6 0.4

0.2

10

5

0.0 -0.2 0.01

-200 -400 -600 -800 -1000 XRD eddy current

-1200 0 0.1 1 Frequency [MHz]

10

-1400 0.0

0.5 1.0 Depth [mm]

1.5

0.0

0.5 1.0 Depth [mm]

1.5

XRD versus High-Frequency Eddy Current shot peened IN100 specimens of Almen 4A, 8A and 12A peening intensity levels

40

200 Almen 8A (XRD)

.

30

0 -200

Almen 12A (XRD)

Residual Stress [MPa]

Cold Work [%] .

Almen 4A (XRD)

-400

20

10

-600

Almen 4A (AECC)

-800

Almen 8A (AECC)

-1000

Almen 12A (AECC)

-1200

Almen 4A (XRD)

-1400

Almen 8A (XRD)

-1600

Almen 12A (XRD)

-1800

0 0

0.1

0.2

0.3 0.4 Depth [mm]

0.5

0.6

0.7

0

0.1

 50 MHz

0.2

0.3

0.4

Depth [mm]

0.5

0.6

0.7