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
high coupling
eddy current
eddy current
eddy current
thermal stability
I2
I1
I
V  ZI
V
Z  i  L*  Rwire

V1
V2
V1   Z11 Z12 
V    Z

 2   12 Z 22 
*
Z12  i  L12
11
12, 21
22
topology
flexible, low self-capacitance, reproducible, interchangeable, economic, etc.
 I1 
I 
 2
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
z = δe
ℓ
t
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” crack
Ti-6Al-4V, 0.026”-crack
Crystallographic Texture
J  E
generally anisotropic
hexagonal (transversely isotropic)
cubic (isotropic)
0   E1 
 J1  1 0
J    0 
 
2 0   E2 
 2 
 J3   0 0 3   E3 
0   E1 
 J1  1 0
J    0 
0   E2 
2
 2 

 J3   0 0 2   E3 
 J1  1 0 0   E1 
J    0 
 
1 0   E2 
 2 
 J3   0 0 1   E3 
x1
θ
x3
σM
σn
σm
basal plane
x2
surface plane
1  2
σ1
conductivity normal to the basal plane
n ()  1 cos 2   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 cos 2 
M  2
a ()  ½ [1 sin 2   2 (1  cos 2 )]
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
0.1
1
Frequency [MHz]
10
0
0.0
-1400
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