6 Eddy Current Inspection - University of Cincinnatipnagy/ClassNotes/AEEM7027... · 6 Eddy Current...
Transcript of 6 Eddy Current Inspection - University of Cincinnatipnagy/ClassNotes/AEEM7027... · 6 Eddy Current...
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