Electromagnetic NDE Peter B. Nagy Research Centre for NDE Imperial - - PDF document

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1

Electromagnetic NDE

Peter B. Nagy Research Centre for NDE Imperial College London 2011

Aims and Goals

Aims 1 The main aim of this course is to familiarize the students with Electromagnetic (EM) Nondestructive Evaluation (NDE) and to integrate the obtained specialized knowledge into their broader understanding of NDE principles. 2 To enable the students to judge the applicability, advantages, disadvantages, and technical limitations of EM techniques when faced with NDE challenges. Objectives At the end of the course, students should be able to understand the: 1 fundamental physical principles of EM NDE methods 2

• peration of basic EM NDE techniques

3 functions of simple EM NDE instruments 4 main applications of EM NDE

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Syllabus

1 Fundamentals of electromagnetism. Maxwell's equations. Electromagnetic wave propagation in dielectrics and conductors. Eddy current and skin effect. 2 Electric circuit theory. Impedance measurements, bridge techniques. Impedance diagrams. Test coil impedance functions. Field distributions. 3 Eddy current NDE techniques. Instrumentation. Applications; conductivity, permeability, and thickness measurement, flaw detection. 4 Magnetic measurements. Materials characterization, permeability, remanence, coercivity, Barkhausen noise. Flaw detection, flux leakage testing. 5 Alternating current field measurement. Alternating and direct current potential drop techniques. 6 Microwave techniques. Dielectric measurements. Thermoelectric measurements. 7 Electromagnetic generation and detection of ultrasonic waves, electromagnetic acoustic transducers (EMATs).

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1 Electromagnetism

1.1 Fundamentals 1.2 Electric Circuits 1.3 Maxwell's Equations 1.4 Electromagnetic Wave Propagation

1.1 Fundamentals of Electromagnetism

SLIDE 4

4

Electrostatic Force, Coulomb's Law

x z y r Q2 Q1 Fe Fe Fe Coulomb force Q1, Q2 electric charges (± ne, e ≈ 1.602 × 10-19 As) er unit vector directed from the source to the target r distance between the charges ε permittivity (ε0 ≈ 8.85 × 10-12 As/Vm)

1 2 e 2

4

x

Q dQ x d r r = πε F e

2

, 2 dQ qdA dA d = = πρ ρ

1 e 3

2

x

Q q x d r

∞ ρ=

ρ ρ = ∫ ε e F

2 2 2 2

, d r r r x dr r x ρ ρ = − = = ρ −

1 e 2

2

x r x

Q q x dr r

∞ =

= ∫ ε e F

1 e

2

x

Q q = ε e F x dQ2 Q1 Fe ρ dρ r infinite wall of uniform charge density q independent of x

1 2 e 2

4

r

Q Q r = πε F e

Electric Field, Plane Electrodes

Qt Fe x z y

e

2

t x

Q q = ε e F infinite wall of uniform charge density q 2

x

q = ε E e E +Q

• Q

A

• Q

q A = charged parallel plane electrodes Q

x

q ≈ ε E e

e t

Q = F E

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5

e t

Q = F E

Electric Field, Point Sources

e 2

4

s t r

Q Q r = πε F e

2

4

s r

Q r = πε E e monopole +Qs +Qs

• Qs

1 3

2

s

Q d E r ≈ πε

2 3

4

s

Q d E r ≈ πε +Qs

• Qs

d E1 E2 E1 dipole

Electric Field of Dipole

z z R R

E E = + E e e

3/ 2 3/ 2 2 2 2 2

/2 /2 4 ( / 2) ( /2)

s z

Q z d z d E z d R z d R ⎡ ⎤ − + ⎢ ⎥ = − ⎢ ⎥ πε ⎡ ⎤ ⎡ ⎤ − + − + ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

( )

2 3 3cos

1 4

s z

Q d E r ≈ θ − πε

3/ 2 3/ 2 2 2 2 2

4 ( / 2) ( /2)

s R

Q R R E z d R z d R ⎡ ⎤ ⎢ ⎥ = − ⎢ ⎥ πε ⎡ ⎤ ⎡ ⎤ − + − + ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

3

3 sin2 8

s R

Q d E r ≈ θ πε

2 2 2

r z R = + cos z r = θ sin R r = θ R z +Qs

• Qs

d θ r r+ r P Ez ER E

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Electric Dipole in an Electric Field

+Q

• Q

pe Fe E

E

E = E e

e d

Q Qd = = p d e

e e

Q = × = × T d F d E

e

Q = F E pe electric dipole moment Q electric charge d distance vector E electric field Fe Coulomb force Te twisting moment or torque Fe

e e

= × T p E

Electric Flux and Gauss’ Law

q charge (volume) density D electric flux density (displacement) E electric field (strength, intensity) ε permittivity ψ electric flux Qenc enclosed charge closed surface S D dS Qenc

S

d ψ = ∫∫D S i = ε D E d d ψ = D S i

S

d dS = S e

enc V

qdV Q ψ = = ∫∫∫ q ∇ = D i

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7

Electric 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 Q Fe dℓ A B

B A AB

U U U W Δ = − =

e

dW = − F i dℓ

B AB A

W Q = − ∫ Eidℓ U V Q =

B B A A

V V V Δ = − = − ∫ Eidℓ

Capacitance

+Q

• Q

E C capacitance V voltage difference Q stored charge Q CV =

+

• S

+

• S

V V V = − = − ∫ Eidℓ Q C V = E +Q

• Q
• A
• Q

E +Q dℓ Q D A A C D E V E ⎫ ≈ ⎪ ⎪ ε ⎪ ≈ ⎬ = ⎪ ε ⎪ ⎪ ≈ ⎭

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Current, Current Density, and Conductivity

I current Q transferred charge t time J current density A cross section area n number density of free electrons vd mean drift velocity e charge of proton m mass of electron τ collision time Λ free path v thermal velocity k Boltzmann’s constant T absolute temperature σ conductivity dQ I dt = dI d = J A i I d = ∫∫J A i

d

ne = − J v

d

dQ ne d dt = − v A i

d

m e = − τ v E v Λ τ =

2

1 3 2 2 mv kT = E dA

2

ne m τ = = σ J E E

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

L L

d d R A A ρ = = ∫ ∫ σ

• i

i i

L R A ρ = ∑ 1 ρ = σ L R A ρ =

+

• S

+

• S

V V V = − = − ∫ Eidℓ

L L

J d V d I I R A = = = ∫ ∫ σ σ

• V

R I = dU dQ P V V I dt dt = = =

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Magnetic Field

B Q Fm dv

e

Q = F E

m

Q = × F v B ( ) Q = + × F E v B F Lorenz force v velocity B magnetic flux density Q charge +I

• I

B pm magnetic dipole moment (no magnetic monopole) N number of turns I current A encircled vector area

m

N I = p A pm

Magnetic Dipole in a Magnetic Field

m

Q = × F v B pm magnetic dipole moment Q charge v velocity R radius vector B magnetic flux density Fm magnetic force Tm twisting moment or torque

m

N I = p A +I

• I

pm Fm B Fm

2 m

2

r v

Qv R R = π × π p e e

2

A R = π Q N I = τ 2 R v π τ =

m

1 2 Q = × p R v

m m

1 2 = × T R F

2 2 m m m

1 1 cos 2 2 T R F d R F

π

= α α = ∫ π

m m

= × T p B

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10

Magnetic Field Due to Currents

2 3

4 4

s s r

Q Q r r = = = πε πε E e r Coulomb Law: = ε D E = μ B H Biot-Savart Law:

2 3

4 4

r

I d I d r r = × = × π π H e e r

• dℓ

dℓ I dℓ r H H magnetic field μ magnetic permeability

2

4

r

I d r = × ∫ π H e e

• Ampère’s Law

2

4

r

I d d r = × π H e e

• enc

S

d Q = ∫∫D S i Gauss’ Law: infinite straight wire

2 2 2 3/ 2

4 4 ( ) I d R I R d d r r R

θ θ

= = π π + H e e

• 2

2 3/ 2

2 2 ( ) I R d I H R R

∞ θ =

= ∫ π π +

• 2

H ds H R I

θ θ

= π = ∫

• dℓ

I dℓ R H r ℓ s 2 I H R

θ =

π Biot-Savart Law: Ampère’s Law: Ampère’s Law:

enc

d I = ∫ H s i

• ∇×

= H J

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N I Φ = μ Λ Є d V N dt Φ = − =

Induction, Faraday’s Law, Inductance

E induced electric field B magnetic flux density t time Є induced electromotive force s boundary element of the loop Φ magnetic flux S surface area of the loop I N Φ

V

μ magnetic permeability N number of turns I current Λ geometrical constant L (self-) inductance I L N Φ =

2

L N = μ Λ

S

d Φ = ∫∫B S i Є d dt Φ = − t ∂ ∇× = − ∂ B E dI V L dt = B Є d = ∫ E s i

• Є

S

d t ∂ = − ∫∫ ∂ B S i

Electric Boundary Conditions

Faraday's law: t ∂ ∇× = − ∂ B E Gauss' law: q ∇ = D i

xt medium I medium II DI θΙ boundary DII DII,t DII,n θΙΙ DI,n DI,t xn xt medium I medium II EI θΙ EII EI,t EII,n θΙΙ EI,n EII,t xn I,n II,n

D D =

I I,n II II,n

E E ε = ε

I,t II,t

E E =

I I,n II II,n

tan tan E E θ = θ

I II I II

tan tan θ θ = ε ε tangential component of the electric field E is continuous normal component of the electric flux density D is continuous

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Magnetic Boundary Conditions

Ampère's law: t ∂ ∇× = + ∂ D H J Gauss' law: ∇ = B i

xt medium I medium II BI θΙ boundary BII BII,t BII,n θΙΙ BI,n BI,t xn xt medium I medium II HI θΙ HII HII,t HII,n θΙΙ HI,n HI,t xn I,n II,n

B B =

I I,n II II,n

H H μ = μ

I,t II,t

H H =

I I,n II II,n

tan tan H H θ = θ

I II I II

tan tan θ θ = μ μ tangential component of the magnetic field H is continuous normal component of the magnetic flux density B is continuous

1.2 Electric Circuits

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Є

Electric Circuits, Kirchhoff’s Laws

Є electromotive force Vi potential drop on ith element Kirchhoff’s junction rule (current law): Kirchhoff’s loop rule (voltage law):

i

V = ∑ = ∫ Ei

• dℓ

I + _

1

R

2

R

4

R

3

R

1

V

2

V

4

V

3

V V

i

I = ∑

enc S

Q d = ∫∫D S i Ii current flowing into a junction from the ith branch + _ Є

1

I

2

I

4

I

1

R

2

R

4

R

3

R

Circuit Analysis

Loop Currents: Kirchhoff’s Laws: + _ Є

1

I

2

I

4

I

1

R

2

R

3

R

1

V

2

V

3

V V + _ Є

1

I

2

I

4

I

1

R

2

R

4

R

3

R

1

i

2

i

4

R

4

V

1 2 4 1 2 4

V V V R R R − − =

1 4

V V V + − =

2 3 4

V V V + − =

3 2 2 3

V V R R − =

1 1 1 2 4

( ) i R i i R V + − − =

2 2 2 3 1 2 4

( ) i R i R i i R + − − =

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DC Impedance Matching

2 g 2 g g

, where (1 ) V R P R R ξ = ξ = + ξ

• 2

2

V P I V I R R = = =

• g

g g g

and V V R I V R R R R = = + +

• 2

g 3 g

1 (1 ) V dP d R − ξ = ξ + ξ

• 2

g max g g

when 4 V P R R R = =

• _

V

g

V

g

R R + P IV = W QV =

AC Impedance

I

V

dI V L dt = I

V

1 V I dt C = ∫ I

V

V R I = V Z i L I = = ω

• V

Z R I = =

• 1

V Z I i C = = ω

• Z

i

V Z R i X Z e I

ϕ

= = + =

• 2

2

V Z R X I = = +

• 1

arg( )

• tan

Z V I

X Z R = ϕ = ϕ ϕ =

( )

( )

I

i t i t

I t I e I e

ω + ϕ ω

= =

• (

)

( )

V

i t i t

V t V e V e

ω + ϕ ω

= =

• { }

Re I I =

• { }

Re V V =

• I

i

I I e ϕ =

• V

i

V V e ϕ =

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15

AC Power

{ }

Re I I =

• (

)

( )

I

i t i t

I t I e I e

ω + ϕ ω

= =

• ( )

cos( )

I

I t I t = ω + ϕ

{ }

Re V V =

• (

)

( )

V

i t i t

V t V e V e

ω + ϕ ω

= =

• ( )

cos( )

V

V t V t = ω + ϕ

* * 0 0

1 1 ( ) ( ) 2 2 P I t V t I V = =

• ( ) ( )

P I t V t =

{ }

Re P P =

• (

) 0 0

1 2

I V

i

P I V e ϕ

− ϕ

=

• 0 0

1 cos( ) 2

I V

P I V = ϕ − ϕ

real notation complex notation correspondence

cos( ) cos cos sin sin α + β = α β − α β cos( ) cos cos sin sin α − β = α β + α β 1 1 cos( ) cos( ) cos cos 2 2 α + β + α − β = α β cos sin

i

e i

α =

α + α reminder:

AC Impedance Matching

V

• g

V

g

Z

• Z
• ≈

{ }

Re P P =

• {

}

2 * g * * g g

1 Re Re 2 2 ( )( ) V Z P I V Z Z Z Z ⎧ ⎫ ⎪ ⎪ = = ⎨ ⎬ + + ⎪ ⎪ ⎩ ⎭

• (

)

* g g g

, Z Z R R X X = = = −

• 2

g max g

8 V P R =

2 g 2

Re 2 4

g g g

V R i X P R ⎧ ⎫ − ⎪ ⎪ = ⎨ ⎬ ⎪ ⎪ ⎩ ⎭

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1.3 Maxwell's Equations

Vector Operations

( )

lim

S S

S

→

⎧ ⎫ ∫ ∇× = ⎨ ⎬ ⎩ ⎭ A A e i

• i

dℓ Curl of a vector: lim

y S x z V

d A A A V x y z

→

⎧ ⎫ ∫∫ ∂ ∂ ∂ ⎪ ⎪ ∇ = = + + ⎨ ⎬ ∂ ∂ ∂ ⎪ ⎪ ⎩ ⎭ A S A i i Divergence of a vector:

x y z

x y z ∂φ ∂φ ∂φ ∇φ = + + ∂ ∂ ∂ e e e Gradient of a scalar:

2 2 2 2 2 2 2

x y z ∂ φ ∂ φ ∂ φ ∇ φ = + + ∂ ∂ ∂ Laplacian of a scalar:

2 2 2 2 x x y y z z

A A A ∇ = ∇ + ∇ + ∇ A e e e Laplacian of a vector:

2

( ) ( ) ∇× ∇× = ∇ ∇⋅ − ∇ A A A Vector identity:

x y z

x y z ∂ ∂ ∂ ∇ = + + ∂ ∂ ∂ e e e Nabla operator:

2 2 2 2 2 2 2

x y z ∂ ∂ ∂ ∇ = ∇ ∇ = + + ∂ ∂ ∂ i Laplacian operator:

y y x x z z x y z

A A A A A A y z z x x y ∂ ∂ ⎛ ⎞ ⎛ ⎞ ∂ ∂ ∂ ∂ ⎛ ⎞ ∇× = − + − + − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ∂ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ A e e e a

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17

Maxwell's Equations

Ampère's law: Faraday's law: Gauss' law: Gauss' law: t ∂ ∇× = + ∂ D H J t ∂ ∇× = − ∂ B E q ∇ = D i ∇ = B i Field Equations: conductivity = σ J E permittivity = ε D E permeability = μ B H Constitutive Equations: (ε0 ≈ 8.85 × 10-12 As/Vm) (µ0 ≈ 4π × 10-7 Vs/Am)

r

μ = μ μ

0 r

ε = ε ε

1.4 Electromagnetic Wave Propagation

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Electromagnetic Wave Equation

Maxwell's equations: ( ) i t ∂ ∇× = + = σ+ ωε ∂ D H J E i t ∂ ∇× = − = − ωμ ∂ B E H ∇⋅ = E ∇⋅ = H ( ) ( ) i i ∇× ∇× = − ωμ σ + ωε H H ( ) ( ) i i ∇× ∇× = − ωμ σ + ωε E E

2

( ) ( ) ∇× ∇× = ∇ ∇⋅ − ∇ A A A

2

( ) i i ∇ = ωμ σ + ωε E E

2

( ) i i ∇ = ωμ σ + ωε H H

2

( ) k i i = − ωμ σ + ωε

2 2

( ) k ∇ + = E

2 2

( ) k ∇ + = H

( ) 0 i t k x y y y

E E e ω − = = E e e

( ) 0 i t k x z z z

H H e ω − = = H e e Example plane wave solution: Wave equations: Harmonic time-dependence: and

i t i t

e e

ω ω

= = E E H H

Wave Propagation versus Diffusion

Propagating wave in free space:

/ ( / ) x i t x y

E e e

− δ ω − δ

= E e

/ ( / ) x i t x z

H e e

− δ − ω − δ

= H e Diffusive wave in conductors: k c ω =

0 0

1 c = μ ε 1 i k i = − ωμσ = − δ δ 1 f δ = π μσ

( / ) 0 i t x c y

E e ω

−

= E e

( / ) 0 i t x c z

H 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:

d 0 0 r

1 c = μ ε ε

r d

c n c = = ε n refractive index

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19

Intrinsic Wave Impedance

( ) 0 i t k x y y y

E E e ω − = = E e e

( ) 0 i t k x z z z

H H e ω − = = H e e ( ) i t ∂ ∇× = + = σ+ ωε ∂ D H J E

( ) z i t k x y y

H ik H e x

ω −

∂ ∇× = − = ∂ H e e ( ) k i i = − ωμ σ + ωε Propagating wave in free space: 377 μ η = ≈ Ω ε Propagating wave in dielectrics:

0 r

n μ η η = ≈ ε ε Diffusive wave in conductors: 1 i i ωμ + η = = σ σδ E i H i ωμ η = = σ+ ωε

Polarization

Plane waves propagating in the x-direction:

( ) ( ) i t k x i t k x y y z z y y z z

E E E e E e

ω − ω −

= + = + E e e e e

( ) ( ) i t k x i t k x z z y y z z y y

H H H e H e

ω − ω −

= + = + H e e e e

y z z y

E E H H η = = −

y z

i i y y z z

E E e E E e

φ φ

= = y z y z y z Ey Ez E 0º (or 180º)

y z

φ − φ = linear polarization elliptical polarization 90º (or 270º)

y z

φ − φ = circular polarization E E

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20

Reflection at Normal Incidence

x y incident reflected transmitted

I

( ) i i0 i t k x y

E e ω − = E e

I

i0 ( ) i I i t k x z

E e ω − = η H e

I

( ) r r0 i t k x y

E e ω + = E e

I

r0 ( ) r I i t k x z

E e ω + = − η H e

II

( ) t t0 i t k x y

E e ω − = E e

II

t0 ( ) t II i t k x z

E e ω − = η H e I medium II medium Boundary conditions: ( 0 ) ( 0 )

y y

E x E x

− +

= = =

i0 r0 t0

E E E + = ( 0 ) ( 0 )

z z

H x H x

− +

= = =

i0 r0 t0

H H H + =

i0 r0 t0 I I II

E E E − = η η η

r0 II I i0 II I

E R E η − η = = η + η

t0 II i0 II I

2 E T E η = = η + η

Reflection from Conductors

x y incident reflected transmitted “diffuse” wave I dielectric II conductor 1 f δ = ≈ π μσ

II I

i n η ωμ η = << η = σ

II I II I

1 R η − η = ≈ − η + η

• negligible penetration
• almost perfect reflection with phase reversal

SLIDE 21

21

Axial Skin Effect

• 0.2

0.2 0.4 0.6 0.8 1 1 2 3 Normalized Depth, x / δ Normalized Depth Profile, F magnitude real part

( )

i t y

E F x e ω = E e ( )

i t z

H F x e ω = H e δ standard penetration depth

/ /

( )

x i x

F x e e

− δ − δ

= 1 f δ = π μσ x y propagating wave diffuse wave dielectric (air) conductor

Transverse Skin Effect

0(

)

z

E E J k r = 1 f δ = π μσ

2

k i = − ωμσ 1 i k = − δ δ

1

2 ( ) k I E a J k a = πσ Jn nth-order Bessel function

• f the first kind

2 1

( ) ( ) 2 ( )

z

k a J k r I J r J k a a = π z r current density conductor rod current, I 2a

1 2 3 4 5 6 7 8 0.2 0.4 0.6 0.8 1 Normalized Radius, r/a Normalized Current Density, J/JDC

a/δ = 1 a/δ = 3 a/δ = 10 magnitude,

DC 2

I J a = π

SLIDE 22

22

Transverse Skin Effect

z r current density conductor rod current, I 2a

• 0.1

1 10 100 0.01 0.1 1 10 100 Normalized Radius, a/δ Normalized Resistance, R/R0

R ∝ ω R R ≈ V Z R i X I = = +

2

R A a = ρ = σπ

• 1

( ) ( ) 2 ( ) J G J ξ ξ ξ = ξ ( ) Z R G k a =

/

lim (1 ) 2

a

a G i

δ→∞

= + δ

/

lim 2

a

R a

δ→∞

= σ π δ

SLIDE 23

23

2 Eddy Current Theory

2.1 Eddy Current Method 2.2 Impedance Measurements 2.3 Impedance Diagrams 2.4 Test Coil Impedance 2.5 Field Distributions

2.1 Eddy Current Method

SLIDE 24

24

Eddy Current Penetration Depth

( )

i t y

E F x e ω = E e ( )

i t z

H F x e ω = H e δ standard penetration depth

/ /

( )

x i x

F x e e

− δ − δ

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

• 0.2

0.2 0.4 0.6 0.8 1 1 2 3 Depth [mm] Re { F} f = 0.05 MHz f = 0.2 MHz f = 1 MHz f = 0.05 MHz f = 0.2 MHz f = 1 MHz

• 0.2

0.2 0.4 0.6 0.8 1 1 2 3 Depth [mm] | F |

1 f δ = π μσ

Eddy Currents, Lenz’s Law

conducting specimen eddy currents probe coil magnetic field s p s

( ) d V dt = − Φ − Φ

p p

∇× = H J

s p s

( ) t ∂ ∇× = −μ − ∂ E H H

s s

= σ J E

p p p

N I Φ = μ Λ

s s

I V ∝ σ

s s s

I Φ = μ Λ

s s

∇× = H J

secondary (eddy) current (excitation) current primary magnetic flux primary magnetic flux secondary p p s

( ) d V N dt = − Φ − Φ

p probe p

( , , , , ... ) V Z I = ω σ μ

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25

2.2 Impedance Measurements

Impedance Measurements

p I p e

( ) ( ) ( ) V K Z I ω ω = = ω Ie Vp Zp Ve Ze Vp Zp Voltage divider: Current generator: Ie

p p V e e p

( ) ( ) ( ) V Z K V Z Z ω ω = = ω +

V e p V

( ) 1 ( ) K Z Z K ω = − ω

SLIDE 26

26

Resonance

Ve R L Vo C

0.2 0.4 0.6 0.8 1 1 2 3 Normalized Frequency, ω/Ω Transfer Function, |K | Q = 2 Q = 5 Q = 10 p 2

( ) 1 i L Z LC ω ω = − ω

p

• e

p

( ) ( ) ( ) ( ) ( ) Z V K V R Z ω ω ω = = ω + ω

2

/ ( ) 1 / i L R K i L R LC ω ω = + ω − ω

2 2

( ) 1 / i Q K i Q ω Ω ω = ω + − ω Ω Ω 1 LC Ω = C R Q R R C L L = = = Ω Ω

• 2

1 1 4Q ω = Ω −

Wheatstone Bridge

3 2 2 e 1 2 4 3

( ) ( ) ( ) Z V Z K G V Z Z Z Z ⎛ ⎞ ω ω = = − ⎜ ⎟ ω + + ⎝ ⎠ Ve V2 Z1 Z4 Z2 Z3 + _ G

3 2 2 1 4

0 if Z Z V Z Z = =

1 4

Z Z R = =

* 2 c

Z i L R = ω +

3 c c

Z i L R = ω + R0 reference resistance Lc reference (dummy) coil inductance Rc reference coil resistance L* complex probe coil inductance

2 3(1

) Z Z = + ξ probe coil reference coil

3 3 3 3

(1 ) ( ) (1 ) Z Z K G R Z R Z ⎛ ⎞ + ξ ω = − ⎜ ⎟ + + ξ + ⎝ ⎠ ( ) ( ) K G K ω ≈ ω ξ

3 2 3

( ) ( ) Z R K R Z ω = +

SLIDE 27

27

Impedance Bandwidth

3 c c

Z i L R = ω + R0 = 100 Ω, Rc = 10 Ω ( ) ( ) K G K ω ≈ ω ξ

3 2 3

( ) ( ) Z R K R Z ω = +

1 2 3 0.1 0.2 0.3 0.4 0.5 Frequency [MHz] Transfer Function, | K0 | Lc = 100 µH Lc = 20 µH Lc = 10 µH c 2 c

/ ( ) 1 ( / ) L R K L R ω ω ≈ + ω

3 c

Z i L ≈ ω

p c

R L ω =

p

1 ( ) 2 K ω ≈

2 c

2R L ω =

1,2

2 ( ) 5 K ω ≈

1 c

2 R L ω =

2 1

4 ω = ω

2 1 c 2 1

6 2

• r 120%

5

r

B B ω − ω = = = ω ω + ω ( , , , ,...) ξ = ξ ω σ μ

2.3 Impedance Diagrams

SLIDE 28

28

Examples of Impedance Diagrams

Im(Z) Re(Z)

L C

Im(Z) Re(Z)

Ω- Ω+ ∞ L C R Ω- Ω+ ∞ R

Im(Z) Re(Z)

R L C Ω ∞ R

Im(Z) Re(Z)

R2 L C Ω ∞ R1 R1+R2 R1

Magnetic Coupling

12 21 22 11

Φ Φ = = κ Φ Φ

2 2 21 22

( ) d V N dt = Φ + Φ

1 1 11 12

( ) d V N dt = Φ + Φ

1 11 12 1 2 21 22 2

V L L I i V L L I ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = ω ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

12 21 11 22

L L L L = = κ

2 21 11 1

N L L N = κ

1 12 22 2

N L L N = κ

1 11 21 11 1

I L N Φ = κΦ = κ

2 22 12 22 2

I L N Φ = κΦ = κ

1 11 11 1

I L N Φ =

2 22 22 2

I L N Φ = I1 N1 N2 V2 Φ

11

V

1

I2 Φ

22

Φ

12

Φ

21 ,

V1 V2

L , L , L

11 12 22

I1 I2

SLIDE 29

29

Probe Coil Impedance

e 22 22 2 n e 22 e 22

R i L L Z i R i L R i L − ω ω = + κ + ω − ω

• 2 2

22 e 22 2 2 n 2 2 2 2 2 2 e e 22 22

(1 ) L L R Z i R L R L ω ω = κ + − κ + ω + ω

• V2

V1 I1 I2

L , L , L

11 12 22

Re 2 2 e 12 1 22 2

V I R i L I i L I = − = ω + ω

12 2 1 e 22

i L I I R i L − ω = + ω

1 11 1 12 2

V i L I i L I = ω + ω

2 2 12 1 11 1 e 22

( ) L V i L I R i L ω = ω + + ω

2 2 12 coil 11 e 22

L Z i L R i L ω = ω + + ω

• 22

2 n 22 e

L Z i R i L ω = + κ + ω

• 1

11 12 1 2 12 22 2

V L L I i V L L I ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = ω ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

1 coil 1

V Z I =

• coil

n 11

(1 ) Z Z i L = = + ξ ω

• coil

ref [1

( , , )] Z Z = + ξ ω σ

• ref

11

Z i L ≈ ω

• 2

2 11 22 12

L L L = κ ( ) κ = κ

Impedance Diagram

22 e

L R ζ = ω /

2 n n 2

Re{ } 1 R Z ζ = = κ + ζ

• 2

2 n n 2

Im{ } 1 1 X Z ζ = = − κ + ζ

• n

n

lim 0 and lim 1 R X

ω→ ω→

= =

2 n n

lim 0 and lim 1 R X

ω→∞ ω→∞

= = − κ

2 2 n n

( 1) and ( 1) 1 2 2 R X κ κ ζ= = ζ= = −

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 Normalized Resistance Normalized Reactance κ = 0.6 κ = 0.8 κ = 0.9 Re=10 Ω Re=5 Ω Re=30 Ω 22 e e

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

n n

1 X R = − ζ conductivity trajectories are semi-circles

2 2 2 2 2 n n

1 2 2 R X ⎛ ⎞ ⎛ ⎞ κ κ + − + = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

SLIDE 30

30

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 “Vertical” Impedance Component 0.32 0.34 0.36 0.38 0.40 0.42 0.28 0.3 0.32 0.34 0.36 0.38 Normalized Resistance Normalized Reactance lift-off lift-off

“physical” coordinates rotated coordinates

n

Z⊥ Δ

n

Z Δ

Conductivity Sensitivity, Gauge Factor

22 e e

3 H, = 1 MHz, 10 , 1 L f R R = μ = Ω Δ = ± Ω

n norm e e

/ Z F R R

⊥

Δ = Δ

• n

abs e e

/ Z F R R Δ = Δ

• 0 (1

) R R F = + ε / / R R F Δ = Δ

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.2 0.4 0.6 0.8 1 Frequency [MHz] Gauge Factor, F absolute normal 0.32 0.34 0.36 0.38 0.40 0.42 0.28 0.3 0.32 0.34 0.36 0.38 Normalized Resistance Normalized Reactance lift-off n

Z⊥ Δ

n

Z Δ

SLIDE 31

31

Conductivity and Lift-off Trajectories

lift-off trajectories are not straight conductivity trajectories are not semi-circles

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 Normalized Resistance Normalized Reactance κ lift-off conductivity e

L R A ≈ σ ( ) κ ≈ κ

e

( ) L R A ≈ σ σ ( , ) κ ≈ κ σ

• finite probe size

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 Normalized Resistance Normalized Reactance κ lift-off conductivity

2.4 Test Coil Impedance

SLIDE 32

32

Air-core Probe Coils

single turn L = a L = 3 a

center

2 I H a =

2

4

r

I d d r = × π H e e

• a

coil radius L coil length

enc

d I = ∫ H s i

• center

/

lim

L a

N I H L

→∞

=

2 axis 2 2 3/ 2

2( ) I a H a z = +

Infinitely Long Solenoid Coil

enc

d I = ∫ H s i

• s

J n I =

1 2

( ) ( )

z z

LH r L H r − = for outside loops (r1,2 > a)

z

H =

1 2

( ) ( )

z z

LH r L H r − = for inside loops (r1,2 < a) constant

z

H =

1 2 s

( ) ( )

z z

LH r LH r L J − =

1 s

( )

z

I H r J n I N L = = = for encircling loops (r1 < a < r2)

inside loop

• utside loop

encircling 2a L

+ Js

_ Js

z

SLIDE 33

33

Magnetic Field of an Infinite Solenoid with Conducting Core

in the air gap (b < r < a) Hz = Js in the core (0 < r < b) Hz = H1 J0(kr) Jn nth-order Bessel function of the first kind

s 1 0(

) J H J kb = + Js

_ Js 2 a 2 b

z

s

( ) ( )

z

J k r H J J k b =

2 2

( ) k ∇ + = H

2

k i = − ωμσ 1 i k = − δ δ

2 2 2

1

z

k H r r r ⎛ ⎞ ∂ ∂ + + = ⎜ ⎟ ∂ ∂ ⎝ ⎠

2 2 s

2 ( ) ( )

b z

H r r dr a b J Φ = πμ + πμ − ∫

z z

B dA H dA Φ = = μ ∫∫ ∫∫

Magnetic Flux of an Infinite Solenoid with Conducting Core

+ Js

_ Js 2 a 2 b

z

s

( ) ( ) ( )

z

J k r H r J J k b = ( )

z z

H H r =

s z

H J =

z

H =

2 2 s

2 [ ( ) ] ( )

b

J J k r r dr a b J kb Φ = πμ + − ∫

1

( ) ( ) J d J ξ ξ ξ = ξ ξ ∫

1 2 2 s

2 ( ) [ ] ( ) b J k b J a b k J k b Φ = πμ + −

1

2 ( ) ( ) ( ) J g J ξ ξ = ξ ξ

2 2 s{

[1 ( )]} J a b g k b Φ = πμ − −

SLIDE 34

34

For an empty solenoid (b = 0): Normalized impedance:

1 1 1

, ,

s L

J nI V i V NV nLV = = ωΦ = =

1 2 2 2 2 s

{ [1 ( )]}

L

V V Z n L i a b g kb n L I J = = = ωπμ − −

2 2 e e

Z i a n L i X = ωπμ =

2 2 2

is called fill-factor ( lift-off) b a κ = ≈

2 n e

{1 [1 ( )]} Z Z i g kb X = = − κ −

2 2 s{

[1 ( )]} J a b g k b Φ = πμ − −

Impedance of an Infinite Solenoid with Conducting Core Resistance and Reactance of an Infinite Solenoid with Conducting Core

2 n n n

{1 [1 ( )]} Z i g kb R i X = − κ − = + Re{ ( )} 1 g kb ≤ ≤ 0.4 Im{ ( )} g k b − ≤ ≤

2 n

Im{ ( )} R g k b = −κ

2 n

1 [1 Re{ ( )}] X g kb = − κ −

n n

1 R X m = − Re{ ( )} 1 Im{ ( )} g k b m g k b − = 1 i k = − δ δ (1 ) b k b i ξ = = − δ

2 2

2 b i⎛ ⎞ ξ = − ⎜ ⎟ δ ⎝ ⎠

0.01 0.1 1 10 100 1000

• 0.4
• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Normalized Radius, b/δ g-function

real part imaginary part

SLIDE 35

35

Effect of Changing Coil Radius

a (changes) b (constant) lift-off b a κ = Normalized Resistance Normalized Reactance 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 b/δ = 1

3 5 10 20 2 κ = 1 0.9 0.8 0.7

a

lift-off ω 2 n

{1 [1 ( )]} Z i g k b = − κ −

Effect of Changing Core Radius

b (changing) a (constant) lift-off

2 n 1 n 2 n

1 R R X m m ≈ − − b a κ =

n 1 2 1

1 , where ( ) 2 a a ω δ ω = ω = = ω σμ Normalized Resistance Normalized Reactance 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

100 400 9 25 ω ωn = 4 κ = 1 0.9 0.8 0.7

b

lift-off 2 n

{1 [1 ( )]} Z i g k b = − κ −

SLIDE 36

36

Permeability

Normalized Resistance Normalized Reactance 1 2 3 4 0.2 0.4 0.6 0.8 1 1.2

ωn = 0.6 1.5 1 2 3 1 µr = 4 µ ω

0.8 b a κ = =

n 1

ω ω = ω

2 2 r s

2 ( ) ( )

b z

H r r dr a b J Φ = πμ μ + πμ − ∫

2 n r

{1 [1 ( )]} Z i g bk = − κ − μ

1 2 r

1 ( ) 2 a a δ ω = = σμ μ

Solid Rod versus Tube

2 2 2 3 r s

2 ( ) ( )

b z c

c H H r r dr a b J Φ = πμ + πμ μ + πμ − ∫

1 0 2 0

( ) ( )

z

H H J k r H Y k r = +

1 0 2 0 s

BC1: ( ) ( ) H J kb H Y kb J + =

1 0 2 0 3

BC2: ( ) ( ) H J k c H Y k c H + =

1 1 2 1 3

BC3: ( ) ( ) 2 k c H J k c H Y k c H + = b a

1 1 2 1

[ ( ) ( )] ( ) k H J k c H Y k c E c

ϕ

− + = σ ∇× = = σ H J E

z

H E r

ϕ

∂ − = σ ∂

2 3

( )2 i H c E c c

ϕ

ωμ π = π solid rod BC1: continuity of Hz at r = b tube BC1: continuity of Hz at r = b BC2: continuity of Hz at r = c BC3: continuity of Eφ at r = c b a c ( )

z z

H H r =

s z

H J =

z

H =

3 z

H H =

SLIDE 37

37

Solid Rod versus Tube

b a c 1, b c a b κ = = η = 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 Normalized Resistance

very thin solid rod tube

Normalized Reactance

thick tube

σ1 σ2 σ1 σ2

Wall Thickness

b a c 1, b c a b κ = = η = 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6

η = 0 solid rod b/δ = 3 b/δ = 2

Normalized Resistance Normalized Reactance

b/δ = 5 b/δ = 10 b/δ = 20 η ≈ 1 thin tube η = 0.2 η = 0.4 η = 0.6 η = 0.8

SLIDE 38

38

Wall Thickness versus Fill Factor

b a c , b c a b κ = η = 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 Normalized Resistance Normalized Reactance

solid rod κ = 0.95, η = 0 solid rod κ = 1, η = 0 thin tube κ = 1, η = 0.99 thin tube κ = 0.95, η = 0.99

Clad Rod

b a c

2 2 core core clad clad s

2 ( ) 2 ( ) ( )

c b c

H r r dr H r r dr a b J Φ = πμ + πμ + πμ − ∫ ∫

clad 1 0 clad 2 0 clad

( ) ( ) H H J k r H Y k r c r b = + ≤ <

core 3 core

( ) H H J k r r c = ≤ < 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 Normalized Resistance Normalized Reactance

copper cladding

• n brass core

solid copper rod solid brass rod brass cladding

• n copper core

d master curve for solid rod d thin wall lower fill factor clad core

, , b c a b σ κ = η = Σ = σ (1 ) d b c b = − = − η

SLIDE 39

39

2D Axisymmetric Models

b a c 2ao 2ai t h ℓ short solenoid (2D)

↓

long solenoid (1D)

↓

thin-wall long solenoid (≈0D)

↓

coupled coils (0D) pancake coil (2D)

• i

1

( ) ( )

a a

I x J x dx

α α

α = ∫

2 2 2 2 6

• i

( ) ( ) ( ) i N I Z f d h a a

∞

ωπμ α = α α ∫ − α

r 1 ( ) 2 r 1

( ) 2( 1) [ ]

h h

f h e e e

−α −α + −α

αμ −α α = α + − + − αμ +α

• 2

2 2 2 r 1

k i α = α − = α + ωμ μ σ Dodd and Deeds. J. Appl. Phys. (1968)

Flat Pancake Coil (2D)

0.05 0.1 0.15 0.2 0.1 1 10 100 Frequency [MHz] (Normal) Gauge Factor

4 mm 2 mm 1 mm

coil diameter

• i

M 2

1 2 a a a f a + = = δ ⇒ = π σμ a0 = 1 mm, ai = 0.5 mm, h = 0.05 mm, σ = 1.5 %IACS, μ = μ0 0.2 0.4 0.6 0.8 1 0.05 0.1 0.15 0.2 0.25 0.3 Normalized Resistance Normalized Reactance

0 mm 0.05 mm 0.1 mm

lift-off

frequency fM

SLIDE 40

40

2.5 Field Distributions

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 field

2 2 r z

H H H = + electric field Eθ (eddy current density)

SLIDE 41

41

Axial Penetration Depth

air-core pancake coil (ai = 0.5 mm, ao = 0.75 mm, h = 2 mm) in Ti-6Al-4V Axial Penetration Depth, δa [mm] 10-2 10-1 100 101 Frequency [MHz] 10-5 10-4 10-3 10-2 10-1 100 101 102

standard actual

1 f δ = π σμ ai

i

• 1

1/e point below the surface at ( ) 2 r a a a = = +

1 2

2 a a ≈

Radial Spread

air-core pancake coil (ai = 0.5 mm, ao = 0.75 mm, h = 2 mm) in Ti-6Al-4V Radial Spread, as [mm] Frequency [MHz] 10-5 10-4 10-3 10-2 10-1 100 101 102

analytical finite element

0.8 1.2 1.6 2.0 1.0 1.4 1.8 1/e point from the axis at the surface ( 0) z =

2

• 1.2

a a ≈

SLIDE 42

42

Radial Penetration Depth

air-core pancake coil (ai = 0.5 mm, ao = 0.75 mm, h = 2 mm) in Ti-6Al-4V Radial Penetration Depth, δr [mm] 10-2 10-1 100 101 Frequency [MHz] 10-5 10-4 10-3 10-2 10-1 100 101 102

standard actual

1 f δ = π σμ

r s 2

a a δ = −

2

• 1.2

a a ≈

Lateral Resolution

ferrite-core pancake coil (ai = 0.625 mm, ao = 1.25 mm, h = 3 mm) in Ti-6Al-4V 1.0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8

experimental FE prediction

Radial Spread, as [mm] Frequency [MHz] 10-2 10-1 100 101

SLIDE 43

43

3 Eddy Current NDE

3.1 Inspection Techniques 3.2 Instrumentation 3.3 Typical Applications 3.4 Special Example

3.1 Inspection Techniques

SLIDE 44

44

Coil Configurations

voltmeter testpiece

• scillator

excitation coil sensing coil

~

voltmeter testpiece

• scillator

coil Zo

~

Hall or GMR detector voltmeter testpiece

• scillator

excitation coil

~ ~

differential coils coaxial rotated parallel

Remote-Field Eddy Current Inspection

Remote Field Remote Field Near Field exciter coil ferromagnetic pipe sensing coil ln(Hz) z low frequency operation (10-100 Hz) Exponentially decaying eddy currents propagating mainly on the outer surface cause a diffuse magnetic field that leaks both

• n the outside and the inside of the pipe.

1

r

f δ = π μ μ σ

/ z z z

H H e−

δ

=

SLIDE 45

45

Time Signal

Main Modes of Operation

single-frequency time-multiplexed multiple-frequency frequency-multiplexed multiple-frequency pulsed Time Signal Time Signal Time Signal excited signal (current) detected signal (voltage)

2 D

τ ≈ μσ

Nonlinear Harmonic Analysis

single frequency, linear response nonlinear harmonic analysis Time Signal Time Signal

H B

ferromagnetic phase (ferrite, martensite, etc.)

SLIDE 46

46

3.2 Eddy Current Instrumentation

Single-Frequency Operation

low-pass filter low-pass filter

• scillator

driver amplifier

+ _

90º phase shifter A/D converter display probe coil(s) driver impedances processor phase balance V-gain H-gain

Vr Vm Vq

m s s r

• q
• cos(

), cos( ), sin( ) V V t V V t V V t = ω − ϕ = ω = ω

[ ]

m r s s

• s o

s s

1 cos( ) cos( ) cos( ) cos(2 ) 2 V V V t V t V V t = ω − ϕ ω = ϕ + ω − ϕ

[ ]

m q s s

• s o

s s

1 cos( ) sin( ) sin( ) sin(2 ) 2 V V V t V t V V t = ω − ϕ ω = ϕ + ω − ϕ

• m r

s s m q s s

cos( ), sin( ) 2 2 V V V V V V V V = ϕ = ϕ

SLIDE 47

47

Nonlinear Harmonic Operation

low-pass filter low-pass filter n divider driver amplifier

+ _

90º phase shifter A/D converter display probe coil(s) driver impedances processor phase balance V-gain H-gain

• scillator

Vr Vm Vq

m s1 s1 s2 s2 s3 s3

cos( ) cos(2 ) cos(3 ) ... V V t V t V t = ω − ϕ + ω − ϕ + ω − ϕ +

r

• cos(

) V V n t = ω

• m r

s s

cos( ) 2

n n

V V V V = ϕ

q

• sin(

) V V n t = ω

• m q

s s

sin( ) 2

n n

V V V V = ϕ

Specialized versus General Purpose

≈ 3 minutes for 81 points ≈ 50 minutes for 21 points measurement time electronic manual frequency scanning ≈ 0.05-0.1% ≈ 0.1-0.2% relative accuracy single spiral coil three pencil probes probe coil 0.1-80 MHz 0.1 – 10 MHz frequency range* Agilent 4294A system* Nortec 2000S system *high-frequency application

SLIDE 48

48

I1 V2 Φ11 V

1

I2 Φ22 Φ12 Φ21

,

Probe Considerations

V Z I = * wire

Z i L R = ω + sensitivity thermal stability

eddy current ferrite-core coil high coupling high coupling eddy current air-core coil high coupling low coupling eddy current flat air-core coil high coupling

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

I Φ

V

1 11 12 1 2 12 22 2

V Z Z I V Z Z I ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

* 12 12

Z i L = ω topology

3.3 Eddy Current NDE Applications

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

SLIDE 49

49

3.3.1 Conductivity

Conductivity versus Probe Impedance

constant frequency 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 Normalized Resistance Normalized Reactance

Stainless Steel, 304 Copper Aluminum, 7075-T6 Titanium, 6Al-4V Magnesium, A280 Lead Copper 70%, Nickel 30% Inconel Nickel

SLIDE 50

50

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 Conductivity [% IACS]

T3 T4 T6 T0

2014

T4 T6 T0

6061

T6 T73 T76 T0

7075 2024

T3 T4 T6 T72 T8 T0

Various Aluminum Alloys

Apparent Eddy Current Conductivity

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

specimen eddy currents probe coil magnetic field 0.2 0.4 0.6 0.8 1.0 0.1 0.2 0.3 0.4 0.5 lift-off curves conductivity curve (frequency) Normalized Resistance Normalized Reactance σ, σ = σ2 σ = σ1 = 0

• = s
• 1

2 3 4 Normalized Resistance Normalized Reactance

SLIDE 51

51

Lift-Off Curvature

inductive (low frequency) capacitive (high frequency)

“Horizontal” Component “Vertical” Component lift-off . conductivity σ2 σ1 σ ℓ = s ℓ = 0 “Horizontal” Component “Vertical” Component . conductivity lift-off σ2 σ1 σ ℓ = s ℓ = 0

Inductive Lift-Off Effect

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 0.1 1 10 100 Frequency [MHz] Relative ΔAECC [%] .

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 0.1 1 10 100 Frequency [MHz] Relative ΔAECC [%] . 63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm 0.0 μm

• 10

10 20 30 40 50 60 70 80 0.1 1 10 100 Frequency [MHz] AECL [μm] .

• 10

10 20 30 40 50 60 70 80 0.1 1 10 100 Frequency [MHz] AECL [μm] . . 63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm 0.0 μm

4 mm diameter 8 mm diameter

1.5 %IACS 1.5 %IACS

SLIDE 52

52

Instrument Calibration

• 0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.1 1 10 100 Frequency [MHz] AECC Change [%] . 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

3.3.2 Permeability

SLIDE 53

53

Magnetic Susceptibility

0.2 0.4 0.6 0.8 1.0 0.1 0.2 0.3 0.4 0.5

lift-off frequency (conductivity)

Normalized Resistance Normalized Reactance

permeability

Normalized Resistance Normalized Reactance 1 2 3 4 0.2 0.4 0.6 0.8 1 1.2

2 3 1 µr = 4 permeability

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 10 20 30 40 50 60 Cold Work [%] Magnetic Susceptibility SS304L IN276 IN718 SS305 SS304 SS302 IN625 cold work (plastic deformation at room temperature) causes martensitic (ferromagnetic) phase transformation in austenitic stainless steels

SLIDE 54

54

3.3.3 Metal Thickness

Thickness versus Normalized Impedance

thickness loss due to corrosion, erosion, etc. probe coil scanning 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6

thick plate

Normalized Resistance Normalized Reactance

thin plate lift-off thinning

• 0.2

0.2 0.4 0.6 0.8 1 1 2 3 Depth [mm] Re { F } f = 0.05 MHz f = 0.2 MHz f = 1 MHz

aluminum (σ = 46 %IACS)

/ /

( )

x i x

F x e e

− δ − δ

=

SLIDE 55

55

Thickness Correction

1.0 1.1 1.2 1.3 1.4 0.1 1 10 Frequency [MHz] Conductivity [%IACS]

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 thickness

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

3.3.4 Coating Thickness

SLIDE 56

56

Non-conducting Coating

non-conducting coating probe coil, ao t d ℓ conducting substrate ao > t, d > δ, AECL = ℓ + t

• 10

10 20 30 40 50 60 70 80 0.1 1 10 100 Frequency [MHz] AECL [μm]

• 10

10 20 30 40 50 60 70 80 0.1 1 10 100 Frequency [MHz] AECL [μm]

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 mm, simulated lift-off: ao = 4 mm, experimental

Conducting Coating

conducting coating probe coil, ao t d ℓ conducting substrate (µs,σs) approximate: large transducer, weak perturbation equivalent depth:

( )

e

1 AECC( ) 2

s s

f f ⎛ ⎞ ≈ σ δ = σ⎜ ⎟ ⎜ ⎟ π μ σ ⎝ ⎠

2

1 ( ) AECC 4

s s

z z ⎛ ⎞ σ ≈ ⎜ ⎟ ⎜ ⎟ π μ σ ⎝ ⎠

s e

2 δ δ = analytical: Fourier decomposition (Dodd and Deeds) numerical: finite element, finite difference, volume integral, etc. (Vic-3D, Opera 3D, etc.) z Je z = δe

SLIDE 57

57

Simplistic Inversion of AECC Spectra

AECC Change [%]

• 0.2

0.2 0.4 0.6 0.8 1 1.2 0.001 0.1 10 1000 Frequency [MHz] AECC Change [%]

• 0.2

0.2 0.4 0.6 0.8 1 1.2 0.001 0.1 10 1000 Frequency [MHz] Depth [mm] Conductivity Change [%]

• 0.2

0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1

input profile inverted from AECC uniform

Depth [mm] Conductivity Change [%]

• 0.2

0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1

input profile inverted from AECC Gaussian

0.254-mm-thick surface layer of 1% excess conductivity

3.3.5 Flaw Detection

SLIDE 58

58

Impedance Diagram

Normalized Resistance

0.2 0.4 0.6 0.8 1

0.1 0.2 0.3 0.4 0.5

conductivity (frequency) crack depth flawless material ω1 lift-off

Normalized Reactance

ω2 apparent eddy current conductivity (AECC) decreases apparent eddy current lift-off (AECL) increases

Crack Contrast and Resolution

probe coil crack 0.2 0.4 0.6 0.8 1 1 2 3 4 5 Flaw Length [mm] Normalized AECC semi-circular crack

• 10% threshold

detection threshold

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

SLIDE 59

59

Eddy Current Images of Small Fatigue Cracks

Al2024, 0.025-mil crack Ti-6Al-4V, 0.026-mil-crack 0.5” × 0.5”, 2 MHz, 0.060”-diameter coil probe coil crack

Crystallographic Texture

= σ J E

1 1 1 2 2 2 3 3 3

J E J E J E σ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = σ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ σ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ generally anisotropic hexagonal (transversely isotropic)

1 1 1 2 2 2 3 2 3

J E J E J E σ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = σ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ σ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ cubic (isotropic)

1 1 1 2 1 2 3 1 3

J E J E J E σ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = σ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ σ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ σ1 conductivity normal to the basal plane 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

2 2 a 1 2

( ) ½ [ sin (1 cos )] σ θ = σ θ + σ + θ

2 2 n 1 2

( ) cos sin σ θ = σ θ + σ θ

M 2

σ = σ

1 2

σ < σ

2 2 m 1 2

( ) sin cos σ θ = σ θ + σ θ x1 x3 x2

basal plane

θ

surface plane

σn σm σM

SLIDE 60

60

Electric “Birefringence” Due to Texture

1.00 1.01 1.02 1.03 1.04 1.05 30 60 90 120 150 180 Azimuthal Angle [deg] Conductivity [%IACS] highly textured Ti-6Al-4V plate equiaxed GTD-111 1.30 1.32 1.34 1.36 1.38 1.40 30 60 90 120 150 180 Azimuthal Angle [deg] Conductivity [%IACS] 500 kHz, racetrack coil

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

SLIDE 61

61

Eddy Current versus Acoustic Microscopy

5 MHz eddy current 40 MHz acoustic 1” × 1”, coarse grained Ti-6Al-4V sample

Inhomogeneity

AECC 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

SLIDE 62

62

Conductivity Material Noise

1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 0.1 1 10 Frequency [MHz] AECC [%IACS]

Spot 1 (1.441 %IACS) Spot 2 (1.428 %IACS) Spot 3 (1.395 %IACS) Spot 4 (1.382% IACS)

as-forged Waspaloy no (average) frequency dependence

Magnetic Susceptibility Material Noise

1” × 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

SLIDE 63

63

3.4 Special Example

Residual Stress Assessment

106 102

intact (no residual stress) with opposite residual stress

Fatigue Life [cycles] 104 108 500 1000 1500

endurance limit service load life time natural life time increased

Alternating Stress [MPa] Residual stresses have numerous origins that are highly variable. Residual stresses relax at service temperatures.

SLIDE 64

64

Surface-Enhancement Techniques

Low-Plasticity Burnishing (LPB) Shot Peening (SP) Laser Shock Peening (LSP) Depth [mm] 0.2 0.4 0.6 1.0 1.2 200

• 200
• 400
• 600
• 800
• 1000

Residual Stress [MPa] SP Almen 12A SP Almen 4A LSP LPB Ti-6Al-4V 0.2 0.4 0.6 1.0 1.2 Depth [mm] Cold Work [%] 40 30 20 10 50 SP Almen 12A SP Almen 4A LSP LPB Ti-6Al-4V

Piezoresistive Effect

Electroelastic Tensor:

1 11 12 12 1 2 12 11 12 2 3 12 12 11 3

/ / / / / / E E E Δσ σ κ κ κ τ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Δσ σ = κ κ κ τ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Δσ σ κ κ κ τ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

11 12

/ /

a ip ip E

Δσ σ η = = κ + κ τ

Isotropic Plane-Stress ( and ) :

1 2 ip

τ = τ = τ

3

τ =

parallel, normal, circular F F δ Adiabatic Electroelastic Coefficients:

* 11 11 th

κ = κ + κ

* 12 12 th

κ = κ + κ

• 40
• 20

20 40 60 80 Time [1 s/div] Axial Stress [ksi] Time [1 s/div] 1.397 1.398 1.399 1.4 1.401 1.402 1.403 Conductivity [%IACS]

IN 718, parallel

SLIDE 65

65

Material Types

parallel

• 0.004
• 0.002

0.002 0.004

• 0.001

0.001 0.002 τua / E Δσ / σ0 normal Copper Ti-6Al-4V parallel

• 0.004
• 0.002

0.002 0.004

• 0.002

0.002 0.004 τua / E Δσ / σ0 normal parallel

• 0.004
• 0.002

0.002 0.004

• 0.001

0.001 0.002 τua / E Δσ / σ0 normal Al 2024 parallel

• 0.004
• 0.002

0.002 0.004

• 0.001

0.001 0.002 τua / E Δσ / σ0 normal Al 7075 Waspaloy parallel

• 0.004
• 0.002

0.002 0.004

• 0.002

0.002 0.004 τua / E Δσ / σ0 normal IN718 parallel

• 0.004
• 0.002

0.002 0.004

• 0.002

0.002 0.004 τua / E Δσ / σ0 normal

XRD and AECC Measurements

• 2000
• 1500
• 1000
• 500

500 0.2 0.4 0.6 0.8 Depth [mm] Residual Stress [MPa] Almen 4A Almen 8A Almen 12A Almen 16A

• 1

1 2 3 0.1 1 10 Frequency [MHz] Conductivity Change [%] Almen 4A Almen 8A Almen 12A Almen 16A 10 20 30 40 50 0.2 0.4 0.6 0.8 Cold Work [%] Almen 4A Almen 8A Almen 12A Almen 16A Depth [mm]

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

• 2000
• 1500
• 1000
• 500

500 0.2 0.4 0.6 0.8 Depth [mm] Residual Stress [MPa] Almen 4A Almen 8A Almen 12A Almen 16A 10 20 30 40 50 0.2 0.4 0.6 0.8 Cold Work [%] Almen 4A Almen 8A Almen 12A Almen 16A Depth [mm]

• 1

1 2 3 0.1 1 10 Frequency [MHz] Conductivity Change [%] Almen 4A Almen 8A Almen 12A Almen 16A

Waspaloy

SLIDE 66

66

Thermal Stress Relaxation in Waspaloy

Waspaloy, Almen 8A, repeated 24-hour heat treatments at increasing temperatures

0.1 0.16 0.25 0.4 0.63 1 1.6 2.5 4 6.3 10 Frequency [MHz] 0.1 0.2 0.3 0.4 0.5 0.6 Apparent Conductivity Change [% ]

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

The excess apparent conductivity gradually vanishes during thermal relaxation!

XRD versus Eddy Current

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.01 0.1 1 10 Frequency [MHz] AECC Change [%] eddy current 0.0 0.5 1.0 1.5 Depth [mm] Cold Work [%] . 5 10 15 20 XRD .

• 1400
• 1200
• 1000
• 800
• 600
• 400
• 200

200 0.0 0.5 1.0 1.5 Depth [mm] Residual Stress [MPa] eddy current XRD

inversion of measured AECC in low-plasticity burnished Waspaloy

SLIDE 67

67

10 20 30 40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Depth [mm] Cold Work [%] . Almen 4A (XRD) Almen 8A (XRD) Almen 12A (XRD)

• 1800
• 1600
• 1400
• 1200
• 1000
• 800
• 600
• 400
• 200

200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Depth [mm] Residual Stress [MPa] . Almen 4A (AECC) Almen 8A (AECC) Almen 12A (AECC) Almen 4A (XRD) Almen 8A (XRD) Almen 12A (XRD)

≈ 50 MHz

XRD versus High-Frequency Eddy Current

shot peened IN100 specimens of Almen 4A, 8A and 12A peening intensity levels

SLIDE 68

68

4 Magnetic NDE

4.1 Magnetic Properties 4.2 Magnetic Measurements 4.3 Magnetic Materials Characterization 4.4 Magnetic Flaw Detection

4.1 Magnetic Properties

SLIDE 69

69

Magnetization

M magnetization V volume χ magnetic susceptibility H magnetic field B magnetic flux density μ0 permeability of free space μr relative permeability pm magnetic dipole moment N number of turns I current A encircled vector area

m

N I = p A +I

• I

m

V ∑ = p M = χ M H

r

( ) = μ + = μ μ B H M H

r

1 μ = + χ

m

1 2 Q = × p R v Q charge v velocity R radius vector

Classification of Magnetic Materials

Diamagnetism:

μr < 1 no remanence

• rbit distortion

e.g., copper, mercury, gold, zinc

Paramagnetism:

μr > 1 no remanence

• rbit and spin alignment

e.g., aluminum, titanium, platinum

Ferromagnetism:

μr >> 1 remanence, coercivity, hysteresis self-amplifying paramagnetism Curie temperature e.g., iron, nickel, cobalt

SLIDE 70

70

Diamagnetism

pm magnetic dipole moment pspin electron spin porb electron orbital motion N number of turns I current A encircled area e charge of proton τ

• rbital period

r

• rbital radius

v

• rbital velocity

Ei induced electric field Fe decelerating electric force m mass of electron n dipoles within unit volume χ magnetic susceptibility v Q Fm B v Q Fe B

i e

F eE =

m

F ev B =

m

• rb

spin

= + p p p

2

• rb

2 Q A e r v p N I A r π = = = − τ π

• rb

2 erv p = −

2 2 2 2

• rb

4 4 e r e r p B H m m μ Δ = − = −

e i

2 2 F d r E r dt e Φ − = π = − π 2 d m dv r dt e dt Φ = π

2

2 m B r r v e π = π Δ 2 er v B m Δ =

• χ ≈ 1-10 ppm

2 2

• rb

4 e r n m μ χ = −

Weak Paramagnetism, Curie Law

m

• rb

spin

= + p p p pm magnetic dipole moment B magnetic flux density Fm magnetic force Tm twisting moment or torque Um potential energy of the dipole kB Boltzmann constant T absolute temperature n dipoles within unit volume χ magnetic susceptibility

m m

= × T p B

m m

U = −p B i

m m 90 90

( ) sin U T d p B d

θ θ

= θ θ = θ θ ∫ ∫

• m

m

cos U p B = − θ

m m

sin T p B = θ

m m0 B

m

( )

U U k T

p U e

− −

=

2 B

3 n m M C H k T T μ χ = = = Curie Law: χ ≈ 5-50 ppm +I

• I

pm Fm B Fm Tm

θ

SLIDE 71

71

Strong Paramagnetism, Curie-Weiss Law:

t i

H H H H M = + = + α

t

C M H T =

t i

M M M M T H H H M C χ = = = − − α Curie-Weiss law:

C

C T T χ = − M H χ = M magnetization H exciting magnetic field χ magnetic susceptibility C material constant T absolute temperature Ht total magnetic field Hi interaction field α material factor TC Curie temperature Curie law: C M H T ≈ C T C χ = − α C T χ ≈

Ferromagnetism

(i) magnetic polarization is produced by collective action of similarly oriented spins within magnetic domains (ii) very high permeability (iii) magnetic hysteresis (v) remnant magnetic polarization (remanence) (vi) coercive magnetic field (coercivity) (iv) depolarization above the (magnetic) Curie temperature

H B Br Hc first magnetization

SLIDE 72

72

Spontaneous Magnetization

N N N N S S S S N S N S S N S N N N S S S S N N

[100] [010] “easy” magnetic axis [001] [110] [111] total internal wall external

U U U U = + +

Magnetic Domains in Single Crystals

easy magnetic axes

H = 0 H H H

1 demagnetization (spontaneous magnetization) 4 technical saturation 3 “knee” of the magnetization curve 2 partial magnetization domain wall movement irreversible rotation reversible rotation H B

1 2 3 5 4

5 full saturation (no precession) thermal precession not shown

SLIDE 73

73

4.2 Magnetic Measurements

Magnetic Sensors

10-2 10-1 100 101 102 103 104 105 5 10 15 20 25 Frequency [Hz] Flux Density [pT/Hz1/2] Hall GMR SDP fluxgate SQUID noise threshold

axial

d V N i N AB dt Φ = − = − ω coil:

SLIDE 74

74

Hall Detector

I I a b x y z

x x

Bz

VH

Fm Fe ( ) Q = + × F E v B ( )

y y x z

F e E v B = − + =

H y

V E a =

x x

I enab v = −

H x y x z z

I V a E av B B enb = = − =

H H x z

R I V B b =

H

1 R en =

Fluxgate

Iexc Vsens B1 B2 B

hard magnetic cores high-frequency excitation low-frequency or dc external magnetic field

B1 + B2 B2 B1 B1 + B2 B2 B1 B = 0 B ≠ 0 t t t t t t

H B sensing voltage (to be low-pass filtered)

SLIDE 75

75

Vibrating-Sample Magnetometer

Vsens B0

vibration (ω) 0 sin(

) d d t = ω

1

( ) [ sin( )] t A B M t Φ = + μ κ ω

2

( ) [ sin( )] t A B M t Φ = − μ κ ω

1 2 sens( )

V t N N t t ∂Φ ∂Φ = − + ∂ ∂ B M = χ μ

sens

( ) 2 cos( ) V t N A B t = − ωχ κ ω B0 bias magnetic flux density M magnetization χ magnetic susceptibility µ0 permeability of free space d specimen displacement d0 specimen amplitude ω angular frequency t time κ geometrical coupling factor A coil cross section Φ1,2 flux in coil 1 and 2 N number of turns Vsens sensing voltage

Faraday Balance

Um magnetic potential energy pm magnetic dipole moment B magnetic flux density M magnetization V volume Ug gravitational potential energy U total potential energy h height W actual weight W’ apparent weight χ magnetic susceptibility H magnetic field µ0 permeability of free space for a single dipole: for a given magnetized volume:

precision scale specimen W’ = W - Fm electromagnet spacer

h

m m

U = −p B i

g m

U U U = + ' dU dB W W M V dh dh = = −

m

U M V B = − U W h M V B = − M H = χ

2

' 2 V dH dH W W V H dh dh μ − = − μ χ = − χ

SLIDE 76

76

4.3 Magnetic Materials Characterization

Magnetic Properties

• 1.5
• 1
• 0.5

0.5 1 1.5

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 Magnetic Field [kA/m] Flux Density [Tesla]

hardened steel soft iron

( , ) ( , )

p p

B B H M H M H M = = μ + μ ferromagnetic materials: para- and diamagnetic materials:

0 (

) B H M = μ + M H = χ

r

B H = μ μ

r

1 μ = + χ

SLIDE 77

77

Initial Magnetization

anhysteretic initial magnetization curve

Flux Density Differential Permeability Magnetic Field Flux Density

B magnetic flux density H magnetic field M magnetization µ0 permeability of free space µd differential permeability M0 saturation magnetization n dipoles per unit volume pm magnetic dipole moment

d

dB dH μ = lim

H

M M

→∞

=

0 (

) B H M = μ +

m

M n p ≤

Retentivity, Coercivity, Hysteresis

Br remanence [Vs/m2] Mr remnant magnetization µ0 permeability of free space Hc coercive field [A/m] Hci intrinsic coercivity U0 magnetic energy density A hysteresis area [J/m3]

0 (

) B H M = μ +

p

( , ) M M H M = technical saturation:

H

H B Br Hc r r

B M = μ

c c

( ) H M H + =

ci

( ) M H =

c ci

H H ≤ dU BdH = U A Δ =

SLIDE 78

78

Texture, Residual Stress

• 2
• 1

1 2

• 300 -200 -100

100 200 300 Magnetic Field [A/m] Flux Density [T] σ = 0 MPa B|| B⊥

• 2
• 1

1 2

• 300 -200 -100

100 200 300 Magnetic Field [A/m] Flux Density [T] σ = 36 MPa B|| B⊥

• 2
• 1

1 2

• 300 -200 -100

100 200 300 Magnetic Field [A/m] Flux Density [T] σ = 183 MPa B|| B⊥

• 2
• 1

1 2

• 300 -200 -100

100 200 300 Magnetic Field [A/m] Flux Density [T] σ = 110 MPa B|| B⊥

mild steel (Langman 1985)

Magnetostriction

Induced magnetostriction: Ms spontaneous magnetization M0 saturation magnetization e spontaneous strain within a single domain ε1,2,3 principal strains

H

1

2 3 e ε =

1 2,3

2 3 e ε ε = − = −

1 2

e ε − ε = Spontaneous magnetostriction:

easy magnetic axes

H = 0

domain s

M M M = ≤

domain domain 1 2,3

, e ε = ε =

volume 1,2,3

3 e ε =

volume

M ≈

SLIDE 79

79

Barkhausen Noise

H = 0 H

domain wall movement H B magnetic field Barkhausen noise

Amplitude Time

• magnetic Barkhausen noise
• acoustic Barkhausen noise

Curie Temperature

ferromagnetic materials (T < TC):

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

T / TC Ms / M0

typical pure metal typical alloy

χ magnetic susceptibility C material constant T temperature TC Curie temperature Curie-Weiss law:

C

C T T χ = −

SLIDE 80

80

4.4 Magnetic Flaw Detection

Magnetic Flux Leakage

Advantages: fast inexpensive large, awkward shaped specimens (particle) Disadvantages: material sensitive poor sensitivity poor penetration depth ferromagnetic test piece sensor Hall cell, etc.) (small coil, exciter coil

SLIDE 81

81

Magnetic Boundary Conditions

xt medium I medium II BI θΙ boundary BII BII,t BII,n θΙΙ BI,n BI,t xn xt medium I medium II HI θΙ HII HII,t HII,n θΙΙ HI,n HI,t xn

Ampère's law: ∇× = H J Gauss' law: ∇ = B i

I,n II,n

B B =

I,t II,t

H H =

I I,n II II,n

H H μ = μ

I I,n II II,n

tan tan H H θ = θ

I II I II

tan tan θ θ = μ μ

Magnetic Refraction

I II I II

tan tan θ θ = μ μ µI/µII =

10 30 100 15 45 60 75 90 15 30 45 60 75 90 30 Ferromagnetic Angle, θI [deg] Nonmagnetic Angle, θII [deg] medium I (ferromagnetic) BI BII θΙΙ θΙ medium II (air) medium I (ferromagnetic) BI BII θΙΙ θΙ medium II (air)

SLIDE 82

82

Exciter Magnets

electromagnet air gap ferromagnetic core H d N I MMF = = ∫

• r H A

Φ = μ μ

r

MMF d A Φ = ∫ μ μ

• m

MMF R = Φ

m r r

1 1

i i i i

d R A A = ≈ ∑ ∫ μ μ μ μ

• H

magnetic field N number of turns I excitation current MMF magnetomotive force Φ magnetic flux ℓ length of flux line µ0µr magnetic permeability A cross section area Rm magnetic reluctance

Yoke Excitation

Detection Methods:

• magnetic particle

(gravitation, friction, adhesion, cohesion, magnetization)

• magnetic particle with ultraviolet paint
• coil
• Hall detector, GMR sensor
• fluxgate, etc.

Lateral Position Tangential Magnetic Field Lateral Position Normal Magnetic Field electromagnet crack N I magnetometer

SLIDE 83

83

Subsurface Flaw Detection

H B

1 2

saturation greatly reduces the differential permeability crack low magnetic field crack high magnetic field

SLIDE 84

84

5 Current Field Measurement

5.1 Alternating Current Field Measurement 5.2 Direct Current Potential Drop 5.3 Alternating Current Potential Drop

5.1 Alternating Current Field Measurement

SLIDE 85

85

Principle of Operation

electric field magnetic flux density axial (x) transverse (y) normal (z) galvanic current injection

≈

magnetometer magnetic injection: primary ac flux

~

~

Bx0

Field Perturbation

magnetic flux density magnetometer axial (x) transverse (y) normal (z) axial flaw cw current Bz < 0 electric current Bz > 0 ccw current axial scanning above flaw

Axial Position Bz [a.u.] Axial Position Bx [a.u.] Bz [a.u.] Bx [a.u.]

SLIDE 86

86

Uniform Field

advantages:

• testing through coatings
• depth information
• limited boundary effects

disadvantages:

• reduced sensitivity
• sensitivity to geometry
• flaw orientation

effect of coating thickness on axial magnetic flux density Bx (ferrous steel, 5 kHz, δ ≈ 0.25 mm, 30-mm-long solenoid) 8 7 6 5 4 3 2 1 5 10 15 20 Coating Thickness [mm] ΔBx [%]

50 × 5 mm 20 × 2 mm 20 × 1 mm

slot size 30 25 20 15 10 5 Slot Depth [mm] ΔBx and ΔBz [%] 0.5 1 1.5 2 2.5

Bx at 5 kHz Bz at 5 kHz Bx at 50 kHz Bz at 50 kHz

Axial Flaw

8 7 6 5 4 3 2 1 10 20 30 40 Slot Depth [mm] ΔBxm per 1 mm Slot Depth [%] 40-mm-long solenoid 12-mm-long solenoid rate of increase of the minimum of Bx with slot depth at the center 2-mm-diameter coil, ferrous steel changes normalized to Bx0 (parallel to B, normal to E)

SLIDE 87

87

Flaw Orientation

0.17 0.16 0.15 0.14 0.13 0.12 0.11 Bx [T] 1 2 3 4 5 Scanning time [a. u.] transverse flaw (normal to B) axial flaw (normal to E) 0.025 0.020 0.150 0.100 0.05

• 0.05

Bz [T] 1 2 3 4 5 Scanning Time [a. u.] transverse flaw (normal to B) axial flaw (normal to E) eddy current mode magnetic flux mode

Magnetic Flux Mode

electromagnet crack N I magnetometer Lateral Position Tangential Magnetic Field Lateral Position Normal Magnetic Field

SLIDE 88

88

5.2 Direct Current Potential Drop

Inductive versus Galvanic Coupling

specimen eddy currents probe coil magnetic field electric current V I I injection current potential drop specimen

advantages of galvanic coupling dc and low-frequency operation constant coupling (four-point measurement) awkward shapes absolute measurements inherently directional

SLIDE 89

89

Thin-Plate Approximation

combined electric current and potential field

2a 2b

t << a ( ) ( ) 2 I E r J r rt ρ = ρ = π ( ) ( ) 2

r r

I dr V r E r dr t r

∞ ∞

ρ = = ∫ ∫ π ( ) ln const 2 I V r r t ρ = − + π

( ) ( )

V V V

+ −

Δ = − ln I a b V t a b ρ + Δ = π −

[ ]

2 ( ) ( ) V V a b V a b Δ = − − +

I (+) I (-) V (+) V (-) I (+) I (-) V (+) V (-)

Lateral Spread of Current Distribution

( ) 2 I J r rt = π (0,0) I J at = π

2 2 2 2

2 (0, ) 2 I a J w a w t a w = π + +

2 2

(0, ) ( ) I a J w a w t = π +

2

(0,0) 2 (0, ) J J w =

2 2 2 2 2

(0,0) 2 (0, ) a w J J w a + = =

2

w a =

2w I (+) I (-) V (+) V (-)

x y

2a

J(0,w) J(0,0)

SLIDE 90

90

Thick-Plate Approximation

2

( ) ( ) 2 I E r J r r ρ = ρ = π

2

( ) ( ) 2

r r

I dr V r E r dr r

∞ ∞

ρ = = ∫ ∫ π ( ) const 2 I V r r ρ = + π t >> a

2a 2b I (+) I (-) V (+) V (-)

≈

combined electric current and potential field

I (+) I (-) V (+) V (-) ( ) ( )

V V V

+ −

Δ = − 1 1 I V a b a b ⎡ ⎤ ρ Δ = − ⎢ ⎥ π − + ⎣ ⎦

[ ]

2 ( ) ( ) V V a b V a b Δ = − − +

Finite Plate Thickness

2a 2b

t

2 2 1/ 2

( ) 2 [ (2 ) ]

n

I V r r nt

∞ =−∞

ρ = ∑ π +

2 2 1/ 2 2 2 1/ 2

1 [( ) (2 ) ] 1 [( ) (2 ) ]

n

I V a b nt a b nt

∞ =−∞

⎡ ρ Δ = ∑ ⎢ π − + ⎣ ⎤ − ⎥ + + ⎦

I (+) I (-) V (+) V (-)

n = 0 n = -1 n = +1 n = -2 n = +2 2t

I (+) I (-) V (+) V (-)

SLIDE 91

91

Resistance versus Thickness

1 lim ln

t

a b t a b

→

+ Λ = π −

2 2

2 lim

t

b a b

→∞

Λ = π − V R I Δ = = ρΛ 0.1 1 10 0.01 0.1 1 10 100 Normalized Thickness, t / a Normalized Resistance, Λ

finite thickness thin-plate appr. thick-plate appr. a = 3b

Crack Detection by DCPD

intact specimen

I (+) I (-) V (+) V (-) ( ) ( )

V V V

+ −

− = Δ t

I (+) I (-) V (+) V (-)

cracked specimen

( ) ( ) c

V V V

+ −

− = Δ c

1 2 3 0.2 0.4 0.6 0.8 1 Normalized Crack Depth, c / t Normalized Potential Drop, ΔVc / ΔV0 a / t = 0.44 1.2 1.8 a = 3b

infinite slot

SLIDE 92

92

Technical Implementation of DCPD

• low resistance, high current
• thermoelectric effect, pulsed, alternating polarity
• control of penetration via electrode separation
• low sensitivity to near-surface layer
• no sensitivity to permeability

power supply polarity switch

+ _

specimen electrodes

Vs

+ _

5.3 Alternating Current Potential Drop

SLIDE 93

93

Direct versus Alternating Current

DCPD ACPD

• higher resistance, lower current
• no thermoelectric effect
• control of penetration via frequency
• higher sensitivity to near-surface layer
• sensitivity to permeability

Thin-Plate/Thin-Skin Approximation

lim ln

f

V a b I t a b

→

Δ ρ + = π −

2a 2b

t << a

I (+) I (-) V (+) V (-)

Re ln V a b I T a b Δ ρ + ⎧ ⎫ ≈ ⎨ ⎬ π − ⎩ ⎭

{ }

min , T t ≈ δ f ρ δ = π μ lim Re ln

f

V f a b I a b

→∞

Δ ρμ + ⎧ ⎫ ∝ ⎨ ⎬ π − ⎩ ⎭

SLIDE 94

94

Skin Effect in Thin Nonmagnetic Plates

t

( ) f f t δ = ≈

t 2

1 f t = πμ σ analytical prediction

a = 20 mm, b = 10 mm, t = 2 mm 100 101 102 103 100 101 102 103 104 105 Frequency [Hz] Resistance [µΩ] 1 %IACS 2 %IACS 5 %IACS 10 %IACS 20 %IACS 50 %IACS 100 %IACS

ft

a = 20 mm, b = 10 mm, σ = 50 %IACS 0.05 mm 0.1 mm 0.2 mm 0.5 mm 1 mm 2 mm 5 mm

ft

100 101 102 103 100 101 102 103 104 105 Frequency [Hz] Resistance [µΩ]

Skin Effect in Thick Nonmagnetic Plates

304 austenitic stainless steel, σ = 2.5 %IACS, experimental 101 102 103 104 100 101 102 103 104 105 Frequency [Hz] Resistance [µΩ]

50 mm 20 mm 10 mm 6.25 mm 2.5 mm 2 mm 1 mm 0.5 mm 0.2 mm 0.1 mm 0.05 mm a = 10 mm, b = 7.5 mm

SLIDE 95

95

Current Distribution in Ferritic Steel

f = 0.1 Hz

FE predictions (Sposito et al., 2006)

f = 50 Hz f = 1 kHz a = 10 mm, b = 5 mm, t = 38-mm, c = 10 mm (0.5-mm-wide notches, two separated by 5 mm)

Thin-Skin Approximation

V Z R i X I Δ = = +

• c

c c

R R K R − Γ − Γ = ≈ Γ ln a b a b + Γ = −

c

2 ln a b c a b + + Γ = −

*

R R ≈ Γ

* c c

R R ≈ Γ

1 2 1 2 3 Electrode Shape Factor, a / b Electrode Gain, Γ0

2b 2a 2b 2a c ln a b R a b ρ + ≈ πδ − 2 ln

c

a b c R a b ρ + + ≈ πδ −

c

1 2 lim

c

c K a b

→

≈ Γ +

*

f R μρ = π

SLIDE 96

96

Technical Implementation of ACPD

low-pass filter low-pass filter

• scillator

differential driver

+ _

90º phase shifter A/D converter specimen electrodes PC processor

Vr Vs Vq frequency range: 0.5 Hz - 100 kHz driver current: 10-200 mA resistance range: 1-10,000 µΩ common mode rejection: 100-160 dB .

a = 0.160” b = 0.080” w = 0.054” 2 d = 0.120” voltage sensing current injection welding weldment d w edge weld clamshell catalytic converter

Application Example: Weld Penetration

NDE [mil] Fracture Surface [mils] 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 weld penetration (w) Weld Penetration [mil] Resistance [µΩ] 50 100 150 200 20 40 60 80 100 120 b = 120 mils 80 mils 100 mils electrode separation (b)

SLIDE 97

97

Application Example: Erosion Monitoring

5 10 15 20 Time [day] 20 21 22 23 24 25 Temperature [ºC] 32.0 32.2 32.4 32.6 32.8 33.0 Resistance [µΩ] 5 10 15 20 Time [day] 20 21 22 23 24 25 Temperature [ºC] 32.0 32.2 32.4 32.6 32.8 33.0 Resistance [µΩ] erosion erosion before compensation after compensation β ≈ 0.001 [1/ºC]

( ) [1 ( )] T T T ρ ≈ ρ + β −

50 60 70 80 90 100 110 120 130 200 400 600 800 Temperature [ºC] Resistivity [µΩ cm]

301 302 303 304 309 310 316 321 347 403

internal erosion/corrosion pipe

SLIDE 98

98

6 Special Methods

6.1 Microwave Techniques 6.2 Dielectric Measurements 6.3 Thermoelectric Measurements

6.1 Microwave Techniques

SLIDE 99

99

Electromagnetic Spectrum

34 19

, 6.63 10 Js, 1.6 10 C E h eV h e

− −

= ν = ≈ × ≈ × microwave IR light cosmic rays X-rays γ rays UV light visible light radio frequency Frequency [Hz] 10 108 106

4

10 1014 1012

10

10 1020 1018

16

1022 1024 Energy [eV] 10 10-6 10-8

• 10

10 100 10-2

• 4

10 106 104

2

108 1010 Wavelength [m] 10 100 102

4

10 10-6 10-4

• 2

10 10-12 10-10

• 8

10-14 10-16

typical lattice constant

Electromagnetic Waves

Plane waves: in dielectrics:

( ) 0 i t k x y y y

E E e ω − = = E e e

( ) 0 i t k x z z z

H H e ω − = = H e e E i H i ωμ η = = σ+ ωε ( ) k i i = − ωμ σ + ωε in conductors:

/ ( / ) x i t x y

E e e

− δ ω − δ

= E e

/ ( / ) x i t x z

H e e

− δ − ω − δ

= H e 1 i k = − δ δ 1 i i ωμ + η = = σ σδ 1 f δ = π μσ 377 μ η = ≈ Ω ε

0 r

n μ η η = ≈ ε ε

( / ) 0 i t x c y

E e ω

−

= E e

( / ) 0 i t x c z

H e ω

−

= H e k c ω =

0 0

1

r

c c n = = μ ε ε

8 0 0

1 3 10 m/s c = ≈ × μ ε

SLIDE 100

100

Reflection/Transmission between Dielectrics

x y incident reflected transmitted I dielectric II dielectric

I II I II

, n n η η η = η =

• strong penetration
• perceivable reflection

I II I II

n n R n n − = +

Reflection from Conductors

x y incident reflected transmitted “diffuse” wave I dielectric II conductor 1 f δ = ≈ π μσ

II I

i n η ωμ η = << η = σ

II I II I

1 R η − η = ≈ − η + η

• negligible penetration
• almost perfect reflection with phase reversal

SLIDE 101

101

Far-Field Measurement Configurations

detector isolator

• scillator

circulator horn antenna specimen

reflection (monostatic radar, pulse-echo)

detector isolator

• scillator

horn antenna specimen

transmission (bistatic radar, pitch-catch) scattering (bistatic radar, pitch-catch)

isolator

• scillator

horn antenna specimen d e t e c t

• r

detector

Near-Field Inspection

detector isolator

• scillator

circulator

• pen-ended

waveguide specimen stand-off distance air backing foam core adhesive substrate skin laminate corrosion damage coating

SLIDE 102

102

(Qaddoumi et al., 1997)

Microwave Image of Rust Under Paint

40 mm × 40 mm area of rust

• n a steel plate

24 GHz, 12.5 mm standoff distance, 0.267 mm of paint 60 40 20 60 40 20 [mm] [mm]

Lock-in Thermography

glass fiber-reinforced polymer plates (50 × 75 mm2) (Diener, 1995)

detector isolator

• scillator

circulator

• pen-ended

waveguide specimen stand-off distance infrared camera lock-in amplifier modulator

microwave raster scan lock-in thermography (phase image)

150-µm-thick delamination bonding defects

SLIDE 103

103

6.2 Dielectric Measurements

Fundamentals

t ∂ ∇× = + ∂ D H J t ∂ ∇× = − ∂ B E Maxwell's Equations: Harmonic solution: i i ωε = σ + ωε

• t

∂ ∇× = σ + ε ∂ E H E t ∂ ∇× = −μ ∂ H E i ∇× = ωε H E

• i

∇× = − ωμ E H i σ ε = ε − ω

• = σ

J E = ε D E = μ B H E electric field H magnetic field D electric flux density B magnetic flux density J electric current density σ electric conductivity ε electric permittivity µ magnetic permeability complex electric permittivity ω angular frequency t time ε

SLIDE 104

104

Electric Polarization

e d

Q Qd = = p d e +Q

• Q

+Q

• Q

E Fe Fe

e e

= × T p E

e t

Q = F E E = ε + D E P

e e 0

V ∑ = = χ ε p P E P electric polarization pe electric dipole moment V volume χe electric susceptibility ε0 permittivity of free space dipole formation dipole rotation

0 r

= ε ε D E

r e

1 ε = + χ

Capacitance

Q D A A C D E V E ⎫ ≈ ⎪ ⎪ ε ⎪ ≈ ⎬ = ⎪ ε ⎪ ⎪ ≈ ⎭

• Q

CV = dQ dV I C dt dt = = 1 V I dt C = ∫

r

ε = ε ε Y i C G = ω +

• 1

Z i C = ω

• Y

i C = ω

• A

G = σ Y i C = ω

• ( )

'( ) ''( ) i ε ω = ε ω − ε ω

• E

Q

• A

I

ideal dielectric lossy dielectric ( ) i σ ε ω = ε − ω

• conducting dielectric

Y i C = ω

• A

C = ε

• ''( )

tan '( ) D ε ω = δ = ε ω

SLIDE 105

105

Complex Electric Permittivity

( ) '( ) ''( ) i ε ω = ε ω − ε ω

• frequency [Hz]

Electric Permittivity [a. u.] + _ ε’ ε’’ _ + dipolar + _ + atomic resonance electronic resonance ionic 103 106 109 1012 1015 1018 _

' s s

lim ( ) lim i

ω→ ω→

σ ε = ε ω = ε − ω

• Capacitive Probes

parallel plate electrodes sensor with guard electrodes Vg basic sensor Rg

≈

Vm Im stray field electrodes Vg Rg

≈

Vm ≈Vm Im

×1

buffer

SLIDE 106

106

Auto-Balancing Bridge

Vg Rg

≈

Im H

device under test

L + _ Rref Im

high-gain

• perational

amplifier 2 m ref

V I R =

• 1

m dut

V I Z =

• 1

dut ref 2

V Z R V =

• 1

V

• 2

V

• dut

Z

• vector

voltmeter vector voltmeter “virtual” ground

Woven Composite

10 20 30 40 0.1 1 10 100 Frequency [kHz] Capacitance [pF]

. coated uncoated

0.001 0.01 0.1 1 10 0.1 1 10 100 Frequency [kHz] Conductance [μS]

. coated uncoated

conductive cloth for electric shielding

SLIDE 107

107

Adhesively Bonded Composite

Pethrick et al., 2002

0.5 1.0 1.5 2.0 2.5 Water Uptake [%] Thickness Variation [%] 2.5 2.0 1.5 1.0 0.5 0.0 10 20 30 40 50 60 70 80 Time1/2 [hr1/2] Water Uptake [%] 2.5 2.0 1.5 1.0 0.5 0.0

intact 122 hr 580 hr 1,007 hr 1,590 hr 5,350 hr

Frequency [Hz] Relative Permittivity 50 40 30 20 10 10-1 100 101 102 103 104 105 106 107 108 109 Frequency [Hz] Dielectric Loss 103 102 101 100 10-1 10-2 10-1 100 101 102 103 104 105 106 107 108 109

intact 122 hr 580 hr 1,007 hr 1,590 hr 5,350 hr

6.3 Thermoelectric Measurements

SLIDE 108

108

Thermoelectric Effect

Seebeck, Peltier, and Thomson effect: coupled electric and thermal flux J electric current density h thermal flux density σ electric conductivity (∇T = 0) κ thermal conductivity (∇V = 0) V voltage T temperature S thermoelectric power closed-circuit Seebeck effect: hA T1 T2 A B hB JA JB I

• pen-circuit Seebeck effect:

T1 T2 A B hA hB JA = 0 JB = 0 VS T0 T0

V + _

S V ST T σ σ −∇ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ σ κ −∇ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ J h V = − σ∇ J T = − κ∇ h ( ) V S T = − σ ∇ + ∇ = J V S T ∇ = − ∇

1 2 1 2

S B A B T T T T T T

V S dT S dT S dT = + + ∫ ∫ ∫

2 2 1 1

S A B AB

( )

T T T T

V S S dT S dT = − = ∫ ∫

Absolute Thermoelectric Power

Temperature [K] 500 1000 1500

• 40
• 30
• 20
• 10

10 20 30 Thermoelectric Power [µV/K]

W (tungsten) Mo (molybdenum) Ag (silver) Cu (copper) Au (gold) Pt (platinum) Pd (palladium)

2 2 1 1

S A B AB

( )

T T T T

V S S dT S dT = − = ∫ ∫

S AB 2 1

( ) V S T T ≈ −

SLIDE 109

109

Contact Thermoelectric Tester

Primary Effect:

• chemical composition

Secondary Effects:

• anisotropy, texture
• fatigue, cold work, plasticity, residual stress, etc.
• pen-circuit Seebeck effect

specimen (A) electrical heating “cold” junction “hot” junction reference electrodes (B)

~ ~ V + _

TEP versus Chemical Composition

Ag Content [%] 20

• 20
• 40
• 60

Thermoelectric Power [µV/K] 20 40 60 80 100 273 K 83 K Ag Content [%] 50 40 30 20 10 Electric Resistivity [µΩ cm] 20 40 60 80 100 293 K 4.2 K

palladium-silver binary alloy

(Rudnitskii, 1956)

SLIDE 110

110

TEP Anisotropy

hexagonal single crystal Zinc, relative to basal plane (Rowe and Schroeder, 1970) Temperature [K]

• 3
• 2
• 1

1 2 3 50 100 150 200 250 300 perpendicular parallel Thermoelectric Power [µV/K]

TEP versus Texture

cold-worked polycrystalline material Ti-6Al-4V, relative to cold work direction (Carreon and Medina, 2006)

50 µm before annealing after annealing 30 60 90 120 150 180 Azimuthal Angle [deg]

• 5.1
• 5.0
• 4.9
• 4.8

Thermoelectric Power [µV/°C] 5 10 15 20 80 60 40 80 60 40 Cold-rolling reduction [%] Difference in TEP [%] gold tip reference copper tip reference before annealing after annealing

SLIDE 111

111

Noncontacting Thermoelectric Tester

closed-circuit Seebeck effect

• relative to surrounding intact material
• no artificial interface
• penetrating (with substantial depth)
• noncontact (with substantial lift-off)

specimen heat thermoelectric current magnetometer

Material Effects versus Geometry

TEP is independent of size and shape C11000 copper diameter 0.375” ∇T ≈ 0.5 °C/cm 2 mm lift-off distance 3” × 3” scanning dimension 18 nT peak magnetic flux before annealing after annealing

plastic zone

milled T ∇ pressed T ∇

SLIDE 112

112

Residual Stress Characterization

shot-peened C11000 copper 5 10 15 20 25 2A 4A 6A 8A 10A 12A 14A 16A Almen Peening Intensity Magnetic Signature [nT]

before relaxation relaxation at 235 ºC relaxation at 275 ºC relaxation at 315 °C 2nd relaxation at 315 °C 3rd relaxation at 460 °C recrystallization at 600 °C

SLIDE 113

113

7 Electromagnetic Acoustic Transducers (EMATs)

7.1 EMAT Principles 7.2 EMAT Instrumentation 7.3 EMAT Applications

Piezoelectricity

+

• +
• +
• +

+

• +
• +

+ +

+ + + + + + +

• - - - - - -

+ + + + + + +

• - - - - - -

Si Si Si O O O

Quartz (silicon dioxide, SiO2)

E b V F σ = A S E

e D E S e K ε ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = σ ⎢− ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

SLIDE 114

114

Electromagnetic Acoustic Transducers

Key Features:

• non-contact/no couplant
• multiple wave modes (including SH)

Disadvantages:

• low sensitivity
• requires special electronics
• material dependent

Advantages:

• easy automation
• high speed scanning
• high reproducibility
• high-temperature inspection
• minimal wear
• less surface preparation required
• easy to customize

(EMATs)

7.1 EMAT Principles

SLIDE 115

115

Principle #1: Lorentz Force

( ) Q = + × F E v B ∇× = H J t ∂ ∇× = − ∂ B E = σ J E Ampère's law: Faraday's law: Ohm’s law: Lorentz force: Je conducting medium Hp He Ip Transmission (I ⇒ F) Reception (v ⇒ V): Je F B0 I B0 Je v V

Principle #2: Magnetization

Fm magnetic force µ0 permeability of free space V volume M magnetization H magnetic field y height χ magnetic susceptibility

specimen electromagnet

y

2

2

m

V dH dH F V M dy dy μ = −μ = −χ excitation current magnetization force no bias strong bias some bias

Time Signal Time Signal Time Signal Fm

SLIDE 116

116

Principle #3: Magnetostriction

Spontaneous magnetostriction:

H = 0

Induced magnetostriction:

H

1,2,3

3 e ε =

1

2 3 e ε =

1 2,3

2 3 e ε ε = − = − 2 4 6 Magnetic Field [104 A/m]

low-carbon steel

Magnetostriction [10-6]

• 20
• 10
• 30
• 40

10 Fe Co Ni

7.2 EMAT Instrumentation

SLIDE 117

117

EMAT Polarization

e

n dA Q ≈ − = − I J v high coupling: n = − × τ I B “surface” traction:

m

Q = × F v B magnetic force: tangential polarization normal polarization Je B0 n I τ τ B0 n I Je

Normal-Beam EMATs

spiral coil radially polarized shear wave rectangular coil linearly polarized shear wave symmetric coil longitudinal wave B0

S N N S

B0

S N

B0

SLIDE 118

118

Angle-Beam Shear EMATs

sin λ θ = Λ periodic permanent magnet horizontally polarized shear wave

S N

Λ θ B0 meander coil vertically polarized shear wave

S N

θ Λ B0

EMAT Electronics

EMATs with permanent or electromagnets driver amplifier

• scillator

+ _ Vs

matching network matching network specimen 0.5 1 1.5 2 2.5 3 Frequency [MHz] 2 4 6 8 10 12 14 16 18 20 Impedance [Ω] resistance reactance

7-turn, 10-mm-diameter spiral coil on ferritic steel

SLIDE 119

119

Impedance Matching

V

• g

V

g

Z

• Z
• ≈

( )

2 g * max g g g g

when , 8 V P Z Z R R X X R = = = = −

• transformer (κ ≈ 1)

12 21 22 11

Φ Φ = = κ Φ Φ

2 2 21 22

( ) d V N dt = Φ + Φ

1 1 11 12

( ) d V N dt = Φ + Φ I1 N1 N2 V2 Φ

11

V

1

I2 Φ

22

Φ

12

Φ

21 , 2 2 1 1

V N V N =

2 2 11 22

( ) d V N dt = Φ + Φ

1 1 11 22

( ) d V N dt = Φ + Φ

2 1 1 2

I N I N =

2 2 2 2 1 1

N Z Z N = ideal transformer (κ = 1)

7.3 EMAT Applications

SLIDE 120

120

Texture Assessment by EMATs

cold-pressed 2024 aluminum, 1.4 MHz, EMAT

η ≈ 0% (annealed)

η = 0.45 % η = 0.8 % η = 1.6 % cavg = 2,850 m/s, 0.2% per division, η = (cmax – cmin)/cavg

Textured Specimen transmitter receiver Rayleigh wave

High-Temperature Monitoring

60 55 50 45 40 35 30 25 20 200 400 600 800 1000 Temperature [K] Stiffness [GPa] C44 C66 230 210 190 170 150 130 200 400 600 800 1000 Temperature [K] Stiffness [GPa] C11 C33 SiC/Ti-6Al-4V composite (Ogi et al., 2001)

SLIDE 121

121

Electromagnetic Acoustic Resonance

(Hirao and Ogi et al., 2003) 50 100 150 SCM 440 steel pure titanium

• 120
• 80
• 40

Stress [MPa]

• 1.0
• 1.1
• 1.2

Birefringence [%] load unload

couplant PZT specimen specimen

EMAT Stress [MPa] 0.05

• 0.05
• 0.10

Birefringence [%] as-received quenched & tempered annealed

Thank You!