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

Principle of Operation

electric field

magneticflux

density

axial (x)

transverse (y)

normal (z)

galvanic current injection

magnetometer

magnetic injection:

primary ac flux

~~

Bx0

Field Perturbation

magneticflux

density

magnetometer

axial (x)

transverse (y)

normal (z)

axial flaw

cw current

Bz < 0

electriccurrent

Bz > 0

ccw current

axial scanningabove flaw Axial Position

Bz

[a.u

.]

Axial Position

Bx

[a.u

.]

Bz

[a.u

.]

Bx [a.u.]

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

00 5 10 15 20

Coating Thickness [mm]

ΔB

x [%

]

50 5 mm

20 2 mm

20 1 mm

slot size

30

25

20

15

10

5

0

Slot Depth [mm]

ΔB

x an

d Δ

Bz

[%]

0 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

00 10 20 30 40

Slot Depth [mm]

ΔB

xm p

er 1

mm

Slo

t Dep

th [

%]

40-mm-longsolenoid

12-mm-longsolenoid

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)

Flaw Orientation

0.17

0.16

0.15

0.14

0.13

0.12

0.11

Bx

[T]

0 1 2 3 4 5Scanning time [a. u.]

transverse flaw(normal to B)

axial flaw(normal to E)

0.025

0.020

0.150

0.100

0.05

0

-0.05B

z [T

]0 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

Tan

gent

ial M

agne

tic

Fie

ld

Lateral Position

Nor

mal

Mag

neti

c F

ield

5.2 Direct Current Potential Drop

Inductive versus Galvanic Coupling

specimen

eddy currents

probe coil

magnetic field

electric current

VI I

injectioncurrent

potential drop

specimen

advantages of galvanic coupling

dc and low-frequency operation

constant coupling (four-point measurement)

awkward shapes

absolute measurements

inherently directional

Thin-Plate Approximation

combined electric current and potential field2a2b

t << a

( ) ( )2

IE r J r

r t

( ) ( )2r r

I drV r E r dr

t r

( ) ln const2

IV r r

t

( ) ( )V V V

lnI a b

Vt a b

2 ( ) ( )V V a b V a b

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

I (+) I (-)

V (+) V (-)

Lateral Spread of Current Distribution

( )2

IJ r

r t

(0,0)I

Jat

2 2 2 2

2(0, )

2

I aJ w

a w t a w

2 2(0, )

( )

I aJ w

a w t

2

(0,0)2

(0, )

J

J w

2 22

22

(0,0)2

(0, )

a wJ

J w a

2w a

2w I (+) I (-)

V (+) V (-)

x

y

2a

J(0,w)

J(0,0)

Thick-Plate Approximation

2( ) ( )

2

IE r J r

r

2( ) ( )

2r r

I drV r E r dr

r

( ) const2

IV r

r

t >> a

2a2b

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

combined electric current and potential field

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

( ) ( )V V V

1 1IV

a b a b

2 ( ) ( )V V a b V a b

Finite Plate Thickness

2a2b

t

2 2 1/ 2( )

2 [ (2 ) ]n

IV r

r nt

2 2 1/ 2

2 2 1/ 2

1

[( ) (2 ) ]

1

[( ) (2 ) ]

n

IV

a b nt

a b nt

I (+) I (-)

V (+) V (-)

n = 0

n = -1

n = +1

n = -2

n = +2

2t

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

Resistance versus Thickness

0

1lim lnt

a b

t a b

2 2

2lim

t

b

a b

VR

I

0.1

1

10

0.01 0.1 1 10 100Normalized Thickness, t / a

Nor

mal

ized

Res

ista

nce,

Λ

finite thickness

thin-plate appr.

thick-plate appr.

a = 3b

Crack Detection by DCPD

intact specimen

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

( ) ( )0V V V

t

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

cracked specimen

( ) ( )cV V V

c

1

2

3

0 0.2 0.4 0.6 0.8 1Normalized Crack Depth, c / t

Nor

mal

ized

Pot

enti

al D

rop,

ΔV

c / Δ

V0

a / t =

0.441.21.8

a = 3b

infinite slot

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

powersupply

polarityswitch

+

_

specimen

electrodesVs

+_

5.3 Alternating Current Potential Drop

Direct versus Alternating CurrentDCPD

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

0lim lnf

V a b

I t a b

2a2b

t << aI (+) I (-)V (+) V (-)

Re lnV a b

I T a b

min ,T t

f

lim Re lnf

V f a b

I a b

Skin Effect in Thin Nonmagnetic Plates

t( )f f t

t 20

1f

t

analytical prediction

a = 20 mm, b = 10 mm, t = 2 mm

100

101

102

103

100 101 102 103 104 105

Frequency [Hz]

Res

ista

nce

[µΩ

]

1 %IACS 2 %IACS 5 %IACS 10 %IAC

S

20 %IACS 50 %IACS

100 %IACS

ft

a = 20 mm, b = 10 mm, σ = 50 %IACS

0.05 mm0.1 mm0.2 mm0.5 mm

1 mm2 mm5 mm

ft100

101

102

103

100 101 102 103 104 105

Frequency [Hz]

Res

ista

nce

[µΩ

]

Skin Effect in Thick Nonmagnetic Plates304 austenitic stainless steel, σ = 2.5 %IACS, experimental

101

102

103

104

100 101 102 103 104 105

Frequency [Hz]

Res

ista

nce

[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

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

VZ R i X

I

c 0 c 0c

0 0

R RK

R

0 lna b

a b

c2

lna b c

a b

*0 0R R *

c cR R

0

1

2

1 2 3Electrode Shape Factor, a / b

Ele

ctro

de G

ain,

0

2b2a

2b2a

c

0 lna b

Ra b

2lnc

a b cR

a b

c0 0

1 2lim

c

cK

a b

* fR

Technical Implementation of ACPD

low-passfilter

low-passfilter

oscillatordifferential

driver

+

_

90º phaseshifter

A/Dconverter

specimen

electrodesPC

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”

voltagesensing

currentinjection

welding

weldment

d

w

edge weld

clamshellcatalytic converter

Application Example: Weld Penetration

NDE [mil]

Fra

ctur

e S

urfa

ce [

mil

s]

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

weld penetration (w)

Weld Penetration [mil]

Res

ista

nce

[µΩ

]

0

50

100

150

200

0 20 40 60 80 100 120

b =

120 mils

80 mils100 mils

electrode separation (b)

Application Example: Erosion Monitoring

0 5 10 15 20Time [day]

20

21

22

23

24

25

Tem

pera

ture

[ºC

]

32.0

32.2

32.4

32.6

32.8

33.0R

esis

tanc

e [µ

Ω]

0 5 10 15 20Time [day]

20

21

22

23

24

25

Tem

pera

ture

[ºC

]

32.0

32.2

32.4

32.6

32.8

33.0

Res

ista

nce

[µΩ

]

erosionerosion

before compensation after compensation

β 0.001 [1/ºC]

0 0( ) [1 ( )]T T T

50

60

70

80

90

100

110

120

130

0 200 400 600 800Temperature [ºC]

Res

isti

vity

[µ

Ω c

m]

301 302 303 304 309 310 316 321 347 403

internalerosion/corrosion

pipe