5 Magnetic Inspection

5.1 Magnetic Laws

5.2 Magnetic Properties

5.3 Magnetic Measurements

5.4 Magnetic Materials Characterization

5.5 Magnetic Flaw Detection

5.1 Magnetic Laws

Magnetic Field

B

Q

Fm

dv

e QF E

m Q F v B

( )Q F E v B

F Lorentz 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 Ip Apm

Magnetic Dipole in a Magnetic Field

+I

-I

pm

Fm

B m Q F v B

m m T p B

pm magnetic dipole moment

Q charge

v velocity

R radius vector

B magnetic flux density

Fm magnetic force

Tm twisting moment or torque

Fm

m1

2N I Q p A R v

Ampère’s Law

infinite straight wire

d

I

dℓ

R

H r ℓ

s

encd I H s

2H ds H R I

2

IH

R

24r

I dd

r

H e e

2 2 2 3/ 244 ( )

I d R I R dd

rr R

H e e

2 2 3/ 202 2( )

I R d IH

RR

Biot-Savart Law:

H magnetic field

I current

Induction, Faraday’s Law, Inductance

Φ magnetic flux

B magnetic flux density

Є induced electromotive force

S surface area of the loop

t time

B

Є

S

d B S

Єd

dt

I N

V

μ magnetic permeability

N number of turns

I current

Λ geometrical constant

L (self-) inductance

N I

Єd

V Ndt

I L

N

dIV L

dt

2L N

5.2 Magnetic Properties

Magnetization

M magnetization

V volume

χ magnetic susceptibility

H magnetic field

B magnetic flux density

μ0 permeability of free space

μr relative permeability

μ magnetic permeability

pm magnetic dipole moment

N number of turns

I current

A encircled vector area

m N Ip A+I -I

m

V

pM

M H

0 0 r( ) B H M H

r 1

B H

0 r

Classification of Magnetic Materials

Diamagnetism:

μr < 1

no remanence

orbit distortion

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

Paramagnetism:

μr > 1

no remanence

orbit and spin alignment

e.g., aluminum, titanium, platinum

Ferromagnetism:

μr >> 1

remanence, coercivity, hysteresis

self-amplifying paramagnetism

e.g., iron, nickel, cobalt

pm magnetic dipole moment

pspin electron spin

porb electron orbital motion

N number of turns

I current

A encircled area

e charge of electron

τ orbital period

r orbital radius

v orbital velocity

Ei induced electric field

Fe decelerating electric force

m mass of electron

χ magnetic susceptibility

Diamagnetism

v e

Fm

B

v e Fe

B

ieF eE

mF ev B

m orb spin p p p

2

orb2

e A e r vp N I A

r

orb2

er vp

2 22 20

orb4 4

e re rp B H

m m

ei2 2

Fdr E r

dt e

2d m dv

rdt e dt

2 2m

B r r ve

2

erv B

m

- χ ≈ 1-10 ppm

Paramagnetism

m orb spin p p p

pm magnetic dipole moment

B magnetic flux density

Fm magnetic force

Tm twisting moment or torque

U potential energy of the dipole

kB Boltzmann constant

T absolute temperature

N moments within unit volume

χ magnetic susceptibility

m m T p B

mU p B

m0 0

( ) sinU T d p B d

m (1 cos )U p B

m m sinT p B

B( )

U

k Tp U e

20

B3

N mM C

H k T T

Langevin model:

χ ≈ 5-50 ppm

+I

-I

pm

Fm

B

Fm

Tm

θ

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

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

5.3 Magnetic Measurements

Magnetic Sensors

10-2

10-1

100

101

102

103

104

105

0 5 10 15 20 25

Frequency [Hz]

Flu

x D

ensi

ty [

pT

/Hz1

/2]

Hall

GMR

SDP

fluxgate

SQUID

noise threshold of key magnetic detectors

axialaxial

dV N i N AB

dt

coil:

ferromagnetic powder, filing

Hall Detector

.

I I

a

b

x

y z

x x

B z

VH

Fm

Fe

( )Q F E v B

( ) 0y y x zF e E v B

Hy

VE

a

x xI env ab

Hx

y x z zI

V a E av B Benb

HH

x zR I BV

b

H1

Ren

5.4 Magnetic Materials

Characterization

Magnetic Properties

-1.5

-1

-0.5

0

0.5

1

1.5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Magnetic Field [kA/m]

Flu

x D

ensi

ty [

Tes

la]

hardened steel

soft iron

( , )pB B H Mferromagnetic materials:

para- and diamagnetic materials: 0 ( )B H M

M H

0 rB H

r 1

Initial Magnetization

anhysteretic initial magnetization curve

Flux Density

Differential Permeability

Magnetic Field

Flu

x D

ensi

ty

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

ddB

dH

0limH

M M

0 ( )B H M

0 mM n p

Texture, Residual Stress

-2

-1

0

1

2

-300 -200 -100 0 100 200 300 Magnetic Field [A/m]

Flu

x D

ensi

ty [

T]

σ = 0 MPa B||

B

-2

-1

0

1

2

-300 -200 -100 0 100 200 300 Magnetic Field [A/m]

Flu

x D

ensi

ty [

T]

σ = 36 MPa B||

B

-2

-1

0

1

2

-300 -200 -100 0 100 200 300 Magnetic Field [A/m]

Flu

x D

ensi

ty [

T]

σ = 183 MPa B||

B

-2

-1

0

1

2

-300 -200 -100 0 100 200 300 Magnetic Field [A/m]

Flu

x D

ensi

ty [

T]

σ = 110 MPa B||

B

mild steel

Barkhausen Noise

H = 0

H

domain wall

movement H

B

magnetic field Barkhausen noise

Am

pli

tud

e

Time

• magnetic Barkhausen noise

• acoustic Barkhausen noise

5.5 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

Magnetic Boundary Conditions Ampère's law:

H J

Gauss' law:

0 B

I,n II,nB B I,t II,tH H

xt

medium I

medium II

BI I

boundary

BII

BII,t

BII,n

II

BI,n

BI,t

xn

xt

medium I

medium II

HI

I

HII

HII,t

HII,n

II

HI,n

HI,t

xn

I I,n II II,nH H I I,n II II,ntan tanH H

I II

I II

tan tan

Magnetic Refraction

I II

I II

tan tan

µI/µII =

10

30

100

0 15 45 60 75 90 0

15

30

45

60

75

90

30

Ferromagnetic Angle, θI [deg]

Nonm

agnet

ic A

ngle

, θ

II [

deg

]

medium I

(ferromagnetic)

BI

BII II

I

medium II

(air)

medium I

(ferromagnetic) BI

BII

II

I

medium II

(air)

Exciter Magnets

electromagnet

air gap

ferromagnetic core

H d N I MMF

0 r H A

0 r

MMF dA

mMMF

R

m0 r 0 r

1 1 i

i i i

dR

A A

H magnetic field

N number of turns

I excitation current

MMF magnetomotive force

Φ magnetic flux

ℓ length of flux line

µ0 µr 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

Tan

gen

tial

Mag

net

ic F

ield

Lateral Position

Norm

al M

agnet

ic F

ield

electromagnet

crack

N I

magnetometer

Subsurface Flaw Detection

H

B

1

2

saturation greatly reduces the differential permeability

crack

1) low magnetic field

crack

2) high magnetic field