4 magnetic nde - university of cincinnatipnagy/classnotes/aeem974 electromagnetic nde... · 4...

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

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

mV

∑=p

M

= χM H

0 0 r( )= μ + = μ μB H M H

r 1μ = + χ

m1

2Q= ×p R v

Q charge

v velocity

R radius vector

Classification of Magnetic MaterialsDiamagnetism:

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

Curie temperature

e.g., iron, nickel, cobalt

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 orbital period

r orbital radius

v orbital velocity

Ei induced electric field

Fe decelerating electric force

m mass of electron

N dipoles within unit volume

χ magnetic susceptibility

vQ

Fm

B

vQFe

B

ieF e E=

mF ev B=

m orb spin= +p p p

2

orb 2

Q A e r vp N I A

r

π= = = −

τ π

orb 2

er vp = −

2 22 20

orb 4 4

e re rp B H

m m

μΔ = − = −

ei2 2

Fdr E r

dt e

Φ− = π = − π

2d m dv

rdt e dt

Φ= π

2 2m

B r r ve

π = π Δ

2

erv B

mΔ =

- χ ≈ 1-10 ppm

2 20

orb 4

e rN

m

μχ = −

Weak Paramagnetism, Curie Lawm orb 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 mU = −p Bi

m m90 90

( ) sinU T p B dθ θ

= θ θ = θ θ∫ ∫

m m cosU p B= − θ

m m sinT p B= θ

m

Bm( )

U

k Tp U e−

=

20

B3

N mM C

H k T T

μχ = = =

Curie Law:

χ ≈ 5-50 ppm

+I

-Ipm

Fm

B

Fm

Tm

θ

Strong Paramagnetism, Curie-Weiss Law:

t iH H H H M= + = + α

tC

M HT

=

t i

M M MM TH H H MC

χ = = =− − α

Curie-Weiss law:c

C

T Tχ =

−

M

Hχ =

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 HT

≈

C

T Cχ =

− α

C

Tχ ≈

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

Spontaneous Magnetization

N N N N

S S S S

N S N S

S S S S

N N S S

S S N N

[100]

[010] “easy” magnetic axis

[001]

[110]

[111]

total internal wall externalU U U U= + +

Magnetic Domains in Single Crystalseasy magnetic axes

H = 0

H

H

H

1 demagnetization(spontaneous magnetization)

4 technical saturation

3 “knee” of the magnetization curve

2 partial magnetization

domain wallmovement

irreversiblerotation

reversiblerotation

H

B

1

2

354

5 full saturation(no precession)

thermal precession not shown

4.2 Magnetic Measurements

Magnetic Sensors

10-2

10-1

100

101

102

103

104

105

0 5 10 15 20 25Frequency [Hz]

Flu

x D

ensi

ty [

pT/H

z1/2 ]

Hall

GMR

SDP

fluxgate

SQUID

noise threshold

axiald

V N i N ABdt

Φ= − = − ωcoil:

Hall Detector

I I

a

b

x

yz

x x

Bz

VH

Fm

Fe

( )Q= + ×F E v B

( ) 0y y x zF e E v B= − + =

Hy

VE

a=

x xI enab v= −

Hx

y x z zI

V a E av B Benb

= = − =

HH

xz

R IV B

b=

H1

Ren

=

Fluxgate

Iexc

Vsens

B1

B2

B

hard magnetic cores

high-frequencyexcitation

low-frequency or dcexternal 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)

Vibrating-Sample Magnetometer

Vsens B0

vibration (ω)

0 sin( )d d t= ω

1 0 0( ) [ sin( )]t A B M tΦ = + μ κ ω

2 0 0( ) [ sin( )]t A B M tΦ = − μ κ ω

1 2sens( )V t N N

t t

∂Φ ∂Φ= − +

∂ ∂

0

0

BM = χ

μ

sens 0( ) 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 mU = −p Bi

g mU U U= +

'dU dB

W W M Vdh dh

= = −

mU M V B= −

U W h M V B= −

M H= χ

20

0'2

VdH dHW W V H

dh dh

μ− = − μ χ = − χ

4.3 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 5Magnetic Field [kA/m]

Flu

x D

ensi

ty [

Tes

la]

hardened steel

soft iron

0 0( , ) ( , )p pB B H M H M H M= = μ + μferromagnetic materials:

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

M H= χ

0 rB H= μ μ

r 1μ = + χ

Initial Magnetizationanhysteretic 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

dHμ =

0limH

M M→∞

=

0 ( )B H M= μ +

0 mM n p≤

Retentivity, Coercivity, Hysteresis

Br remanence [Vs/m2]

Mr remanent 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 magnetization:

HH

B

Br

Hc

r 0 rB M= μ

c c( ) 0H M H+ =

ci( ) 0M H =

c ciH H≤

0dU B dH=

0U AΔ =

Texture, Residual Stress

-2

-1

0

1

2

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

Flu

x D

ensi

ty [

T]

σ = 183 MPaB||

B⊥

-2

-1

0

1

2

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

Flu

x D

ensi

ty [

T]

σ = 110 MPaB||

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

12

3

eε =

12,3 2 3

eεε = − = −

1 2 eε − ε =

Spontaneous magnetostriction:

easy magnetic axes

H = 0

domains 0M M M= ≤

domain domain1 2,3, 0eε = ε =

volume1,2,3 3

eε =

volume 0M ≈

Barkhausen Noise

H = 0

H

domain wallmovementH

B

magnetic field Barkhausen noise

Am

plit

ude

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 Tχ =

−

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

Magnetic Boundary Conditions

xt

medium I

medium II

BIθΙ

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:

0∇ =Bi

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

I I,n II II,nH Hμ = μ I I,n II II,ntan tanH Hθ = θ

I II

I II

tan tanθ θ=

μ μ

Magnetic Refraction

I II

I II

tan tanθ θ=

μ μ

µI/µII =

1030

100

0 15 45 60 75 900

15

30

45

60

75

90

30Ferromagnetic Angle, θI [deg]

Non

mag

neti

c A

ngle

, θII

[deg

]

medium I(ferromagnetic)

BI

BIIθΙΙ

θΙ

medium II(air)

medium I(ferromagnetic)

BI

BII

θΙΙ

θΙ

medium II(air)

Exciter Magnets

electromagnet

air gap

ferromagnetic core

H d N I MMF= =∫

0 r H AΦ = μ μ

0 rMMF d

A

Φ= ∫

μ μ

mMMF

R =Φ

m0 r 0 r

1 1 i

i i i

dR

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

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

gent

ial M

agne

tic

Fiel

d

Lateral Position

Nor

mal

Mag

neti

c F

ield

electromagnet

crack

N I

magnetometer

Subsurface Flaw Detection

H

B

1

2

saturation greatly reduces the differential permeability

crack

low magnetic field

crack

high magnetic field