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
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