Transcript MExxxElectromagnetic NDE - University of Cincinnati

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
pm  N I A
+I
pm
magnetic dipole moment
N
number of turns
I
current
A
encircled vector area
Q
charge
v
velocity
R
radius vector
M
magnetization
V
volume
χ
magnetic susceptibility
H
magnetic field
B
magnetic flux density
μ0
permeability of free space
μr
relative permeability
-I
pm 
M 
1
Q R v
2
 pm
V
M  H
B  0 (H  M)  0 r H
r  1  
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
Curie temperature
e.g., iron, nickel, cobalt
Diamagnetism
p m  porb  pspin
QA
e r2 v
porb  N I A 
 

2r
B
er v
porb  
2
Q
v
Fm

Fe
Q
Fe  eEi
v
porb electron orbital motion
I
current
A
encircled area
e
charge of proton
τ
orbital period
e
r
orbital radius
er
B
2m
v
orbital velocity
Ei
induced electric field
Fe
decelerating electric force
m
mass of electron
n
dipoles within unit volume
χ
magnetic susceptibility
m
B  r 2  2  r v
v 
pspin electron spin
number of turns
F
d
 2  r Ei   2  r e
dt
e
B
magnetic dipole moment
N
d
m dv
 2r
dt
e dt
Fm  ev B
pm
 e2 r 2
e2 r 2
porb  
B  0
H
4m
4m
 e2 r 2
orb   n 0
4m
- χ ≈ 1-10 ppm
Weak Paramagnetism, Curie Law
p m  porb  pspin
Tm  pm B
B
Tm  pm B sin 
Fm
pm
-I
θ


90
90
U m   T ()   pm B  sin  d 
Tm
+I
Um   pm B cos 
Fm
U  U m0
 m
kB T
p (U m )  e
Curie Law:
n 0 m 2
M
C
 


H
3 kB T
T
χ ≈ 5-50 ppm
Um  pm B
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
Strong Paramagnetism, Curie-Weiss Law:
 
Curie law:
M 
 
M
H
C
H
T
C
T
Ht  H  Hi  H   M
C
M  Ht
T
M
M
M
 


MT
H
H t  Hi
 M
C
Curie-Weiss law:
 
C
T  C
 
C
T  TC
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
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
B
Br
first magnetization
H
Hc
Spontaneous Magnetization
[001]
[111]
[010] “easy” magnetic axis
[100]
[110]
N N N N
N N S S
N S N S
S S S S
S S N N
S N S N
Utotal  Uinternal  Uwall  Uexternal
Magnetic Domains in Single Crystals
easy magnetic axes
1 demagnetization
(spontaneous magnetization)
H=0
domain wall
movement
B
4
2 partial magnetization
H
irreversible
rotation
3 “knee” of the
magnetization curve
H
reversible
rotation
4 technical saturation
H
thermal precession not shown
5 full saturation
(no precession)
5
3
2
1
H
4.2 Magnetic Measurements
Magnetic Sensors
noise threshold
Flux Density [pT/Hz1/2]
105
104
Hall
103
GMR
102
SDP
101
100
fluxgate
10-1
SQUID
10-2
0
5
coil:
10
15
Frequency [Hz]
V  N
d
  i  N ABaxial
dt
20
25
Hall Detector
z y
x
F  Q (E  v  B)
Bz
Fy   e ( E y  vx Bz )  0
V
Ey  H
a
b
Ix
Ix
Fe
Fm
a
VH
I x   enab vx
VH  a E y   a v x Bz 
VH 
RH I x
Bz
b
RH 
1
en
Ix
Bz
e nb
Fluxgate
B1
hard magnetic cores
B low-frequency or dc
B
high-frequency
Iexc
excitation
external magnetic field
B2
H
sensing voltage
V
(to be low-pass filtered) sens
B≠0
B=0
B1
B1
t
t
B2
B2
t
t
B1 + B2
B1 + B2
t
t
Vibrating-Sample Magnetometer
vibration (ω)
Vsens
B0
B
M   0
0
d  d0 sin(t )
1(t )  A[B0  0 M sin(t )]
2 (t )  A[B0  0 M sin(t )]

2
Vsens (t )   N 1  N
t
t
Vsens (t )   2 N A B0  cos(t )
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
electromagnet
specimen
spacer
W’ = W - Fm
h
precision scale
Um
magnetic potential energy
pm
magnetic dipole moment
B
magnetic flux density
M
magnetization
for a single dipole:
Um  pm B
V
volume
for a given magnetized volume:
Um   MV B
Ug
gravitational potential energy
U  Ug  Um
U
total potential energy
h
height
W
actual weight
W’
apparent weight
χ
magnetic susceptibility
H
magnetic field
µ0
permeability of free space
U  W h  MV B
dU
dB
W' 
 W  MV
dh
dh
M  H
 V dH 2
dH
W '  W    0 V H
   0
dh
2
dh
4.3 Magnetic Materials
Characterization
Magnetic Properties
para- and diamagnetic materials:
B  0 (H  M )
M  H
B  0 r H
r  1  
ferromagnetic materials:
B  B( H , M p )  0 H  0 M ( H , M p )
1.5
hardened steel
Flux Density [Tesla]
1
0.5
soft iron
0
-0.5
-1
-1.5
-5 -4
-3 -2 -1 0 1 2 3
Magnetic Field [kA/m]
4
5
Initial Magnetization
anhysteretic initial magnetization curve
Flux Density
Flux Density
Differential Permeability
Magnetic Field
B
magnetic flux density
H
magnetic field
M
magnetization
B  0 (H  M )
µ0
permeability of free space
lim M  M 0
µd
differential permeability
M0
saturation magnetization
n
dipoles per unit volume
pm
magnetic dipole moment
d 
dB
dH
H 
M0  n pm
Retentivity, Coercivity, Hysteresis
B  0 (H  M )
M  M (H , M p )
B
technical saturation:
Br
H
H
Hc
Br  0 Mr
Br
remanence [Vs/m2]
Hc  M (Hc )  0
Mr
remnant magnetization
M (Hci )  0
µ0
permeability of free space
Hc
coercive field [A/m]
Hci
intrinsic coercivity
U0
magnetic energy density
A
hysteresis area [J/m3]
Hc  Hci
dU0  BdH
U0  A
Texture, Residual Stress
mild steel (Langman 1985)
2
2
σ = 36 MPa
1
Flux Density [T]
Flux Density [T]
σ = 0 MPa
B||
B
0
-1
-2
1
B
0
-1
-2
-300 -200 -100 0
100 200
Magnetic Field [A/m]
300
-300 -200 -100 0
100 200
Magnetic Field [A/m]
2
300
2
σ = 110 MPa
σ = 183 MPa
B||
1
Flux Density [T]
Flux Density [T]
B||
B
0
-1
-2
-300 -200 -100 0
100 200
Magnetic Field [A/m]
B||
1
B
0
-1
-2
300
-300 -200 -100 0
100 200
Magnetic Field [A/m]
300
Magnetostriction
Spontaneous magnetostriction:
M domain  M s  M 0
easy magnetic axes
M volume  0
H=0
1domain  e,
domain
0
2,3
volume 
1,2,3
Induced magnetostriction:
1 
e
3
2e
3

e
2,3   1  
2
3
H
1  2  e
Ms
spontaneous magnetization
M0
saturation magnetization
e
spontaneous strain within a single domain
ε1,2,3
principal strains
Barkhausen Noise
B
H=0
H
domain wall
movement
H
Barkhausen noise
Amplitude
magnetic field
• magnetic Barkhausen noise
• acoustic Barkhausen noise
Time
Curie Temperature
 
Curie-Weiss law:
C
T  TC
χ
magnetic susceptibility
C
material constant
T
temperature
TC
Curie temperature
ferromagnetic materials (T < TC):
1.2
1.0
Ms / M0
typical alloy
0.8
typical pure metal
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
T / TC
1.0
1.2
1.4
4.4 Magnetic Flaw Detection
Magnetic Flux Leakage
exciter coil
sensor
(small coil,
Hall cell, etc.)
ferromagnetic test piece
Advantages:
Disadvantages:
fast
material sensitive
inexpensive
poor sensitivity
large, awkward shaped specimens (particle)
poor penetration depth
Magnetic Boundary Conditions
Gauss' law:
Ampère's law:
 B0
 H  J
xn
xn
medium II
medium II
BII
II
II
BII,n
BI,t
boundary
BII,t
BI,n
HII
HI,t
xt
BI I
HII,n
xt
HII,t
I
HI,n
HI
medium I
medium I
BI,n  BII,n
H I,t  H II,t
I H I,n  II H II,n
tan I H I,n  tan II H II,n
tan I
tan II

I
 II
Magnetic Refraction
BII
tan I
tan II

I
 II
II
Nonmagnetic Angle, θII [deg]
90
µI/µII =
75
medium II
(air)
10
30
100
60
45
I
30
medium I
(ferromagnetic)
BI
15
0
0
15
30
45
60
75
Ferromagnetic Angle, θI [deg]
90
BII
II
medium II
(air)
BI
medium I
(ferromagnetic)
I
Exciter Magnets
air gap
ferromagnetic core
electromagnet
 H d  N I  MMF
H
magnetic field
  0 r H A
N
number of turns
I
excitation current
MMF
magnetomotive force
Φ
magnetic flux
MMF

ℓ
length of flux line
µ0 µr
magnetic permeability
1 d
1

 i

0  r A
0 i ri Ai
A
cross section area
Rm
magnetic reluctance
MMF  
Rm 
Rm 

d
0  r A
Yoke Excitation
N
I
Detection Methods:
electromagnet
magnetometer
magnetic particle
(gravitation, friction, adhesion,
cohesion, magnetization)

magnetic particle with ultraviolet paint

coil

Hall detector, GMR sensor

fluxgate, etc.
Normal Magnetic Field
Tangential Magnetic Field
crack

Lateral Position
Lateral Position
Subsurface Flaw Detection
B
2
1
H
saturation greatly reduces the differential permeability
low magnetic field
high magnetic field
crack
crack