DEPTH PROFILING OF MACHINED SURFACES USING CROSS
CORRELATION OF BARKHAUSEN NOISE BUTTERFLY
CURVES
N. Meyendorf4 andH. Roesner2
University of Dayton Research Institute - Center for Materials Diagnostics,
University of Dayton, 300 College Park, Dayton, OH 46469-0121
2
Fraunhofer Institute for Nondestructive Testing IZFP, Saarbrucken, Germany
ABSTRACT. The Barkhausen noise technique was used to characterize machined surfaces of
small diameter tensile specimens. The Barkhausen noise butterfly curves measured for
specimens with different surface finishing (grinding, lathe working) at several different
analyzing frequencies were compared to those obtained on electro-polished specimens.
Microstructure modifications at the surface by machining are the reason for a complex structure
of the butterfly curves, especially, those achieved at high analyzing frequencies. A new
analyzing technique was developed based on cross correlation of a Barkhausen noise butterfly
curve with a curve of a reference material. Depth profiling results achieved by this method
showed excellent agreement with x-ray diffraction measurements.
INTRODUCTION
Depth profiling of property gradients like hardness or stress is a challenge for
NDE. State-of-the-art techniques are based on multi-parameter approaches, which
require an empiric calibration on calibration specimens with known property gradients.
Usually, 6 to 10 calibration specimens are required for proper calibration of the
instrument. These calibration specimens should be identical to the specimen under
examination (same base metal properties, same surface and same shape) [1]. For many
applications, such a set of calibration specimens is not available or is very expensive.
Therefore, techniques, which require only a reduced calibration expenditure, could be
very beneficial for NDE.
If the measured NDE parameter will change linearly with the property to be
measured, it should be sufficient to know the signal response of the NDE method for the
surface of the test specimen and the base material of the test specimen. The depth
information should be obtained from methods that determine NDE parameters with
variations in penetration depth, like multi-frequency eddy current or a frequency
analysis of the Barkhausen noise signal. Unfortunately, all parameters measured with
these above electromagnetic techniques are strongly nonlinear [2]. The following
experiments will demonstrate that the cross correlation of Barkhausen noise butterfly
curves may be suitable for generating such a linear signal response, which is required
for reconstruction of a depth profile of residual stress or another material properties.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
1697
2.8
2.6
Half-width in °2Theta
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0
20
40
60
80
Distance to Surface in µm
100
120
100
Residual Stress in MPa
0
-100
-200
-300
-400
E
(ground)
c
-500
-600
0
D
(r = 0,25; S = 900 m/m in; w ith chilling)
(rEF ~ 0,25; S = 900 m/min; with chilling)
(r = 0,4; Ss = 1500 m/m in; w ith chilling)
E 0,4; = 1500 m/min; with chilling)
(r-p=
(r = 0,25; S = 1500 m /m in; without chilling)
E 0,25; S = 1500 m/min; without chilling)
(r-jj,=:
(r = 0,4; S = 1500 m /m in; without chilling)
E
A
A
B
B
C
20
40
60
80
D istance to Surface in µm
100
120
FIGURE
FIGURE1:1:X-ray
X-raydefraction
detractionresults
resultsofofmachined
machinedmini
minitensile
tensilespecimens
specimens[3].
[3].
EXPERIMENTS
EXPERIMENTS
Specimen
SpecimenPreparation
Preparationand
andDestructive
DestructiveCharacterization
Characterization
The
TheBarkhausen
Barkhausennoise
noisetechnique
techniquewas
wasused
usedtotocharacterize
characterizesurface
surface damage
damage due
due to
to
machining
machiningofofminiaturized
miniaturizeddogbone
dogbone specimens.
specimens. When
When test
test material
material isis limited
limited and
and
specimens
specimensmust
mustbebemachined
machinedwith
withdiameters
diametersless
lessthan
than22mm,
mm, surface
surface modifications
modifications can
can
have
havea asignificant
significanteffect
effectononmechanical
mechanicalparameters
parameterstotobe
bedetermined.
determined. The
The specimens
specimens in
in
the
thecurrent
currentstudy
studywere
weremachined
machinedfrom
fromfine
finegrain
grainferritic
ferritic steel.
steel. The
The steel
steel was
was tempered
tempered
and
andaged,
aged,resulting
resultinginina abainitic,
bainitic,martensitic,
martensitic,microstructure.
microstructure. Small
Small tensile
tensile specimens
specimens
with
witha adiameter
diameterofof2 2mm
mmand
andananeffective
effective length
lengthofof26
26mm
mmwere
were prepared
prepared from
from these
these
materials.
materials.The
Thefollowing
followingtechniques
techniqueswere
wereused
usedfor
forthe
thesurface
surfacefinishing:
finishing:
••
••
••
••
Electro-polishing,
Electro-polishing,
Grinding,
Grinding,
Latheworking
workingwith
withchilling,
chilling,
Lathe
Latheworking
workingwithout
withoutchilling.
chilling.
Lathe
Metallographicand
andscanning
scanningelectron
electronmicroscopic
microscopic examinations
examinations indicated
indicated that
that
Metallographic
by
lathe
working,
a
surface
layer
of
up
to
80
um
is
damaged
and
grinding
damages
by lathe working, a surface layer of up to 80 µm is damaged and grinding damages
approximatelya asurface
surfacelayer
layerofof77µm.
|im. Electro-polishing
Electro-polishing isis expected
expected to
to be
be the
the only
only
approximately
technique,
which
does
not
generate
surface
damage
so
that
material
properties
at
the
technique, which does not generate surface damage so that material properties at the
surface
should
be
identical
to
the
bulk
material
properties.
Figure
1
shows
the
results
of
surface should be identical to the bulk material properties. Figure 1 shows the results of
1698
Analyzing frequency fa = 1kHz - 10 MHz
Analyzing frequency fa = IkHz -10 MHz
Electrodes
Electrod
I2
x1, σ1
H2
x2, σ2
H1, I2
Sensor Gap
Electromagnet
Coil, Magnetization Frequency fs = 1 - 300 Hz
Coil, Magnetization Frequency fs = 1 - 300 Hz
FIGURE
data analyses.
analyses.
FIGURE2:2:Experimental
Experimentalsetup
setupand
andprinciple
principle of
of data
the
specimens. The
Theresults
resultsindicate
indicatestrong
stronggradients
gradients
thex-ray
x-raydiffraction
diffraction studies
studies of
of similar
similar specimens.
ininstresses
and
especially
compressive
stresses
close
to
the
specimen
surfaces;
half
stresses and especially compressive stresses close to the specimen surfaces; thethe
half
width
the depth
depth of
of damage
damageand
andplastic
plasticdeformation
deformation
widthofofthe
thedetected
detected x-ray
x-ray line
line shows
shows the
generated
From both
both viewgraphs,
viewgraphs,ititisisobvious
obviousthat
thatthethe
generatedby
bythe
the machining
machining process.
process. From
highest
working with
with chilling
chillingand
andthe
thelowest
lowestdamage
damage
highestdamage
damageisis generated
generated by
by lathe
lathe working
resultsfrom
fromgrinding
grinding[3].
[3],
results
BarkhausenNoise
NoiseExperiments
Experiments
Barkhausen
Barkhausennoise
noiseisis generated
generated in
in ferromagnetic
is is
Barkhausen
ferromagneticmaterials
materialsififthe
themagnetization
magnetization
changed
by
an
external
field.
Movement
and
jump
of
Bloch
walls
generate
internally
changed by an external field. Movement and jump of Bloch walls generate internally
localizededdy
eddycurrents,
currents,which
which can
can be
be detected
detected as
onon
toptop
localized
as pulses
pulseswith
withananinductive
inductivesensor
sensor
of
the
specimen
surface.
The
noise
generated
during
demagnetization
processes
has
a a
of the specimen surface. The noise generated during demagnetization processes has
broad frequency spectrum from several kilohertz up to several megahertz [1, 4].
broad frequency spectrum from several kilohertz up to several megahertz [1, 4].
Therefore, the variation of the analyzing frequency should allow extracting information
Therefore, the variation of the analyzing frequency should allow extracting information
of different surface layer depth of the inspected material.
of different
layer depth
the inspected
material.
Ansurface
electromagnet
wasofused
to magnetize
the specimens periodically and to
An
electromagnet
was
used
to
magnetize
the specimens
generate the Barkhausen noise (Figure 2). A disadvantage
of thisperiodically
technique isand
the to
generate
the
Barkhausen
noise
(Figure
2).
A
disadvantage
of
this
technique
is
generation of stray fields at the interfaces between the pole shoes and the specimen thatthe
generation
stray
fields at signal.
the interfaces
between
pole shoes
specimen
that
can affectofthe
measuring
Therefore,
this the
technique
does and
not the
allow
scanning
can
affect
the
measuring
signal.
Therefore,
this
technique
does
not
allow
scanning
across the surface. A new magnetization principal to generate Barkhausen noise was
across
surface.
A new magnetization
principalwere
to generate
was
used the
to image
inhomogeneities.
Two electrodes
attachedBarkhausen
to the endsnoise
of the
used
to
image
inhomogeneities.
Two
electrodes
were
attached
to
the
ends
of
specimens. The magnetization current between 10A and 40A through the specimenthe
specimens.
magnetization
current between
10A and
the specimen
generates a The
magnetic
field in circumferential
direction.
An40A
audiothrough
sensor close
to the
generates
a magnetic
fieldwas
in circumferential
direction.
An signal
audio was
sensor
close to
to athe
surface of
the specimen
used to detect the
noise. The
overlaid
surface
of theoscillating
specimenvoltage
was used
to detect
theoscillating
noise. The
signalfield
wasand
overlaid
to a
periodically
generated
by the
magnetic
its upper
harmonics. oscillating
The Barkhausen
noise
has been
by frequency
filtering
a high
periodically
voltage
generated
byextracted
the oscillating
magnetic
field with
and its
upper
harmonics. The Barkhausen noise has been extracted by frequency filtering with a high
1699
M [V]
M [V]
Electropolished
7
fA = 10 MHz
6
f A =10MHz
fA = 40 -60 kHz
Ground
6
Lathe worked
-10
Lathe worked
4
3
3
2
2
1
1
-20
Ground
5
5
4
-30
Electropolished
7
M[VJ
00
00
0
10
20
-30
30
-20
-
-10
10
H [A/cm]
20
30
H [A/cm]30
20
H[A/cm]
FIGURE 3: Barkhausen noise butterfly curves for the specimens with different surface finishing for a
Barkhausen
curves for
the specimens
with different surface finishing for a
veryFIGURE
high (10 3:
MHz)-left
and noise
a low butterfly
(40-60kHz)-right
analyzing
frequency.
very high (10 MHz)-left and a low (40-60kHz)-right analyzing frequency.
pass filter. This signal is then rectified and analyzed as a function of the time dependent
pass filter.
signal(see
is then
rectified
analyzed
a function
the to
time
dependent
magnetic
fieldThis
strength
Figure
2). and
A Hall
probeassensor
was of
used
measure
the
magnetic
field
strength
(see
Figure
2).
A
Hall
probe
sensor
was
used
to
measure
the
tangential magnetic field. The resulting curves, with these characteristic butterfly
tangential
magnetic
field.
The
resulting
curves,
with
these
characteristic
butterfly
shapes, were analyzed in terms of the amplitude maximum and by the shape of the
shapes,
were
analyzedtechniques
in terms of
amplitude
maximum and by the shape of the
curve
due to
correlation
(seethenext
paragraph).
curveItdue
to
correlation
techniques
(see
next
paragraph).
was necessary to analyze the Barkhausen noise with different analyzing
It to
was
necessary
to analyze the
Barkhausen noise
withused
different
analyzing
frequencies
obtain
depth information.
A narrow-band
filter was
to extract
noise
frequencies
to
obtain
depth
information.
A
narrow-band
filter
was
used
to
extract
noise
from only one analyzing frequency or frequency range. With the digital signal
from only one analyzing frequency or frequency range. With the digital signal
acquisition system used for the experiments the whole Barkhausen noise spectrum was
acquisition system used for the experiments the whole Barkhausen noise spectrum was
obtained during one measurement. Frequency analysis was performed later by digital
obtained during one measurement. Frequency analysis was performed later by digital
signal processing. Characteristic butterfly curves have than been calculated for the
signal processing. Characteristic butterfly curves have than been calculated for the
different
differentanalyzing
analyzingfrequencies.
frequencies.The
Thebutterfly
butterflycurves
curvesmeasured
measured from
from late
late worked
worked and
and
ground
specimens
showed
very
complex
structure,
especially,
for
high
ground specimens showed very complex structure, especially, for high analyzing
analyzing
frequencies
(see
Figure
3)3)
due
frequencies
(see
Figure
duetotothe
theheavy
heavysurface
surfacedamage
damagegenerated
generated by
by the
the machining
machining
process.
process.
RESULTS
AND
DISCUSSION
RESULTS
AND
DISCUSSION
and HCM
TheThe
conventional
conventionalBarkhausen
Barkhausennoise
noiseanalyzing
analyzingtechnique
technique using
using M
MMax
Max and HCM
cannot
reflect
the
complex
structure
of
the
curves
shown
in
Figure
3.
However,
cannot reflect the complex structure of the curves shown in Figure 3. However, the
the
curves
forfor
different
analyzing
frequencies
curves
different
analyzing
frequenciescontain
containuseful
usefulinformation
information for
for depth
depth profiling.
profiling.
Therefore,
a new
data
processing
Therefore,
a new
data
processingtechnique
techniquewas
wasdeveloped
developedtotoanalyze
analyze the
the Barkhausen
Barkhausen
noise
curves.
idea
was
noise
curves.The
The
idea
wasto tocompare
comparea anoise
noisebutterfly
butterflycurve
curvetotothe
the curve
curve from
from the
the
undamagedreference
referencematerial.
material. The
Theelectro-polished
electro-polished specimen
specimen was
was chosen
chosen as
as this
undamaged
reference
material.
reference
material.
It is
well
knownin inelectrical
electricalengineering,
engineering,that
thatcross
cross collation
collation techniques
techniques are
are
It is
well
known
useful
compare
two
signalsand
andget
geta ametric
metricofofsimilarity
similarity[5].
[5]. The
Theparameter
parameter K
K as
as aa
useful
to to
compare
two
signals
function
a cross
correlation
functionofoftwo
twodata
datasets
setsx(i)
x(i)and
andy(i)
y(i)(formula
(formula 1).
1).
function
of of
k isk aiscross
correlation
function
å [( x(i) − x
m
) * ( y (i − k ) − y m )]
i
K(k)= =
K(k)
å ( x(i) − x
i
m
)2
å ( y (i − k ) − y
m
)2
i
Barkhausen-noise
butterfly
curves
and M2, we can simplify:
ForFor
twotwo
Barkhausen-noise
butterfly
curves
MMI
1 and M2, we can simplify:
1700
(1)
M [V]
M[V]
Cross correlation to
reference curve
Cross
correlation to
M
1(H)
reference
curve
Reference curve M1(H)
(electropolished)
, Reference curve Mj(H)
(electropolished)
1
K
KMax
0.8
0.6
0.6
- 30
- 20
-10
0
10
20
30
H [A/cm]
0.4
H[A/cm]
Original BN Curves
M(H)
Original BN Curves M(H)
0.2
k
0
-1200
-800
-400
0
400
800
1200
Cross Correlation Function K(k)
Cross Correlation Function K(k)
FIGURE 4: Barkhausen butterfly curves for specimens that where lathe worked with and without
FIGURE 4: Barkhausen butterfly curves for specimens that where lathe worked with and without
chilling in comparison to electro-polished material and cross correlation between lathe worked and
chilling in comparison to electro-polished material and cross correlation between lathe worked and
electro
polished
(reference)
material.
electro
polished
(reference)
material.
K(k)
=
K(k)=
E1 =
1
E1 E 2
åM
1
(H ) ⋅ M 2 (H − k )
H
å M 1 2(H)
E2 =
H
å M 2 2(H)
(2)
(2)
H
formula
a simplificationforforBarkhausen
Barkhausen noise
noise butterfly
butterfly curve
TheThe
formula
(2) (2)
is aissimplification
curvedata
datasets.
sets.
formula
applied
comparethetheBarkhausen
Barkhausen noise
noise curves
curves for
The The
formula
waswas
applied
to to
compare
for lathe
lathe worked
worked
without
chilling(M(M
) to the Barkhausen noise reference curve MI
metalmetal
withwith
andand
without
chilling
2) 2 to the Barkhausen noise reference curve M1
(electro-polished)
in
Figure
4.
(electro-polished) in Figure 4.
Because
of the
symmetry
Barkhausennoise
noisebutterfly
butterfly curves,
curves, the
Because
of the
symmetry
of of
Barkhausen
the peak
peakofofthe
the
cross correlation function should be located at k = 0. Because of small asymmetries of
cross correlation function should be located at k = 0. Because of small asymmetries of
the Barkhausen noise curves, the center peak of the cross correlation function is shifted.
the Barkhausen
the center
peak that
of the
cross
is shifted.
The two sidenoise
peakscurves,
corresponds
to k values
reflect
thecorrelation
shift of thefunction
Barkhausen
noise
The peak
two side
peaks
corresponds
to
k
values
that
reflect
the
shift
of
the
Barkhausen
noise
that means the shift of HCMpeak that means the shift of HCM.
00
1-Kmax [in %]
0
-0.02
-0.02
„ -0.04 -
100
50
50
100
150
150
-0.04
^ -0.06-0.06
7 -0.08 -0.08
J -0.1 -
——•• grinding
*"-0.1
-0.12
——•grinding
without chil.
——A with chil.
-0.14 -0.12
without chil.
with chil.
-0.16
-0.14
Penetration depth [in mico-meter]
-0.16
FIGURE 5: Maximum of the cross-correlation as function of the eddy current penetration depth
Penetration depth [in mico-meter]
calculated from the analyzing frequency.
FIGURE 5: Maximum of the cross-correlation as function of the eddy current penetration depth
calculated from the analyzing frequency.
1701
10 -
7
l=j
£
*V
14 12 10
8
6
4
A
-
X"
AX*£
* grinding
• without chil.
2 - S&
A with chil.
jS
0 - ————— n-—————,—————,——-——i
0
100
200
300
4(
Av. Res. Stress [in MPa(-1)l
FIGURE 6: K^ compared to the average residual stress in a surface layer equal to the calculated eddy
current penetration depth.
We selected the maximum amplitude of the cross correlation function Kmax as a metric
for similarity for the Barkhausen noise curves. Kmax was calculated for several butterfly
curves measured at the analyzing frequencies 10 MHz, 2.5 MHz, 0.4 MHz, 150 kHz
and 50 kHz. In Figure 5, these results are displaced as the function of the calculated
eddy current penetration depth that corresponds to the analyzing frequency. For a better
comparison to the x-ray results in Figure 1, the difference of 1 minus Kmax is displayed.
Figure 6 compares these results to the average residual stresses for the corresponding
surface layer calculated from the x-ray diffraction measurement. An excellent linear
correlation was found between the average residual stresses, calculated from the x-ray
diffraction measurements and the correlation coefficient of the Barkhausen noise
butterfly curve for the same surface layer.
The data analysis procedure discussed above includes two major simplifications:
•
•
A constant sensitivity for the whole surface layer corresponding to the eddy
current depth for the Barkhausen noise technique is assumed.
By calculating the eddy penetration depth, a constant permeability has to be
assumed.
Both are very rough approximations to reality. However, this excellent linearity
can allow us to determine depth profiles of residual stresses and probably also other
material quantities by only two measurements without a complex calibration procedure.
SUGGESTED PROCEDURE FOR DEPTH PROFILING
Based on the above results, we suggest the following procedure for depth
profiling of ferromagnetic material:
Two Barkhausen noise butterfly curves are measured for a wide frequency range
and stored in a digital data processing system. One curve is from a specimen that
represents the base metal properties PQ. The other is the specimen with the unknown
property gradient below the surface P(z). The stress (or any other property that has to
be determined) has to be measured by a conventional technique (for example, x-ray
diffraction) for the reference specimen (P0) and for the surface of the unknown
1702
specimen (Pg). Barkhausen butterfly curves for different analyzing frequencies are
calculated from the original date for both the reference material and the specimen to be
inspected. The cross correlation function is now calculated for each pair of butterfly
curves resulting from the same analyzing frequency for the unknown specimen and the
reference material. The peak values of the correlation functions Kmax depend upon the
analyzing frequencies and the corresponding material depth z calculated from the eddy
current penetration depth Kmax(z). Kmax for the highest analyzing frequency is assumed
to be characteristic for the surface property PS and called Ks. The property gradient to
be measured P(z) (for example the stress gradient) can now be calculated by the
following formula (3):
P(z) - (Ps -Po)*[(l-KM(z)) /(1-Ks)] + Po
(3)
P(z) is the average of the measured property for the surface layer with the thickness z.
A deconvolution is required to calculate the real property gradient.
SUMMARY
Barkhausen noise technique was employed to characterize the surface of small
tensile test specimens. The butterfly curves have proven to be very sensitive to
microstructure modifications and stress gradients at and close to the surface due to the
machining process. Especially, for high analyzing frequencies, the Barkhausen noise
butterfly curves show characteristic variations in shape, which are not analyzed using
the conventional Barkhausen noise method. A new analyzing technique based on crosscorrelation of Barkhausen noise butterfly curves was developed. This technique
compares the butterfly curve of the inspected specimen to the one of a known reference
material (for example, an electro-polished specimen). Depth profiling can be achieved
by variation of the analyzing frequency of the Barkhausen noise signal. The calculated
frequency dependent and depth dependent maximum of the correlation function
KMaxShowed a linear relation to the average stress in the surface layer measured by the
x-ray diffraction technique. This linearity of the cross correlation parameter is the basis
to calculate surface gradients without a large set of calibration specimens.
ACKNOWLEDGEMENTS
Research was sponsored by the German Reactor Safety Program and conducted
at the Fraunhofer Institute for Nondestructive Testing. The authors acknowledge Dr.
Schmidt and Dr. Pfeiffer from the Fraunhofer IWM for preparing the samples,
mechanical, metallographic, and x-ray tests, as well as Dr. Altpeter and Melanie Kopp
from IZFP for supporting the Barkhausen noise experiments and discussing the results.
The authors also acknowledge Dr. Victoria Kramb and Cindy O'Brien for help
preparing this paper.
REFERENCES
1. I. Altpeter, W.A. Theiner and B. Reimringer: "Harte- und
Eigenspannungsmessungen mit magnetischen zerstorungsfreien Prufverfahren "; in
1703
"Eigenspannungen", ed. V. Hauk, Dt. Gesellschaft fur Metallkunde, pp. 83-103
(1983).
2. S. Tiitto: "Magnetic Methods; Handbook of measurements of residual stresses'^
SEM, The Fairmont Press, Inc.
3. M. Kienzler, "Untersuchung von Einflussen aus der Herstellung und Bearbeitung
kleiner Zugproben aufdas Spannungs-Dehnungsverhalten "9 Master Theses, IWM,
Freiburg (1996).
4. J. Bender, <fBarkhausen Noise and Eddy Current Microscopy (BEMI): Microscope
Configuration, Probes and Imaging Characteristics"; Review of Progress in
Quantitative Nondestructive Evaluation, Vol. 16, (1997).
5. H. Kronmiiller:, "Methodender Mefitechnik"\ Schnacker-Verlag, Karlsruhe, 2.
Edition (1984).
1704