THE EFFECT OF PLASTIC DEFORMATION AND RESIDUAL
STRESS ON MAGNETIC BARKHAUSEN NOISE SIGNALS IN MILD
STEEL
Thana Rahim, Lynann Clapham
Department of Physics, Queen's University, Kingston, Ontario, Canada K7L 3N6
ABSTRACT. This study was conducted to investigate the effects of plastic deformation on
magnetic Barkhausen noise (MEN) signals in mild steel. A number of mild steel samples were
subjected to different degrees of uniaxial plastic deformation up to 30% strain. Angular MEN
measurements were done on those samples. The results indicated that plastic deformation introduces
a magnetic easy axis depending on the degree of plastic deformation. A significant progression
towards magnetic isotropy (no magnetic easy axis) was observed after heat-treating the samples at
low temperatures 450° C, 475° C, and 500° C. The activation energy associated with the anisotropy
decrease was calculated from the low temperature annealing results using an Arrhenius-type
analysis. This was found to be 99 Kcal/mol, which is consistent with recovery-type processes.
INTRODUCTION
Magnetic Barkhausen Noise (MEN) is a non-destructive technique used for
detecting residual and applied stress [1], determining a magnetic easy axis [2] and
evaluating microstructure characteristics such as grain size and carbon content [3]. MBN is
produced by abrupt changes in magnetization within ferromagnetic materials during the
application of a time varying magnetic field. These changes are produced by the
irreversible motion of domain walls when they move across pinning sites. Pinning sites
may be grain boundaries, inclusions, defects, dislocation tangles, etc. MBN is an effective
method for determining the stress state in ferromagnetic materials due to its high sensitivity
to elastic strain.
An important result of plastic deformation is the creation of elastic residual stresses
[4]. Stefanita's work [5] showed that for up to 40% strain in steels, the effects on MBN
were due entirely to residual elastic stresses introduced during plastic deformation.
Pipelines typically have an axial magnetic easy axis formed during pipe
manufacture. Earlier work [6] showed that low temperature 'stress relief heat treatments
(450-500°C) could reduce and eventually eliminate this easy axis, leaving the pipe wall
magnetically isotropic. In this earlier study, however, the degree of initial plastic strain
was not well characterized, since it resulted from the manufacturing process. The present
study was designed to introduce controlled uniaxial deformation (from 0-30% strain) into
well-characterized mild steel samples. The magnetic anisotropy was carefully studied as it
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
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developed during plastic deformation and then as it was gradually reduced and eliminated
during low temperature heat treatment.
EXPERIMENTAL METHOD
Sample Preparation
Fourteen hot rolled mild steel samples were obtained from a local supplier. The
mechanical properties of the material were a yield strength of 230 MPa, an ultimate tensile
strength of 303 MPa, and a Young's modulus of 200 GPa. Sample dimensions were 279
mm x 83 mm x 3mm. Samples were cut such that the longitudinal (applied stress) direction
coincided with the rolling direction. The samples were sanded to a 1200 grit finish using
progressively finer grade silicon carbide sand paper to produce a flat deformation free
surface for MEN measurements. An 800 kN capacity Riehle uniaxial tensile testing
machine was used to apply tensile loading. The samples were plastically deformed to levels
of plastic strain from 0% to 30%.
Magnetic Barkhausen Noise Measurements
The MEN experimental apparatus used to produce and measure the Barkhausen
noise signals is shown in Figure 1. An 800 turn primary coil of AWG 31 magnet wire was
wound around a ferrite U shaped steel laminate core. This was used to produce the
magnetic excitation field. The distance between the outside edges of the U core was 22
mm. A pick-up coil located between the poles of the U core magnet was used to detect the
MEN signals. The output of the pick-up coil was sent to a 10K gain preamplifier and
through a band pass filter (3-200 kHz). A personal computer that has a resident digital
oscilloscope board was used to collect and analyze the signals.
The MEN voltage pulses were analyzed by integrating the square of voltage with
respect to time. The parameter resulting from this analysis is termed the MBNEnergy.
In this work, an "angular" MEN measurement technique was used to determine the
magnitude and direction of the magnetic easy axis in each sample. This involved rotating
the MEN probe by angular increments of 10° around a fixed axis. The data is analyzed as a
polar plot, with data fitted using the following equation [7]:
MBN
(i)
Energy
L
Electromagnet
MBN pick-up Coil
FIGURE 1. Experimental set-up for measurement of magnetic Barkhausen noise.
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where 9 is the angle of the magnetic field with respect to the reference (rolling/applied
stress) direction, a is related to the angular dependent variation of the MEN measurement,
and P is the parameter associated with the isotropic background. A magnetic easy axis
coincides with the elongation direction of the angular MBNnnergy plot. The direction of this
easy axis (with respect to the reference direction) is<|).
Heat Treatment
After deformation and initial MEN measurements, samples were heat treated at
three different temperatures for periods of time ranging from 1 to 220 hours, followed by
air-cooling. The temperatures used in this work were 450°, 475°, and 500° C, temperatures
typically associated with stress relieving in steels [8-11].
Microstructure Examination
Samples were prepared for optical microscopy using standard techniques.
Microstructures are shown in Figure 2 for the a) undeformed sample, b) 30% plastically
deformed sample, and c) 30% plastically deformed and annealed sample. A typical
ferrite/grain boundary pearlite steel microstructure was observed in all cases. All three
samples were microstructurally identical as viewed with an optical microscope, with no
observable changes due either to deformation or heat treatment.
FIGURE 2. Photomicrographs of (a) Undeformed sample, (b) 30% plastically deformed sample before
annealing, (c) 30% plastically deformed sample after annealing for a period of 1 hour at 500° C and aircooled.
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RESULTS AND DISCUSSION
Figure 3 shows the polar plots of the angular MBNEnergy measurements for the
samples plastically deformed up to 30%. The solid lines in the figure represent the best fit
to equation 1. This figure indicates that the undeformed sample has no magnetic easy axis,
i.e. it displays isotropic magnetic behaviour. Subjecting the material to plastic deformation
introduces magnetic anisotropy into the material. The release of tensile loading creates a
compressive residual stress along the original stress axis (the axial direction). As seen in
Figure 3a, this compressive stress state in turn produces an easy axis in the transverse
direction [2] that progressively increases with higher deformation levels.
After deformation, samples were subjected to different low temperature "recovery"
annealing treatment from 450°-500 °C for one to 220 hours. As indicated previously in
Figure 2, the microstructure appears identical before and after these annealing treatments.
Figure 3b shows polar plots of the angular MBNEnergy results for the plastically deformed
samples after annealing the samples at 450 °C for a period of 220 h. This figure indicates
that annealing the sample at this low temperature has relieved much of the residual
compressive stress from the samples, resulting in a return to magnetic isotropy.
In order to characterize the extent of magnetic anisotropy a parameter termed
ratio is introduced, as described by the following equation [6]:
MBN Energy ratio = MBN Energy (e = 90°)
(2)
where 6 is the angle of the MBN excitation field with respect to the reference
(rolling/applied stress) direction. This equation describes the ratio of MBNEnergy along the
rolling direction to that in the transverse direction. Figure 4 shows the MBNEnergy ratios as a
function of strain, for the plastically deformed samples before and after annealing.
Annealing times were 220 hours at 450 °C, 84 hours at 475 °C and 1 hour at 500 °C. This
figure indicates that annealing the samples at 450 °C for up to 220 h produces only
moderate changes in the magnetic anisotropy, while annealing at higher temperatures (475
a)
b)
FIGURE 3. Polar plot of angular MBNEnergy variation for different plastic strains, a) after deformation but before
annealing the samples, b) after annealing the samples for a period of 220 hours at 450° C. The magnitude of
plastic strain is 2% (V), 9.8% (a), and 30% (•). Also shown is the angular MBNEnergy result for the undeformed
sample (•). The solid lines represent the lines of best fit to equation 2.
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——————-B-. ..6_......
annealing at 450° C
Plastic Strain %
FIGURE 4. Variation of MBNenergy ratio as a function of plastic strain before annealing the samples (o),
after annealing the samples for a period of 220 h at 450 °C (D), after annealing the samples for a period of 84
h at 475 °C (V), and after annealing the samples for a period of 1 h at 500 °C (•).
and 500°C) produces a more significant progression towards magnetic isotropy. It should
also be noted that the undeformed 'control' samples did not change with annealing,
remaining completely isotropic.
The activation energy for this process can be calculated from the annealing results
using an Arrhenius-type analysis similar to that used by Andeymi et al [10] for recovery
studies on extruded mild steel bar, and Clapham et al [9] for pipeline steels. From the
angular MBNEnergy plots it was possible to calculate the "time for a 50% reduction in
anisotropy", termed (T ), for each temperature, r was determined to be 1 h at 500 °C, 84
h at 475 °C, and 220 h at 450 °C. Using an Arrenius analysis, the equation:
T = AeXP i-RT
(3)
is plotted with In T vs 1/T (K"1). An Arrenius plot of the data is shown in Figure 5. The
slope of the line of best fit through the data is:
d(lnr)
R
Q
(4)
where R is the gas constant in cal/mole/K and Q is the activation energy in cal/mole. The
activation energy was calculated to be 99 Kcal/mole.
GENERAL DISCUSSION
As mentioned earlier, magnetic anisotropy is introduced
due to compressive
residual stresses created during unloading of the uniaxially deformed samples. Consistent
with earlier studies [2], this produces a magnetic easy axis in the transverse direction,
which is becomes more pronounced as the deformation increases. It is also possible for
MEN to change due to increasing dislocation density, however earlier work [5] indicated
that this does not occur in these steels for deformation levels below 30%.
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0.00142 »~
0.0014.
0.00138
0.00136
E
!
0.00134.
0.00132 •
0.0013.
0.00128 -
FIGURE 5. Arrhenius plot for various low temperature experimental data (450, 475, and 500 °C) exhibiting
temperature 1/T (K"1) as a function of time T(s) to the plastically deformed samples, 2% (A), 9.8% (•), and
30% (+), time for a 50% reduction in anisotropy.
The magnetic anisotropy can be reduced by subjecting the material to low
temperature heat treatments. This leads to stress relief due to dislocation rearrangement
through a mechanism termed polygonization. This is commonly known as 'recovery' in
metallurgical terminology. The temperature directly affects the recovery process, since
increasing temperature facilitates dislocation movement. These processes take place on a
very small scale in the microstructure and cannot be viewed optically, hence the lack of
microstructural changes in Fig. 2.
The earlier study of Andeyemi et al [10] identified an activation energy of 32-80
Kcal/mol for recovery processes in extruded mild steels. Later work on pipeline steels by
Clapham et al found that magnetic anisotropy changes were associated with an activation
energy around 100 Kcal/mol. This suggested that such anisotropy changes were due to
recovery processes leading to stress relief in these materials. The activation energy
determined from the present work (99 Kcal/mol) indicates that, again, recovery is the
mechanism responsible for the magnetic anisotropy changes in these mild steel samples.
We conclude that in these samples magnetic easy axis forms due to compressive residual
elastic stresses created during unloading after applied tensile plastic deformation.
Magnetic isotropy returns when the elastic residual stresses are relieved with low
temperature heat treatments.
SUMMARY
The magnetic anistotropy in mild steel samples was investigated using MEN
measurements. Samples were initially magnetically isotropic, yet developed a magnetic
easy axis after uniaxial deformation and unloading. Compressive residual stresses were
identified as the source of the magnetic anisotropy. These stresses, along with the
magnetic anisotropy, were removed by typical 'stress relieving' heat treatments. Activation
energy studies indicated that the return to magnetic isotropy was associated with recovery
processes in the microstructure.
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ACKNOWLEDGMENT
The authors would like to gratefully acknowledge the support of the Gas Research
Institute (now the Gas Technology Institute, GTI) Chicago, USA, Pipeline Inspection
International (PII)5 and the Natural Sciences and Engineering Council (NSERC) of Canada.
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