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Materials Science and Engineering A313 (2001) 145 – 152
www.elsevier.com/locate/msea
Magnetic and X-ray diffraction measurements for the
determination of retained austenite in TRIP steels
L. Zhao
a,b,
*, N.H. van Dijk
c
, E. Br¨ck
d
, J. Sietsma
b
, S. van der Zwaag
a,b
a
Netherlands Institute for Metals Research
,
P
.
O
.
Box
5008,
Rotterdamseweg
137,
GA Delft
,
The Netherlands
b
Laboratory for Materials Science
,
Delft Uni
ersity of Technology
,
Rotterdamseweg
137, 2628
AL Delft
,
The Netherlands
c
Interfaculty Reactor Institute
,
Delft Uni
ersity of Technology
,
Mekelweg
15, 2629
JB Delft
,
The Netherlands
d
Van der Waals
—
Zeeman Institute
,
Uni
ersity of Amsterdam
,
Valckenierstraat
65, 1018
XE
,
Amsterdam
,
The Netherlands
Received 6 June 2000; received in revised form 20 December 2000
Abstract
The accurate determination of the volume fraction of retained austenite is of great importance for the optimization of
transformation induced plasticity (TRIP) steels. In this work, two aluminium-containing TRIP steels are studied by means of
magnetization and X-ray diffraction (XRD) measurements. By fitting the field dependence of the approach to saturation in the
magnetization curves, the saturation magnetization is determined, which is linearly related to the volume fraction of retained
austenite. Moreover, information with respect to the microstructure can be obtained from the fitting parameters and the
demagnetizing factor for the magnetization curve. The volume fractions obtained from the magnetization measurements are
compared with data from XRD measurements. A discussion of the data suggests that magnetization measurements lead to more
reliable results and a more sensitive detection of the retained austenite than XRD measurements. © 2001 Elsevier Science B.V.
All rights reserved.
Keywords
: TRIP steels; Retained austenite; Magnetization; Microstructure
1. Introduction
austempering is the result of the suppression of the
formation of carbides during the bainitic transforma-
tion, due to the presence of the alloying elements such
as aluminium and silicon. The enrichment of carbon in
the austenite increases its thermal stability and conse-
quently, the austenite can be retained upon cooling to
room temperature [1 – 5].
A quantitative determination of the volume fraction
of the existing phases, especially the retained austenite,
is essential for the evaluation of the TRIP steel proper-
ties. Experimental methods that have been reported in
the literature include X-ray diffraction (XRD) [1 – 6],
neutron diffraction [7], optical microscopy combined
with image analysis [8], scanning electron microscopy
(SEM) [9], M¨ ssbauer spectroscopy [9,10], dilatometry
[11], and magnetization measurements [12,13]. A sum-
mary of the characteristics of these techniques is pre-
sented in Table 1. Among them, the XRD method is
the most frequently used as it is a suitable technique
and XRD facilities are widely available. Other tech-
niques are usually applied in order to overcome the
The development of steels during the last decade
have shown that transformation induced plasticity
(TRIP) steels constitute a new category of sheet or strip
steels, in terms of their high strength and enhanced
formability. These excellent mechanical properties
mainly arise from a martensitic transformation of
metastable retained austenite, induced by external
stress. The TRIP steels possess a multi-phase mi-
crostructure, consisting typically of ferrite, bainite and
retained austenite. The microstructure is formed after
intercritical annealing and a subsequent isothermal an-
nealing in the bainitic transformation region, called
austempering. The carbon content in austenite is en-
hanced both during the intercritical annealing and dur-
ing the austempering. The carbon enrichment during
* Corresponding author. Tel.: +31-15-2782268; fax: +31-15-
2786730.
E
-
mail address
: l.zhao@tnw.tudelft.nl (L. Zhao).
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S0921-5093(01)00965-0
146
L
.
Zhao et al
. /
Materials Science and Engineering A
313 (2001) 145–152
shortcomings of the XRD method. However, these
methods have their own limitations with respect to the
determination of the volume fraction of retained austen-
ite in the TRIP steels with a multi-phase microstructure.
For instance, the M¨ ssbauer spectroscopy measure-
ments require a very thin foil (20 – 50
from the approach to saturation and the demagnetizing
factor of the magnetization curve. The reliability and
accuracy of the measurements will be discussed, and
compared with the results obtained from the XRD
method.
m), which leads
to a different internal stress condition, in comparison to
bulk samples. This may influence the results, since the
retained austenite is very stress-sensitive. Dilatometry
measurements make it possible to detect the fraction of
transformed phase in-situ from the length change, but
the measurement accuracy is not high since the knowl-
edge of lattice parameters is limited and transformation
plasticity may also affect the net dilatation. Magnetiza-
tion measurements have intrinsic advantages as they are
accurate and probe the bulk of the materials.
The present work aims to determine the volume
fraction of retained austenite in TRIP steels by means of
magnetization measurements. Furthermore, informa-
tion with respect to the microstructure can be obtained
2. Background
Magnetic methods, such as magnetization measure-
ments and thermo-magnetic analysis, are often used in
metallurgical studies [13]. In magnetization measure-
ments, the saturation magnetization can be obtained
from the magnetization curve. The difference in satura-
tion magnetization of specimens with and without
austenite is directly related to the volume fraction of
non-ferromagnetic retained austenite. This is due to the
fact that ferrite, as well as martensite and cementite, is
ferromagnetic at temperatures below the Curie tempera-
ture (for pure ferrite
T
C
=770°C and for cementite
T
C
=210°C), while the austenite is paramagnetic [14].
The magnetization measurements give a relation be-
tween measured magnetization (
M
) and applied mag-
netic field (
H
), as schematically shown in Fig. 1. One
can distinguish three different parts of the curve. In the
first part, indicated by the line ‘ab’, the relation between
M
and
H
is almost linear. In this field region, the
magnetic field inside the sample is reduced by the stray
fields of the magnetized sample. The inverse of the
initial slope is the so-called demagnetizing factor, which
depends on the shape of the sample, on the volume
fraction of the existing phases, as well as on their
microstructure. In the case of a microstructure consist-
ing of a continuous ferromagnetic matrix, in which
inclusions of phases with different magnetic properties
are embedded, the effective demagnetizing factor,
N
eff
,is
estimated by [15,16],
Table 1
A comparison of the characteristics of different techniques for an
analysis of the volume fraction of retained austenite
Observed
Probed volume
Accuracy
quantity
X-ray
Diffraction
Surface layer
Normal
diffraction
peaks
Neutron
Diffraction
Bulk
Normal
diffraction
peaks
Metallography/
SEM
Color-etched
Surface layer
Low
grain
M¨ ssbauer
Transmission
Thin foil
High
Magnetization
spectra
Saturation
Bulk
High
Dilatometry
magnetization
Length change
Bulk
Low
N
eff
=(1−
f
)
N
m
+
fN
p
(1)
Fig. 1. Schematic illustration of the magnetization curve.
where
f
is the volume fraction of the inclusions, for
example, the retained austenite or the cementite. The
so-called macroscopic demagnetizing factor,
N
m
, de-
pends on the sample shape, and decreases with increas-
ing the dimensional ratio (
r
) between the length and the
width of the sample when the field is applied along the
length of the sample. The microscopic demagnetizing
factor,
N
p
, represents the shape anisotropy of the inclu-
sions and their orientation distribution [13]. For in-
stance,
N
p
=0 if needle-like or plate-like inclusions are
oriented with the long axis parallel to the magnetization
direction. When the inclusions are randomly oriented,
an average value of
N
p
=1/3 is expected, independent of
the shape. A deviation from
N
p
=1/3 is, therefore, a
sign of texture inside the sample, but not vice versa,
because
N
p
=1/3 when the shape of the inclusions is
spherical.
L
.
Zhao et al
. /
Materials Science and Engineering A
313 (2001) 145–152
147
Table 2
Chemical composition (wt.%) of the TRIP steels Al1.8 and Al1.4P
a
Code
C
Mn
Al
Si
P
N
Ac
1
Ac
3
Al1.8
0.20
1.53
1.8
0.02
0.005
0.004
761
1037
Al1.4P
0.18
1.52
1.4
0.02
0.081
0.0055
747
1017
a
The starting and finishing temperatures of the ferrite to austentie transformation, Ac
1
and Ac
3
(°C), have been determined by dilatometry
experiments [21].
The second part of the curve, indicated by ‘bc’ in Fig.
1, is the transition region characterized by domain wall
movements and the reorientation of spins following the
domain wall movement. The characteristics of the tran-
sition thus depend on the existing preferred orientation
(texture). The approach to saturation, shown as the line
‘cd’ in Fig. 1, is used for the determination of the
volume fraction of retained austenite. In this region, a
rather large increase in
H
is required to produce a
relatively small increase in
M
. This behavior is associ-
ated with microstructural effects, and depends on rota-
tions and reorientation of spins. The approach to
saturation is usually described by [13,17]
3. Experimental
1−
H
−
H
2
The two aluminium containing TRIP steels examined
in this investigation were produced via hot rolling and
air cooling, and had an as-received thickness of 6 mm.
The composition of the materials is shown in Table 2.
The materials were machined to cylinders with a diame-
ter of 5 mm and a length of 10 mm for heat treatments
under vacuum in an 805a type B¨ hr dilatometer. In
order to design the appropriate thermal schedules, the
transformation temperature (Ac
1
and Ac
3
) were deter-
mined by dilatometry. The results are listed in Table 2.
The samples were pre-annealed for 10 min at 900°C,
which is in the two-phase region, and then quenched at
25°Cs
−1
to 400°C, held at this temperature for 0, 0.5,
1.0, 1.5, 2.0, 3.0, 5.0 and 10.0 min, respectively, and
subsequently cooled at approximately 2°Cs
−1
M
=
M
s
(2)
where
M
s
is the saturation magnetization. The parame-
ters
a
(in A m
−1
)and
b
(in A
2
m
−2
) are positive
constants, which can be ascribed to different physical
origins. Parameter
a
arises from nano-scale microstruc-
tural effects such as inclusions, voids, point defect
and/or microstresses, and parameter
b
from the crystal
anisotropy.
The volume fraction of retained austenite,
f
, can be
determined by a comparison of the
M
s
values in the
austenite-containing sample,
M
s
(
c
), and in the austen-
ite-free sample
M
s
(
f
),
f
=
M
a
−
M
s
(
c
)
M
a
to room
=1−
M
s
(
c
)
M
s
(
f
)
(3)
temperature.
The magnetization measurements were performed in
a Quantum Design SQUID magnetometer (MPMS-5S).
In SQUID magnetization measurements, an applied
magnetic field is used to induce a magnetization in the
sample. The sample magnetization produces stray
fields, which are subsequently probed up to a very high
accuracy by a superconducting SQUID device. The
equipment is calibrated periodically with standard
nickel and palladium spheres (with a sensitivity of
1×10
−11
A·m
2
). During the measurement of the cylin-
drical sample, the magnetic field was applied to a
maximum value of 5 T (
H
=3.98×10
6
Am
−1
)and
then decreased stepwise to zero field, i.e. from 5 to 0.25
T in steps of 0.25 T, from 0.25 to0Tinsteps of 0.05
T. The measurements were performed in decreasing
field in order to create a well-defined field history for
the magnetization. The measuring temperature was reg-
ulated at 26.85
=
M
s
(
f
)/
M
a
is the ratio between the satura-
tion magnetization of the austenite-free sample and that
of ferrite (
M
a
). The austenite-free sample contains be-
sides ferrite also a small volume fraction of cementite,
which can be estimated from the composition of the
materials using the lever-rule. The coefficient
thus can
be obtained from the published data of the saturation
magnetization of the ferrite (
M
a
=1.714×10
6
Am
−1
[13] for pure iron) and cementite (
M
s
=0.99×10
6
0.05°C. The relative error of the mea-
sured data is smaller than 0.5%. As-received material
was considered to be austenite-free, which was confi-
rmed by XRD measurements. In order to fit the ap-
proach to the saturation of the measured magnetization
data and the physically significant parameters described
in Eq. (2), a linear least-squares fitting of the ‘cd’ line in
Fig. 1 is applied, and the fitting error is obtained from
the standard definition [20].
After the magnetization measurements, disks with a
diameter of 5 mm were cut along the transverse direc-
A
=1−
f
+
f
[
M
s
/
M
a
].
In the derivation of Eq. (3), it is assumed that the
amount of cementite precipitates is negligible after
austempering of the TRIP steels, since the addition of
alloying elements such as aluminium significantly sup-
presses the formation of cementite during the bainitic
transformation [1 – 5].
[18,19]) via the relation
where
m
−1
148
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Zhao et al
. /
Materials Science and Engineering A
313 (2001) 145–152
tion of the cylinder samples and polished for the XRD
measurements. Very low force was applied during cut-
ting and mechanical polishing in order to avoid stress-
induced transformation of the retained austentie. The
XRD measurements were performed on a Siemens’
X-ray diffractometer using CoK
0.2×10
6
Am
−1
and the fits
to Eq. (2) are shown in Fig. 2. From the fits, the
saturation magnetization
M
s
was obtained with a rela-
tive error less than 0.2%. It was found that the
M
s
values in the as-received steels (1.533×10
6
Am
−1
for
the Al1.8 sample and 1.475×10
6
Am
−1
for the Al1.4P
sample) were about 11 and 14% smaller than the
M
s
of
pure iron, which is 1.714×10
6
Am
−1
[13]. This is due
to the presence of cementite with a lower
M
s
, (leading
to a decrease of around 1%) and the addition of
alloying elements including carbon, manganese, alu-
minium, phosphorous and silicon in the TRIP steels, as
well as the sample size effect. Taking the dependence of
M
s
on composition as reported in literature [18,22] and
assuming no partitioning of the alloying elements, a
decrease of
M
s
of 7.2 and 6.2% is calculated for both
steel grades. Nevertheless, since
M
s
for the Al1.8 sam-
ple is larger than the one for the Al1.4P sample, the
decrease in
M
s
is not simply proportional to the
amount of aluminium, which is the main difference in
composition for these two steels. The effect of the third
factor leading to a decrease of the experimental value of
M
s
, viz. the relatively large sample size, was investi-
gated by measurements on cylindrical samples of 1 mm
in diameter and 2 mm in length. It was found that the
M
s
values in the small samples were approximately 3%
larger than those obtained from the large samples.
However, the sum of these three effects (11% for the
Al1.8 and 10% for the Al1.4P sample) is still lower than
the measured decrease of the
M
s
value for the Al1.4P
sample. This may be due to non-linear effects as the
alloys contain a combination of different elements.
The volume fraction of the retained austenite is cal-
culated from the saturation magnetization,
M
s
, using
Eq. (3). The coefficient
radiation. A more
detailed description of experimental conditions and re-
sults of the XRD measurements has been published
elsewhere [21].
4. Results
4.1.
Volume fraction of retained austenite
The magnetization as a function of the applied mag-
netic field was measured for both compositions and all
Fig. 2. Measured magnetization as a function of the applied magnetic
field for Al1.8 samples. The open circles represent the as-received
(AR) sample, the solid diamonds the sample without austempering (0
min), and open squares the sample with austempering at 400°C for 3
min. the lines correspond to fits with Eq. (2).
=
M
s
(
c
)/
M
a
is estimated to be
0.987 for the Al1.8 sample and 0.989 for the Al1.4P
sample, based on the chemical composition of the
materials in Table 2 and the published
M
s
values for
ferrite and cementite. It is interesting to note that the
value of
is insensitive to variations in
M
a
caused by
alloying elements as they affect
M
s
(
f
) in a similar way
for small concentrations. This is also true for the evalu-
ation of the fraction of retained austenite determined
by Eq. (3) as the alloying concentrations are equal in
the TRIP samples and the austenite-free sample.
Fig. 3 shows the calculated fraction as a function of
the austempering time in the Al1.8 and Al1.4P samples.
One can see that the fitting errors are nearly negligible,
since the standard deviation (S.D.) is 0.002, indicating
that the measured data are accurate with respect to the
determination of the volume fraction of retained
austenite, even though some deviations in the magne-
tization curve are observed. It is noteworthy that simi-
lar results, but with lower accuracy, are obtained when
the magnetization at the maximum applied magnetic
field is used instead of
M
s
in Eq. (3).
Fig. 3. The volume fraction of retained austenite
f
as a function of
austempering time. The experimental error is smaller than the symbol
size.
austempering times applied. Three representative mag-
netization curves at
H
L
.
Zhao et al
. /
Materials Science and Engineering A
313 (2001) 145–152
149
ues. One can also see that a higher aluminium concentra-
tion leads to a higher fraction of retained austenite. A
higher aluminium concentration also increases the hold-
ing time required to obtain the maximum. These two
trends may be related to each other, and are attributed
to the increased suppression of carbide formation with
increasing aluminium concentration.
4.2.
Relation between the M
–
H cur
e and the
microstructure
Fig. 4. Parameters a and b as a function of the austempering time at
400°C for the Al1.8 samples. ‘AR’ stands for the as-received sample.
In addition to providing the
M
s
value, the magnetiza-
tion measurements can also reveal information on the
microstructure. From the fitting procedure, one obtains
the microstructure related parameters,
a
and
b
,asde-
scribed in Eq. (2). Fig. 4 shows the variation of these
parameters during austempering and the errors resulting
from the fitting procedure for the Al1.8 samples.
Although the strong mathematical correlation be-
tween the two parameters affects the values obtained, it
may be concluded that the absolute values of
b
/
H
2
are
always smaller than those for
a
/
H
in the relevant range
for
H
. This indicates that domain rotation is more
influenced by nano-scale microstructural aspects, such as
voids, inclusions, point defects and microstresses, than
by the crystal anisotropy. The difference between
a
/
H
and
b
/
H
2
is smaller in the as-received than in the
as-quenched samples. This might be due to the decrease
in microstress and the fraction of inclusions as a result
of intercritical annealing. The difference between
a
/
H
and
b
/
H
2
increases during the bainitic transformation
before the maximum volume fraction, showing the in-
crease of microstress, and possibly the inclusions, result-
ing from the phase transformation.
In the low magnetic field range of the magnetization,
indicated by the ‘ab’ line in Fig. 1, the observed magne-
tization can be related to the presence of demagnetiza-
tion fields. The effective demagnetizing factor,
N
eff
,is
deduced from the inverse slope of the
M
–
H
curve in low
magnetic fields, as a function of the volume fraction of
retained austenite, and the results are shown in Fig. 5.
As can be seen, all demagnetizing factors range between
0.140 and 0.155. In the present cylindrical samples with
a height of 10 mm, a diameter of 5 mm and a high
permeability (10
2
Fig. 5. The effective demagnetizing factor
N
eff
as a function of
volume fraction of retained austenite
f
The dependence of the volume fraction on the austem-
pering time reveals valuable information regarding the
transformation behavior in the two steels. About 5.6 and
2.5% of austenite are retained in the as-quenched
(austempering time zero) Al1.8 and Al1.4P samples,
respectively. In the first stage of austempering, the
volume fraction retained austenite increases with in-
creasing austempering time, and reaches a maximum
value. This indicates that more austenite is retained as
a result of its increased stability due to the increased
carbon concentration. The carbon enrichment arises
from the suppression of carbide formation during the
bainitic transformation. For the annealing time leading
to the maximum in retained austenite, the carbon enrich-
ment moves the martensite starting temperature of the
austenite to a temperature below room temperature. For
longer annealing times, the fraction decreases, gradually
for the Al1.8 samples and more rapidly for the Al1.4P
samples. The martensite starting temperature is still
below room temperature, but the fraction of retained
austenite decreases as the bainitic transformation contin-
o
[13]), a geometrical demagne-
tizing factor,
N
m
, of 0.14 [13,18] is expected for a sample,
which is homogeneously magnetized along the cylindri-
cal axis. Further analysis of published data [13] reveals
that the derivative of the geometrical demagnetizing
factor with respect to the dimensional ratio
r
is d
N
m
/
d
r
=−0.075 in the vicinity of
r
=2. This indicates that
the shape differences in the samples due to the limited
accuracy of machining or due to the phase transforma-
tions during the heat treatment procedure [23] have a
negligible effect on
N
m
with respect to the measured
demagnetizing factor.
10
3
in Al1.8 and Al1.4P samples.
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