ISIJ International, Vol. 43 (2003), No. 3, pp. 378–385
Microtexture of Thin Gauge Hot Rolled Steel Strip
Roumen PETROV,1) Leo KESTENS,1) Patricia C. ZAMBRANO,2) Martha P. GUERRERO,2) Rafael COLÁS1,2) and
Yvan HOUBAERT1)
1) Department of Metallurgy and Materials Science, Ghent University, Technologiepark 903, B-9052 Zwijnaarde (Gent),
Belgium. E-mail: Roumen.Petrov@rug.ac.be
2) Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de
Nuevo León, A.P. 149-F, 66451 San Nicolás de los Garza, N.L., Mexico.
(Received on July 22, 2002; accepted in final form on October 23, 2002 )
A series of trials were conducted on a compact rolling mill to evaluate the properties and characteristics
of carbon steel strip hot rolled to less than 2 mm in thickness from thin cast slabs. Steels of two different
compositions were studied, the first one, a low carbon steel, was rolled to a total reduction ranging from 94
to 98 %, final thickness ranging from 1.06 to 2.69 mm, whereas the second one was a Nb bearing microalloyed steel rolled to a total reduction of around 96 %. The rolling trials were complemented by means of
computer modelling to get a deeper understanding of the process. It was found that the ferritic grain size of
the low carbon strips varied from 7 to 10 m m, with the finer sizes found in the thinner strips, the grain size
of the microalloyed steel was found to be 3.6 m m. Analysis of the texture of the hot rolled strips indicated
that the ferrite in the low carbon resulted from the transformation of recrystallized austenite, in comparison,
low intensity transformation texture from unrecrystallized austenite was found in the Nb bearing steel. The
observed texture data correlate with the R-values measured.
KEY WORDS: hot rolling; steel; texture; microstructure.
{113}具110典 texture component has detrimental effects on
both characteristics. A number of studies has proven that
the {332}具113典 transformation texture component sharpens
when the substitutional solutes, like Mn and Ni, are added
to the steel together with Nb,2,3) when the cooling rate increases3–5) and when the austenite grain size decreases.3)
Improvements in thin slab casting, hot direct charging together with hot rolling techniques and practices have resulted in the production at an industrial scale, of hot rolled
strips of gauges thinner than 2 mm. Such processing implies that the reductions of thickness in the originally cast
slab is higher that 96 %. Furthermore, hot direct charging of
thin cast slab does not permit the common isotropic transformations that take place in conventionally processed material.6)
The goal of the present work is to study the influence of
processing parameters on the microstructure and texture of
two carbon steels, one plain and the other with Nb addition,
which were cast into thin slabs and hot rolled in a compact
strip mill to different final thickness.
1. Introduction
The standard processing route for steel strips thinner than
2 mm with narrow dimensional tolerances and high surface
quality includes, as a rule, hot rolling, pickling, cold rolling
and annealing. The main functional properties for cold
rolled and annealed steel strips are their strength, toughness
and formability. The latter is often characterized by the
deep drawability of the material, which strongly depends on
the texture of the steel sheet. The texture of cold rolled and
annealed strips usually displays two main texture components: the {111} fibre (ND fibres) that has a beneficial effect on the deep drawability and the {001} texture fibre,
which has a detrimental effect.1)
In some cases when the requirements for high surface
quality are not very strong, hot rolled thin strips can be a
viable economical alternative for cold rolled steel strips.
This replacement will be more effective when the mechanical properties of the hot rolled thin strips, i.e. strength and
toughness, are high enough and are combined with low values of plastic anisotropy. Such a combination of properties
may be achieved by means of thermo-mechanical treating
that results in a fine-grained microstructure with a specific
texture. Significant grain refinement is possible to obtain by
lowering the transformation temperature in the steel, for instance by the use of accelerated cooling after hot rolling,
controlled rolling in combination with microalloying or by
solid solution strengthening. A widely accepted opinion is
that the development of a {332}具113典 transformation texture component in hot rolled sheets enhances both toughness and formability in steel strips,2) whereas the
© 2003 ISIJ
2. Experimental
Two low carbon steels, designated as A (plain carbon)
and B (with higher Mn and Nb contents), were hot rolled in
an industrial six-stand continuous rolling mill to different
final thickness. All the samples were hot rolled directly
after being cast into slabs of around 50 mm in thickness.
Figure 1 shows a schematic diagram of the mill from
which the samples were taken. Full details of the mill can
be found elsewhere.6) Three different rolling schedules were
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ISIJ International, Vol. 43 (2003), No. 3
Fig. 1.
Schematic diagram of the thin slab rolling mill.
used with steel of composition A (identified as A1, A2 and
A3), whereas only one schedule, similar to that of A2, was
applied with steel B. All the samples from either type of
materials were cut at room temperature from the coiled
product. Coiling of the strips take place at the end of the
run out table, which is equipped with a cooling system. The
cooling system consists of a series of low pressure laminar
water headers located on the top of the strip and low pressure water jet headers from the bottom side. The number of
headers being used was controlled by the operators to assure coiling temperature below 650°C. The chemical composition of the steels is shown in Table 1 and the parameters of the rolling schedules together with the measured R
and Dr-values are shown in Table 2. The value of critical
temperatures A1⫽718°C and A3⫽860°C were calculated
with the equations proposed by Andrews.7) The temperature
changes in the strips during rolling were predicted by computer modelling,8) as this approach allows to have an idea
whether the final rolling temperature (FRT) stays within the
austenite phase field or within the two phase, a ⫹g , region.
The values shown in Table 2 indicate that the final rolling
temperatures predicted by the model were above A3, without entering the intercritical region for the rolling schedules
A1, A2 and B, but not for the thinnest sample (A3), on
which the final pass may have been imparted in the intercritical region.
Evaluation of the forming characteristics of the hot rolled
steels was carried out by testing tensile samples cut parallel, perpendicular and at 45° with respect of the rolling direction. Individual measurements of the instantaneous
width and thickness to the samples were made to obtain the
strain values as referred to the width and thickness (e w and
e t respectively) of the samples. The plastic strain ratio r was
determined by:
r⫽
Table 1.
Table 2.
Processing parameters and R-values for the strips.
εw
....................................(1)
εt
Following the procedure described in a previously published work.9)
The average value of r was determined from the data collected by testing samples cut along the different directions:
R⫽
Composition of the steels.
r0 ⫹ r90 ⫹ 2r45
4
rolling direction. The plastic anisotropy of the sheet (Dr)
was calculated by:
...........................(2)
Dr⫽
where R represents the average value of r and the sub-indexes 0, 90 and 45 indicate the angle with respect to the
r0 ⫹ r90 ⫺ 2r45
..........................(3)
4
The full details of the experimental procedure can be found
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ISIJ International, Vol. 43 (2003), No. 3
elsewhere.10)
The microstructure of the samples was examined in the
cross section of the samples after standard sample preparation procedure and 2% nital etching. The plane for observation was perpendicular to the transverse direction as it is
schematically shown in Fig. 2. A, B, C and D indicate the
position of points located in the centre of the cross section
of the strip (A), the centre of the upper surface (B), the centre of the side wall (C) and the corner (D) (cf. Fig. 2). In the
centre of the plane that includes points A and B a local microtexture measurements by means of orientation imaging
microscopy (OIM) were performed. The samples for OIM
were electrolytically polished after a final step of mechanical polishing with 1 m m diamond paste and etched in 2 %
nital. The OIM attachment was installed on a Philips XL30
ESEM with an LaB6 filament and the electron backscattering diffraction (EBSD) patterns were acquired and analysed
by means of the commercial TSL OIM* software.11) The
orientation data of at least 3 local measurements of each
sample were summarized and further post processed by
means of FHM-MTM software developed by Van Houte12)
in order to represent the texture of the strips by means of
the orientation distribution functions (ODFs). Every ODF
created in this way represents statistically reliable texture
data.
Fig. 2.
3. Results
The temperature evolution in different zones of the hot
rolled strips predicted by the computer model8) is shown in
Fig. 3. The temperature at the end of rolling was measured
in point B and it is marked on the diagram. The average
grain size of austenite, represented by the average grain diameter, was also modeled. The predictions for the austenite
grain size, together with the ferrite grain diameters that
were measured in the hot rolled thin strips, are shown in
Fig. 4.
The microstructure of hot rolled strips obtained by means
of optical metallography (OM) in the middle thickness of
the strips is shown in Figs. 5(a)–5(d). The average ferrite
grain diameters calculated from the EBSD data are shown
in Fig. 6(a), whereas Fig. 6(b) displays the grain diameter
in the central zone and in the surface of the strip A2. The
definition of grains in the OIM post processing software
differs from the conventional one commonly used in metallography and needs further explanation. The determination
of grains by OIM is based on an algorithm that groups
neighboring similarly oriented points into grains. The software identifies the orientation of every point, and checks
whether such a particular orientation falls within the tolerance allowed for by the operator to decide whether that
point, together with neighboring points is a part of one single grain. The minimum number of points required to decide if a group of closely oriented points should be considered as a grain (minimum grain size) is defined by the operator, as well as the minimum misorientation angle that determines if the measured neighboring points belong to the
same grain or not. The procedure is repeated until the
boundaries between connected points can be established.
As a consequence of this method it is possible to observe
one single grain with a large intragranular orientation gradient accumulated over a certain distance by low point-topoint misorientations. This approach allows a more precise
determination of the grains with different level of misorientation than the classical metallographic methods, but the re-
Schematic diagram of the strip with the position, which
were sampled for microstructural observation.
Fig. 3.
Predicted temperature changes in the cross section of the strips A1 and A3 during hot rolling plotted versus the
distance from the beginning of the rolling line. The dotted line displays the position of calculated Ac3 temperature
and the black square displays the temperature measured at the end of rolling.
* TSL OIM is a trade mark of TexSem Laboratories Inc., Draper, UT, USA.
© 2003 ISIJ
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ISIJ International, Vol. 43 (2003), No. 3
Fig. 4.
Evolution of the average austenite grains in different zones of the strip predicted by the model of Zambrano et
al.8) and measured average grain size of the ferrite at room temperature (white dots).
Fig. 5.
Microstructure of the middle thickness of the strips; (a) steel B, t⫽2.18 mm; (b) steel A3, t⫽1.06 mm; (c) steel
A2, t⫽1.92 mm; (d) steel A1, t⫽2.69 mm.
the averaged data for every strip were plotted vs. the total
strain together with the predicted one by the model austenite grain size (cf. Fig. 7). The average grain size calculated
by means of the linear interception method was presented
also in this figure (white dots) and it coincides very well
with the data derived from the OIM measurement.
Figures 8(a)–8(d) display the ODF in the j 2⫽45° section of Euler space (Bunge notation) measured in the middle thickness of each strip and in Figs. 9(a) and 9(b) some
most important ferrite texture components are represented
in j 2⫽45° section of the Euler space (Fig. 9(a)) together
with the g -phase orientations from which they might
emerge in accordance with the Kurdjumov–Sachs orienta-
sults are strongly dependant on the definitions, ranges and
values set by the operator. The grains data in this work were
obtained using a grain tolerance angle of 5° and the minimum grain size was chosen to be 2 measuring points, which
were at a distance of 1 m m apart. These parameters are
commonly used in this type of analysis.11) All data points
with a confidence index (CI) lower then 0.05 were excluded
from the analysis as dubious. The CI quantifies the reliability of the indexed pattern. The data displayed on Figs. 6(a),
6(b) are taken from one representative measurement of
every sample, which includes more than 1 000 grains.
Afterwards, the average grain diameter for each sample was
calculated from at least 3 to 6 different measurements and
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ISIJ International, Vol. 43 (2003), No. 3
Fig. 6.
Fig. 7.
(a) Grain size distribution in terms of area fraction for steels B (Dav⫽3.6 m m), A3 (Dav⫽7.2 m m), A2 (Dav⫽9 m m)
and A1 (Dav⫽10 m m); (b) grain diameter measured in the center of the strip and in the edge zone (strip A2 Dav
center⫽9 m m, Dav edge⫽7 m m); (c) number of grains and area fraction of the grains plotted vs. grain diameter for
steel B.
Changes in average austenite grain diameter DA, average
ferrite grain diameter DF and DA/DF ratio as a function of
the rolling reduction in the thin strip from the plain carbon steel. The white dots display the data for the average
ferrite diameter measured by the linear intersection
method.
tion relationships (Fig. 9(b)).
The ODF of steel B (with 0.023% Nb), Fig. 8(a), shows
a maximum of 2⫻ (1⫻ represents the random texture level)
at {001}具110典, which corresponds to the rotated cube orientation and it is a characteristic ferrite component transforming from a recrystallized cube austenite orientation. The
texture components {113}具110典 with an intensity of 2.5⫻
and {332}具113典 with 3⫻ are also present in the strips of
steel B, and are associated with the transformation of ferrite
© 2003 ISIJ
Fig. 8.
382
Middle thickness texture of the strips; (a) B, t⫽2.18 mm;
(b) A3, t⫽1.06 mm; (c) A2, t⫽1.92 mm; (d) A1,
t⫽2.69 mm. Iso-intensity levels 0.8–1.0–1.3–1.6–2.0–
2.5–3.2–4.0–5.0–6.4.
ISIJ International, Vol. 43 (2003), No. 3
Fig. 9.
(a) j 2⫽45° section of the Euler space with the most important ferrite texture components. The arrow points to the
zone with ferrite b -fibers (shaded); (b) selected BCC product orientations in the j 2⫽45° section showed together
with FCC parent orientations from which they originate.14)
from deformed austenite, which is assumed to display a
characteristic b -fibre texture of the deformed FCC metal.
The textures of the strips from steel A were found to vary
with the processing parameters. Figure 8(b) displays the
texture of the sample A3 with a thickness of 1.06 mm. The
maximum intensity, 8⫻, is observed at the {001}具110典 rotated cube component and 2⫻ at the component with Euler
angles j 1⫽10° F ⫽80° and j 2⫽45°, which differs approximately ⬃10° from the ideal position of the rotated Goss
({110}具110典) component. Rotated cube, Goss and rotated
Goss are characteristic texture components of the ferrite
transformed from cube austenite component (cf. Fig. 9(b)).
The {332}具113典 and {558}具3 11 5典 transformation components emerging from the deformed austenite are also presented in the ODF but with low intensity (1.6⫻) though.
Steel A2 with a final thickness of 1.9 mm, which was finished at 885°C displays almost the same type of texture as
the sample A3, i.e. the typical texture of ferrite transformed
from a cubic austenite component (Fig. 8(c)). The texture is
characterized by a strong rotated cube {001}具110典 (6.4⫻)
combined with a Goss and a rotated Goss component with
intensities of 2.5⫻ and 3.2⫻ respectively. The relatively
weak fibre texture component with maximums of 1.6⫻ on
{332}具113典 and {558}具3 11 5典 can be identified as transformation products from unrecrystallized austenite.
The texture of the strip A1 (Fig. 8(d)) with a thickness of
2.69 mm is the weakest one among the plain carbon steel
sheets. It displays a maximum of 2.5⫻ on RD fibre {113 to
114}具110典, which spreads towards the {111}具112典 component forming a continuous series of orientations which constitutes the ferrite b -fibre. The ferrite b -fibre is the transformation product from the austenite b -fibre, which represents
the characteristic texture components of the deformed FCC
material with high stacking fault energy (SFE).15,16) A rotated cube recrystallization texture component {001}具110典 is
also presented in the ODF with the intensity of 2⫻.
which strongly influences the toughness of the steels as well
as their forming characteristics, and therefore it was used
for the quantitative characterization of the microstructure.
The average grain diameter Dav, calculated on the basis of
EBSD measurements is used to define the grain size. This
parameter changes significantly as a function of the chemical composition of the steel and the processing parameters.
A general observation is that the measured ferritic grain diameter corresponds sufficiently well to the predicted
austenite grain diameter on the final rolling stage (cf. Fig.
4) and the microstructures in the cross section of the hot
rolled strips consist of homogeneously distributed ferritic
grains, i.e. no differences between the microstructure and
grain size in the middle thickness and in the surface layers
of the strips were observed (cf. Fig. 6(b)).
Strong grain refinement is observed in steel B, which
contains 0.023%Nb. The average grain diameter Dav measured in this steel (Fig. 6(a)) is 3.6 m m. It is 2.5 times smaller than the average grain diameter measured in strips A1,
A2 and A3 (compare the data in Fig. 6(a)). Most of the microstructure of steel B consist of grains smaller than 5 m m,
which include between 75 and 95 % of all number of grains
(see Fig. 6(c)), but cover only 30% of the area.
OIM allows to discriminate grain orientations with regard to the grain size. Such an exercise was made with the
microstructure of steel B. Figure 10 shows the microstructures for the grains that have a size smaller than 3 m m, Fig.
10(a), where it can be noticed that the small grains show
the tendency to be distributed in chains, which may correspond to some of the previous austenite grain boundaries,
or are concentrated in regions with elongated shapes along
the rolling direction, which may correspond to previous
austenite grains. The grains that have a diameter higher
than 10 m m are represented in Fig. 10(b). It may be possible
that such large grains of ferrite emerged from highly
strained austenite, and were the first to be transformed.
Hence, after transformation, these grains will have a growth
advantage in comparison to the ones transformed later on.
The grain size distribution observed in the final ferritic
structure may bear a legacy to the retardation of recrystallization of the parent austenite phase, as a consequence of
4. Discussion
4.1. Microstructure
The grain size is an important structural parameter,
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ISIJ International, Vol. 43 (2003), No. 3
istic of the accumulated plastic deformation in the parent
austenite prior to transformation. The data in Fig. 7 show
that austenite grains of a given size produce ferrite grains
of smaller size as the total accumulated strain increases, i.e.
the DA/DF ratio increases with an increase of the rolling reduction.
4.2. Texture
The ODF of steel B, which was calculated on the basis of
5 different local measurements, is shown in Fig. 8(a) and
displays two important components of ferrite that were generated from deformed austenite. The {332}具113典 ferrite texture component, which is considered as a favorable orientation from the viewpoint of drawability1,2) (high R value) is
presented with an intensity of 2.5⫻. The {112}具131典 component, which also represents a transformation product
from deformed austenite, appears with a maximum intensity of 3.2⫻. This component, together with the rotated cube
that was observed with an intensity of 2⫻, are considered
to have a detrimental effect on the R-value.2)
The analysis of the distribution of the texture components among grains of different size was done by calculating the ODF from grains smaller than 3 m m and larger than
10 m m, as they can be clearly discriminated in steel B. The
ODF plots shown in Figs. 10(c) and 10(d) correspond to the
smaller and larger grains shown in Figs. 10(a) and 10(b),
respectively. The transformation texture components of the
deformed austenite {332}具113典 (shifted to {554}具225典),
{111}具112典 displaying an intensity of 6⫻ and {001}具010典
with an intensity of 4⫻ are the strongest components in the
ODF of the grains larger than 10 m m, whereas the
{001}具110典 and {110}具110典 components appear with intensities of 3⫻, respectively (Fig. 10(d)). According to some
authors2,13,15) these texture components could emerge from
either deformed or recrystallized austenite (see Fig. 9(b)),
but the later is less probable, taking into account the Nb
content of steel B, the rolling parameters and the model
predictions.
The ODF of the grains smaller then 3 m m (Fig. 10(c))
displays almost equal intensity of both ferrite texture components that could emerge from deformed austenite
({223}具110典 and {332}具113典) with intensity of 2–3⫻ and
from recrystallized austenite ({001}具110典 and {110}具110典)
with intensity of 2–3⫻.
Considering the data of the grain size diameter and how
the texture components are distributed among them it can
be concluded that the strong deformed grains are among
the first to transform into ferrite and hence, they have a
growth advantage with respect to later transformed grains
that might have emerged from the partially recrystallized
austenite.
The textures of plain carbon steel strips are shown in
Figs. 8(b), 8(c) and 8(d). In general the textures of the strips
A3 and A2 differ significantly from the texture of the Nb
steel, whereas the texture of strip A1 looks similar to it. The
intensity of the texture increases with the increase of the
total rolling reduction and the thinnest strip A3 displays the
strongest texture. Two main groups of texture components
are presented in the ODFs of the plain carbon steel. The
first group corresponds mainly to transformation products
emerging from recrystallized austenite (i.e. rotated cube,
Fig. 10. Image quality maps showing all grains smaller than
3 m m (a) and all grains larger than 10 m m (b) together
with the corresponding ODFs gathered from small
grains (c) and large grains (d).
microalloying with Nb, as well as for finish rolling in the
intercritical a ⫹g region.13)
The ferrite grains in plain carbon steel are larger than
those in the Nb containing steel B, their average diameter
vary from 7.2 m m, for strip A3, to 10 m m, for strip A1. The
metallographic observations did not show significant differences between the microstructure (grain size and shape) in
the surface and in the middle thickness of the strips (Fig.
6(b)), but somehow, the grains close to the surface are
slightly smaller in diameter than those at mid thickness. A
relatively weak grain refining effect was observed in the
plain carbon strips as a function of the rolling reduction,
which can be associated with the increased dislocation density in the parent austenite phase prior to the transformation. An indirect proof of this assumption is the difference
between the austenite grain size predicted by the computer
model and the grains measured in the final ferrite. Figure 7
displays the ratio DA/DF for the strips of plain carbon steel
A1, A2 and A3, where DA is the average austenite grain diameter before the transformation predicted by the model8)
and DF is the size of the ferrite. It can be considered that
with increase of this ratio more ferrite grains (with a small
diameter) are nucleated from a single austenite grain, assuming that there is no grain growth during coiling.
Because coiling was executed at temperatures below
650°C, such assumption seems reasonable. Therefore, the
number of ferrite grains emerging from a single austenite
grain will be a function only of the deformed substructure
of the austenite, and can be used as a qualitative character© 2003 ISIJ
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ISIJ International, Vol. 43 (2003), No. 3
hot rolling of hot charged-thin cast slabs is studied in this
work. Two types of steels were studied, plain carbon steel,
subjected to total hot rolling reduction of 94 to 98%, and
Nb containing steel finish rolled to a total reduction of
94%. It was found that the final grain size on hot rolled
plain carbon steels ranged from 7 to 10 m m, was dependant
on the total amount of reduction during hot rolling.
Significant grain refining was observed to occur in the Nb
containing steel in which the average grain size was
3.6 m m.
A low intensity transformation texture from deformed
austenite was observed in the Nb containing steel, whereas
the type and intensity of ferrite texture in the plain carbon
steels depends on the thermo-mechanical history of the
steel strip. When the reduction at elevated temperatures is
higher the ferrite texture intensifies and possesses all typical transformation components from the recrystallized
austenite phase. When the strain at elevated temperature is
low the texture is weak and additional transformation components emerging from deformed austenite are dominant.
The observed texture data of plain carbon steel are in good
correlation with the results from R-value measurements.
The data confirm that by proper control of the processing
parameters it is possible to obtain thin hot rolled strips with
fine grains and appropriate texture providing satisfactory
deep drawability.
Fig. 11. Changes in true strain per pass for the different strips as
a function of the rolling temperature. The last pass in
strips A1, A2 and A3 is at rolling strain of 0.25.
rotated Goss and Goss). The intensity of the rotated cube
component is stronger in the thinner strips A3 and A2 displaying a value of 8 and 6.4⫻ respectively and only 2⫻ in
the thickest strip A1. The rotated Goss and Goss components are concurrently present only in the texture of strip
A2, whereas the rotated Goss component with a certain deviation from the exact position is observed also in the texture of the thinnest strip A3. The transformation components from deformed austenite are weak in the textures of
the strips A3 and A2 but they are the strongest components
in the texture of the strip A1 with a thickness of 2.69 mm,
which displays the highest R-value. Hence, the improvement of the R-value in the thickest strip is due to the two
main reasons: (i) a general decrease of the intensity of unfavorable components and (ii) the development of the
{111}具112典 texture component which has a positive effect
on the deep drawability.2) For better understanding the texture formation in hot rolling of thin strips, it is necessary to
know also the strain distribution among the different passes. Figure 11 displays the evolution in the reduction of the
strips thickness presented by the true strain for every rolling
pass. Strips A2 and A3 were subjected to higher reductions
at elevated temperatures than strip A1 but in the final pass
all strips received an almost identical rolling strain of 0.25.
If the reduction at elevated temperatures is higher the intensity of the ferrite transformation texture from recrystallized
austenite is stronger (cf. Figs. 11 and 8(b), 8(c), 8(d)), because the high temperature deformation intensifies the recrystallization of the austenite. Hence, taking into account
the texture data in Figs. 8(b), 8(c) and 8(d) and the data in
Fig. 11 it is possible to assume that recrystallization in the
thickest strip A3 develops weaker than in the thinnest
strips, as far as it was subjected to the lower strain. In a
later stage it will be possible to employ the present data to
extend the g -recrystallization model8) to a fully quantitative
texture dependant description
Acknowledgements
PCZ, MPG and RC thank the support provided by
CONACYT, Mexico, and Hylsa, S.A. de C.V., for the material.
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