Materials Science and Engineering A 539 (2012) 294–300
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Materials Science and Engineering A
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tudy on hot deformation behavior of carbon structural steel with flow stress
ian Wang ∗, Hong Xiao, Hongbiao Xie, Xiumei Xu, Yanan Gaotate Key Laboratory of Metastable Materials Science and Technology, National Engineering Research Center for Equipment and Technology of Cold Rolling Strip,chool of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
r t i c l e i n f o
rticle history:eceived 11 May 2011eceived in revised form 1 January 2012ccepted 23 January 2012vailable online 31 January 2012
a b s t r a c t
The hot deformation behaviors of carbon structural steel were investigated using isothermal compressiontests performed on a Gleeble 3500 thermal-mechanical simulator at temperatures of 950–1050 ◦C, andstrain rates of 0.01–0.5 s−1. Austenite grain growth behavior under different heating conditions was alsostudied. The relationships among average grain size, soaking temperature, and time were determined.The flow stress under dynamic recrystallization (DRX) conditions was analyzed, and the critical strain, asa function of the deformation parameters, was measured. The dependence of peak strain on strain rate
and temperature obeys a hyperbolic sine equation with a Zener–Hollomon parameter. Using regressionanalysis, the DRX activation energy was determined and the DRX grain size model of the steel wasconstructed. Meanwhile, an approximate model based on the flow curves was investigated to determinethe recrystallized fraction under different conditions, after which the DRX kinetics model was established.The model predictions show good agreement with the experimental results.
ot deformation
. Introduction
Carbon structural steels have been used in industry, but theirelatively low strength constrains their wide application. In theast few decades, considerable work has been done on attainingltrafine-grained low-carbon steels to increase their strength givenhat grain refinement is the only way to obtain both high strengthnd good ductility [1]. A useful technique is to induce dynamicecrystallization (DRX) during hot deformation [2,3]. Future steelaterials are expected to be characterized by ultrafine grains,
igh purity, and high homogeneous distribution. The strength andongevity of steel double under no increase in production costs,o decrease in toughness and plasticity, and reduced consump-ion of alloy resources and energy. The core theory and technologyie in the realization of ultrafine grain properties [4,5]. DRX is ofnterest because it softens metals during hot forming and playsn important role in microstructural evolution [6–8]. However,icrostructural changes can affect the macroscopic characteristics
f a workpiece. In addition, these changes influence the mechani-al properties of the end-product; such properties include strength,uctility, toughness, and resistance against corrosion. Thus, inves-igating the DRX behavior and austenite microstructural evolution
f metals is highly important.
No systematic research on critical strain εc, activation energy Q,nd grain growth mechanisms of carbon structural steels has been
conducted. To this end, the grain growth mechanisms that takeplace during heating, the kinetics of DRX during hot deformationare investigated, and the final grain size after DRX is completed forsome types of carbon structural steel. The findings of this study canserve as reference for further research.
2. Experimental procedure
The composition of the Q235A steel used in this research is0.17 C, 0.22 Si, 0.68 Mn, 0.009 P, and 0.006 S. All the values areexpressed in wt%. The hot deformation behaviors of Q235A carbonstructural steel were investigated using isothermal compressiontests performed on a Gleeble 3500 thermal-mechanical simulatorat temperatures of 950–1050 ◦C and strain rates of 0.01–0.5 s−1.Fig. 1(a) shows the heat treatments and deformation process of thesteel. All the samples were first heated to 1200 ◦C at a heating rateof 10 ◦C/s. This temperature was held for 180 s to ensure uniformtemperature and desired grain size of the specimens. The spec-imens were then cooled to different deformation temperatures.After being held for 90 s in the tested temperature, the specimenswere deformed to various strains at strain rates of 0.01–0.5 s−1.The specimens were immediately quenched in water to capture themicrostructure of the hot deformed material. Optical micrographswere obtained from the cross-sectional surface of the deformedspecimens that were cut parallel to the compression axis. In addi-
tion, when the recrystallization was completed, the new structurebecame metastable so that austenite grains grew and reduced thegrain boundary energy per unit volume. To investigate the growthbehavior of austenite grain and the mechanisms that underlie grain
J. Wang et al. / Materials Science and Engineering A 539 (2012) 294–300 295
Fig. 1. The experimental schedules employed in the thermo-mechanical simulationtests. Schematic representation of the method for study on grain growth modelis shown in (b) and (c)). (a) Schematic of hot deformation for various strain ratesas
gat1tc
3
3D
attassda
ttp
Z
Fig. 2. Stress–strain curves for Q235A steel at various strain rates and tempera-tures (a) T = 950 ◦C, ε̇ = 0.01 s−1, 0.05 s−1, 0.1 s−1; (b) T = 1000 ◦C, ε̇ = 0.05 s−1, 0.1 s−1,
−1 ◦ −1 −1 −1
nd temperatures, (b) schematic of hot deformation for fixed temperature, and (c)chematic of hot deformation for fixed time.
rowth in the tested steel, hot deformations at fixed temperaturesnd times were designed. Fig. 1(b) and (c) shows the procedure forhe compression tests. A set of specimens was heated to 1000, 1050,100, 1150, and 1200 ◦C for 40 s, whereas another set was exposedo temperatures held at 950 ◦C for 10–240 s after deformation toonstruct the grain growth model after recrystallization.
. Results and discussion
.1. Determination of the activation energy and critical strain ofRX
The stress–strain curves of the steel tested at different temper-tures and strain rates are shown in Fig. 2. The curves indicatehe effect of work hardening and microstructural evolution inhe specimens [8,9]. As is shown in the figure, both strain ratend deformation temperature have a considerable effect on flowtress. Flow stress increases with the increase in strain rate at theame deformation temperature and strain. By contrast, flow stressecreases with the increase in temperature at the same strain ratend strain.
The Arrhenius equation is widely used in describing the rela-ionships among strain rate, flow stress, and temperature at highemperatures. It can also be expressed with the Zener–Hollomonarameter (Z) as follows [10–13]:
= ε̇ exp(
Q
RT
)= A[sinh(˛�p)]n. (1)
0.5 s ; (c) T = 1050 C, ε̇ = 0.01 s , 0.05 s .0.1 s ).
According to Eq. (1), ε̇ can be described as:
ε̇ = A[sinh(˛�p)]n exp(−Q
RT
), (2)
where A and ˛ are the material dependent constants, n is the stress
exponent, and �p denotes the peak stress. Q is the activation energyof hot working, R represents the universal gas constant, and T is the
296 J. Wang et al. / Materials Science and Engineering A 539 (2012) 294–300
ar
ε
a
ε
nhdnF
s
∂
w
Fig. 3. Relationship between ln(strain rate) and �p .
bsolute temperature. At low stress, Eq. (2) is reduced to a powerelationship [14,15], expressed as:
˙ = A′�n′exp
(−Q
RT
), (3)
nd at high stress, to an exponential relationship:
˙ = A′′ exp(ˇ�) exp(−Q
RT
). (4)
The constants ˛ and n′ are related to ˇ = ˛n′ so that ˛ and′ can be simply determined from experimental data at low andigh stresses. At constant deformation temperatures, the partialifferentiation of Eqs. (3) and (4) yields the following equations:′ = ∂ ln(ε̇)/∂�p, ˇ = ∂ ln(ε̇)/∂ ln(�p), which can be observed inigs. 3 and 4 [16]; n′ = 4.6697, ˇ = 0.0584, ˛ = ˇ/n′ = 0.0125.
Taking natural logarithms to obtain partial derivatives on bothides of Eq. (2), the following formula can be obtained:
(ln ε̇) = n ∂[ln sinh(˛�p)] − Q
R∂(
1T
)(5)
If T is constant, Eq. (5) can be rewritten as:
1 ∂ ln[sinh(˛�p)]
n
=∂ ln ε̇
. (6)
Thus, a linear relationship exists between ln sinh(˛�p) and ln ε̇hen T remains constant. In accordance with the relationship
Fig. 4. Relationship between ln(strain rate) and ln �p .
Fig. 5. Relationship between ln sinh(˛�p) and ln(strain rate).
curves of ln sinh(˛�p) and ln ε̇ (Fig. 5), the value of n can be esti-mated because n equals to the reciprocal of the linear slope. Fig. 5shows that the value of n increases with the increase in deforma-tion temperature. The average value of n is 4.029, as determined bycalculation. A linear relationship exists between ln sinh(˛�p) and1/T when ε̇ is constant, according to Eq. (5):
Q = Rn
{∂[ln sinh(˛�p)]
∂(1/T)
}. (7)
According to the relationship curves of ln sinh(˛�p) and 1/T(Fig. 6), the linear slope increases with the increase in strain rate,and the average value of the slopes is 9920.1. Because the value ofn has been calculated, the average value of Q, 332.13 kJ/mol, can beobtained using Eq. (7).
The prerequisite for studying DRX is knowing its critical strain.Using stress–strain curves is a simple method for determining thecritical strain of the initiation of DRX. The initiation of DRX proceedsunder the following condition:
∂
∂�
(− ∂�
∂�
)= 0. (8)
where � is the conventional strain hardening rate, and (∂�/∂�) in Eq.(8) indicates that the initiation of DRX corresponds to the inflection
point in the � − � curve and the minimum point in the −(∂�/∂�) − �curve [12,17]. Fig. 2 shows the true stress versus the true straincurves of the tested steel at different deformation temperaturesand strain rates. The −(∂�/∂�) − � curves can be obtained from the
Fig. 6. Plots of ln sinh(˛�p) versus 1/T at different strain rates.
J. Wang et al. / Materials Science and Engineering A 539 (2012) 294–300 297
FT(
sD
ri
ε
Z
ig. 7. Determination of the critical strain for DRX, −(∂�/∂�) − � curves ((a)= 950 ◦C, ε̇ = 0.01 s−1, 0.05 s−1, 0.1 s−1; (b) T = 1000 ◦C, ε̇ = 0.05 s−1, 0.1 s−1, 0.5 s−1;
c) T = 1050 ◦C, ε̇ = 0.01 s−1, 0.05 s−1, 0.1 s−1).
tress–strain curves, and are shown in Fig. 7. The critical strain ofRX can be determined from this figure.
Critical strain εc or the dependence of the onset of dynamicecrystallization on strain rate and temperature has been empir-cally demonstrated [18–20] as follows:
c = a · Zb (9)
= ε̇ exp(
c
T
). (10)
Fig. 8. Comparison between the measured values and calculated values for εc .
where c equals to (Q/R), in which Q is the activation energyof hot working, R is the universal gas constant. The criti-cal strain of DRX increases with increasing strain rate anddecreasing temperature. The formula for the critical strain of DRXis obtained using the Levenberg–Marquardt and universal globaloptimization (UGO) methods, where a = 2.28084626759453E-5,b = 0.197768954663879, and c = 59597.3709706269. Fig. 8 showsthe comparison of the measured and calculated values of εc.
εc = 2.2808 × 10−5
(ε̇ exp
(59597
T
)0.1978)
(11)
3.2. DRX Kinetics
At high temperatures and low strain rates, the DRX phenomenonis increasingly evident. The volume fraction of dynamic recrystal-lization X can be expressed as [11,21–23]:
X = 1 − exp
[−kd
(ε − εc
εp
)nd]
(ε ≥ εc). (12)
where kd, nd, are the material dependent constants. Determiningthe recrystallized fraction under different deformation conditionson the basis of microstructures is difficult because this requiresextensive metallography and measurements. The stress–straincurves can provide some information regarding the recrystallizedfraction. The softening fraction occurring in the deformation pro-cess, X, is given by Eq. (13) [24]:
X = �rec − �
�∗ss − �ss
, (13)
where �rec and �∗ss are the instantaneous and steady flow stresses
assuming that dynamic recovery pertains to only the softeningmechanism; � and �ss are instantaneous and steady flow stressesfor DRX. �∗
ss and �ss are displayed in the schematic of stress–straincurves shown in Fig. 9. � and �ss can be obtained from thestress–strain curves in Fig. 2. �∗
ss cannot be easily determined, butits value is nearly equal to that of �p. Thus, this study uses �p
instead of �∗ss. �rec can be obtained by extending the front region
of the stress–strain curves where the strain is lower than the criti-cal strain, according to the mathematical model that describes the
region as follows[25–28]:
�2rec = �∗2
ss + (�20 − �∗2
ss ) exp(−˝ε), (14)
298 J. Wang et al. / Materials Science and Engineering A 539 (2012) 294–300
wps
˝
a
X
mFli
l
tTm
Fs
Fig. 11. Comparison between predicted and experimental recrystallized volume
Fig. 9. Schematic diagram of the stress–strain curve for DRX.
here �0 is the initial stress, ˝ denotes the dynamic recoveryarameter, which is dependent on deformation temperature andtain rate, and can be calculated by converting Eq. (14) into:
= ln[(�2rec − �∗2
ss )/(�20 − �2
ss)]−ε
. (15)
In terms of Eqs. (13)–(15), the recrystallized fraction can bepproximately denoted by Eq. (16) after using �p instead of �∗
ss:
= �rec − �
�p − �ss. (16)
We obtain the recrystallized fraction under different defor-ation conditions using Eq. (16) and the stress–strain curves in
ig. 2. To determine kd and nd, the plots of ln[− ln[1 − X]] versusn[(ε − εc)/εp] are used (Fig. 10) for selected conditions ε̇ and T. Thiss accomplished using the following equation:
n[− ln[1 − X]] = kd ln
[(ε − εc)
εp
]+ ln nd. (17)
The value of kd is 3.53389 and that of nd is 2.1989. Fig. 11 shows
he comparison of predicted and measured recrystallized fractions.he predicted result is in good agreement with the experimentaleasurement.
ig. 10. Defermination of the constants kd and nd at different temperatures andtrain rates.
fraction in the deformed at (a) 950 ◦C and (b) 1050 ◦C.
3.3. Determination of the grain size model for DRX
DRX grain sizes were measured under various deformation con-ditions. It decreases with the increase in strain rate and the decreasein temperature. To model the dependence of the DRX grain sizeon temperature and strain rate, the following relationship is used[29,30]:
D = BZ−k, (18)
where Z is the Zener–Hollomon parameter, and both B and k areconstants. Using the non linear regression methods, the formulafor the recrystallized grain size of DRX is obtained: B = 41032.73,k = 0.2247.
Ddrx = 41032.73 · Z−0.2247 (19)
The DRX grain sizes calculated using the derived model and themeasured grain sizes are shown in Fig. 12. The calculated results
are in good agreement with the measured values. Fig. 13 shows thedynamically recrystallized grain sizes under different deformationconditions.
J. Wang et al. / Materials Science and Engineering A 539 (2012) 294–300 299
Fig. 12. Comparisons between calculated and measured grain sizes for differentr
3
warroohas
d
Fig. 14. The dependence of grain growth on heating temperature.
ecrystallization behaviors.
.4. Grain growth model
As shown in Figs. 14 and 15, austenite grains gradually growith the increase in heating temperature; holding time also has
n important effect on the growth of austenite grain. The growthate decreases with increasing time, and the decrease is initiallyapid before it slows down at longer durations. The aforementionedbservations are similar to the normal grain growth behavior ofther steels [31,32]. Taking the effect of heating temperature andolding time on austenite grain size into account, the kinetics ofustenite grain growth has been known to obey the following clas-
ical relationship [31–34]:
mt − dm
0 = k0t exp(−Q ′
RT
), (20)
Fig. 13. The dynamically recrystallized grain size
where dt is the average grain size at time t, d0 is the initial grainsize, Q′ represents the grain growth activation energy, k0 is thepre-exponent factor, and R denotes the general gas constant. Inaccordance with the measured grain sizes, the optimal values ofm, k0, and Q′ in Eq. (20) are determined using regression analysis.Then, the grain growth model of the tested steel is expressed asfollows:
d1.979 = d1.9790 + 1.423 × 1013t exp
(−268200RT
). (21)
The grain sizes predicted using Eq. (21) agree well with themeasured values, as shown in Fig. 16.
s under different deformation conditions.
300 J. Wang et al. / Materials Science and En
Fig. 15. The dependence of grain growth on holding time.
4
btt
((
(
[[[[[[
[[[
[
[[[[[[[
[
[[[30] H.Y. Kim, W.H. Sohn, S.H. Hong, Mater. Sci. Eng. A 251 (1998) 216–225.
Fig. 16. Comparison of measured grain diameters with calculated ones.
. Conclusions
Using a Gleeble 3500 thermo-mechanical simulator, the DRXehavior of Q235A steel are investigated under different deforma-ion conditions through hot compression tests. The results of theseests are summarized as follows.
(i) DRX occurs in all the deformation specimens of Q235A steel. The
deformation was performed at temperatures of 950–1050 ◦Cand strain rates of 0.01–0.5 s−1. Decreasing strain rate andincreasing deformation temperature can promote the occur-rence of DRX.
[[[[
gineering A 539 (2012) 294–300
ii) The DRX activation energy of Q235A steel is 332.13 kJ/mol.iii) The relationship between the critical strain of DRX and defor-
mation conditions can be described by Eq. (11).iv) The recrystallized fraction under different deformation condi-
tions can be approximated by Eq. (16). The DRX kinetic modelfor Q235A steel was constructed in this paper.
(v) The growth mechanisms of the austenite grain growth processwere also determined.
Acknowledgments
The authors appreciate the support of the Natural Science Foun-dation of Hebei Province of China (E2009000397) and the NationalNatural Science Foundation of China (51075353). The authors alsogratefully acknowledge the support of the State Key Laboratory ofMetastable Materials Science and Technology of Yanshan Univer-sity.
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