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Research ArticleEvolution of Dynamic Recrystallization in
5CrNiMoVSteel during Hot Forming
Zhiqiang Hu and Kaikun Wang
School of Materials Science and Engineering, University of
Science and Technology Beijing, Beijing 100083, China
Correspondence should be addressed to Kaikun Wang;
[email protected]
Received 31 May 2019; Revised 30 October 2019; Accepted 21
November 2019; Published 9 January 2020
Academic Editor: Michael J. Schu ̈tze
Copyright © 2020 Zhiqiang Hu and Kaikun Wang. /is is an open
access article distributed under the Creative CommonsAttribution
License, which permits unrestricted use, distribution, and
reproduction in anymedium, provided the original work isproperly
cited.
/e dynamic recrystallization (DRX) behavior of 5CrNiMoV steel
was investigated through hot compression at temperaturesof
830–1230°C and strain rates of 0.001–10 s− 1. From the experimental
results, most true stress-strain curves showed thetypical nature of
DRX that a single peak was reached at low strains followed by a
decrease of stress and a steady state finally atrelatively high
strains. /e constitutive behavior of 5CrNiMoV steel was analyzed to
deduce the operative deformationmechanisms, and the correlation
between flow stress, temperature, and strain rate was expressed as
a sine hyperbolic typeconstitutive equation. Based on the study of
characteristic stresses and strains on the true stress-strain
curves, a DRX kineticsmodel was constructed to characterize the
influence of true strain, temperature, and strain rate on DRX
evolution, whichrevealed that higher temperatures and lower strain
rates had a favorable influence on improving the DRX volume
fraction atthe same true strain. Microstructure observations
indicated that DRX was the main mechanism and austenite grains
could begreatly refined by reducing the temperature of hot
deformation or increasing the strain rate when complete
recrystallizationoccurred. Furthermore, a DRX grain size model of
5CrNiMoV was obtained to predict the average DRX grain size
duringhot forming.
1. Introduction
Hot work die steel is a kind of metal material widely usedfor
forging dies, hot extrusion dies, and die-casting dies,which makes
the metal heated above the recrystallizationtemperature or the
liquid metal into a workpiece. On ac-count of the strict property
requirements in the course ofserving, it is necessary to precisely
control the micro-structure in the forging process. In order to get
the opti-mum microstructure in terms of properties, such
asstrength, ductility, impact toughness, and thermal stability,the
deformation process parameters such as temperature,strain per pass,
strain rate, and initial grain size must bewell selected. When the
metal is subjected to plastic de-formation at high temperature
larger than half meltingtemperature, dynamic recrystallization
(DRX) is the mainapproach of microstructure control and
mechanicalproperty improvement [1–4]. /erefore, detailed
research
on the DRX behavior of metals during hot working isessential to
optimizing processing parameters.
Considerable investigations have been done on DRXkinetics, and
those research studies concentrate on revealingthe relationships
between the deformation conditions andthemicrostructures by
analyzing the true strain-stress curvesobtained from hot
compression tests. Recrystallizationmodels were constructed based
on the hot compression testswith wide temperature and strain rate
ranges to predict DRXevolution [5–8]. For a more accurate dynamic
recrystalli-zation model, it was of great importance to obtain the
criticalconditions for DRX, which was usually identified by
usingthe θ − σ and (dθ/dσ) − σ curves [9–11]. Wu and Han
[12]presented a kinetics model, and a third-order
polynomialexpression was fitted to determine the critical condition
forthe onset of dynamic recrystallization. Gan et al.
[13]structured the kinetics equations of DRX and a
constitutivemodel to predict the flow stress behavior, of which
fifth order
HindawiAdvances in Materials Science and EngineeringVolume 2020,
Article ID 4732683, 13
pageshttps://doi.org/10.1155/2020/4732683
mailto:[email protected]://orcid.org/0000-0002-9619-8183https://orcid.org/0000-0002-2062-5804https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2020/4732683
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polynomial fitting and nonlinear curve fitting were,
re-spectively, presented for determining the critical strain
andextrapolating work hardening stress. /e research studiesnot only
estimated the recrystallized volume fraction andgrain size based on
DRX models but also compared thecalculated results with the
experimental values [14, 15]./ese investigations fully verified the
accuracy of the DRXmodels in predicating DRX evolution, as well as
its wideapplicability. Besides, Luo et al. [16] analyzed the
dynamicrecrystallization (DRX) behavior of the AFA alloy
underdifferent deformation conditions by combining techniquesof
electron back-scattered diffraction (EBSD) and trans-mission
electron microscopy (TEM), and the results showedthat the
nucleation mechanisms of DRXmainly included thestrain-induced grain
boundary (GB) migration, grainfragmentation, and subgrain
coalescence. Aashranth et al.[17] proposed a novel technique, known
as flow softeningindex (FSI), to assess DRX, and found that FSI
values wereassociated with the grain growth, intermediate FSI
valuesassociated with DRX, and high FSI values associated with
thework-hardening and flow localisation phenomena. /esenew
analytical methods also played an important role in thequalitative
or semiquantitative study of dynamic recrystal-lization during hot
deformation.
5CrNiMoV steel is a die steel mainly used for making allkinds of
large forging dies. Although 5CrNiMoV steel hasbeen widely used in
industrial applications, the hot defor-mation process of the steel
has been less investigated andonly little information on the
dynamic recrystallization(DRX) behavior or flow stress behavior of
the steel has beenreported. So far, the influence of annealing,
forging state, andquenching tempering state on the microstructures
of steelmatrix composites (SMCs) with 5CrNiMo steel as matrixwas
investigated by the metallographic analysis method [18]./e changes
in strength, hardness, and impact ductility of5CrNiMo steel after
the addition of different contents of RELa element were
investigated [19]. Besides, activation en-ergies for plastic
deformation of the low alloy steel Din56CrNiMoV7 (5CrNiMoV) were
studied using tensile testsin the temperature range 660–800°C [20].
To supplement theresearch on the forming property of hot work die
steel5CrNiMoV, the present study explored the DRX behaviorand
microstructure evolution at different deformationconditions based
on the isothermal hot compression tests.And a constitutive
equation, a DRXmodel, and a DRX grainsize model were constructed to
predict the DRX evolution.
2. Materials and Methods
/e 5CrNiMoV steel used in this research, with a
chemicalcomposition (wt.%) of 0.54C - 0.25Si - 0.72Mn - 0.012P
-0.003S - 0.96Cr - 1.58Ni - 0.36Mo - 0.074V - (bal.)Fe, wassampled
from a 15 t large forged die. Cylindrical specimensfor hot
compression tests with a diameter of 10mm and aheight of 15mm were
machined. /e prior austenite mi-crostructure of the water-cooled
samples after holding at1230°C for 180 s is revealed in Figure
1(a). Single-passthermosimulation compression experiments were
carriedout with a Gleeble 3500 thermomechanical simulator,
according to the process illustrated in Figure 1(b). Duringthe
process, argon was used to protect the specimens fromsurface
oxidation. Tantalum foil and high-temperature lu-bricate were used
between the anvils and the specimens toreduce the friction./e
specimens were heated to 1230°C at aheating rate of 10°C·s− 1 and
held for 3min and then cooledto the experiment temperature at the
cooling rate of 10°C·s− 1./en, the specimens were held at the
forming temperaturefor 30 s to get a uniform temperature
distribution. /ecompression experiments were performed at strain
rates of0.001, 0.01, 0.1, 1, and 10 s− 1, at temperatures of 830,
930,1030, 1130, and 1230°C, respectively, to a maximum truestrain
of 0.8. After deformation, the specimens were im-mediately quenched
in water to preserve the final deformedmicrostructure. /e quenched
specimens were sliced alongthe axial section. /e sections were
polished and etched in asolution of picric acid (5 g) +H2O (100ml)
+HCl(2ml) + benzene sulfonic acid (2 g) at 50°C for 3-4min./en, the
optical micrographs were recorded in the centreregion of the
samples using a metalloscope, and the averagerecrystallized grain
size of specimens was measured usingthe software Image-Pro Plus,
according to the line inter-ception method described in ASTM
E112-96 standards.
3. Result and Discussion
3.1.Analysis of True Stress-Strain. /e typical true
stress-straincurves were obtained at different strain rates and
temperatures,as shown in Figure 2./e flow stress was significantly
influencedby forming temperature, strain rate, and true strain.
Generally,as the true strain increased, the true stress increased
almostperpendicularly during the initial stage and then slowly
in-creased to a peak stress, before finally dropping to a
relativelysteady state [21]. As seen from Figure 2(a), at a given
defor-mation temperature of 1230°C, the flow stress increasedwith
theincrease of the strain rate. At the strain rates of 0.001 s− 1,
0.01 s− 1,and 0.1 s− 1, the flow curves showed a single peak
followed by adecrease of stress and finally reached a plateau,
which impliedthe occurrence of the full dynamic recrystallization
(DRX)phenomenon [22, 23]. At the strain rates of 1 s− 1 and 10 s−
1, theflow curves showed dynamic recovery (DRV) character withouta
peak stress. However, DRX was previously observed in de-formed
samples whose flow curves showed no strongly definedpeak. As seen
from Figure 2(b), at the same strain rate of 0.1 s− 1,the flow
stress decreased with the increase of deformationtemperature. All
the true stress-strain curves demonstratedworkhardening with a
maximum in the flow stress followed bysoftening, and the peak flow
stress and the strain at flow curvesdecreased as the test
temperature increased. It was due to the factthat the increase of
deformation temperature increased the rateof the vacancy diffusion,
cross-slip of screw dislocations, andclimb of edge dislocations.
Besides, large hot work dies weregenerally forged at high
temperature and relatively low strainrate, andDRXwas the prime
softeningmechanism for hot workdie steel 5CrNiMoV at the evaluated
conditions.
3.2. &e Constitutive Behavior. Zener and Hollomon
dis-covered that true stress-strain relationship not only
2 Advances in Materials Science and Engineering
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depended on the chemical composition but also relied on
thematerial deformation temperature and strain rate. /eyintroduced
Zener–Hollomon parameter Z, also known asthe temperature
compensated strain rate [24], to considerthe effects of true
strain, deformation temperature, andstrain rate on the deformation
behaviors. /e relationshipamong the flow stress, the deformation
temperature, and thestrain rate in the plastic deformation process
of metallicmaterials can be expressed by
Z � _ε expQactRT
� A(sinh(ασ))n, (1)
where _ε is strain rate (s− 1), σ is the true stress (MPa)
(usuallytaken as the peak stress), R is the universal gas
constant(8.314 J/(mol.K)), T is the absolute temperature (K), Qact
isthe activation energy of deformation (J/mol), andA, α, and nare
constants independent of temperature. /e value of αwas determined
through serial computation to be 0.0128using α � β/n1, where n1 was
obtained by linear fitting ln _ε
and ln σ (Figure 3(a)) and β was the average slope of ln
_εversus σ (Figure 3(b)).
To obtain the activation energy Qact and material con-stants A
and n, the natural logarithm of both sides ofequation (1) was
taken, and it is shown in the followingequation:
ln _ε � lnA + n ln(sinh(ασ)) −QactRT
. (2)
When the temperature (T) was constant, materialconstant n was
expressed as follows, with relevant straightlines for different
conditions shown in Figure 3(c):
n �z ln _ε
z(ln(sinh(ασ)))
T
. (3)
/e activation energy Qact indicated the natural defor-mation
ability of steel and was calculated as follows, withrelevant
straight lines at different conditions shown inFigure 3(d):
120T = 1130°C
10s–1
1s–1
0 .1s–1
0 .01s–1
0 .001s–1
100
True
stre
ss (M
Pa) 80
60
40
20
00.0 0.2 0.4 0.6
True strain0.8
(a)
1230°C
1130°C
1030°C
930°C
830°C
ε· = 0.1s–1200
True
stre
ss (M
Pa) 150
100
50
00.2 0.4 0.6
True strain0.8
(b)
Figure 2: Typical true stress-strain curves of hot work die
steel 5CrNiMoV at different deformation conditions.
(a)
Tem
pera
ture
(°C)
10°C/s
10°C/s
30s
Compression
Water quenching
Hot deformation temperature:
Strain rate:
830, 930, 1030, 1130, 1230°C
0.001, 0.01, 0.1, 1, 10
Strain:0.7
Time (s)
1230°C, holding 180s
(b)
Figure 1: (a) /e prior austenite grains of as-received 5CrNiMoV
steel. (b) Schematic diagram of hot compression test.
Advances in Materials Science and Engineering 3
-
Qact � R∗ n∗z(ln(sinh(ασ)))
z(1/T)
_ε. (4)
/e average activation energy Qact and material constantnwere
determined as 390.238 kJ/mol and 4.927, respectively.As was known
that the average activation energy Q was usedto describe the
required energy to reach, such as the peakpoint of flow curve and
the occurrence of DRX, it could bethe activation energy for DRV,
DRX, or a combination ofthem with other phenomena such as dynamic
precipitationand their corresponding microstructural mechanisms.
/eaverage activation energy (Qd) for hot deformation wasseparated
into thermal (Qth) and mechanical (Qmech) parts./e thermal
activation was found necessary to propel dif-fusion and help
dislocations bypass the short-range barriers
such as the solute atoms. /e mechanical energy could
helpdislocations overcome strong long-range obstacles such
asdislocation tangles [25]. Assuming Qth was constant andequal to
the activation energy for diffusion (Qdif ), Qth of5CrNiMoV steel
was calculated as 322.86 kJ/mol accordingto the empirical formula
[26]./e acquired average apparentactivation energy Q of 5CrNiMoV
steel at different defor-mation was 390.238 kJ/mol, and the average
mechanicalenergy (Qmech) was about 67.378 kJ/mol. For the existence
ofthe mechanical energy (Qmech), which depends on the ap-plied
stress and therefore varies with the deformationtemperature and
strain rate (Figure 3(d)), the apparentactivation energy is often
much larger than any imaginedatomic mechanism [27]. For example,
the linear regressionof the data resulted in the values ofQ� 435.3
and 374 kJ/mol
5.5
5.0
4.5
4.0lnσ
3.5
3.0
2.5–8 –6
830°C930°C1030°C
1130°C1230°C
–4 –2 0 2lnε·
4
(a)
σ
250
200
150
100
50
0–8 –6
830°C930°C1030°C
1130°C1230°C
–4 –2 0 2lnε·
4
(b)
3
2
1
0ln(s
inh(ασ
))
–1
–2–8 –6
830°C930°C1030°C
1130°C1230°C
–4 –2 0
�e average n = 4.99
n = 5.1
n = 5.61
n = 5.07
n = 4.45
n = 4.74
2lnε·
4
(c)
3
2
1
0ln(s
inh(ασ
))
–1
–2
�e average Q = 390238kJ/mol
Q = 357583
Q = 320765
Q = 398154
Q = 459643
Q = 422072
0.00
065
0.00
070
0.0010.010.1
110
0.00
075
0.00
080
0.00
085
0.00
090
1/T0.
0009
5
0.00
100
(d)
Figure 3: Relationships between (a) ln _ε and ln σ, (b) ln _ε
and σ, (c) ln _ε and ln(sinh(ασ)), and (d) ln(sinh(ασ)) and
1/T.
4 Advances in Materials Science and Engineering
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for the VCN200 and AISI 4135 steel compressed at the
samedeformation condition. It was revealed that the
differentapparent activation energies were attributed to about
30%difference between the carbon equivalents of the steel [28].
Besides, according to equation (3), the value of n wasconstant
with strain rate. As shown in Figure 3(c), it wasobserved that the
value of n for 5CrNiMoV steel presented arising trend on the whole
with temperature rising, which wasprobably for the increase in rate
of DRX with temperatureincreasing. Many investigations indicated
that this differencestemmed from the dissimilar dynamic softening
mechanismsof the materials [25, 29]. /e average value of
materialconstant n was exactly close to 5, which indicated that
thedeformation mechanism was mainly controlled by the glideand
climb of dislocations. Moreover, to be proposed as anindex to the
microstructural evolutions, it showed that thedeformation mechanism
was discontinuous dynamic re-crystallization (DDRX). Besides, the
peak stress points havebeen used to find the regression n values
after the initiation ofDRX, which could lead to a little decrease
in value of n fromthe theoretical value of 5 to 4.927 [30, 31]. /e
Zener–Hollomon parameter for this steel was expressed as
follows:
Z � _ε exp390238
RT . (5)
Besides, another material constantAwas calculated to
be7.405×1013, which was obtained by plotting lnZ versusln(sinh(ασ))
at different deformation conditions, as shownin Figure 4. In
summary, substituting the constants Q, A, α,and n into equation
(1), the constitutive equation for hotwork die steel 5CrNiMoV could
be expressed as
_ε � 1.17 × 1014(sinh(0.0128σ))4.927 · exp −390238
RT .
(6)
Furthermore, the constitutive equation of flow stress canbe
written as
σ �1
0.0128ln
Z
1.17 × 1014
1/4.927
+Z
1.17 × 1014
2/4.927+ 1
1/2⎫⎬
⎭,
Z � _ε exp3902388.314T
.
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(7)
3.3. Dynamic Recrystallization Kinetics. In the hot
forgingprocess, dislocation continually increased and
accumulatedwiththe increasing deformation amount. When it reached a
criticalvalue, DRX nuclei would form and grow up near
grainboundaries, twin boundaries, and deformation bands.
Oncerecrystallization occurred in the region, the dislocation
densityof it would reduce by rearrangement and annihilation of
dis-location [32]./epeak stress-strain, critical stress-strain,
steady-state stress, and saturated stress on the true stress-strain
curve
are illustrated in Figure 5(a). Here, the uppermost curve (σsat)
isregarded as resulting from the operation of dynamic
recoveryalone. It represents the assumed work-hardening behavior
ofthe un-recrystallized regions and can be derived from the
work-hardening behavior prior to the critical strain (εc). /e
criticalstrain (εc) for DRX depends on the composition of
thematerial,grain size prior to deformation, and deformation
condition(temperature and strain rate). DRX is initiated at the
criticalstrain (εc) and critical stress (σc) after which it leads
tomore andmore softening and is responsible for the difference
between theDRV and DRX curves [33, 34]. /e onset of DRX can
berecognized by an inflection point in the curve of work-hard-ening
rate (θ, θ � zσ/zε) versus flow stress (σ). /is methodeliminates
the need for extrapolated flow stress data, and thesecritical
points can be precisely located on the flow curves.Typical
work-hardening curve at temperature 1230°C and strainrate 0.1 s− 1
is shown in Figure 5(b), from which it was easy todetermine the
values of the steady stress (σs) and the saturationstress (σsat) of
DRV, the critical stress (σc) and the peak stress(σp) of DRX, and
the corresponding critical strain (εc) and peakstrain (εp) of DRX.
With the method described above, char-acteristic stresses and
strains at different deformation conditionswere obtained and are
shown in Table 1.
/e Avrami model is frequently used to evaluate thekinetics of
crystallization and growth of lipids. However, it isdifficult to
apply to the entire range of the crystallizationevent, mainly
because the rate of crystallization and thedimensionality of growth
in the model are assumed to belinear and constant according to the
assumptions [35, 36]. Itis generally admitted that DRX follows
Avrami’s law, and themost common expression to quantitatively
interpret thisphenomenon is expressed as equation (8). It was used
topredict recrystallized fraction for strains greater than εc dueto
the effect of dynamic recrystallization. And the value ofXDRX
should be equal to one when the steady state wasreached.
XDRX � 1 − exp − kdε − εcεp
nd
, ε≥ εc, (8)
Equation
InterceptSlopeResidual sum of squarePearson’s r
y = a + b ∗ x
32.39295 ± 0.11954.9273 ± 0.10855
7.357270.99446
InZ
45
40
35
30
25
3210–1–2ln(sinh(ασ))
Figure 4: Relationships between lnZ and ln(sinh(ασ)).
Advances in Materials Science and Engineering 5
-
where XDRX is the DRX volume fraction, kd and nd are thematerial
constants, and εc and εp are the critical strain andpeak strain,
respectively. /is expression, which is modifiedfrom the Avrami’
equation, means that XDRX depends on thestrain and other
deformation conditions [37]. /e value ofXDRX was determined from
the flow-curve analysis. /emethod for determining XDRX by analyzing
the flow stresscurves is illustrated in Figure 5(a). /e following
expressionwas adopted to determine the DRX volume fraction:
XDRX �σsat − σσsat − σs
, (9)
where σsat denotes the flow stress and its softening effect
thatonly results from dynamic recovery (without DRX), σs is
thesteady-state stress under the DRX conditions, and σ is the
truestress. Substituting characteristic stresses at different
deforma-tion conditions into equation (9),XDRX was obtained. Taking
thelogarithm of both sides of the expression, we get the
following:
ln − ln 1 − XDRX( ( � ln kd + nd lnε − εcεp
. (10)
As shown in Figure 6, the material constants at
differentdeformation conditions were ascertained through thelinear
regression analysis. However, the material param-eters under
different deformation conditions differedgreatly. It is known that
kd and nd are not constants andclearly depend on the temperature,
strain rate, and thechemical composition of the steel [35]. To
improve theaccuracy of the model, they were described as a function
ofZ. Figure 7 shows the plots of the parameters ln nd and ln
kdversus lnZ. An approximate linear relationship betweenln nd and
lnZ and ln kd and lnZ was observed. More often,the value of nd and
kd declined with increase in Z, and thevalue of Z depended on the
deformation condition. As wasknown that increasing temperature or
decreasing strainrate gave rise to the increase of Z therefore
leads to theincrease of XDRX. It was indicated that the two
parametersnd and kd depended on the deformation temperature
andstrain rate. In other words, the two parameters showed animpact
on the recrystallization volume fraction. By re-gression analysis,
the dependences of nd and kd wereexpressed as follows:
σ
σp
σsat – σ σsat – σs
σsat
σs
σc
εc εp ε
(a)
300 T = 1230°C, ε = 0.1s–1
200
θ(M
Pa)
100
30 40σ(MPa)
σp
σsat
σc
σs
50 60
0
(b)
Figure 5: (a) Schematic plot showing the peak stress-strain,
critical stress-strain, steady-state stress, and saturated stress
on the true stress-strain curve. (b) Work-hardening rate with
respect to stress: determination of σc, σsat, σp, and σs.
Table 1: Values of characteristic strains and stresses at
different deformation conditions.
T (°C) _ε (s− 1) σp (MPa) εp (MPa) σc (MPa) εc (MPa) σs (MPa)
σsat (MPa)
930 0.001 63.60 0.256 62.33 0.187 56.55 65.3930 0.01 81.70 0.263
78.55 0.192 68.8 85.2930 0.1 118.65 0.373 116.57 0.272 108.48
119.81030 0.001 39.00 0.121 36.06 0.073 29.27 42.61030 0.01 57.87
0.181 56.44 0.147 44.81 59.71030 0.1 83.98 0.25 82.36 0.181 75.05
85.81130 0.001 23.31 0.084 22.41 0.065 17.98 24.31130 0.01 38.21
0.13 36.20 0.096 29.52 40.41130 0.1 55.27 0.242 53.88 0.165 40.23
56.31230 0.001 15.65 0.064 14.80 0.046 11.42 16.71230 0.01 26.44
0.108 25.37 0.075 17.92 27.21230 0.1 45.04 0.172 44.54 0.148 30.56
45.7
6 Advances in Materials Science and Engineering
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nd � 0.536Z0.032,
kd � 0.0235Z0.1056. (11)
Deformation temperature and strain rate had an ap-preciable
impact on the critical strain and the peak strain.For each of the
DRX characteristic true stress-strain curves, acritical strain and
a peak strain were obtained [13]. Fur-thermore, the relationships
between the peak strain and thedeformation conditions and the
critical strain and the de-formation conditions can be,
respectively, expressed as theexponential function of the
Zener–Hollomon parameter.Figure 8 shows the plots ln εp and ln εc
versus lnZ. By linearfitting, relevant material parameters were
obtained and thedependences εp of and εc on Z were written as
follows:
εp � 0.002335Z0.14057
,
εc � 0.00166Z0.14144
.(12)
Besides, the relationship between εp and εc can be
usuallydescribed as follows:
εc � Cεp, (13)
where C is the constant. /e value of material constant C
wasusually between 0.3 and 0.9, which had been previously
reportedfor steel. By substituting the values of εp and εc into
equation (13)and regression analysis (Figure 9), the value ofCwas
calculated tobe 0.727, and the relationship between εp and εc was
expressed as
εc � 0.727εp. (14)
Until now, all the parameters needed for the determi-nation of
XDRX have been obtained or expressed as functions
of Zener–Hollomon parameter. Finally, the kinematic modelof DRX
of 5CrNiMoV steel can be expressed as follows:
XDRX � 1 − exp − kdε − εcεp
nd
, ε≥ εc,
nd � 0.536Z0.032,
kd � 0.0235Z0.1056,
εp � 0.002335Z0.14057,
εc � 0.00166Z0.14144,
Z � _ε exp3902388.314T
.
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(15)
2
1
0
ln(–
ln(1
– X
DRX
))
–1
–2
–3
–1.5 –1.0 –0.5 0.5 1.0 1.5 2.0ln((ε – εc)/εp)
0.0
930°C, 0.001s–1
930°C, 0.01s–1
930°C, 0.1s–1
1030°C, 0.001s–1
1030°C, 0.01s–1
1030°0, 0.1s–1
1130°C, 0.001s–1
1130°C, 0.01s–1
1130°C, 0.1s–1
1230°C, 0.001s–1
1230°C, 0.01s–1
1230°C, 0.1s–1
Figure 6: Relationships between ln(− ln(1 − XDRX)) andln((εc −
ε)/εp) at different deformation conditions.
EquationInterceptSlopePearson’s r
y = a + b ∗ x–0.62333 ± 0.170.03209 ± 0.005
0.90474
lnn d
0.6
0.5
0.4
0.3
0.2
0.1
lnZ24 26 28 30 32 34 36 38
(a)
0.0
–0.2
–0.4
–0.6
–0.8
–1.0
–1.2
lnk d
lnZ24 26 28 30 32 34 36
EquationInterceptSlopePearson’s r
y = a + b ∗ x–3.74872 ± 0.28150.10563 ± 0.00946
0.97305
(b)
Figure 7: Relationships between (a) ln nd and lnZ and (b) ln kd
andlnZ.
Advances in Materials Science and Engineering 7
-
3.4. Microstructure Observations. /e optimal metallogra-phy has
been selected to observe microstructure evolution.Figures
10(a)–10(e) show the microstructure of 5CrNi-MoV steel deformed at
a constant temperature of 830°Cand strain rates of 0.001, 0.01,
0.1, 1, and 1 s− 1. /e redarrows in Figure 10 illustrate the new
recrystallized DRXgrains. It should be noticed that DRX grain size
decreasedevidently with increasing strain rate, as it enhanced
boththe work-hardening rate and dislocation density,
therebyproducing more nuclei per unit volume and the energystored.
However, at the strain rate of 0.1, 1, and 10 s-1, DRXbehavior
stayed incomplete and the unrecrystallizationgrains are illustrated
in Figure 10 by the white arrows. Itwas for that higher strain
rates, to some extent, broughtless time for the movements of grain
boundaries anddislocations, which restrained the growth of DRX
nuclei[38, 39].
Figures 11(a)–11(e) show the microstructure of5CrNiMoV steel
deformed at a constant strain rate of
1 s− 1 and the temperature of 830, 930, 1030, 1130, and1230°C.
/e red and white arrows in Figure 11 illustratethe new
recrystallized DRX grains and un-recrystallizedgrains,
respectively. At the temperature of 830°C, therewere still
un-recrystallized grains. As the temperature wasincreased to 930°C,
many elongated grains disappeared,and the microstructure was
gradually replaced by fineDRX grains. For the increased deformation
temperatureof 1030, 1130, and 1230°C, growth of the grains turned
tobe easier. As shown in Figures 11(c)–11(e), big grainswere formed
and tiny grains between the grain bound-aries were observed, which
indicated the growth ofrecrystallized grains. It was pointed that
because re-crystallization activation energy increased with
defor-mation temperature, dislocation motion and crystal slipwere
promoted, which enhanced grain-boundary mi-gration, facilitating
nucleation and growth of DRX grains[40]. In summary, although it
was possible to cause in-complete recrystallization by reducing the
temperature ofhot deformation or increasing the strain rate, it
showedfavorable impact on grain refinement when
completerecrystallization occurred.
It was observed that the complete DRX grain size
usuallyincreased with the increases of the deformation temperature
orthe decreases of the strain rate. /e average dynamic
recrys-tallization grain size of 5CrNiMoV steel at different
defor-mation conditions was measured by the
quantitativemetallography method according to the ASTM standard.
/emeasured results are listed in Table 2. /e average grain size
ofdynamic recrystallization depended on the deformation
tem-perature and the strain rate. It can be expressed as
follows:
DDRX � a3 _εm3 exp
Q3
RT , (16)
where DDRX denotes the average grain size of dynamic
re-crystallization (μm), Q3 is the activation energy for
graingrowth (J/mol), _ε is the strain rate (s− 1), T is the
deformationtemperature (K), R is the gas constant (8.314
J/(mol.K)), and
lnε p
–1.0
–1.5
–2.0
–2.5
lnZ24 26 28 30 32 34 36 38
EquationInterceptSlopePearson’s r
y = a + b ∗ x–6.05973 ± 0.40.14057 ± 0.01
0.95863
(a)
lnε c
–1.5
–2.0
–2.5
–3.0
lnZ24 26 28 30 32 34 36 38
EquationInterceptSlopePearson’s r
y = a + b ∗ x–6.40107 ± 00.14144 ± 0.0
0.93731
(b)
Figure 8: Relationships between (a) ln εp and lnZ and (b) ln εc
and lnZ.
0.30
0.25
0.20
0.15
0.10
0.05
ε c
εp0.1 0.2 0.3 0.4
EquationInterceptSlopePearson’s r
y = a + b ∗ x0.00124 ± 0.00720.72734 ± 0.0349
0.98868
Figure 9: Relationships between εp and εc.
8 Advances in Materials Science and Engineering
-
a3 and m3 are the material constants. Taking the
naturallogarithm of both sides of equation (16), we get
thefollowing:
lnDDRX � ln a3 + m3 ln _ε +Q3
RT. (17)
/rough the linear regression analysis of lnDDRXversus ln
_ε(Figure 12(a)) and lnDDRX versus 1/T(Figure 12(b)) respectively,
the values were as follows:
m3 � − 0.1674 and Q3 � − 102593 J/mol. After determiningthe
material parameters m3 and Q3, a3 was obtained as173,488 from the
relationships between DDRX and_εm3 exp[Q3/RT] (Figure 13). /e model
of dynamic re-crystallization grain size of 5CrNiMoV steel can
beexpressed as follows:
DDRX � 173488_ε− 0.1674 exp
− 102.594 × 103
RT . (18)
Figure 10: Optical microstructure of 5CrNiMoV steel deformed at
the temperature of 830°C: (a) _ε� 0.001 s− 1, (b) _ε� 0.01 s− 1,
(c) _ε� 0.1 s− 1,(d) _ε� 1 s− 1, and (e) _ε� 10 s− 1.
Advances in Materials Science and Engineering 9
-
Figure 11: Optical microstructure of 5CrNiMoV steel deformed at
the strain rate of 1 s− 1: (a) T� 830°C, (b) T� 930°C, (c)
T�1030°C,(d) T�1130°C, and (e) T�1230°C.
Table 2: Average dynamic recrystallization grain size (μm).
Temperature (°C) 0.001s− 1 0.01 s− 1 0.1 s− 1 1 s− 1 10 s− 1
830 6.75 5.51 3.71 2.25 1.85930 20.98 14.18 9.69 6.68 4.361030
42.83 27.86 20.23 13.23 9.491130 83.53 55.67 38.85 26.31 18.871230
149.20 98.21 70.30 46.24 33.94
10 Advances in Materials Science and Engineering
-
4. Conclusion
Based on the isothermal compression tests on the Gleeble3500
thermal simulator in the range of temperatures 830,930, 1030, 1130,
and 1230°C and strain rates 0.001, 0.01, 0.1,1, and 10 s− 1, the
dynamic recrystallization (DRX) kinetics of5CrNiMoV steel was
investigated./e following conclusionswere drawn from the present
study:
(1) True stress-strain curves obtained by hot compressiontests
exhibited the typical characteristics of dynamicrecovery or dynamic
recrystallization. /e tempera-ture and strain rate had significant
influences on thetrue stress which increased with decreasing
deformation temperature and increasing strain rate./e
constitutive behavior of 5CrNiMoV steel wasanalyzed to deduce the
operative deformationmechanisms. Its apparent activation energy
Q(390.238 kJ/mol) was larger than that calculated basedon the
empirical formula for the lattice self-diffusionin 5CrNiMoV steel.
/e value of material constant nwas exactly close to 5, which
indicated that the de-formation mechanism was mainly controlled by
theglide and climb of dislocations. By further analysis oftrue
stress-strain curves, the Arrhenius-type consti-tutive equation
with Zener–Hollomon parameter forthe steel was constructed as
follows:
σ �1
0.0128ln
Z
1.17 × 1014
1/4.927
+ Z1.17×1014 2/4.927
+ 1 1/2
,
Z � _ε exp3902388.314T
.
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(19)
(2) Characteristic stresses and strains on the true
stress-strain curves at different deformation conditionswere
obtained, and the dependences of the criticalstrain, peak strain,
and materials constant kd and ndon the Zener–Hollomon parameter
were investi-gated. To quantitatively analyze the impact of
thestrain and other deformation conditions on the DRXvolume
fraction, a modified model from the Avrami’equation was established
as follows:
lnD
DRX
6
5
4
3
2
1
830°C930°C1030°C
1130°C1230°C
lnε·–8 –6 –4 –2 0 2 4
(a)lnD
DRX
5
4
3
2
1
0
0.001s–10.01s–10.1s–1
1s–110s–1
1/T0.00080.0007 0.0009
(b)
Figure 12: Relationships between (a) lnDDRX and ln _ε and (b)
lnDDRX and 1/T.
DD
RX
160
120
80
40
0
ε· m3exp(Q3/RT)0.0000 0.0004 0.0008
EquationInterceptSlopePearson’s r
y = a + b ∗ x2.22178 ± 2.4731173488.35157 ± 8
0.97086
Figure 13: Relationships between DDRX and _εm3 exp(Q3/RT).
Advances in Materials Science and Engineering 11
-
XDRX � 1 − exp − kdε − εcεp
nd
, ε≥ εc,
nd � 0.536Z0.032,
kd � 0.0235Z0.1056,
εp � 0.002335Z0.14057,
εc � 0.00166Z0.14144,
Z � _ε exp3902388.314T
.
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(20)
(3) Microstructure observations indicated that DRX wasthe main
mechanism of work softening for steelsduring large deformation and
austenite grains weregreatly refined by reducing the temperature of
hotdeformation or increasing the strain rate whencomplete
recrystallization occurred. And the DRXgrain size model of 5CrNiMoV
steel could beexpressed as follows:
DDRX � 173488_ε− 0.1674 exp
− 102.594 × 103
RT . (21)
Data Availability
/e data used to support the findings of this study are in-cluded
within the article.
Conflicts of Interest
/e authors declare that there are no conflicts of
interestregarding the publication of this paper.
Acknowledgments
/is work was financially supported by the National KeyResearch
and Development Program of China(2017YFB0701803 and 2016YFB0701403)
and the State KeyLaboratory of Nickel and Cobalt Resources
ComprehensiveUtilization.
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