EvolutionofDynamicRecrystallizationin5CrNiMoV ...downloads.hindawi.com/journals/amse/2020/4732683.pdf · models in predicating DRX evolution, as well as its wide applicability.Besides,Luoetal.[16]analyzedthedynamic

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

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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

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.


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)).


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


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:


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


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.


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


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


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


y = a + b ∗ x0.00124 ± 0.00720.72734 ± 0.0349

0.98868

Figure 9: Relationships between εp and εc.


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.


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


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


y = a + b ∗ x2.22178 ± 2.4731173488.35157 ± 8

0.97086

Figure 13: Relationships between DDRX and _εm3 exp(Q3/RT).



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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EvolutionofDynamicRecrystallizationin5CrNiMoV ...downloads.hindawi.com/journals/amse/2020/4732683.pdf · models in predicating DRX evolution, as well as its wide applicability.Besides,Luoetal.[16]analyzedthedynamic