Materials Science & Engineering A 565 (2013) 126–131

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Materials Science & Engineering A

0921-50

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E-m

journal homepage: www.elsevier.com/locate/msea

The metadynamic recrystallization in the two-stage isothermal compressionof 300M steel

J. Liu a, Y.G. Liu a, H. Lin b, M.Q. Li a,n

a School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR Chinab Beijing Institute of Aeronautical Materials, Beijing 100095, PR China

a r t i c l e i n f o

Article history:

Received 23 October 2012

Received in revised form

27 November 2012

Accepted 28 November 2012Available online 7 December 2012

Keywords:

300M steel

Two-stage compression

Metadynamic recrystallization

Volume fraction

93/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.msea.2012.11.116

esponding author. Tel.: þ86 29 88460465; fa

ail address: honeymli@nwpu.edu.cn (M.Q. Li)

a b s t r a c t

The two-stage isothermal compression are carried out at the deformation temperatures of 1173–1373 K,

strain rates of 0.1–5.0 s�1, and a strain of 0.69 and the inter-pass times of 0.2–5.0 s after the first stage

isothermal compression in order to investigate the metadynamic recrystallization of 300M steel. The

experimental results show that the metadynamic softening fraction rapidly increases with the increasing of

deformation temperature and strain rate. According to the present experimental results, the kinetic equation

for the metadynamic recrystallization of 300M steel is proposed. The volume fraction in the metadynamic

recrystallization Xm is presented as follows: Xm¼1�exp[�0.693(t/t0.5)0.69], and the time for the metady-

namic softening fraction of 50%, t0.5¼9.7�10�7_e�0:27 exp[14103/(RT)]. The calculated results are in a good

agreement with the experimental, which indicates that the present kinetic equation can be used to

characterize the metadynamic recrystallization behavior in the isothermal compression of 300M steel.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

The 300M steel as one of the ultrahigh strength steel is widelyused in aircraft landing gear due to its good balance of highstrength, fracture toughness, fatigue strength and good ductility.For 300M steel, the austenite grain coarsening occurs easily in hotforging. Coarse grains have an adverse effect on plasticity, strengthand toughness of 300M steel, thus obstructing the development ofhigh performance and complex component of 300M steel.

Many investigations have laid a foundation for controlling coarsegrains in forging of 300M steel by investigating the growth behaviorof austenite grains and the deformation mechanisms of 300M steelin the isothermal compression. Zhang et al. [15] obtained the growthbehavior of austenite in the heating process of 300M steel, andpointed out that grain size of austenite increased with the increasingof heating temperature and holding time, and presented the growthmodel of austenite in 300M steel: d¼4.04�106t0.7exp[�1.32�105/(RT)]. Luo et al. [16] investigated the flow stress, the apparentactivation energy for deformation and the growth behavior ofaustenite in the isothermal compression of 300M steel.

In forming processes, the hot rolling and forging processes oftenconsist of several successive deformation passes, including inter-passperiods between deformation passes. During the inter-pass periods inhot forging, three distinct softening mechanisms may take place foraustenite: static recovery, static recrystallization and metadynamicrecrystallization [1,2,11]. Metadynamic recrystallizaton takes place

ll rights reserved.

x: þ86 29 88492642.

.

when the nuclei formed by dynamic recrystallization during defor-mation grow [3,4]. Metadynamic recrystallization behavior betweendeformation passes are important phenomena causing the changes ingrain characteristics (i.e. size and distribution) of metals. So under-standing metadynamic recrystallization behavior during hot rollingand forging processes is an important point in controlling coarsegrains, so as to manufacture the high quality products.

Most researches [5–7] pointed out that strain rate was theprimary parameter affecting metadynamic recrystallization kinetics,with a small effect of temperature but insensitivity to strain. Raoet al. [8] predicted the softening behavior of medium-carbon steelunder hot working conditions in multistage compression by theoffset-stress method, back-extrapolation stress method and strain-recovery method. Based on the above-mentioned studies, Lin et al.[9] investigated the metadynamic recrystallization behavior of42CrMo by using the two-pass isothermal compression, and set upkinetic equation of metadynamic recrystallization. Elwazri et al. [10]investigated the kinetics of metadynamic recrystallization in vana-dium microalloyed high carbon steels, and found that there is atransition strain region between where both static and metadynamicrecrystallization take place during the inter-pass time, and revealedthat V and Si have a strong solute drag effect on the kinetics ofmetadynamic recrystallization. Djaic and Jonas [11] studied the effectof inter-pass time and processing parameters (deformation tempera-ture and strain rate) on microstructure evolution during inter-passperiods between deformation passes. Jung et al. [12] formulatedequations for metadynamically recrystallized grain size and graingrowth by single compression. Lin and Chen [13] investigated theeffect of deformation temperature, strain rate on the microstructureevolution during metadynamic recrystallization in hot deformed

Table 1The chemical composition of as-received 300M steel (wt%).

C Si Ni Mn Cr Mo V Cu S P

0.39 1.61 1.82 0.69 0.91 0.42 0.07 0.06 0.0012 0.0089

Fig. 1. Experimental procedure for the two-stage isothermal compression.

J. Liu et al. / Materials Science & Engineering A 565 (2013) 126–131 127

42CrMo steel, and established the grain size model for metadynamicrecrystallization. Beladi et al. [14] proposed a novel mechanism ofmetadynamic softening during annealing of a fully dynamicallyrecrystallizd austenitic Ni–30Fe.

The present work aims to investigate the metadynamicrecrystallization behavior in the two-pass isothermal compres-sion of 300M steel. The effects of deformation temperature, strainrate on metadynamic recrystallization behavior are investigatedby using the two-stage isothermal compression. The experimentaldata are used to obtain the kinetic equation which can calculatethe metadynamic softening fractions in the two-pass isothermalcompression of 300M steel. The comparisons between the experi-mental and the calculated results show that the kinetic equationcan be used to characterize the metadynamic recrystallizationbehavior in the isothermal compression of 300M steel.

2. Experiments

The chemical composition (wt%) of as-received 300M steelwith a diameter of 22.0 mm is shown in Table 1. The Ac1

temperature and Ac3 temperature of 300M steel are 1021 K and1075 K respectively [15,16]. The cylindrical specimens of 300Msteel with a diameter of 8.0 mm and height of 12.0 mm weremachined. The two-pass isothermal compression was carried outon a computer-controlled, servo-hydraulic Gleeble-1500 thermo–mechanical simulator.

As shown in Fig. 1, the compression specimens were heatedto 1473 K at a heating rate of 10 K s�1, held for 5 min prior tocompression to ensure full austenitizing and a uniform grain size,then cooled at a cooling rate of 10 K s�1 to deformation tempera-ture and held for 1 min. The first stage compression wereperformed at the deformation temperatures of 1173 K, 1273 K,and 1373 K, strain rates of 0.1 s�1, 1.0 s�1, and 5.0 s�1, and astrain of 0.69. As the strain reached to 0.69, the specimens wereheld at a given deformation temperature for inter-times of 0.2 s,0.5 s, 1.0 s, and 5.0 s after unloading. Then the second stagecompression started, the deformation temperatures and strainrates of the second stage were same as that in the first stage. Toprevent the occurrence of dynamic recrystallization, the strain inthe second stage were determined as 0.16. After the second stageisothermal compression, the specimens were rapidly quenchedin water.

3. Results and discussion

3.1. Flow stress–strain curves

The selected flow stress–strain curves obtained in the two-stagecompression of 300M steel at different times, deformation tem-peratures and strain rates are shown in Fig. 2. For all the experi-mental conditions, the yield flow stress in the second stagecompression is higher than or the same as that in the first stagecompression. It can be seen from Fig. 2(a) that the yield flow stressof 300M steel in the second stage compression generally decreasewith the increasing of inter-pass time at the same heat treatmentand deformation conditions. Those results suggest that muchmetadynamic softening occurs with the increasing of inter-pass

time. As inter-pass time increases to 5.0 s, the flow stress–strain inthe second stage compression is the same as that in first stagecompression, which means that full metadynamic softening occurs.In case of no metadynamic softening, the flow stress–strain curve inthe second stage compression coincides with the extrapolated onein the first stage compression [17]. There are two reasons to explainthe changes of the flow stress–strain curves in the following: thefirst one is that metadynamic softening occurs and dislocationdensity before the second stage compression decreases with theincreasing of inter-pass time, so the yield flow stress in the secondstage compression decreases with the increasing of inter-pass time.The another one is that the grain size before the second stagecompression increases with the increasing of inter-pass time due tometadynamic softening which can cause the dynamically refinedmicrostructure to coarse. Meanwhile, it is well known that the yieldflow stress in the deformation process decreases with the increas-ing of grain size. Thus, if the inter-pass time is long enough to allowthe full metadynamic softening to destroy the dislocation structureestablished in the first stage compression, the flow stress–straincurve in the second stage compression is the same as that in thefirst stage compression in order to rebuild the dislocation structure.It is also observed that the flow stress in the two-stage compressionof 300M steel is sensitive to deformation temperature and strainrate in Fig. 2(b) and (c). The flow stress decreases markedly with theincreasing of deformation temperature at certain strain rate, andincreases gradually with the increasing of strain rate at certaindeformation temperature. This suggests that metadynamic soft-ening is significantly affected by the deformation temperature andstrain rate. In addition, it can be seen form Fig. 2(c) that fullmetadynamic softening occurs at a deformation temperature of1373 K.

3.2. Effect of the processing parameters on the metadynamic

softening

The interrupted deformation method is based on the principlethat the yield flow stress at the high deformation temperatures issensitive to the microstructure evolution. In order to quantify themetadynamic softening fraction, the 0.2% offset-stress method isadopted in the present study. The metadynamic softening frac-tion, X is determined by applying the offset-stress method asfollows:

X ¼sm�s2

sm�s1ð1Þ

where sm (MPa) is the flow stress at the end point in the firststage compression, s1 (MPa) and s2 (MPa) are the offset yield

0

35

70

105 1.0 s

0.5 s

5.0 s

Flow

stre

ss/M

Pa

Strain

0.2 s

Deformation temperature: 1373 KStrain rate: 1.0 s-1

0

50

100

150

200

1373 K

1273 K

Flow

stre

ss/M

Pa

Strain

1173 K

Strain rate: 5.0 s-1

Inter-pass time: 5.0 s

0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

0.0 0.2 0.4 0.6 0.80

30

60

90

120

150

0.1 s-1

1.0 s-1

Flow

stre

ss/M

Pa

Strain

5.0 s-1

Deformation temperature: 1373 KInter-pass time: 5.0 s

Fig. 2. Flow stress–strain curves in the two-stage compression of (a) 300M steel at different inter-pass time, (b) deformation temperature, and (c) strain rate.

J. Liu et al. / Materials Science & Engineering A 565 (2013) 126–131128

flow stresses for the first and second stage compression respec-tively (Fig. 3).

Fig. 3. Determination of the metadynamic softening fraction using the 0.2% offset-

stress method.

3.2.1. Deformation temperature

Fig. 4 shows the effect of deformation temperature on meta-dynamic softening fraction of 300M steel at the deformationtemperatures of 1173 K, 1273 K, 1373 K, and a strain rate of0.1 s�1. Obviously, it can be seen from Fig. 4 that metadynamicsoftening fraction increases with the increasing of deformationtemperature. At an inter-time of 1.0 s, the metadynamic softeningfraction is only 37.9% at a deformation temperature of 1173 K,and it increases to 85.2% at a deformation temperature of 1373 K.In addition, it is also observed that the velocity of metadynamicsoftening at a deformation temperature of 1373 K is higher thanthose at the other deformation temperatures. 100% metadynamicsoftening fraction achieves at a deformation temperature of1373 K and an inter-time of 5.0 s. The full metadynamic softeningeffect occuring in the short time reveals that metadynamic soft-ening at high deformation temperature is rapid. Meanwhile, at adeformation temperature of 1173 K and an inter-pass time of5.0 s, the metadynamic softening fraction is only 50% and therate of metadynamic softening rapidly decreases, which maymean that the full metadynamic softening cannot occur at this

deformation condition. The two reasons can explain the effect ofdeformation temperature on the metadynamic softening fractionin the following: the first one is that the nucleation of dynamicrecrystallization is the thermally activated process, the higher thedeformation temperature, the easier the formation of dynamicnuclei. The another one is that as the deformation temperatureincreases, the diffusion of atoms speed up, and the migration ofmobile boundaries becomes easier, in which it benefits to thegrowth of dynamically formed grains.

0 1 2 3 4 5

0.2

0.4

0.6

0.8

1.0

Met

adyn

amic

sof

teni

ng fr

actio

n/%

Inter-pass time/s

1173 K 1273 K 1373 K

Strain rate:0.1 s-1

Fig. 4. Effect of the deformation temperature on the metadynamic softening.

0 1 2 3 4 5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Met

adyn

amic

sof

teni

ng fr

actio

n/%

Inter-pass time/s

0.1 s-1

1.0 s-1

5.0 s-1

Deformation temperature:1173 K

Fig. 5. Effect of the strain rate on the metadynamic softening.-1

0

1

2

1173 K 1273 K 1373 K

ln(ln

(1/(1

-Xm

)))

lnt

Strain rate:1.0 s-1

-2 -1 0 1 2

0.0

0.9

1.8

2.7

0.1 s-1

1.0 s-1

5.0 s-1

ln(ln

(1/(1

-Xm

)))

Deformation temperature:1373 K

J. Liu et al. / Materials Science & Engineering A 565 (2013) 126–131 129

3.2.2. Strain rate

The effect of strain rate on metadynamic softening fraction at adeformation temperature of 1173 K is shown in Fig. 5. It can beseen from Fig. 5 that metadynamic softening fraction increaseswith the increasing of strain rate. For different strain rates of0.1 s�1, 1.0 s�1 and 5.0 s�1 as an inter-pass time is 5.0 s, meta-dynamic softening fraction are 51.7%, 64.8%, 70.3% respectively.Main reason for effect of the strain rate on the metadynamicsoftening fraction is that the rate of dislocation generationincreases with the increasing of strain rate [18]. The tangleddislocation structures hinder the dislocation movement, leadingto the difficulty for the occurrence of dynamic recovery at highstrain rates. Then, the reduced extent of dynamic recoveryoccurring at high strain rate may in turn produces a high dis-location density and increases the driving force for metadynamicrecrystallization.

-2 -1 0 1 2

-0.9

lnt

Fig. 6. Relationship between ln(ln(1/(1�Xm))) and ln t: (a) deformation tempera-

ture, and (b) strain rate.

3.2.3. Inter-pass time

The effects of the inter-pass time on the metadynamic soft-ening fraction are shown in Figs. 4 and 5. It can be seen thatmetadynamic softening fraction rapidly increases with theincreasing of inter-pass time and the velocity of metadynamicsoftening becomes slow at the inter-pass time above 1.0 s. With

the increasing of inter-pass time, the dynamically recrystallizdgrains grow and the amount of metadynamically recrystallizedgrains appear so as to contribute to the softening in the deforma-tion process of 300M steel. Because the dislocation densitydecreases, the driving force for metadynamic softening decreaseswith the increasing of inter-pass time. So the velocity of meta-dynamic softening becomes slow.

3.3. Kinetic equation of metadynamic recrystallization

The Avrami equation can be applied to characterize therecrystallization softening behavior involving nucleation andgrowth. Although the metadynamic softening does not involve anucleation step, it can be defined by the Aravmi equation in thefollowing form [19]:

Xm ¼ 1�exp �0:693t

t0:5

� �n� �ð2Þ

where Xm is the volume fraction in the metadynamic recrystalli-zation (%), and the value of Xm is assumed to be same as themetadynamic softening fraction X, t is the inter-pass time (s), n isthe material dependent constant, t0.5 is the time for the metady-namic softening fraction of 50% (s), which can be expressed asfollows:

t0:5 ¼ A_epexpQm

RT

� �ð3Þ

-2.1 -1.4 -0.7 0.0 0.7 1.4

-2.1

-1.4

-0.7

0.0

0.7

1.4

Cal

cula

ted

lnt 0

.5

Experimental ln t0.5

Fig. 9. The comparison of the experimental and the calculated ln t0.5 (solid lines

J. Liu et al. / Materials Science & Engineering A 565 (2013) 126–131130

where Qm is the apparent activation energy for metadynamicrecrystallization (kJ mol�1), T is the absolute deformation tem-perature (K) and R is the gas constant (J mol�1 K�1), p and A arethe material dependent constants.

Taking the natural logarithm on the both sides of Eq. (2) twicegives,

ln ln1

1�Xm

� �� �¼ ln0:693þnlnt�nlnt0:5 ð4Þ

and substituting the values of the metadynamic softening fractionX and corresponding inter-pass time into Eq. (4), the plots ofln(ln(1/(1�Xm))) versus ln t are shown in Fig. 6. Calculating byusing the linear regression method, the average value of n is 0.69.

Taking the natural logarithm on the both sides of Eq. (3) gives,

lnt0:5 ¼ lnAþpln_eþ Qm

RTð5Þ

the values of t0.5 at the experimental conditions can be conductedfrom the relationship between Xm and corresponding inter-passtime. Fig. 7 shows the effect of deformation temperature T on t0.5.It is obvious that Qm can be estimated as 141 kJ mol�1 by usingthe linear regression method.

Substituting the values of t0.5 and strain rate into Eq. (5), thevalue of p can be obtained as �0.27 from the slopes in Fig. 8

0.72 0.75 0.78 0.81 0.84 0.87

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5 0.1 s-1

1.0 s-1

5.0 s-1

lnt 0

.5

1/T (103·K-1)

Fig. 7. Relationship between ln t0.5 and 1/T.

-3 -2 -1 0 1 2-2.25

-1.50

-0.75

0.00

0.75

1.50 1173 K 1273 K 1373 K

lnt 0

.5

ln(strain rate·s-1)

Fig. 8. Relationship between ln t0.5 and ln _e.

which show a linear relationship between ln t0.5 and ln e. Then A

can be achieved as 9.7�10�7 based on the above-computedmaterial constants (p, Qm).

represent the calculated results; symbols represent the experimental results).

0 1 2 3 4 5

1373 K

Met

adyn

amic

sof

teni

ng fr

actio

n/%

Strain rate:1.0 s-1

1173 K

1273 K

0.0

0.2

0.4

0.6

0.8

1.0

Inter-pass time/s

0 1 2 3 4 50.0

0.3

0.6

0.9

1.2

5.0 s-1

1.0 s-1

Met

adyn

amic

sof

teni

ng fr

actio

n/%

Inter-pass time/s

0.1 s-1

Deformation temperature: 1373 K

Fig. 10. The comparison of the experimental and the calculated metadynamic

softening fraction at (a) different deformation temperatures, and (b) strain rates (solid

lines represent the calculated results; symbols represent the experimental results).

J. Liu et al. / Materials Science & Engineering A 565 (2013) 126–131 131

Eqs. (2) and (3) can be represented as follows:

Xm ¼ 1�exp �0:693t

t0:5

� �0:69" #

ð6Þ

t0:5 ¼ 9:7� 10�7 _e�0:27exp141303

RT

� �ð7Þ

The comparison of the calculated and the experimental t0.5 atdifferent deformation conditions is shown in Fig. 9. The maximumand average difference between the calculated and experimental t0.5

are 16.9% and 8.7% respectively. The comparisons of the calculatedand the experimental Xm at different deformation temperatures andstrain rates are shown in Fig. 10(a) and (b) respectively. Themaximum and average difference between the calculated andexperimental Xm are 17.9% and 3.1% respectively. The calculatedresults are in a good agreement with the experiment, which indicatesthat the model for the metadynamic recystallization behavior in theisothermal compression of 300M steel can be obtained by thepresent kinetic equation.

4. Conclusions

The two-stage isothermal compression of 300M steel has beenconducted in the deformation temperatures ranging from 1173 Kto 1373 K and strain rates ranging from 0.1 s�1 to 5.0 s�1 aimingto investigate the effects of deformation parameters on themetadynamic recrystallization behavior. According to the experi-mental results, the kinetic equation is obtained to characterizethe metadynamic recrystallization behavior. The research resultsare in the following: (1) the metadynamic softening fractionincreases with the increasing of deformation temperature, strain

rate and inter-pass time, (2) the full metadynamic softeningcannot occur at a deformation temperature of 1173 K and strainrate of 0.1 s�1, (3) the full metadynamic softening occurs at adeformation temperature of 1373 K and strain rates in the presentwork, (4) the volume fraction in the metadynamic recrystalliza-tion Xm is presented as follows: Xm¼1�exp[�0.693(t/t0.5)0.69],and the time for the 50% metadynamic softening fraction,t0.5¼9.7�10�7_e�0:27 exp[141303/(RT)]. The calculated resultsare in a good agreement with the experimental.

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