Vol. 11 No. 4 J . C E N T . S O U T H U N IV . T E C H N O L . Dec. 2004

Article ID: 1005 - 9784(2004)04 - 0 3 5 3 - 0 5

Kinetics for static recrystallization after hot working of 0 . 3 8 C - 0 . 9 9 C r - 0 . 1 6 M o steel e

I.I X i o n g ( ~ ~]~)1 Z H A N G H o n g - b i n g ( ~ N ~ ) 2, RUAN X u e - y u ( ~ N ~ ) ~, I .UO Zhong-hua(~)~4:i~) ~, Z H A N G Y a n ( ~ ~ ) 3

(1. Department of Plasticity Technology, Shanghai Jiaotong Universi ty, Shanghai 200030, China; 2. Department of Materials Engineering, Shanghai Institute of Technology, Shanghai 200233, China;

3. State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China)

Abstract: The restoration mechanisms for static recrystallization of work-hardened austenite were investigated by using double-pass compression tests performed on medium carbon steel containing chromium and molybdenum. The

softening fraction was defined by 2 ~ offset method. The results show that Avrami exponent of about 0.21 is insen- sitive to deformation temperature, indicating that the action of steel grade should be considered. The time of 50°~ recrystallization (t0.5) decreases noteworthily with the increase of deformation temperature. Apparent activation en- ergy for static recrystallization of 195 kJ/mol , which is close to that of vanadium microalloyed steel, is obtained by calculating. The increasing trend of the driving force for recrystallization is opposite to that of the deformation tem-

perature, which is attributed to the number of operative slip system increasing as temperature increasing.

Key words: hot working; steel; softening fraction; recrystallization; restoration mechanism; work-hardened

CLC number: TG 312 Document code: A

1 INTRODUCTION

The chief aim of hot working is to change original metals into the metal products possessing wanted shape and properties by changing the shape and microstructure of metals at elevated tempera- ture. There are dynamic recovery and dynamic re- crystallization during hot working. For multi-pass deformation, between passes if the former strain is less than the critical strain, static recovery and static recrystallization will occur without meta dynamic recrystallization. Static recrystallization between passes has a particularly important influ- ence on the subsequent microstructures and on the restoration of flow stress ElI , thereby the effects of deformation parameters and chemical components on static recrystallization have been studied by many researchers in recent decades L: to]. The direct method (metallographic method) and the indirect method (thermomechanical test method) were used to investigate the progress of static recrystalliza- tion. The former can directly offer data, but it is laborious and time consuming, and in many cases even impossible to be used E3'lt]. The latter , gener- ally double-pass test , computing softening frac tions according to stress - strain curve, has an im- perfection difficult to distinguish recovery and re-

crystallization. Compared with the double-pass thermomechanical method, another mechanical tes- ting method, stress relaxation, conquers the prob- lem caused by recovery and consumes less time, whereas the relationship between the stress present during recrystallization and softening fraction has been uncertain Fll-t:g , thus enough evidence is nee- ded to testify its reliability. Usually the static re- crystallization kinetics is described by Avrami equation E14]

arv = 1 - - e x p I - - B (7[-f)n I (1)

where cry is the recrystallized fraction, B = - - ln(1 f ) , f is the specified recrystallization fraction, n is Avrami exponent , t is the isothermal holding time between deformation passes, and tf is the time for a specified recrystallization fraction. Therefore , the dependence of n and t¢ on deforma- tion parameters should be known to completely de- scribe recrystallization kinetics, tf is defined as fol lows~ ls] .

h=As PdgZrexp ( R ~ ) (2)

where Z, Zener-Hollomon parameter , is equal to eexp(Qd~f/RT), Qaef is the deformation activation energy, e is the equivalent strain, ¢ is the strain rate, d0 is the initial grain size, Q~rx is the activa-

@ Foundation item: Project(50275094) supported by the National Natural Science Foundation of China; project(03HZ01) supported by the

Emphasized Item of Development Foundation of Science and Technology of Shanghai City, China

Received date: 2003 - 12 - 25 ; Accepted date: 2004 - 04 - 07

Correspondence: LI Xiong, Doctoral candidate ; Tel: -- 86-21-62813430 ; E-mail : li_xiong@ peoplemail, com. cn

• 354 • J o u r n a l C S U T Vol . 11 No. 4 2004

tion energy for static recrystall ization, R is the gas constant , T is the absolute t empera ture , and A , p , q, r are parameters dependent on material. Be- cause r has a very weak effect on strain rate E~6~, which suggests that r - ~ 0 , thus Z~-~I . General ly , let f be equal to 0. 5, Eqns. (1) and (2) can be evolved as follows:

x v = l - - e x p [ - - O . 6 9 3 ( k ) ~] (3)

to .5=A~-Pdqexp(~Z~ ) (4)

In the previous work most studies of static re- crystallization were concentrated in C-Mn steels , Nb microalloyed steels , V microalloyed steels and stainless steels[115], whereas Cr-Mo structural steels were not involved. The purpose of the pres- ent s tudy is to investigate the behavior of static re- crystallization in 0 .38C-0 .99Cr -0 .16Mo steel. Double-pass compression tests were used to exam softening behavior of the austenite during the in terpass holding times.

2 MATERIALS AND EXPERIMENTAL METHODES

2 .1 Materials and experimental procedure The steel used in the exper iment , provided by

way of hot-rolled s ta te , was forged into round bar in d ia -mete r of 10 m m and then machined into small cylindrical compression specimens with 8 mm in diameter and 15 m m in length. The chemical composit ion of the steel is listed in Table 1.

Table 1 Chemical composit ion of steel w / %

C Si Mn Cr Mo P S

0 . 3 8 0. 23 0 . 6 4 0 . 9 9 0 . 1 6 0. 008 0. 009

The thermomechanical method is quicker and easier than the metal lographic method, so that the in terrupted compression technique was used to s tudy the static softening in the present study. In order to assess the extent of res torat ion, double- pass compress ion exper iments were carried out using a Gleeble-1500 thermomechanical simulator. The specimens were heated to 1 200 °C and kept for 5 min to get requisite grain size of austeni te , then cooled to deformation tempera tures ranging from 975 °C to 1 075 °C. The time intervals be- tween passes were from 5 s to 1 000 s. A constant strain per pass (s) of 0 .2 and a constant strain rate of 1 s -1 were applied. The schematic diagram of double-pass compression tests is shown in Fig. 1.

2 . 2 Data processing Ordinarily the softening fraction between the

deformation passes is measured by the back extra- polation method , the mean flow stress method and

m

E ~e

Fig. 1

1200 °C 5rain ~ Strain rate: ls l

10 °C/s~ ~1= ~=0.2

,0s % 975-1 075 °C 5-1"000 s \ /20° s

Time/s

Schematic diagram of double-pass compression tests

the offset method. The softening fraction (XBE) can be calculated by the back extrapolat ion method as fol lows.

O" m -- O'BE XBE - - ( 5 )

am -- a o where am is the flow stress corresponding to the end of the first pass , aBE is the s t ress corresponding to the intersection of initial strain curves before and after it is t ranslated onto the second strain curve to make coincident, ac~ is the yield stress in the first pass. The softening fraction was under- est imated when the back extrapolat ion was em- ployed, and the trend be came more intense as the reerystallized fraction increases [2'3J.

The softening fractional evaluated in light of the mean flow stress method is calculated perform- ing integration on stress - strain curve. The sof- tening parameter , x~, can be calculated by the fol- lowing expression.

~m - - ~e xo - - (6)

~m - - ~1

where al and #z are the mean flow stresses in re- spect of the first and seeond passes , respectively, am is the mean stress in a hypothetical second pass evaluated from the continuous curve and corre- sponds to zero softening. The mean flow stress is calculated according to the following expression:

a -- a& (7)

During calculating am value, the stress - strain curve in the first pass needs to be extrapolated. Here it is arbi t rary because it is artificially inter- fered.

For the offset method , the softening fraction is calculated by the following express ion.

O" m - - O" 2 Zo,-- (8)

O" m - - 0 " 1

where 0 1 and a2 are the offset s t resses of 0. 2 and 2% strain in the first and second passes , re- spectively. By 0. 2 ~ offset me thod , the effect of the recovery was underes t imated so that the sol-

LI Xiong, et al: Kinet ics for stat ic reerystal l izat ion af ter hot work ing of 0 . 3 8 C 0 . 9 9 C r - 0 . 1 6 M o steel • 355 °

tening fractions calculated were more than the re- crystallized fraction E~'I~] , and that the precisions in calculation were often disturbed by the "no i se" that sometimes appears in the early part of flow curve at high temperature E~6]. 2 ~ offset method is comparatively insensitive to recovery, and the sof- tening fractions calculated by it fit well to the re- crystallized fractions L~'16] .

Consequently, 2O/oo offset method is used to compute the static recrystallized softening rate. Within admissible error , the recrystallized fraction Xv is considered approximately equal to the soften- ing fraction. Because the strain applied is less than critical strain required by dynamic reerystalliza- t ion, dynamic and meta-recrystallization could not happen and would not be considered while calculat- ing the static recrystallized fraction.

3 R E S U L T S A N D D I S C U S S I O N

The double-pass compression test was per formed to exam the restoration by static recrystal- lization. Since the true strain value of 0. 2 in the first pass is well below that required to initiate dy namic recrystallization in Cr-Mo steel, the hot working is finished at the work-hardening stage, the work-hardened austenite is then softened only by the static recovery and recrystallization without metadynamic recrystallization during isothermal holding after deformation. For the various deform- ation temperatures and the various time intervals between passes, the softening fraction determined by 2°/00 offset method is shown in Fig. 2. These specimens have a mean initial austenite grain size of 140 htm. It can be seen that the curves display the sigmoid-shaped behavior as the deformation tem- perature is increased to 1 075 °C, and the softening fraction is increased with the increase of the hold- ing time.

The dependence of l n l n [ 1 / ( l - - x v ) ] on lnt is shown in Fig. 3. According to Fig. 3, n value and t0.5 value can be obtained. Taking non-exponent

0 8 = 1 075 .~ 2

0.6

'=~ 0.4 f ~' 0.2

to 5

o J 10 100 1 600

Ti me/s

Fig. 2 Effect of temperature on softening fraction

items as a side of Eqn. ( 3 ) , and taking the log- ari thm twice of both sides, the following expres- sion, is obtained.

lnln[1/(1--xv)]=nlnt+lnO. 693--nlnt0~ (9) where n is the slope, (ln0. 693--nlnt0.~) is the intercept. After the slope and the intercept are measured, t0.~ can be determined. Fur thermore , to.5 can also be got from Fig. 2. The change of t0.s with the deformation temperature is plotted in Fig. 4. As shown in Fig. 4, t0.~ value decreases as deformation temperature increases, showing that static recrystallization can progress at a greater rate at higher temperature. It is well known that recovery and recrystallization are thermally-activa- ted processes, thereby the occurrence of static re- crystallization is sensitive to temperature, to.~ val- ues rooted from Figs. 2 and 3 are discrepant, which mainly results from the errors existing in the for- mer during fitting curves.

1.0

0.5

,~ 0.0

_~ 0.5

1.0

Fig. 3

-1.5

1 075 °C

25 °C

°C A • •

I I I I

I 3 5 7 In(t/s)

Dependence of ln lnE1 / (1 - -Xv) ] on lnt

"V~r,

300

200

1 O0

0

960

l - - Rooted from Fig.3 Rooted from Fig.2

I

,0'00 ,0'40 lo8o Temperature/°C

Fig. 4 Dependence of t0.5 on deformation temperature

Avrami exponent n measured under various deformation conditions, about 0. 21 (see Fig. 3 ) , with a similar result discovered by Garcia-Mateo et al [~7] , is much less than that of the previous study. These values reported in literatures are listed in Table 2. Theoret ical ly, this exponent is between 1 . 0 - 2 . 0 , 2 . 0 - 3 . 0 o r 3 . 0 4. 0 for linear, planar

and polyhedral growth of grains, respective- ly[! 1'1~]. Laasraoui et al [2] thought tha t , under the condition of static recrystall ization, n value is inde- pendent of the deformation parameters and chemi- cal composit ion, which is around 1.0 . Per t tu la et al In2 considered that in the case of grain boundary nucleation, the exponent obtained for static recrys- tallization is typically between 1 .0 and 2 .0 and if an exponent is below 1 .0 , some recovery effect can be included. Howeve r , alloying elements in solu- tion were thought to retard the progress of recov- ery through solute-drag effects on dislocation mo- bility [~9]. In addit ion, unlike 0.2 °//0 offset method , in which 20 °//00 of softening was a t t r ibuted to recov- ery [4] , 2 °//00 offset method nearly avoided the effect of recovery [31. I t can he seen f rom Table 2 tha t , for different steel grades and different deformation pa ramete r s , n value varies f rom 0.4 to 2 .0 , which should not be simply at t r ibuted to recovery for due to the finite effect of recovery. The role of single alloy element was largely noticed [2' a, 11, 20], but the

combination of alloy elements was ignored. T h u s , fur ther work is required to evaluate the role of the material and the deformation parameters upon the value of the exponent.

Table 2 n values of Avrami equation

Steel n value Ref.

Stainless steel 2 . 0 1

L o w C steel; Nb steel; Nb-B steel; 1 .0 2 Cu-Nb-B steel

0 . 1 C - 1 . 4 2 Mn 0 .31Si -0 . 0 3 5 N b 0 . 8 - 1 .3 3

0 . 1 7 C - 0 . 7 4 M n - 0 . 012Si -0 .01Ni-0 . 019Cr ; 2 . 0 4 0 . 0 4 C - 0 . 3 M n - 0 . 000 9Si-0. 025Ni-0. 033Cr

Sta inless s teel ; C -Mn steel; 0 . 7 - 1 . 3 11 Nb steel ; A r m o iron

0 . 2 4 C - 1 . 5 6 M n - 0 . 2 8 S i 0 . 1 8 V - 0 . 5 - 1 . 1 17 0. 019AI-0. 009 9N

0 . 3 3 C 1 . 4 9 M n 0 . 2 5 S i - 0 . 2 4 V 0 . 4 - 1 . 1 17 0. 027A1 0. 010 ON

0 . 4 7 C 0 . 7 8 M n - 0 . 2 4 S i - 0 . 025A1-0. 009 ON 0 . 7 - 1 .2 17

~ 4

--.= 3

i i / i

0.90 0.92 0.94 0.96 (RT)-,/(10-s mol.J i)

Fig. 5 Dependence of lnt0 ~ on 1 / ( R T )

The driving force (Fsr , ) for recrystallization can be est imated from Re{. [ 17 ] .

12.5/xo 2 F~rx-- G (11)

where Aa is the increase of s t ress obtained from the flow curve during working hardening, G is the shear modulus of austenite with an approximate value of 4 X 1 0 4 MPa c5]. The deformat ion tempera- ture influences the driving force through Aa term. The recrystallization forces were calculated from 975 °C to 1 075 °C, and are shown in Fig. 6.

Nb microal loyed steel

0 . 1 9 C 1 . 2 9 M n - 0 . 287Si; 0 . 1 2 C - 1 . 4 2 M n - 0 . 362Si-0. 042V

0 . 9 19

0 . 7 20

Fig. 6

In te rms of Eqn. ( 4 ) , the following expression is deduced to est imate the activation energy for static recrystall izaion.

Qsrx lnt0 5 = In (A¢- Pd q ) + R-T ( 10 )

The dependence of lnt0s on 1/(RT) is plotted and fitted into a line, f rom the slope of the line, the activation energy of Q~rx = 195 k J / m o l was mea- sured, as shown in Fig. 5. This value is not con- sistent with other data reported in the l i teratures for Nb steels c2] and stainless steel L1] , hut in agree- ment with that of V microalloyed steel [~9' 21]

3

z

2

1 960 1 000 1 040 I 080

Temperature/°c

Dependence of recrystall ization force on deformation tempera ture

• 356 • Journal OSUT Vol. 11 No. 4 2004

From Fig. 6, the driving force for recrystalli- zation decreases with the increase of deformation temperature . This is because the number of opera- tive slip system increases with increasing tempera- ture [~] , result ing in Aa being smaller. These values are in accordance with the results in Ref. [17] .

4 CONCLUSIONS

1)A lower value of Avrami exponent is meas- ured by 2% offset me thod , which is insensitive to deformation temperature . The result indicates that the effect of steel grade should be considered.

I.I Xiong, et al: Kinetics for static recrystallization after hot working of 0.38C-0.99Cr 0. 16Mo steel • 357 •

2 ) T h e t ime of 5 0 ~ ree rys ta l l i za t ion at var ious

de fo rma t ion t e m p e r a t u r e s , t , .5, is computed . T h e

acce lera t ion of t,,5 decreases as the de fo rma t ion

t e m p e r a t u r e increases.

3) A p p a r e n t ac t iva t ion ene rgy for s ta t ic recrys-

ta l l iza t ion of 195 k J / m o l are d e t e r m i n e d , which is

close to that of the r epor t ed V mic roa l loyed steels.

4) T h e dr iv ing force for rec rys ta l l i za t ion de-

creases wi th increas ing de fo rma t ion t e m p e r a t u r e ,

which resu l t s f rom the n u m b e r of opera t ive slip

s y s t e m increas ing as de fo rma t ion t e m p e r a t u r e in-

creasing.

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