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Formulation

Hot Rolling

of Static

Process

Recrystallization

of Steel Plate*

of Austenite

inBy Atsuhiko YOSHIE,** Hirofumi MORIKAWA,** Yasumitsu

and Kametaro ITOH***Synopsis

A critical condition for static recrystallization of austenite (r) in plate

rolling process has been formulated in terms of the change in average dis-location density. The latter was calculated from the decrease in stress

due to recovery and recrystallization observed by the double deformation

tests. The main results are summarized as follows:

(1) The relation among stress, strain and average dislocation density

has been formulated. By the present formulation, deformation stress for

practical conditions of the controlled rolling of plate can be calculated as

a function of temperature, strain, strain rate and r grain size.

(2) The behavior of static recovery and recrystallization taking place

during holding period after deformation has also been formulated as a

function of dislocation density. This formulation makes it possible to

estimate the critical condition for static recrystallization during an interval

time between the successive rolling passes of plate.

(3) Deformation conditions such as temperature, strain, strain rate,

Y grain size and interval time between passes affect the critical condition

for recrystallization. The shorter interval time elevates the temperature

limit of non words: hot deformation; static recrystallization; austenite; plate

rolling; incubation time; mathematical **I. Introduction

Controlled rolling process has become one of the

important processes in steel plate production. Espe-cially the total reduction in the temperature range of

non recrystallization has been increased for improving

the mechanical properties. Therefore, it is indis-pensable for the process design to make clear the

critical condition for recrystallization of austenite

(r) in hot rolling.

As seen in the schematic illustration of Fig. 1, the

critical condition for static recrystallization of r is

considered to be a function of temperature, stored

strain, strain rate in rolling and r grain size as well

as chemical compositions of steels. In higher tem-perature range, the critical strain (&cr) for recrystalliza-tion is smaller than the strain in each pass of com-mercial plate rolling. As a result, recrystallization

starts during the interval time before the next pass.

In lower temperature range, however, recrystalliza-tion does not begin until an accumulated strain of

several passes exceeds ~cr because the strain of each

rolling pass does not usually exceed 8er.

The critical conditions for recrystallization have

been investigated by many authors. Some authors'-3>

have observed the microstructure of steels quenched

after hot rolling and shown the maps of rolling condi-*

tions which are divided into recrystallization range

and non recrystallization range. This method, how-ever, requires the growth of recrystallized grains to

observable size to define the onset of recrystallization,

so the observed start of recrystallization may be

apparent and different from its true start (i.e., nuclea-tion). Moreover, when a lower hardenability steel

is employed or a specimen is heavily deformed, it is

difficult to discern prior r grain structure because

quenched r transforms to martensite insufficiently.

For these reasons, the critical condition derived from

microstructural observation might not be accurate.

Other authors4,5~ have performed the double defor-mation tests and reported an empirical criterion of

recrystallization : a value of softening ratio specified

at the inflection in a softening ratio res. time curve.

However, the physical meaning of the specific value of

softening ratio in this method is indefinite. Recently

some authors6-$~ have formulated mathematically

the behavior of recrystallization in hot rolling process

in terms of the changes in observed microstructure.

The critical condition for static recrystallization, how-ever, was not described quantitatively, because theFig.1. Schematic illustration of the critical conditions for

recrystallization of Y in hot rolling process (on

assumption that chemical composition, strain rate

and austenite grain size are constant).Based on the paper presented to the 110th ISIJ Meeting, October 1985, 51500, at Niigata University in Niigata. Manuscript

received on August 29, 1986; accepted in the final form on March 13, 1987. © 1987 ISIJ

* * Plate, Bar, Shape & Wire Rod Research Laboratory, R & D Laboratories-II (stationed at Higashida), Nippon Steel Corporation,

Edamitsu, Yahatahigashi-ku, Kitakyushu 805.

* * * Plate Technical Division, Nippon Steel Corporation, Otemachi, Chiyoda-ku, Tokyo chArticle(425)(426) Transactions ISIJ, Vol. 27, 1987incubation period of recrystallization was not taken

into account in their calculation.

In the present report the critical condition for

recrystallization in hot rolling process has been

expressed in a mathematical model by taking the

incubation period into consideration. The model

has been derived not from the change in observed

microstructure but from the decrease in the stress

observed in the present double deformation tests.

In order to estimate the critical condition, the

observed stress has been related to the average dis-location density (p) because the relations among

p, strain and

authors.7'9"°>stress have been clarified by many

II. Mathematical Model

1. Procedure of Mathematical Analysis

Figures 2(a) and 2(b) shows a schematic illustra-tion of the changes in average dislocation density

and stress-strain curves in double deformation tests. 11)

Average dislocation density increases with deforma-tion and decreases during interval time due to the

progress of recovery and recrystallization.

assumption that stress (a) corresponds to p, the value

On the

of p at each point (for example, point A or B in Fig.

2(a)) can be calculated from the observed j (for ex-ample, stress-strain curves A or B in Fig. 2(b)).

Senuma et al. 12) formulated deformation resistance

of hot strip steel as a function of p. At the 1st step

of the present analysis, the relation between r and

p is formulated in the same way.

the decrease in p due to recovery and recrystallization

At the 2nd step,

is formulated as a function of time after deformation

including undetermined coefficients. At the 3rd step,

the values of undetermined coefficients are determined

from the decrease in p during interval time calculated

through the observed a in double deformation tests.

With these procedures, progress of recovery and recrys-tallization after deformation is formulated mathe-matically. The schematic illustration of the pro-cedures of analysis is also shown in Fig. 2.

2. Relation among Deformation Stress, Strain and Average

Dislocation Density

Deformation stress during hot working is expressed

as

a = a'id+ae .........................(1)

where a'id is an internal stress and oe is an effective

stress. As the latter term can be neglected when r

is deformed at high temperature,9> the relation be-tween a and p is expressed as10)

a ale = ap1~2, .. ...................(2)

where a is a constant.

Next, the relation between strain (e) and p will be

derived. Strain hardening and dynamic recovery

proceed simultaneously with hot deformation.

change in p is formulated into the following differential

The

equation.

dp = (op/or)dr+(op/ot)dt ..................(3)Fig. 2. Schematic i

llustration ofthe procedure of the the rolling strain of plate is relatively small, p is

assumed to be proportional to E.13) Therefore the rate

of strain hardening (op/oe) is expressed as

op/or=b ............................(4)

where b is a function of temperature ( T)9) and

b = b° exp (Qb/RTT) ...................(5)

where b° : a constant, Qb : an apparent activation

energy and R : the gas constant (8.314 J. mol-1 K-1).

Dislocation configuration corresponds to e and multi-plication of dislocation depends on T.

of strain rate (s) and r grain size (Dr) are neglected

The effect

because their contributions are assumed to be small.

The rate of dynamic recovery is expressed as14)

op/ot = -cpn .........................(6)

where c is a function of T, and Dr, C coDrae s exp (Qe/RT) ~ ...............( )

where co, me and ne are constants, and Qe an apparent

activation energy. The effect of D1 and are assumed

to be expressed in the form of power function because

their dependence on c is not clear. On the same

assumption, the similar functional forms are adopted

in Eqs. (10), (14) and (15), which will be discussed

below. The opportunity for annihilation of disloca-tions with opposite Burgers-vector (n=2 in Eq. (6))

is very few because dislocations hardly cross-slip in

mainly due to climbing and absorption at grain

boundary (n=1 in Eq. (6)). With the combination

of Eqs. (4) and (6) with n=1, the relation between

p and

deformation asis formulated for a constant through the

p = b/c(1 _ e-eE)+ po e-eE(8)where po is the dislocation density of annealed steel.

From Eqs. (2) and (8), stress-strain relations of any

deformation conditions of the controlled rolling of

plate in r temperature range can be calculated.3. Relation between Static Recovery and Average

Disloca- tion Density

The annihilation rate of p during static

recovery

after deformation is expressed in the same

form asthat of dynamic recovery as14)op/ot = -d .p ,(9)where t is time after deformation andd = doDmdEnd exp (Qd/RT) ,(10)where do, and and nd are constants, and Qd an apparent

activation energy. When p =Pd at t = 0 and p = po at

t=oo, the relation between p and t is formulated intop = (pd-po) eXp (-d •t)+po ,(11)where pd is a dislocation density just after hot defor-mation.4. Relation between Static Recrystallization and Average

Dislocation Density

After static recrystallization starts at t = z (z : incu-bation period), p decreases according to Eq. (12) due

to progress of recrystallization and becomes po after

recrystallization completes.p = (po-pr)X +pr ,(12)where X is the fraction recrystallized, and pr is the

dislocation density according to Eq. (11). The

value of X is expressed as a function of t into the

following equation. 16)X =1-exp {-e(t-z)'),(13)where e is a function of T, e, and Dr as in the form ofe = eo DmeBne gee exp (Qe/RT),(14)TransactionsIs",Vol.27,1987(427)where eo, me, ne and le are constants, and Qe an ap-parent activation energy.

function of T, e, s and Dr, asIncubation period, z, is a

T =-ODmTEnv&z exp (QTIRT),(15)where z-o, mt, nz and l= are constants, and Q an

apparent activation energy. The value of n in

Eq. (13) is assumed to be a constant value of 2, on

the basis of the present experimental data and the

report of other authors.7,17)

By substitution of Eq. (13) into Eq. (12), the

relation among p, e, t and z is obtained. By expand-ing the term of t and z into series and neglecting

the terms of higher order after twice logarithmic

calculation, it is possible to obtain a linear equation

of p, e, t and z-. The values of e and z are determined

by regression analysis with the series of p calculated

from the observed stress at s=0.05 (a o o5) in the

2nd pass of double deformation tests in. which T, ~,

and DY are constant and t a variable. The constants

included in Eqs. (14) and (15) are also obtained by

regression analysis with the calculated e and z for

different T, a, E and Dr.

With the combination of the equations mentioned

above, static recovery and recrystallization behavior

and the critical condition of recrystallization can be

calculated. This mathematical model can be applied

to multi-pass rolling, because p can be calculated

consistently from the beginning to the end of rolling

. Materials and Experimental Methods

The chemical composition of steels used are shown

in Table 1. The high hardenability steel A contain-ing Ni, Mo and B was employed for the comparison

between microstructure and deformation stress and

Nb steel B was employed for this formulation which

was a typical steel for plates produced by controlled

rolling. Single or multi deformation tests were

performed by using a compression type hot deforma-tion simulator. 18) Specimens were machined from

continuous casting slabs to the column with a size

of 7 mm diameter and 12 mm height.

The specimens were heated in an induction furnace

to the heating temperature (HT) at a heating rate of

5°C/s, and held for 10 min followed by cooling to

each deformation temperature (DT) at a cooling rate

of 5°C/s. The fluctuation of temperature in the speci-men is proved to be within 5°C during heating and

cooling and within 2°C during holding. Then single

or multi axial compressions were performed at DT

immediately. Strain, deformation speed, interval

time during deformation and temperature were

precisely

case of double deformation test, stress-strain curves

controlled through a computer. In the

of the 2nd pass were measured just after holding time

ranging 1 1 000 s after the 1st pass. The prior r

grain boundaries were observed in some specimens

quenched just after the same holding chArticle (428)TransactionsISIJ,Vol.27, 1987Table alcompositionsof thesteels.(wt%) y-v.v

Fig.3. Progress of recrystallization duringintervaltime after the1st deformation.1 V, Results

1. Comparison between Microstructure and Deformation

Stress

Steel A was employed for the observation of the

prior

after deformation.

r grain boundaries

Figures 3 and 4 are the optical

of a quenched specimen

microstructures of the quenched specimens and the

observed stress-strain curves, respectively. These

figures show the decrease in deformation stress in the

2nd pass due to the progress of recrystallization.

Figure 5 shows the relation among the time after the

1st pass, the fraction of r recrystallized, X, and

6E-0.05 of the 2nd pass. The value of X was measured

from the micrographs. Figure 5 reveals that the

decrease in a for t < 10 s is caused by recovery and that

for t >_ 10 s by recovery and recrystallization. From

these data, however, it is impossible to determine

exactly the true start of recrystallization as mentioned

before.

2. Formulation of Recovery and Recrystallization Behavior

of 0.01 % Nb Steel

Steel B was employed for this formulation. Table

2 shows the experimental conditions used.

Chemical analysis of the specimens quenched just

after holding for 10 min at the heating temperature

ranging 95O- 1 200°C confirmed that Nb was com-pletely

HT is considered to affect Q only through Dr.

dissolved even at HT=950°C. Therefore

In

this experiment, Dr varied from 12.5 to 300 sm

according to HT from 950 to 1 200°C. The possible

effect of Nb precipitation on ~E=0,05 by holding at a

certain temperature before deformation was also

investigated. Its effect, however, was very small

because both C and Nb contents were relatively small N 4 V Ul F i, i 1 1 ~ l Ig V V ~, L 1 ~ V V V VI, C~ V. V A7

Fig.4. Variation of stress-strain curves with interval . 5.

Effect of interval time on 0,=O.05 and X.

Table 2. Experimental conditions for steel the steel B. Therefore precipitation hardening

can be neglected and only strain hardening is caused

by retardation of recovery and recrystallization

through the variation of 6 with Nb.

The constants included in Eqs. (2), (5) and (7)

were obtained by regression analysis mentioned

before. The units of observed data are kg/mm2 for

Q and sm for Dr. Table 3 shows the values of con-stants. The effect of Dr, m~ and ~, n~ on the rate of

dynamic recovery are relatively small. The depen-dence of DT on deformation resistance which is usuallyTransactionsISIJ,Vol.27,1987(429)Table nts for Eqs.(2), (5), (7), (10), (14) and (15)for steel sed as Misaka's type equation'9> is divided into

the dependence of strain hardening, Qb and that of

dynamic recovery, Q~ . As these values are of the

same order of magnitude but of the opposite sign,

7 increases with decrease in DT. The values of

constants included in Eqs. (10), (14) and (15) are

also shown in Table 3. The effect of Dr, and and

~, nd are also small on the progress of static recovery.

The effect of ~, l~ on the progress of recrystallization

is by far larger than that of Dr and E. The value of

l3 is close to that of experimental formula by the

other author.20~3. Comparison between Experimental Data and Calculated

Results

Figure 6 shows the stress-strain curves of various

deformation conditions. Calculated results by using

Eqs. (2)' (8) are in good agreement with the experi-mental data in every case. Figure 7 illustrates the

decrease in ~E=0.05 at the 2nd pass due to the progress

of recovery after deformation. Calculation was per-formed on assumption that only recovery progressed.

Experimental data are consistent with the calculated

results before the start of recrystallization and deviate

with the progress of recrystallization. In the lower

DT, Fig. 7(a), the incubation period for recrystalliza-tion is considered to be between 20 and 100 s for

=0.2 and between 10 and 20 s for a=0.4. In the

higher DT, Fig. 7(b), recrystallization starts in much

shorter period after deformation. Figure 7 reveals

that the larger e and the higher DT result in the

shorter incubation period.

Figure 8 shows the decrease in cr, 0,05 due to

recovery and recrystallization during holding time

after deformation. The progress of both recovery

and recrystallization were calculated in this case.

Lines and solid triangles represent calculated results

from Eqs. (11), (12) and (15). Good agreement

between experimental data (open marks) and calcu-lated results proves that this mathematical model is

effective to estimate the recovery and recrystalliza-tion behavior in plate rolling process.V. DiscussionFig. 6. Effect of FIT, DT, and Eon . 7. Decrease

to recovery

in deformation

of in

the 2nd pass due1. Effect of Nb on Deformation Stress

The decrease in observed stress between the 1st

and the 2nd pass arises from the difference between

softening due to recovery and recrystallization and

precipitation hardening of Nb. Their contributionFig. 8. Decrease

to recovery

in deformation stress in the 2ndpass dueand chArticle(430 Transactions ISU, Vol. 27, 1987can not be discerned because of their interactions.

Figure 9 shows the effect of Nb content on a E-0.05

obtained by the single deformation test of 0.10%C-1.00%Mn steel. The stresses of specimens held for

500 s at 800°C for precipitation before the deforma-tion were nearly equal to the stresses of the specimens

without holding. From Fig. 9, stress increment is

proportional

solution hardening.

to the Nb content in accordance with

As the present specimen con-tains only 0.01 % Nb, the precipitation hardening is

expected to be no more than 1 kg/mm2, which is

within the error of observed stress.

Precipitation behavior of Nb(CN) may differ

before and after deformation.21~ In this respect,

DeArdo et al.22~ reported that Nb (CN) selectively

precipitates at grain boundary and subgrain boundary

of 1'. Therefore the effect of these precipitates on

deformation stress might be negligibly smaller than

that of coherently precipitated Nb(CN) in matrix.

Though the precipitation hardening of Nb(CN) is

neglected in the present model, experimental data

are consistent with the results of calculations.

2. Critical Condition of Recrystallization after Deformation

Incubation period, z, is calculated as a function

of ~, 7 and Dr in Eq. (15). As a result, effect of

deformation conditions on the critical conditions for

recrystallization can be analyzed by Eq. (15). Figure

10 shows the effect of 6 on z. In the multi-stage defor-mation test, s in the abscissa is the stored strain

calculated with Eq. (8). Calculated results indicate

that the higher DT and the smaller Dr result in the

shorter incubation period. Figure 11 shows the crit-ical conditions for static recrystallization of r. The

right upper sides of the lines are the recrystallization

ranges and the left lower sides are the non recrystal-lization ranges. If an interval time between defor-mation is longer than the incubation period (param-eter in Fig. 11), recrystallization starts during the

interval time. Therefore a short interval time elevates

the temperature limit of non recrystallization. Figure

12 shows the relation between applied deformation

strain and stored strain at the start of recrystallization.

The difference between these strains indicates the

decrease in dislocation density due to recovery during

the incubation period. Figure 13 shows the effect

of s on the softening ratio (S) in double deformationFig. of Nb content on a,_o.o5 in the1st just at the start of recrystallization. The ratio

S is described as

S = (Um-6n)I(~m-~0) ................ (16)

where 6,n is the peak stress in the 1st pass, and o and

7 fl are the yield stress of the 1st and 2nd passes,

respectively. These stresses are calculated from Eqs.

0'n were taken as 6f-o(2), (8), (11) and (15). In the calculation, 6o and

respectively. Djaic and Jonas,4~ and Ouchi et a1.5~

.o5 for the 1st and 2nd pass,

reported that static recrystallization started at a

specific value of S, O.20'0.30. As the strain at the

1st pass were 0.14 or 0.20 respectively in their experi-ments, the values of S calculated by the presentt model

are nearly 0.2-'0.3. From Fig. 13, however, the

value of S changes widely with the variation of

deformation conditions. A general criterion of recrys-Fig. of strain . alconditions for recrystallizationof . 12. Comparison between applied

deformation strain

and stored strain at the start of .13. Effect of deformation conditions on softening ratio

at the start of ation is not necessarily described in terms of

a specific value of S. On the other hand, the present

model predicts satisfactorily the critical condition of

recrystallization for comprehensive conditions of hot

rolling of . Conclusion

The critical condition of static recrystallization of

r in plate rolling process has been formulated in terms

of the change in average dislocation density calculated

from the decrease in deformation stress due to recovery

and recrystallization in the double deformation tests.

The results are summarized as follows :

dislocation

(1) The relation among stress, strain and average

density and the change in dislocation

density due to strain hardening and dynamic recovery

during deformation have been formulated. By the

present formulation, the deformation stress for prac-tical deformation conditions of controlled rolling canTransactionsISIJ,Vol.27,1987(431)be calculated as a function of temperature, strain,

strain rate and r grain size.

lization during holding period after deformation has

(2) The behavior of static recovery and recrystal-also been formulated as a function of dislocation

density. This formulation successfully predicts the

critical condition of recrystallization during the inter-val time between the successive rolling passes of plate.

strain rate, r grain size and interval time between

(3) Deformation conditions such as temperature,

passes affect the critical condition of recrystallization.

A smaller interval time elevates the temperature

limit of non recrystallization.

tallization such as a specific value of softening ratio

(4) An empirical criterion for the start of recrys-is not always valid, because the softening ratio

changes largely with deformation conditions.

Acknowledgements

The authors wish to thank Dr. H. Sekine, Dr. H.

Mimura and Dr. T. Senuma, Nippon Steel Corp.,

for their helpful NCES

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