Model for Prediction of Microstructural Events During Rod Hot Rolling of Austenitic Stainless Steel

487

CANADIAN METALLURGICAL QUARTERLY

MODEL FOR PREDICTION OF MICROSTRUCTURALEVENTS DURING ROD HOT ROLLING OF

AUSTENITIC STAINLESS STEEL

T. EL-BITAR1, A. ISMAIL1, I. RASHID2 and M.R. EL-KOUSSY3

1Central Metallurgical R & D Institute, CMRDI, Cairo, Egypt2ARCOSTEEL, El-Sadat City, Egypt

3Faculty of Engineering, Cairo University, Egypt

(Received August, 2001; in revised form May, 2002)

Abstract A mathematical model is constructed representing the non-executable equations to deter-mine the mean flow stress (MFS) using both Sims and Ekelund approaches. The model considers theredundant strain calculations. Solving the equations of the model develops a numerical solution and con-sequently the MFS is then calculated. The numerical values are taken from the rod mill logs, particular-ly when the interpass times are short, since the laboratory equipment cannot be used. The calculated MFSvalues are then related to the inverse of the absolute rolling temperature to determine the non-recrystal-lization temperature (T

nr), the strain accumulation and the cyclic softening / dynamic recrystallizing

zones of the austenitic stainless steel.At the finishing and prefinishing stages, the accumulated deformation and the deformation heating

affect temperature raising. However, at both stages, the coefficients of friction (m) decrease as the effectof the rolling velocity becomes predominant. The MFS values calculated by Ekelund are always higherthan those calculated by Sims. The T

nris detected as 1143 C. However, between 1143 and 1081 C, with

0.03 seconds interpass time, a stress accumulation zone is detected. At the high strain rate, 103 s-1, in thetemperature range 1063 and 1018 C, dynamic recrystallization is initiated. At higher strain rates (1200-1500 s-1), cyclic softening / dynamic recrystallizing is initiated. The finishing temperature is found to bethe most attributable to the grain size, whereas, the sub-grain structure is mainly due to multi-passesdeformation.

Rsum On construit un modle mathmatique reprsentant les quations non-excutables pourdterminer la contrainte moyenne dcoulement (MFS) utilisant lapproche de Sims et celle dEkelund.Le modle considre les calculs de dformation redondants. En rsolvant les quations du modle, ondveloppe une solution numrique et, consquemment, la MFS est ensuite calcule. On utilise lesvaleurs numriques des journaux dentres du laminoir, particulirement quand le temps entre lespasses est court, puisquon ne peut pas utiliser lquipement de laboratoire. Les valeurs calcules deMFS sont ensuite relies linverse de la temprature absolue de laminage pour dterminer latemprature de non-recristallisation (T

nr), laccumulation de dformation et les zones cycliques de

ramollissement/recristallisation dynamique de lacier inoxydable austnitique.Aux tapes de finissage et de pr-finissage, la dformation accumule et la chaleur de dformation

ont pour effet dlever la temprature. Cependant, aux deux tapes, le coefficient de friction (m)diminue mesure que leffet de vlocit de laminage devient prdominant. Les valeurs de MFScalcules par Ekelund sont toujours plus leves que celles calcules par Sims. On dtecte T

nr 1143 C,

cependant, entre 1143 et 1081 C, avec 0.03 s dintervalle de passe, on dtecte une zone daccumulationde contrainte. un taux lev de dformation, 103 s-1, dans la gamme de temprature entre 1063 et1018 C, la recristallisation dynamique est initie. des taux de dformation encore plus levs (1200-1500 s-1), ladoucissement/recristallisation dynamique cyclique est initi. On trouve que la tempraturede finissage est attribuable principalement la taille de grain, alors que la structure du sous-grain estprincipalement due la dformation par passes multiples.

Canadian Metallurgical Quarterly, Vol 41, No 4 pp 487-496, 2002 Canadian Institute of Mining, Metallurgy and Petroleum

Published by Canadian Institute of Mining, Metallurgy and PetroleumPrinted in Canada. All rights reserved

T. EL-BITAR, A. ISMAIL, I. RASHID and M.R. EL-KOUSSY

INTRODUCTION

The mean flow stress (MFS) is usually used to detect theevents that take place during hot rolling [1]. Thesemicrostructural events are like recrystallization, strainaccumulation and g-a phase transformation [2]. Forinstance, three critical temperatures of steel rolling are rec-ognized [3]. These are the temperatures below which therecrystallization of austenite no longer takes place, T

nr, and

the start, Ar3, and finish, Ar1, of the austenite to (a +

Pearlite) transformation. Boratto et al. [3], were the first todevelop the procedure used to determine the T

nr, A

r3 andA

r1 temperatures. These critical temperatures are locatedon the inverse points of the curve relating the MFS to theinverse of the absolute temperature [4]. Consequently, frac-tional softening and grain size can be expected [5].Different mathematical modules and numerical modelshave been developed to detect the MFS from the mill logs[6,7]. Most of these models use Sims approach [8] to cal-culate the MFS.

The most controlling factor separating conventionalrolling and dynamic recrystallization rolling is the lengthof the interpass intervals and in particular whether this islonger or shorter than 1 second [5]. Long interpass timeprocesses are those that involve reversing mills or whenearly in the reduction process in the tandem mills. On theother hand, in the rod finishing rolling, although the nomi-nal pass strains are below the critical strain for dynamicrecrystallization (DRX), the interpass times are too shortfor significant amounts of conventional static recrystalliza-tion (SRX) to occur [9]. As a result, the strain accumulatesfrom pass to pass until DRX is initiated. At the completionof a pass involving DRX, the recrystallization that occursis no longer dynamic, rather it is metadynamic (MRX)[10]. On the bases of previous works [11, 12], the MRXprocess generates fine austenite grain sizes at high valuesof Zener-Hollomon parameter which are at high strain ratesand relatively low temperature.

Physical simulation of rolling schedules by mean oftorsion tests has proved to be very powerful in the designof rolling passes for reversing mills [3]. However, the highstrain rates associated with the finishing stages cannotreadily be achieved using laboratory equipment [13]. Theshort interpass time processes are those that involve con-tinuous mills, particularly when these are located at the fin-ishing end of an operation, so that the stock is moving rel-atively quickly. Under these conditions, the strain rates canbe as high as 100-1000 s-1 (in the finishing stands of rodmills) [14] and the associated deformation times are of theorder 1 ms.

Most of the previously published models were dealingwith hot flat rolling; however, there are few modelingworks on the rod hot rolling. The aim of the present workis to construct a model for the evaluation of MFS from the

rod mill logs, particularly when the interpass times are tooshort, to detect the non-recrystallization temperature, thestrain accumulation and softening zones of the austeniticstainless steel.

In the present work, a previously constructed constitu-tive model for flat hot rolling [15] has been adapted andvalidated to cope with rod hot rolling [16]. The results ofthe adapted model are compared with those obtained frommill logs. The adapted model has been developed by intro-ducing further equations that help precise computation ofdifferent parameters instead of treating them either as con-stant terms or neglecting their effects [16].

MODEL EQUATIONS

The mathematical model mainly depends on Simssapproach [8] and the developed Orowan method [15]. Theroll pressure can be calculated at the exit side by usingSimss approach

(1)

However, it can be calculated at the entry side as

(2)

By definition, the neutral point is that which lies on thearc of contact between the exit and entry sides.Furthermore, the normal roll pressure at the exit side (S+ )is equal to that at the entry side (S-). More succinctly, at theneutral point S+ = S- where the right hand side of bothEquations 1 and 2 is equal to each other and the angle qbecomes the neutral angle (f

n), then

(3)

where

(4)X Z hh

k

k

fexit

b

entry

= -

-

-

21

2

1

1

1

2m

s

s

ln

f n

hR

hR

X=

2 2

2tan

Sk

hh

Rh

Rh

Rh

-

- -

= +

+

-

p

q j

41

2 2

12

1

2

12 1

2

12

ln

tan . tan .

Sk

hh

Rh

Rh

+-

= +

+

p

j

41

2 2

12 1

2

12

ln tan .

488


and

(5)

where a is the bite angle

(6)

at the same time

(7)

then

(8)

However, due to the excessive loads acting upon the rolledstock, the working rolls behave elastically and the rollradius, R, increases to R according to the formula devel-oped by Hitchcock [17] where

(9)

where P is the rolling force, W is the width and c is an elas-tic constant and is equal to

(10)

where n is Poissons ratio and E is the Young modulus forthe working roll material. c has different values accordingto the roll material, [18].

c= 2.21 x 10-4 mm2/kg for steel rolls.c= 2.53 x 10-4 mm2/kg for chilled cast iron rolls. c= 4.35 x 10-4 mm2/kg for cast iron rolls.

The roll flattening R should not be more than 2R.

The coefficient of friction (m) is one of the factorsaffecting the location of the neutral point on the arc of con-tact. This coefficient is influenced by the rolling tempera-ture t in C which is proposed by Ekelund [19] with the fol-lowing relationship;

(11)

where K=1 for the steel rolls, t should not be less than 700C and v the roll velocity in m/s. and not more than 5.0.

(12)

(13)

As previously stated in Equations 12 and 13, Ekelundpaid attention to both m and Dh. Sims did not care about m,but he paid attention to the thickness difference (Dh) [8].

(14)

where

(15)

The strain rate can be calculated by the following equa-tion [8,20].

(16)

where

(17)

ROLL MILL AND DATA COLLECTION

Numerous data are collected from the roll mill of theARCOSTEEL Company in Egypt. These data cannot readi-ly be achieved using laboratory equipment [13]. The roll millconsists of 32 stands. The mill stands are divided into 10stands for the roughing stage, 4 stands for the intermediaterolling stage and 8 stands for finishing stage to produce bars.It is also possible to use the remaining 10 stands for the pre-finishing stage for the production of wires. The mill has hor-izontal roll stands followed by vertical ones. Consequently,the width of the rolled stock is considered as the input thick-ness for the next stand. The initial billet dimensions were162.3 162.3 mm. The shape and dimension of the groovesin rolls as well as the effective roll radius (R) are given inTable I. The roll mill is completely automated and computercontrolled and monitored. The rolling temperature (t) is

e =

-h hh

1 2

1

e

p

e

e e

=

-( )-

260

1 111

U Rh

ln

Q hh h

h hh

Rh

Yh h

Sims =-( )

-

-

-

-

2

1 2

1 1 2

2 2

2

1 2

4

4p

p

. tan ln

MFS PW R h QSims Sims

( ) =

32 D

Q . R h . hh hEkelund

= + -

+1 16 12

1 2

m D D

MFS PR h

( ) =

EkelundEkelundW QD

m = -( )K t1 05 0 005. . - 0.056 v

cE

=

-( )16 1 2np

= +

R R P cW h

1 ..D

Y h R n= + -( )2 2 1 cosf

f n

h YR

= -

-

-cos 1 112

a = -

-

-cos 1 11 22

h hR

Z Rh

Rh

=

-22

1

2tan a

MODEL FOR PREDICTION OF MICROSTRUCTURAL EVENTS DURING ROD HOT ROLLING 489




taken as the mean value of the temperatures recorded at theexit side of the roll bite. The rotational roll speed (U) is usedto compute the rolling velocity (v) which is the bar velocityat the exit side of the roll bite. The rolling force (P) is con-sidered as the mean of two values recorded with the aid ofload cells mounted on both roll necks.

MATERIAL

The rolled material is austenitic stainless steel billets toproduce 6.0 mm diameter wires. The steel chemical com-position is presented in Table II.

490

Table I Some data extracted from mill logs

Pass Pass Effective Exit bar h1 h2 Rolling Rotational Rolling shape roll radius width mm mm temp. (t) roll speed force

(R) (W) C (U) (P)mm mm rpm ton

R1 Box 286.05 171.0 162.3 120.0 1194 8.8 166.6R2 Box 282.20 140.0 171.0 140.0 1178 11.1 139.9R3 Box 291.65 141.8 118.5 88.0 1165 14.3 189.0R4 Box 295.05 112.0 141.8 112.0 1156 17.4 132.7R5 Box 231.35 111.2 90.1 69.0 1148 29.2 128.8R6 Box 226.75 86.0 111.2 86.0 1143 37.9 93.1R7 Ov 241.00 76.2 70.2 58.0 1000 15.4 116.5R8 O 237.60 67.3 76.2 67.3 996 19.4 77.2R9 Ov 245.65 60.3 67.3 43.0 988 25.7 115.6R10 O 242.80 53.2 60.3 53.2 992 31.8 67.1I1 Ov 201.85 47.2 53.2 33.5 966 51.4 78.1I2 O 199.30 41.5 47.2 41.5 973 62.5 46.9I3 Ov 205.15 39.4 41.5 25.0 970 81.1 69.6I4 O 202.75 32.6 39.4 32.6 983 100 40.1F1 Ov 207.15 30.6 32.6 20.0 973 129.3 51.9F2 O 204.60 25.2 30.6 25.2 988 160.8 32.3F3 Ov 158.65 25.7 25.2 15.0 995 268.3 38.1F4 O 156.20 19.8 25.7 19.8 1018 340.8 21.8F5 Ov 159.40 21.7 19.8 12.0 1012 395.4 27.1F6 O 156.95 16.7 21.7 16.7 1034 476.8 14.6F7 Ov 159.60 17.8 16.7 11.0 1041 523.9 18.4F8 O 157.85 14.6 17.8 14.6 1056 616.6 11.1

PF1 Ov 102.00 15.6 14.6 9.4 1047 1098.4 11.5PF2 O 100.95 12.4 15.6 12.4 1063 1348.1 6.8PF3 Ov 84.70 12.7 12.4 8.0 1063 1921.8 8.0PF4 O 84.05 10.6 12.7 10.6 1064 2271.2 4.6PF5 Ov 85.15 10.4 10.6 6.8 1064 2777.9 6.4PF6 O 84.65 8.9 10.4 8.9 1067 3282.9 3.6PF7 Ov 85.80 8.9 8.9 5.5 1067 4034.3 6.0PF8 O 85.10 7.4 8.9 7.4 1072 4767.8 3.6PF9 Ov 86.15 7.3 7.4 4.6 1075 5831.5 4.9PF10 O 85.65 6.1 7.3 6.1 1081 6891.7 3.1

Table II Chemical composition of steel

Element C Si Mn Ni Cr Mo Cu Al P S Nwt. % 0.03 0.3 1.8 9.36 18.3 0.4 0.35 .003 .020 .025 .079

NUMERICAL EVALUATION

The numerical evaluation is the executable form of themodel equations. The calculations are presented by thecommercial Excel software technique. The model is pro-vided with the initial rolling values as shown in Table I. Itis constructed to go through the different equations of themodel in a consecutive manner to solve these equationswith the help of the provided initial rolling values at eachstand. The model thoroughly calculates the neutral angle(j

n) and consequently the neutral thickness (Y) by using

not only Sims theory, [8], but also by Ekelund assumptions[19]. The roll elastic behaviour due to excessive rollingloads is taken into consideration [17]. Steel rolls were usedwith a Hitchcock constant (c) equal to 2.21x10-4 mm2/Kg[18].

EXECUTION OF MODEL EQUATIONS

Table III summarizes the numerical values resulting fromthe execution of the model equations at each of the millstands.

RESULTS AND DISCUSSIONS

Interpass times (t) as well as rolling temperatures (t) areconsidered as important factors affecting the MFS valuesand consequently influence the final properties of the rolledmaterial. Figure 1 represents both interpass time (t) androlling temperature (t) at the different stands of the roll mill.The interpass time decreases continuously from one stand tothe other. On the right hand side of the same figure, therolling temperature falls down to the end of the roughingstage. Afterwards, the rolling temperature rises again.



Table III Some calculated values from rolling data

Pass Flatten. 1000/T Bite. Interpass Roll Nom. Redun. Total Strain Neutral Neut. MFS Fric. MFS Roll K-1 angle time (t) velocity Strain Strain Strain Rate, angle thick. (Sims) Coef. (Ekel.)

radius (a) Sec. (v) (e.) (jn). (Y), Kg/mm2 (m) Kg/mm2

(R') Rad m/sec s-1 rad mm

R1 287.51 0.682 0.387 0.41992 0.26 0.349 0.097 0.446 0.81 0.125 124.5 8.23 0.438 8.08R2 284.21 0.689 0.333 0.28642 0.33 0.231 0.083 0.314 0.83 0.117 143.9 10.21 0.443 9.73R3 294.47 0.695 0.325 0.21678 0.44 0.343 0.081 0.424 1.52 0.112 91.7 12.58 0.443 12.25R4 297.64 0.700 0.319 0.17528 0.54 0.273 0.080 0.353 1.55 0.112 115.8 11.67 0.442 11.21R5 234.16 0.704 0.303 0.09905 0.71 0.308 0.075 0.383 3.02 0.108 71.7 14.79 0.436 14.35R6 228.90 0.706 0.335 0.08444 0.90 0.297 0.084 0.381 3.48 0.116 89.1 13.17 0.428 12.83R7 247.66 0.786 0.226 0.14000 0.39 0.221 0.055 0.276 1.58 0.088 59.9 24.72 0.528 22.25R8 244.37 0.788 0.194 0.09542 0.48 0.143 0.047 0.191 1.58 0.079 68.8 22.90 0.525 20.52R9 249.93 0.793 0.316 0.11736 0.66 0.517 0.078 0.595 3.87 0.106 45.8 19.75 0.519 18.60R10 252.33 0.791 0.171 0.05142 0.81 0.145 0.041 0.186 2.93 0.071 54.5 27.03 0.509 24.26I1 205.60 0.807 0.314 0.05828 1.09 0.534 0.078 0.612 7.97 0.105 35.8 20.64 0.506 19.68I2 208.09 0.803 0.169 0.02579 1.30 0.148 0.040 0.188 5.95 0.070 42.5 29.64 0.490 26.82I3 210.00 0.805 0.285 0.03351 1.74 0.585 0.070 0.655 14.75 0.096 27.0 22.22 0.467 22.00I4 210.86 0.796 0.183 0.01751 2.12 0.219 0.044 0.263 12.37 0.074 33.7 27.47 0.440 25.85F1 213.31 0.803 0.247 0.01826 2.80 0.564 0.060 0.624 26.29 0.087 21.6 23.06 0.407 24.17F2 215.33 0.793 0.163 0.00966 3.44 0.224 0.039 0.263 22.80 0.066 26.1 30.48 0.363 30.34F3 163.75 0.789 0.254 0.00905 4.46 0.599 0.062 0.661 55.45 0.088 16.3 25.33 0.303 30.57F4 162.69 0.775 0.194 0.00544 5.57 0.299 0.047 0.346 52.44 0.076 20.7 28.23 0.261 31.59F5 165.05 0.778 0.222 0.00535 6.60 0.578 0.054 0.632 91.15 0.079 13.0 23.12 0.264 29.49F6 163.06 0.765 0.178 0.00357 7.83 0.300 0.043 0.343 79.63 0.070 17.5 23.63 0.253 26.85F7 165.99 0.761 0.189 0.00345 8.75 0.482 0.046 0.528 122.69 0.071 11.8 22.28 0.250 28.06F8 166.09 0.752 0.143 0.00221 10.19 0.230 0.034 0.264 100.85 0.059 15.2 25.42 0.242 28.42

PF1 105.17 0.758 0.227 0.00197 11.73 0.513 0.055 0.569 225.96 0.082 10.1 22.07 0.247 27.90PF2 104.75 0.749 0.179 0.00127 14.24 0.267 0.043 0.310 202.20 0.071 12.9 23.82 0.239 26.85PF3 87.39 0.749 0.228 0.00114 17.04 0.506 0.056 0.562 389.06 0.083 8.6 22.87 0.239 29.11PF4 88.03 0.748 0.155 0.00065 19.98 0.201 0.037 0.238 304.99 0.064 11.0 26.74 0.238 29.13PF5 88.13 0.748 0.214 0.00074 24.76 0.524 0.052 0.576 616.40 0.078 7.3 22.56 0.238 29.22PF6 89.65 0.746 0.134 0.00039 29.09 0.181 0.032 0.213 464.29 0.056 9.2 28.12 0.237 30.60PF7 89.54 0.746 0.200 0.00047 36.23 0.562 0.048 0.610 1008.49 0.073 5.9 24.58 0.237 32.81PF8 91.18 0.743 0.133 0.00027 42.47 0.215 0.031 0.246 791.07 0.055 7.6 32.00 0.234 35.92PF9 90.73 0.742 0.180 0.00029 52.58 0.544 0.043 0.587 1588.54 0.067 5.0 25.71 0.233 34.62PF10 93.36 0.739 0.121 0.00017 61.78 0.215 0.028 0.243 1262.44 0.050 6.3 34.91 0.230 39.79


It is evident that the interpass time decreases as a resultof the reduction in the cross-sectional area and consequent-ly increases in the length of the rolled stock. Hence, therolls rotational speed would increase from one stand to theother (as shown in Table I) to cope with the elongation ofthe rolled stock.

Due to high amounts of accumulated deformation espe-cially after the roughing stage, the deformation heating gen-erated leads to a temperature rising of the rolled stock. At thesame time, after the roughing stage, the interpass timedecreases sharply from one stand to another (0.1 to 0.0001sec.). Short interpass times and the high amount of deforma-tion heating compensate for the loss in stock temperatureduring rolling and even lead to temperature riising. Thisprocess favours the deformation process of the austeniticstainless steel as it exhibits high resistance to deformation bylosing its high temperature [21].

Figure 2 represents both the rolling velocity (v) and thecoefficient of friction (m) at the different roll mill stands.The rolling velocity increases up to pass 6 when the veloci-ty decreases then rises again continuously to cope with the

increase in stock length due to the accumulated reduction inthe cross-sectional area from stand to stand. The drop invelocity at stand 6 is due to a lopper effect which existsbetween stands 6 and 7.

On the other hand, the coefficient of friction (m) decreas-es throughout the roughing stands and begins to rise sharplyat stand 7 due to the loss of some of the rolling temperatureand velocity as a side effect of the lopper existence.Afterwards, m decreases again where the effect of the rollingvelocity becomes predominant over the effect of rolling tem-perature (Equation 11) [18].

Figure 3 shows a presentation of the rolling force at dif-ferent mill stands. The presentation is a comparison betweenthe measured values at the mill logs and the prediction froman adapted model [20] constructed for rod hot rolling calcu-lations. The predicted values are always lower than thosemeasured. However, the difference in value is much higherat the roughing stage than at the intermediate and finishingrolling stages. However, the two curves have the same trend,where the trend of the rolling force decreases continuouslyfrom one stand to the other as the cross-sectional area of therolled stock decreases. The difference in rolling forcebetween the measured and predicted values occurs becauseit is difficult to represent and measure the actual amount ofreduction in cross-sectional area in rod rolling processeswhere the actual amount of reduction is much more than thattheoretically measured at each stand [22]. This difficultyleads to a deficiency in modeling the rod rolling processes.

One of the targets of the present work is to evaluate themean flow stress (MFS) for each pass by both Sims andEkelund approaches. The MFS is presented against the reci-procal of the absolute value of the rolling temperature inFigure 4. This presentation reflects clearly the behaviour ofthe austenitic stainless steel during deformation under thespecified conditions. The MFS values calculated by Ekelundare always higher than those calculated by Sims. This isbecause Ekelund considered the value of the friction coeffi-cient and Sims did not pay attention to it.

492


Interpass time Rolling temperature, C

Stand number

Inte

rpas

s tim

e, se

c. 10.1

0.01

0.001

0.00010 5 10 15 20 25 30 35

Rol

ling

tem

pera

ture

, C

1200

1100

1000

900

Coeficient of friction Rolling velocity, m/s

Stand number

Coef

ficie

nt o

ffric

tion 0.6

0.5

0.4

0.3

0.2

0.10 5 10 15 20 25 30 35 R

ollin

g ve

loci

ty, m

/sec100

10

10

0.1

Fig. 1. Interpass time and rolling temperature at different stands

Fig. 2. Coefficient of friction and rolling velocity at the different millstands

Mill log dataPredicted data

Pass number

Rol

ling

forc

e, to

n

200

175

150

125

100

75

50

25

00 5 10 15 20 25

Fig. 3. Presentation of rolling force at different mill stands for both milllog and predicted data



It is clear that point 1 represents the temperature of thenon-recrystallization (T

nr) process where the MFS begins to

rise sharply. Up to point 1, 1148 C, fully static recrystal-lization should take place after each rolling pass where theinterpass time and rolling temperature in this region are rel-atively high and permit for this conventional recrystalliza-tion [13]. This process is indicated as the rate of increase inMFS with 1/T is relatively low. When strain hardening isoccurring at a temperature below T

nrthere is a sharp increase

in slope as is evident from point 1 to point 2, (1081 C) [5].The interpass time in that region markedly decreases from0.1 to 0.03 seconds and consequently the strain rate increas-es greatly from 1.5 to 14.75 s-1, where there would not be achance for stress annihilation, [13], but rather stress accu-mulation. At the end of the strain hardening region, the mate-rial exhibits softening [23] from point 2 to point 3 (1063 C).This softening occurs as a result of dislocation densitydecrease and vanishing damaged substructures. However,the grains still pancaked.

However, when dynamic recrystallization is initiated(followed by metadynamic recrystallization), the rate ofincrease of the mean flow stress drops away from that asso-ciated with the strain accumulation from point 3 to point 4(1018 C) where the strain rate becomes very high on theorder 103 s-1 [14], which would lead to dynamic recrystal-lization. Consequently, the austenite grain size is refined to agrain size of the order of 15 to 20 mm quite independent ofthe initial grain size,[24]. From point 4 to point 5 (966 C)where the strain rate becomes around 1200-1500 s-1, theaustenite grain size is refined in successive recrystallizationevents [24] that is the material exhibits cyclic softening /dynamic recrystallizing [23].

Figure 5 represents the microstructure of a 6.0 mmdiameter wire produced at a rolling temperature of 1081 Cwith a 1262 s-1 strain rate. The micrograph revealsaustenitic coarse grains with sub-grain structures. Thecoarse grains were created as a result of a high finishingrolling temperature (1081 C). However, the sub-grainstructure is due to the multi-pass deformation withincreased strain rate from one pass to another. The sub-

grain structure emphasis which has been discussed in therange between points 3 and 4 in Figure 4.

On the other hand, finishing rolling at a lower rollingtemperature (988 C) with a moderate strain rate (22.8 s-1)would result in a high Zener-Hollomon parameter (Z) valueaccording to the following formula

Z= e. Exp [ Qdef / RT]

where Qdef is the activation energy for deformation.Consequently, high values of the (Z) parameter favours theinitiation of dynamic recrystallization with fine austeniticgrains [25 ].

This is clearly represented in Figure 6, which is amicrostructure of a 25 mm diameter rod after passing standF2 at the previous deformation conditions. The microstruc-ture presented in Figure 6 represents point 5 in Figure 4.

SimsEkelund

1000/T, K-1Mea

n flo

w st

ress

, Kg/

mm

2 45403530252015105

00.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 0.85

(2)1081 C

(1)1148 C

(3)1063 C

(4)1018 C

(5)966 C

Fig. 4. MFS calculated by both Sims and Ekelund approaches against1000/T

Fig. 5. Microstructure of a 6.0 mm wire 100 (rolling temperature 1081C with 1262 s-1 strain rate)

Fig. 6. Microstructure of a 25 mm diameter rod 100 (rolling tempera-ture 988 C with 22.8 s-1 strain rate)

T. EL-BITAR, A. ISMAIL, I. RASHID and M.R. EL-KOUSSY494


Both microstructures presented in Figures 5 and 6 con-firm what was detected in Figure 4 ensuring that the finish-ing temperature is the most attributable to the grain size;whereas, the sub-grain structure is mainly due to multi-pass-es deformation. All that was reported regarding themicrostructure emphasizeses that the detection ofmicrostructure events during hot deformation by the MFS temperature relationship is a reliable method.

CONCLUSIONS

1. At the finishing and prefinishing stages, the accumulat-ed deformation and the deformation heating affect temper-ature rising.

2. The coefficients of friction (m) decrease throughout theroughing stands and begin to rise sharply at the intermedi-ate process. Afterwards, m decreases again as the effect ofthe rolling speed becomes predominant.

3. The MFS values calculated by Ekelund are alwayshigher than those calculated by Sims.

4. The Tnr

is detected as 1143 C.

5. Between 1143 and 1081 C with 0.03 second interpasstime, there would not be a chance for stress annihilation butrather stress accumulation.

6. At a high strain rate, 103 s-1, in the temperature range1063 and 1018 C, dynamic recrystallization of the austen-ite grains is initiated.

7. As the strain rate continues increasing (1200-1500 s-1),the steel exhibits cyclic softening / dynamic recrystallizing.

8. The finishing temperature is the most attributable to thegrain size; whereas, the sub-grain structure is mainly due tomulti-passes deformation.

NOMENCLATURE

Symbol Meaning Units

MFS mean flow stress Kg/mm2t rolling temperature CT absolute rolling temperature KT

nrnon-recrystallization temperature C

m coefficients of friction DRX dynamic recrystallization SRX static recrystallization MRX metadynamic recrystallization S+ normal roll pressure at the exit side Kg/mm2

S- normal roll pressure at the entry side Kg/mm2a bite angle rad.f

nneutral angle rad.

h1 bar thickness before rolling MM2h2 bar thickness after rolling MM2W bar width MM2c elastic constant R effective roll radius MM2R flattened roll radius MM2K

exit flow stress at the exit side Kg/mm2K

entry flow stress at the entry side Kg/mm2sf forward tension Kg/mm2sb backward tension Kg/mm2Y thickness at the neutral angle MM2v roll velocity mm/secU rotational roll speed Rpmov oval pass shape o round pass shape t interpass time secx nominal strain x

rredundant strain

xt total strain x

. strain rate sec-1P Rolling force tonZ Zener-Hollomon parameter Qdef activation energy for deformation erg

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Model for Prediction of Microstructural Events During Rod Hot Rolling of Austenitic Stainless Steel

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