IS[J International, Vol. 32 (1 992), No. 3, pp, 440-449

Application of

trolled Cooling

Mathematicalof Wire Rods

Modelling

and Barsto Hot Rolling and Con-

Ettore ANELLl

Department of Structural Steel Metallurgy, CENTROSVILUPPOMATERIALl,P. O, Box I0747

(Received on September2. 1991; accepted in final form on December20. 1991)

Roma-Eur, Italy.

A set of integrated mathematical mode[s for simulating hot rolling and controlled cooling of wire rodsand bars has been developed through extensive laboratory ~esearch work and validation against carefu]Iy

monitored results from industrial mills.

Experimental tests have been carried out on C-Mnand eutectoid steels selected as representative of thevarious applications of wire rods and bars.

Static and dynamic recrystailization of austenite, fraction of transformed austenite, final microstructuresand mechanical properties are all calculated by modelling physical phenomenaand using quantitativerelationships betweenthe microstructural and kinetic parameters and the process variables, i.e. strain, strain

rate, temperature and time.

Themodelshave boen applied to predict the microstructure evolution during hot rolling and to investigate

the effect of working conditions and recrystallization mechanismson the formation of heterogeneousaustenitic microstructures.

Theeffects of the cooling patterr, on the temperature profile and the austenite phase transformation havea]so been studied to prevent: coarse pearlite and martensite formation at the centre of wire rods which havecores enriched in Cand Mn; surface hardening of bars whenwater tube cooling systems are used to controlthe temperature at the cooling beds.

The models provide an important insight into the process that is beneficial to enhancethe quality of longproducts.

KEYWORDS:mathematical modelling; hot rolling; controlled cooling; wire rod; bar; recrystallization

kinetics; grai n size evolution; phasetransformation; mechanical properties; C-Mn and eutectoid steels; storedstrain; hot torsion testing.

1. Introduction

-A comprehensive steel rolling model should makeaccurate predictions of the effects of process variables

on temperature distribution, microstructural evolution

and thelr consequent effects on product propertles.

Considerable research has been devoted to computermodelling of hot rolling, including both thermome-chanical and metallurgical aspects. The specific ad-

vances madein this field have been recently discussedduring two international conferences.1'2)

The work at CENTROSVILUPPOMATERIALI(CSM)was initially concentrated on the development ofmicrostructure and hot strength models for plate roliing

of CMnand microalloyed steels.3'4) The constitutlve

relations for microstructure evolutlon prediction werecoupled with tempcrature and deformation models to

optimize rolling schedules and improve rolling force

prediction at ILVA's plate mill N0.2 (ILVA is the majorItalian steelmaking company), Taranto Steel Works.Both finite difference computing method (FDCM)3'4)and finite element method(FEM)5,6) were employed to

model strain and temperature evolution.

This work summarises the extension of the thermo-mechanical and microstructural modelling to bar andwire rod rolling mills, where the very high stock speedand short interpass times, especially in the final stage ofrolling, favours strain accumulation. Furthermore the

high temperature gradients across the section, increasedby the introduction of additional water cooling systems,lead to amicrostructural gradient along the rod diameter.

In the paper, a set of models specifically designed topredict the thermal and microstructural evolution of

C-Mnsteel long products is outlined and their ap-plication to improve the quality of the final productsis discussed.

2. ExpenmentalWorkExperimental tests and rolling trials have been car-

ried out on C-Mnand eutectoid steels for bars and wirerods (Table l) in order to develop the models throughlaboratory research work andvalidation against carefully

monltored results from Industrial mills.

2.1. Laboratory Tests

Specimenstaken from billets have been austenitized

O1992 ISIJ 440

ISIJ International. Vol. 32 (1992). No. 3

Table l. Chemical composition of steels (wto/o).

Chemical composition ("/*)

Steel UseC Mn Si Cr B Ti Al

ES17QC29BIC43FP69FF82

FF82K

Welding wire

FastenersForgingSteel cordRopesandPrestressed

concrete

O. IO0.300.400.71

0,85

0.82

l .70

0.92

O.700.660.62

0.74

0.85

0.300.25

0.24

0.25

0.21

0,04O, 14

O.15

0.03

0.03

0.24

0,0024 0,050.0050.0250.03

0.0050.03

0.01

at temperatures ranging from 900 to 1250'C for 2, 15

and 120min and subsequently water quenchedin order

to define empirical grain growth laws.

Hot torsion tests have been performed on specirnens

having different austenitic grain sizes (dy =20~40/Im),

varying both the deformation temperature (T=900l 150'C) and the amountof strain (8=0.21-0.64), in or-der to quantify the effect of the main metallurgical andprocess parameters on the softening kinetics and relevant

structural modifications. Themethodologydeveloped byIRSID7) and based on the performance of double hottorsion tests has been adopted for analyzing recrystalli-

zation kinetics. The size of the recrystallized austenitic

grain has been measuredby metallographic methodsonspecimens quenchedimmediately after recrystallization

had been completed.The characteristics of the austenite phase transforma-

tion under isothermal conditions (TTT diagrams) havebeen determined by dilatometry.

2.2. Industrial Trials

The verification and calibration of the models havebeen performed by comparing calculated values withactual bar and wire rod mill data from ILVA's plants,

Piombino steel works.On-1ine surface temperature measurements have

been madeby portable infrared pyrometers previously

calibrated against a black body at the laboratory. Themeasurementshave been carried out, with the emissivity

set at 0.83, at different positions along the bar and wire

rod mills, at the entry and exit side of water coolingsections (spray or tubular type) and along the Stelmor

conveyor.Specimens for austenitic microstructure evaluation

were taken and water quenchedat various stages of the

rolling process using the mill shears. A few wire rodspecimens were taken before the onset of phase trans-

formation, by stopping the Stelmor conveyor for a fewseconds and cutting off the end wraps which have beenimmediately water quenched.

3. Mathematical Models

Thefollowing sections describe the submodelsfor grain

growth, static anddynamicrecrystallization, transforma-tion and structure-property relationships. Thesemodels

can be used singly or linked in sequencewith the outputdata of one model working as input data for the nextmodel. The flow chart of the Integrated mathematical

DIUJ~TSOAK,NG

EMPERATURE

CONTROL8YSTEMOFREHEATING

FURNACE

T,1E,,,,OPtIYSICALCON8TANTSANDHOTItOUJNGPARAUETERS

THE,tU(hMECHAMCALNODEL

THERMALEVOLUT]ONOf I,LLETS

TFtAN81ENTRADIALD,STRIDUTION

OFTEMPERA11JRE

AUSTENITiCGR'LIN

GRowrHMODEL

INIT[AL AUSTEN,TICGRAINSiZE

HOTROLUNGMICROSTRUCTURAL,10DEL

FOREACHPAss:

- VOLUMEPer OFRECRYSTAUJZED,,ATERiAL

- AUSTENITICGRAINstzE- AceuMULATEDSTAAIN

441

COOUNGDATA=-uENGTHOFCOOUNGZONES

-HEATTRANSFER

OEFFICtENT

r~~~~~rlCOOUNGMODEL

ITrDIAGRAUS

AD,ALTEMPERA11JRANDAUSTENITE

TftANSFORMATIONEVOLUTION

FINALM~l:ROSTRUCTUREANDMECHANICAL

PROPERTIES

Fig, l. Flow chart of mathematical models.

models is shownin Fig. l.

3.1. Grain Growth ModelThis model is used to predict the initial austenitic- grain

size of those C-Mnsteels which show a continuousgrowth.

Theaverage size of austenitic grains (dv in pm) is givenfor isothermal treatments by the relationship:

dv=kl•tk2exp( QIRT) ..........(1)

where t is the time in hours, Tthe absolute temperatureand R the gas constant. The constants kl, k2, and Q.have been identified for each steel on the basis of

measurementsof dy Performed on samples subjected todifferent austenitization treatments (Table 2).

The austenitic grain size which results from a specific

thermal evolution can be calculated from Eq. (1)

approximating the reheating curve by a series ofisothermal segments of length At. If in the time step ti

to ti +At the temperature increases from Ti to Ti+ 1,the

increase in the austenitic grain size is calculated from the

following series of equations:

d ......(2)=kl(t* +At)k2 exp(- Q~/RTi+ 1)""vi + l

1/k2 ......(3)t* = (dyil(kl • exp( - Q~/RTi+

1))" --

O 1992 ISIJ

ISIJ lnternationai, Voi,

Table 2.

32 (1992), No. 3

Values of empirical coefricients.

LowCsteel

ES 17MediumCsteel

QC29B FP69High Csteel

FF82

ygrain

growth

kl

k2

Qo(KJ/mol)

9.1 x 106

O, 18

126

**

*

7.9 > 104

O. 19

69

4.1 x 107

O, 12

141

Strain to peakstress (ep)

ab

4.83 x 10~30.09

2.73 x l0~30,20

l.84 x lO~ 30.24

1.84 x 10~30.24

Time to 50 olo

recryst. (t50)

d

fQ1

1.4 x lO~ 14

- I.9

l.l

33.0 x 103

3.2 x l0~9

- 1.6

0.9

18.4 x 103

7.3 x 10~12

- 1.9

0,6

27.2 x 103

4,5 x lO~s

I.O

0.6

6,9 x 103

Recryst, volumefraction exponent(n)

ghmQ2

21.3

0.54

-0.25-2.2 x 103

12.2

0.04

-0.lO-2.6 x 103

6.2 x 104

O43

- O.04

- 13.6 x 103

6.1 x 106

0.02

-0.30

- 18.4 x 103

Recryst. grainsize (dyrox)

pq

Q3

l 150

-0.3O.39

-6.5 x 103

84

-0.60.33

-3.5 x 103

95.5

-0.5O.39

-3.5 x 103

95.5

-O.50.39

-3.5 x 103

* Steel QC29Bcontains Ti which wasadded to protect B. Its grain growth behaviour is described by the following equation:

dv =95[1 -exp[-7.4 x l0~3 (T- I 133)]]

where d~ is in pmand T is in K.

where t* is the fictitious time required to reach theprevious grain size dvi at the newtemperature Ti+1'

For microalloyed steels under reheating conditionswhich lead to abnormal grain growth other empiricalrelationships must be used.8)

3.2. ThermomechanicalModelFEMenables the local strains, strain rates and tem-

perature to be computed. At present only preliminarystudies exist. Therefore the strain (e) and strain rate (~)

during a pass have beenassumedto be the ones expectedfor homogeneousstrain and the key variable is thereforethe temperature.

Themodelis basedonnumerical integration by FDCMof the Fourier heat equation. The temperature distri-

bution in the stock section is evaluated using an equiv-alent round section. Algorithms originally designed forsteel plate and suitably modified to account for the dif-

ferent geometry are used to predict the thermome-chanical cycle for a given location in the cross sectionof the stock. These data are used as input data for themicrostructural model.

3.3. Hot Rolling Microstructural ModelThemodelestimates the austenitic structure developed

during each pass (i,e. austenitic grain size of eachhomogeneousstructure, volume fraction of recrystalliz-

ed grains, amountof residual strain accumulated) as afunction of the thermal and mechanical conditions(T, 8, ~). The set of equations forecasting the austenitic

structure is applied sequentially according to logic

procedures equivalent to those proposed for flat-rolled

products. In the program, structures which differ sig-

C 1992 ISIJ 442

nificantly one from the other are treated as separatefeatures

.

3'4)

Onthe basis of laboratory test results, static recoverywasassumedto produce 20 o/o softening during each passin the roughing stage. Its effect during the finishing stagewasneglected. For each homogeneousstructure, a checkis madeto control whether the total strain (inclusive ofthe residual strain accumulated during previous passese,) is smaller (static recrystallization) or greater (dynamicrecrystallization) than the critical strain required for theonset of dynamic recystallization (8dy"). The 8dy" valuesare calculated on the basis of the hot torsion test resultsusing the following equations:

8p=a ' dbv' Zo. i s

... .... . .

.(4)

edy~=c'8p ..............(5)

wh~reZ=~• exp(QIRT) is the ZenerHollomonparame-ter in s~1, eF is the strain to peak stress, a and barecoefficients which dependon steel composition (Table 2)

and c=edy~/ep=0.85.

3.3, I .Static Recrystallization

Under isothermal conditions, the volume percent ofmaterial undergoing static recrystallization (R o/~) within

a certain time t (in s) from the finish of hot deformationhas been calculated with the following Avrami-typeequation:

Ro/o = 100 •(1 -exp[ -0.693(t/t50)"]) "-"""'(6)

The values of the exponent n and of the 50 olo'' ,,

recrystallizatron trme "tso" havebeencalculated in termsof operating parameters T, 8 and dv With the followingequations:

ISIJ International, Vol.

t50 =d•8' ' d~•exp(Q1/T)......

..........(7)

n=g'8h'd'y"•exp(Q2/T).......

..........(8)

The empirical coefficients of Eqs. (7) and (8) dependon steel composition (Table 2).

Since the strain rates applied during the finishing passesof the rolling sequencewere far higher than those adoptedfor the hot torsion tests (~ = 3.6/s), the following equation,has been used to calcuiate the actual value of time for

50 o/o recrystallization:

(8 '

=t50(~) t503'6

..(9)

where r=0.20-0.28.9•10) The influence of ~is significant

only for the time t50 9)

With regard to the recrystallized austenitic grain size

the hot torsion results havebeenanalyzed mathematicallyusing an expression of the type developed for a C-Mnsteel,3) with the addition of the term ~o.1 to allow for

the strain rate effect9):

dv"'=p'~~0.1. q d . ....(lO)8 ' ~•exp(Q3/T)

.. .....

where dv (Pm) is the austenitic grain size prior to de-

formation and the coefficients are shownin Table 2.

In the case of partial recrystallization, the grains aresmaller than those of a completely recrystallized material

and are calculated from the following relationship:

d' =d • fRo/o /lOO11/3..........

(1 l)y"* y"* \ / ' """

For the fraction of material that does not recrystallize

before the subsequent pass, the model calculates aneffective size value which allows for elongation of the

original grains and for the volume available to the

work-hardened austenite4):

dy. I 06 d (1 R~/lOO)1/3 exp(-8) ......(12)

Once recrystallization is complete, further grain

growth takes place as a function of time and tempera-ture. The relationship proposed by Sellarslo) has beenused in the model.

3.3.2. DynamicRecrystallization

The information available is very limited and thefollowing features have consequently been adopted for

formulating the model:

- The onset of dynamic recrystallization occurs when8> 8dy".

- The kinetics of dynamic and metadynamic recrys-tallization are described by the parameters t50 and n,

calculated with the samelaw as established for static

recrystallization. Although this hypothesis concern-ing dynamic recrystallization mayappear arbitrary,

nevertheless it can be considered as the lower limit ofthe actual behaviour of the material.

Theformula proposedby SenumaandYadall) is usedfor estimating the size of the dynamic recrystallized

grains. This formula describes the "peculiar" growthpatterns observed experimentally, i,e. very high growthrates during the first few seconds and subsequently

very slow growth.

443

32 (1992), No. 3

3.4. Controlled Cooling and Phase TransformationModel

Modernmills have special cooling sections in order toprevent grain growth and control the temperature at

which air cooling starts. For these reasons a computingalgorithm having a structure giving a high flexibility for

simulating different operational conditions has beendeveloped to forecast the thermal and microstructureevolution during the cooling after hot rolling.

The general Fourier heat equation, which takes into

account the heat generated by the phase transforma-tion, is integrated by finite differences, describing con-currently the evolution of the austenite during cooling.

Thepowerequations presented in Ref. 12) were used to

compute the heat capacities and coefficients of ther-

mal conductivity at different temperatures for the var-ious microconstituents. The sharp decrease in the heatcapacity of ferrite just above the Curie temperature Tcwasnot taken into account since all of the transforma-tions started below Tc. The austenite transformation is

determined by considering the cooling curve as a series

of micro-isotherms and applying the laws governing theisothermal austenite transformation, derived by TTTdiagrams, in accordance with the procedures proposedby other authors.i3'14)

Different boundary conditions can be selected forvarious cooling zones, each characterized by its lengthand rod travelling speed. The heat flow at the surface(~*) can be calculated by the following relationship:

~*=h(T*- T.)........

.....,....(13)

where T* is the surface temperature, T~ is the air orwater temperature, h is a combined heat transfercoefficient which includes a heat transfer coefficient byconvection heat flow (h*) and a radiation heat transfercoefficient (h.):

h=h*+h......

...........(14)

Thevalues of h. along the Stelmor conveyor havebeenfound to be dependentprimarily on the cooling air fiowrate and therefore on the opening of the fan baffles.

Figure 2shows the variation of h, with fan opening for

d cs•rr•dI aIP

RS

o!:: 150E_

,Q

~loo

~:

Fig. 2

50

o

fRS

ba) sin9le wire rod 200

tcS ~150 :T

O:~_

~ 100~r'

b] overlapped Wire rcds (~

WIRERODDIAMETER= 11 mm50

p > 50 mm

oO 25 1007550

FANOPENING( pct )Convection heat transfer coefficient (h*) on the Stelmor

conveyor calculated using surface temperature mea-surements. Pis a measureof wire rod overlapping (see

graph inset).

Q1992 ISIJ

ISIJ International, Vol.

specific working conditions. Wire rods which are notoverlapped showa heat transfer coefficient, h, about 20 o/o

higher.

Theonset of phase transformation is calculated on thebasis of the Scheil's hypothesis,13'14) No difference is

madebetween ferrite and pearlite. However, the volumefraction formed between Bs and Ms is identified asconsisting of bainite and the volume fraction formedbelow Msas consisting of martensite.

The fraction of austenite which transforms to ferrite

and pearlite or to bainite is calculated according toAvrami's lawl 5):

2~,

-,Vi = I - exp bd./TTT

t (1 5)dy

in which Vi represents the fraction of austenite tha~transforms at the temperature Ti. Thecoefficients bi andni Vary with temperature and are derived from the TTTdiagram determined for a grain size d./TTT' The modelfollows the procedure proposed by Agarwal andBrimacombel3) where each TTTcurve is approxlmatedto a series of linear segments in logarithmic scale tosimplify ca]culation of coefficients bi and ni. The frac-tion of austenite transformed at temperature Ti aboveMsis calculated by solving Eq. (15) at time ti; this timevalue is equal to the sumof the time interval At (duringwhich the temperature value is Ti) andof the "equivalent"time required for the transformation at temperature Ti ofan amountof austenite equal to that transformed duringthe entire previous time.

For temperatures be]ow Ms, the fraction of austenitethat transforms to martensite is calculated with theequation proposed by Koistinen and Marburgeri4)

Vy=(1 -~Vi)[1 -exp[-0.01 10(Ms- T)]] ...(16)

where Ms is the martensite start temperature and(1 -~Vi) is the fraction of untransformed austenite.

Using a steel of similar composition to the eutectoidsteels employedin the present investigation, Iyer et a!. 16)

calculated the interiamellar spacing of pearlite using:

s(mm)=I.8 • 10~2

..........(17)

ATE('C) """'

Thesameformula wasadopted in this work, wlth thc

average undercooling relative to A*1 (A TE) being takenas the average between the maximumvalue at the startof transformation and the minimumvalue at the peakof recalescence.

The dependenceof ferrite grain size (d*) on austenitegrain size and average cooling rate (CR) in steels havinga ferritepearlite microstructure was found to be:

d*=Ad~•4(1 -exp(0.075dy))CR 0.14 ..........(18)

where the constant Avaries with composition, d. and dv

are expressed in ,lm and CRin 'C/min. Since the threesteels considered had comparable calculated Ar3 tem-peratures,17) the effect of their compositional differ-

ences on d. was neglected on the assumption that C,

Mnand Si act on d. mainly through their effect on Ar3.

32 (1992), No. 3

3.5. Mechanical Properties-Structure Relationships

Microstructural parameters estimated by the modelsare converted to mechanical property information usingvarious empirical regression formulas.

The hardness of each phase is calculated from thechemical composition according to the expressions de-veloped by Creusot-Loire.18) The total hardness is cal-

culated using a linear mlxture law.

Theductility of pearlitic steels fs mainly controlled bythe austenitic grain size d .yOn the basis of experimental data the followingequation has been obtained for the reduction ofarea (Z) of eutectoid steels:

Z(o/o)=25.2-0.36• 106t+2.48d~1/2 .............(19)

where dy and t (cementite thickness) are expressed in

mm.The cementite thickness t is a function of carboncontent and interlamel]ar spacing of pearlite.

The ultimate tensile strength (UTS) of pearlitic steels

dependson the interlamellar spacing and wascalculatedaccording to the equations proposedby Gladman,19'20)

4. Validation of Models

A set of equations with empirically determined co-efficients were worked out to relate the heat transfercoefficient to the operating conditions of the mill. Anexample of the predicted temperature profiles througha bar mill comparedwith experimental surface temper-atures is shownin Fig. 3. Ali the calcu]ated values werefound to be in good agreement with the correspond-ing measured values (relative differences of less than5olo).

Figure 4showsa comparison between the calculatedand measuredsurface temperature values of high-carbonand boron steel wire rods on the Stelmor conveyor underspecified operating conditions.

The predictions madeby the model are in very goodagreement with the experimental values, since the de-viations match the spread of the experimental data(1 ATI 20'C).

Figure 5showsa comparison between calculated andmeasuredmeanaustenite grain sizes. Thepredictions arefairly accurate (standard deviation 10 o/o) considering thatthey cover 26 rods of different steels, rolled to differentdiameters, investigated at two different points (centre

O

UJa:

DFCaEUJOL:~UJh

r ~I

CENTERi

, I MEAN

e ISURFACE

120O

1100

1000

90O

l iI* !

,

i_le

tlp'rtal'ntll'

1vllu"l I f +-i

O IOO50

DISTANCE(m)Frg. 3. Temperature profile during hot rolling of 42mmdi-

ameter bars.

(~:) 1992 ISiJ 444

ISIJ International. Vol. 32 (1992), No. 3

TC•C)

ooo

800

7oo

8oo

500

CALCEXP STEEL ~ RS FRTLHT cs FANOPENING(Pct. )l,~ ec eI,11 c ,,, t 1 : g 4 5 c , , 12 13

, FPf- ss TS 100O • Io o., , o o o 15 IQe 100 o o o 50

A FF,2 11. s t, s tO1O 175 o]2 30 $0 1OO1 ,oo 10- ,oo so 50 1OO

A Ff ,2K 1t. s 1••S 10CO •so O12 o 2s 7s 15 1s 1, 1s ,s ,o 1OO

I FPC, IS.O 12., l d. •10 o,eo 100 100 ,oo 100 ,oo 1 1 t 1 ,oo

o QC,,l 10.S al 1OeO No 0,0 7 INSULATEDCOVER

RS=rotling 8peedFRT=ftntshing rolting temperature

LHT-Ilyina held temperltureI~

'o. CS=conveyortpeed,~ ,e.

,~;~~' 'd•.

~~* *\ \~••~

~\ ~~1.~\' .

oo

D, oo

D,-,~Ci~ I :;~~*

\AL~~~~~ ,~' -~r-

ao

\ ~!~ *~ ~~ ~'~

\t 2 3 4 5 6 7 8 12 t3

60

Fig. 4.

Comparison between calculated and measured surface

temperatures of wire rods during controlled cooling.

o 20 40

70MEANAUSTENITICGRAI N SIZE

E~Q,

ul

C,O

LOl

10Q,

fO

:~

O

50

50

40

so

20

io

o

o

///'Ao o oA (~10 8~

o ol)

. !~9'(Fle

JL(E)

.Q. '

e ,•. ROD RODCENTERSVRFACE~

~igh Csteel o eO, iC-i.7Nn-O BSi A JL ~O,

3C-O,9Mn-B D l

o io 20 30 (Io 50 50 70measurea 9rain slze (Hm)

Comparisonbetween calculated and measuredmeanaustenitic grain sizes in full-scale trials.

E:~

UJNCO

ZC,:OOFZUJh,,,:,C

iao

ieo

i~o

i20

iOo

eo

50

~0

20

O

*

r

r

q

o\

ROUGHINGTRAIN

(a)

dl 'u""

A$40o 1'o l

1't INTERMEDIATETRA'N

50

o 2 si 4 s E 7 a 9 io li 12i

PASSNUMBER

Fig. 5.

and surface).

An example of the predicted austenite grain size ev-olution during rolling is shown in Fig. 6. During the

roughing stage (Fig. 6(a)), the interpass times aresufficiently long to allow for complete recrystalliza-

tion with progressive grain refining. During finishing

(Fig. 6(b)), only partial recrystallization occurs despite

the very rapid kinetics, since the interpass times be-

come progressively shorter (t sec). Refining ofthe austenitic structure during the finishing stage is clear-

ly brought on by the occurrence of partial static recrys-tallization processes, followed by dynamic recrystalli-

zation of the strongly work-hardened fraction ofmaterial. This leads to the formation of a heterogeneousstructure (even if the grains are initially all of the samesize) within a few seconds after the last pass, owing to

the high growth rate of the dynamically recrystallized

grains.

Detailed analysis of the structure of I I and 5.5mmdiameter rod specimens, quenched 15-20 sec after the

E:~

,,,

ZC,:(,

OFZUJhC,,

D,

40

30

20

10

o

t

2"d INTERM.

TRAIN(b)

A

A

lII

~

'Q"' - HA"DENEOA Ef 0.4{V 8r> 04AusTE'I'TE

STAT'enEc'lysTAuJzATo" ADYNA'IIC IECIYSTAUJZATWdV

"EA" s'zE tv

V

A FtNISHINGMILL

VVV ' ltJF,

Fig. 6.

ii i2 ia i4 i5 i5 i7 ia ig ao 2i 22 23

PASSNUMBERPredicted evolution of austenitic grain

roughing, (b) finishing.

a4 25

size: (a)

end of rolling, revealed that the measured grain size

distributions followed a bimodal pattern as predicted

by the model (Table 3).

In order to test the reliability of the model moreradically (especially with regard to the kinetics asso-ciated with the very high growth rates of dynamically re-

crystallized grains), mill conditions were set up for

blocking the rod in the water box facing the exit of thc

445 C ~992 ISIJ

ISIJ International, Vol. 32 (1992), No. 3

finishing stand. In this way, it waspossible to freeze the

austenitic structure of a high carbon steel within 0.5 secfrom the end of rolling. Metallographic examination oflongitudinal and transversal sections of the rod revealedthe presence of a fully recrystallized structure consistingof two different grain populations as predicted by therecrystallization model (Table 3).

5. Industrial Applications

Theability of the proposed "complete model" in sim-ulating the industrial processes and its potential use-fulness in designing and solving problems have beendemonstrated by significant examples of calculation ofhot rolling andcontrolled cooling of wire rods andbars.

5.1. Hot Rolling

Examplesof the effect of hot rolling practice on theformation of heterogeneous austenitic structures have

Table 3. Comparison between calculated and measureddata relative to heterogeneous austenitic structuresin high-carbon steel rods.

been already discussed. Local heterogeneity increaseswith billet temperature and becomesprogressively morepronounced from the surface to the centre of the rod(Table 4)

.

The model is also able to predict the variation of the

meanaustenite grain size along the stock diameter dueto the thermal gradient. Figure 7shows the comparisonof experimental and calculated meangrain sizes in a17mmdiameter rod. Theagreement is good despite thefact that the strain variation is not considered.

The positive effect of reducing the billet soakingtemperature and the rolling speed for the refinement ofaustenitic grains of 21 mmdiameter bars is shown in

Table 5. A reduction in austenitic grain size of about30 o/o can be obtained.

5.2. Controlled Cooling of Wire RodsThe influence of wire rod diameter, cooling practices

and axial segregation on microstructure and strength has

Wire rodTime after Experimental

diametersend of valuesrolling Volume dv

(mm) (s) ("/*) (~m)

Calculatedvalues

Volume d),

(o/o) ('tm)

E

UJNCO

ZaC

OZUJ

:

70

17 mmDIAMETERROD

60

50

5.5

11.O

55

17

22

0.5

79.7

20.3

51.2

48.8

59.0

41 .O

23.9

l I.4

36.4

l8.7

21 812.8

68.4

31.6

71.8

28 258.8

41.2

31.6

l0.9

31.9

l7.7

20.2

10.6

Fig. 7.

40

30

cllcutlted

/e

1"P~~ ""ItL1' "' 'I'

\ \., ,,bl 'b

/ 'xporimental ~F.f CENTER

8.5 8fO.O

DISTANCE(mm)Comparisonof experimental and calculated austenitic

grain size profile along the rod diameter (high-carbonsteel).

Table 4. Calculated austenitic grain size heterogenelty (a)

of 5.5mmrods for different billet soaking tem-perature

Table 5. Predicted effect ofsoaking temperature androllingspeed on austenitic grain size of 21 mmdiameterbars.

Rodsurface Rodceuter

Billet soakingI 140

temperature ('C)d}, (~m) 17.9

a (pm) 7.6

1190

22. l9. l

l 140

28.5

l I.9

l 190

31.l

13.2

Soakingtemperature

('C)

Rollingspeed(m/s)

Meangrain size (~m)

Surface Center

1200

l 160

12

968

. 348

. 578.4

58.8

T'C

900

800

700

60o

500

400

STEELFP82

FANOPENING100 '/-

~\ T1..~

\ t4ll

\ \\ ll\ \l 'i\ t\

\ ,1 \\\

\ ,l

c=~5mm\. Il-+/11 ~\

If \\l, \'J'l

'l'l

ll

*"+ ) ll7////////

~ 7~j ///

~~•/;/i//

/I~(_7""~1*

c= 15mm

c=11 5mm

100

80

6o

40

2o

o

l 2 4 6 B753

40 m

UJHzUJ~(,):)

oUJ

Scc

oLL,,)

zcE: Fig. 8.h Predicted effects of wire rod diameter on local temperature

and fraction of transformed austenite.

O 20

C 1992 ISIJ 446

ISIJ International, Vol. 32 (1992), No. 3

been investigated.

5.2.1. Effect of Wire-rod DiameterFor equal cooling conditions (all fans turned on), an

increase in rod diameter from 5.5 to 15mmcauses anincrease of the estimated mean pearlite formationtemperature from 610 to 650'C (Fig. 8). This in turncauses an increase of calculated lamellar spacing froms= 150nmto s=230nmand corresponding reduction in

mechanical strength (AUTS= - 55 MPa).

5.2.2. Effect of Cooling Practices

The models have been used in a specific applicationaimed to reduce the cooling rate downto the point wherethe strength of the wire rod could still be guaranteed tobe greater than I 030MPa.The reduction of the coolingrate was planned to prevent the formation of brittle

structures in the segregation zones of 5.5mmdiameterrods (see Sec. 5.2.3). Figure 9 shows the calculated

temperature and strength values, relative to the originalsituation and to the newpractice singled out with themodel, compared with the experimental data. Theseresults confirm the model capacity to yield reliable

information for selecting the optimum on-1ine coolingpractice.

T('C )

900

8oo

700

eoo

500

Another practical problem in wire rod mill is to avoidthe formation of bainite or martensite in steels with highhardenability such as boron steels for fasteners. Aninsulated cover and low conveyor speeds are usuallyadopted to give very dense loops and thus low coolingrates.

In Fig. 10 the effects of laying headtemperature (LHT)and conveyor speed (CS) on the temperature profile andtransformed austenite fraction are shown for l0.5mmdiameter rods.

The phase transformation is not completed in theinsulated zone and the formation of acicular micro-structure cannot be avoided whencritical values for LHTand CSare reached.

If low LHTvalues are difficult to be obtained thesimulation suggests that it is convenient to shift theinsulating cover a few meters to favour a rapid tem-perature decreaseup to the start of phasetransformation,

5.2.3. Central Segregation Effects

Formation of bainite and martensite, which give rise

to problems during drawing, is favoured by high coolingrates and by the increase of local hardenability dueto segregation of elements such as Cand Mnat the

FANOPENINGPERCENTAGE~iCAL. EXP STEEL RS FRT LHT cs

,nl'l oc ecm,,, ml 1 2 3 , 5 6 7 8 12 13

FPeg 55 7G IQ7Q 9oo 09 o o o 75 10o loo o Olo 50A ,

s fp69 55 76 lo40 870 o9 o 25 25 25 5o 5o o o o 50o

UTS tUPa) UTS tMPaLEXP CALC

A 1065-1095 1090

B IO3O-1050 1050

t)RS=rotling speed

\~.FRT=tinishing ralting temperature

LHT=1ayinahead temperature

l .CS=conveyorspeed

l

2 6 83 4 5 t2 13

Fig. 9.

Predicted temperature profile of 5.5 mmdiameterhigh-carbon steel wire rods along Stelmor con-veyor.

o 20 40 60

T("C )

~,oo

Uoo

700

bOO

STEELQC29BEXPCAL LHT

"C510

9]o

8,0

cs

Q10

ool

QO,

COVLH

1 - 21

1 - 21

1- 24

Wire rod diam.

\ 910 OOI 7 24/

\~ O / /"\ / /

~:~~ /

*~ - _ P.J-_-7-- _/ ,/~ L= !~1- -

INSULArINGCovbRs

= 10.5 mm

tOo

tlo

60

40

20

o

(l

UJhZUJFc,,

:)

OUJ:~Q:

OLL,1)

Za:

h

60

Fig. 10.

Temperature and austenite evolution duringretarded cooling on the Stelmor conveyor for

boron steel wire rod.

o 20 40 m

447 @1992 ISIJ

ISIJ lnternational, Vol. 32 (1 992), No. 3

fP6S $FeA ~~ RS LHT cs FANOPENiNGPERCENTAGEFP" l,,, llt*t* t tc m l~ , 2 J d$ s G 1 I 12 l9

A D l 5. 5 75 B70 o. 9 o o o 75 100 IOO o o o 50

T('C ) B (; e 5.5 75 870 o. 9 o o o 75 50 5o 50 o o 50

c A dlL ~5 75 870 o. 9 o o o 25 25 25 25 25 o 50

900STEEL c~ Mn~ Si~ Cf~

FP6S o. 1 o. 6 o. 2800SEG~FPf- 1.O 1,1 0,2

700 Ps Pt

/600

..~f4

(a) Bs

50o1 2 3 J' 5 6 8 ,2 13

o 20 40 60

SEGR L) RS LHT cs FANOPENINGPERCENTAGEFf82K FF•2X mm 'c t 2 a d' s G 1 8 12 t:,

o l 55 75 870 09 O o o o 25 25 o 25 o 50T('C ) D

E o , 55 75 870 09 o o o Q 25 o Q 25 Q 50

900STEEL c~ M,11, Si~ Crl,

FF82X 0•2 o.7 o. 2 o,,5800

SEGaFFt2K 1.0 1. 1 0.2 'L9

70o PsP1

pf

(P*B)t600 (P•B)I

~, B: 'O~(b) B: 5ole

500l 2 3 4 5 8 7 8 t2 ,3

20 10 m 60o

Fig. 11.

Predicted effect of central segregation andtemperature profile and final microstructure

diameter high-carbon steel wire rods.

cooling onof 5.5mm

centreline of the wire rod. Figure ll shows the modelresults for 5.5 mmdiameter rods which are moreproneto the formation of undesirable phases since they can becooled rapidly. The effect of segregation on phasetransformation kinetics was taken into account byshifting the start and end of transformation according to

available information21) on the influence of chemicalcomposition derived from TTTdiagrams.

Toprevent the formation of bainite and/or martensiteit is necessary to modify the cooling practice, starting

from the point on the Stelmor conveyor where pearlite

starts to form on the rod surface. From that pointonwards, the airflow rate of the fans should be reduceddrastically for a conveyor length sufficient to ensure the

transformation to pearlite of the austenite in the central

segregation zone (Fig. I l(a)).

In the case of a morehardenable steel (Fig. I l(b)), it

is necessary to shut downtwo fans at the onset of pearlite

transformation. This operation reduces drastically the

formation of bainite, which otherwise would amounttoover 100/0. Setting the baffies of fan No. 8 to a 250/0

opening contributes to keeping the temperature of the

pearlite transformation within mediumva]ues (640'C),

thereby avoiding the formation of coarse pearlite.

5.3. Bar Cooling

Very rapid cooling systems are required to reduce the

stock temperature for controlling grain growth after hot

O

GC:Dh,:a:aJJ

:EUJh

Fig.

1100

1000

900

800

700

6OO

500

400

300

200

100

O

Ma

MEAN

[1:l10 m

[]5m

[]5m

CENTER

SURFACE

ROLLINGSPEED= 41 m! I

h = 17 kW/ (m2 •C ,

O 10 20 30 40 5O 6O 70 80

DISTANCE(m)12. Predicted effect of cooling system layout

perature profile of 32mmdiameter bar.

90 Ioo

on tem-

rolling as the usual distances between finishing roll andcooling bed are rather small. However, if severe cooling

occurs temperatures can reach values lower than 400'Cand martensite formation could result at the surface.

In Fig. 12 the effect of the cooling systern layout(heat transfer coefficient of 17kW/(m2.C) on tempera-ture profiles of 32mmdiameter bar is shown.

Twocooling sections, 5mlong each, instead of onelO mlong cooling zone, succeed in achieving lower stock

temperatures without inadmissible undercooling of the

bar surface, avoiding martensite formation.

~ 1992 ISIJ 448

ISIJ International. Vol. 32 (1 992), No. 3

6. Conclusions

Asystem of mutually integrated mathematical modelshas been applied for investigating the relationships be-

tween process variables and the thermal and micro-structural homogeneity of wire rods and bars.

Thepresence of thermal gradients along the diameterof the rod and the effect of different recrystallization

mechanismscan lead to the formation of heterogeneousaustenitic structures.

Using the model, it has been possible to quantify theeffects of rod diameter and cooling practices on the mi-crostructure and temperature profile along the Stelmor

conveyor.The degree to which bar surfaces can be cooled by

water tube systems avoiding martensite formation hasbeen determined.

Amongthe practical objectives already achieved,

or which can be achieved in the short term by ap-plying the microstructural mathematical model, are:

- optimization of the hot rolling and cooling practicesfor the materials currently in production;

- identification of controlled cooling conditions for newsteels, with a consequent reduction of industrial ex-periments;prediction of the improvements obtainable troughplant modifications (e,g. Introduction of additionalcooling systems in the mill to reduce finish rolling

temperature);

- identification of simplified models for on-1ine use.

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449 @1992 ISIJ