ISIJ international, Vol. 35 (1 995). No. 9, pp. 1100-1 108

Integrated Model for Calculating

Parameters of Steel during Rolling

Microstructural and Formingin Continuous Mills

W. LEHNERTand N. D. CUONGInstitut fOr Metallformung, Technische Universitat Bergakademie Freiberg, Bernhard-von-Cotta-Str. 4,

Deutschland. E-mail: Lehnert@imf.tu-freiberg,de

(Received on March30. l995, accepted in final form on April 24. l995)

09596 Freiberg,

Theforming conditions strongly influence the product quality. The integrated simulation model "Rod andWire", which was specially developed, tested and adapted for the Tolling of rods and wire, allows thepreliminary calculation of important local microstructural and forming parameters. The simulation model"Rod and Wire" comprises several modules: deformation and speed fields, temperature distribution in thedeformation zone and the delay time, microstructural parameters (grain size, recrystallized fration) andtransformation structure, strength of selected steel grades. The results of simulation can be used as a basisfor the material evaluation of plants and processes. By examples, it wasshownhowthe effect of process-related influences on product quality can be accurately determined and quantified.

KEYWORDS:hot rolling; high speed rolling; microstructure, recrystallization; Iocal forming parameters;simulation.

1. Introduction

The preliminary calculation of the microstructureforming during hot deformation is of special importancewith respect to the optimization of the technologiesallowing the manufacture of products with defined me-chanical and technological parameters. In most cases,the formation of a unifoim fine-grained microstructureis essential. For steel grades with an allotropic phasetransformation, a uniform fine-grained austenitic struc-

ture, which can be obtained by temperature-controlled(normalizing) rolling, allows to obtain a fine-grained

secondary microstructure. Dueto the complexity of the

involved processes, the extent and the kinetics of the

microstructural evolution can be described by mathe-matical modelling only, and only mathematical simu-lation can produce a clear idea of the controlling rela-

tionships.

The forming conditions in rod and wire rolling are

very different from those in strip and plate rolling. Im-portant characteristics are:

- inhomogeneous deformation distribution over the

cross section due to groove rolling,

- average reduction in cross-sectional area fixed by

groove sequence,

- higher reference deformation rate (up to 3500s~ i),

- shorter deformation times and delay times with in-

creasing numberof passes,

- strong heating of the rolling stock in the last passes,and

- Iimited temperature control.

Amongthese characteristics controlling the real struc-

C 1995 ISIJ 1100

ture of the materials, the determination of the local

forming parameters is of special importance in rod andwire rolling, and not only for microstructural simulationbut to the extent that they have to be taken into accountwhendeterming the material constants relevant for the

assessmentof the microstructure.

Theproposed integrated simulation model is basedonthe assumption that the local forming parameters (e.g.

temperatue, forming degree and deformation rate) arethe first to be determined for rod and wire rolling in

continuous mills (Fig. l). The processes of micro-structural formation were investigated on a four-standmill under the conditions of high-speed rolling mills. Byassigning the local microstructural and forming param-eters, the material-dependent parameters can be de-

termined for the microstructural model. In view of the

complexity of the individual calculation modules, this

article cannot discuss all details of the integrated model;these are described in publications.1 ~ 3) In the following,the most important steps and special characteristics ofthe proposed integrated model for the calculation oflocal microstructural and forming parameters will bedescribed.

2. Process Model

The process model comprises three important modelunits:

- modelunit for the calculation of local forming degreesand deformation rates,

- model unit for the calculation of the temperature field

in the deformation zone, and

ISIJ International. Vol, 35 (1 995). No. 9

Boundary. theory

Flow ct[rve model

Viosioplastic investigations

Modei for the caleuh,tion oflocaldeformation and deformation r~,te

e, e A, p,C=f( S,Material)

\/.

\

~L

/ fii*I

ir

rT~~~~rS~~I Model for calculation of the

--' temperature ficld in the defonn~$tion zonebalanee IT]ethod

Finite difference

method

Rolling tests

Assig]Iment of local

lllicrostructL[ral andfonning para]neters

Material parameters

Model fQr Calculation of the

temperature field during delay time

e, t, ~

Microstructural modei

J),,

/_),t

' X

Fourier heat

conductionequation

.:UJ

l

/

I

a) Rolling gap division.

Y

i

I

J:(

Model of mechauical

propertles

zRa, Rm,A, Z

Material Process Equipment

Fig, l. Freiberg integrated model for calculating local

microstructural and forming parameters.

- model unit for the calculation of the temperature field

during delay time.

Theparameters calculated by each model unit form the

assumptions and input values for the next model unit.

2.1. Modelfor the Calculation of Local FormingDegreesand Deformation Rates

This model is based on the boundary theory of plas-ticity mechanics in combination with the finite differ-

ence method(FDM). The speed field in the rolling gapcan be better illustrated if the entrance andexit plane arelimited by curved surfaces rather than planes (Fig.

2a)). In a simplified way, a plane state of deformationis assumedfor a longitudinal strip element. This as-surnption can be brought in agreement with reality if

the deformation process is subdivided into longitudinalstrips of equal width (Fig. 2b)) andeach strip is analyzedseparately. The three-dimensional deformation zone is

reduced to the plane rolling gap. In Fig. 2c), the defor-

mation rate tensor T~ and the reference deformationrate were derived for a strip for the case that all longi-

tudinal elements experience the samechange in length.

The calculation wasperformed numerically by dividingthe rolling gap in a multitude of small surface elements(Fig. 2a)). The inhomogeneity of deformation, whichcan be interpreted as the proportion between the actualreference forming degree and that obtained in paral-lelepipedal deformation, was confirmed by visioplastic

investigations at different rolling temperatures andmaterials. Threadedpins were inserted in the specimens

11ol

!:tJJ

b) Rolling stock division for rolling circular stock in

an oval groove.

If/~;

J~!Lhfl'Fi~)i~~~,c

vrlv ' cos ev"v 'uh

' I .dvr

v

al~~ ~elT'2r dr'rr dr

~ vr

v ! ' uerr

-~'~'~_

:'-~ !de ' Crr O gre

!:i i~elrl: ' O OT~-

l_;:~r{drl r ' '

~ee

~vl Ot82 '

~/~~T~~~1r2r+

~2e* 2 Er2g

~v 1ltl5S'r~Lv ,~r~~~Le

c) Deformation rates in rolling'

Fig' 2. Calculation of local deformation rates'

to be rolled. For Id/h~ =2.7, the cumulative referenceforming degree and the e-values are indicated in Figs. 3and 4. Dueto the inhomogeneouslongitudinal deforma-tion, the central zones are subjected to higher deforma-tion rates and forming degrees than the surface zones.After reaching a maximum,~then decreases in the di-

rection of the rolling stock outlet.

C 1995 ISiJ

ISIJ International, Vol. 35 (1995). No. 9

1,0

O,8

.::o 0,6

~> 0,4(~

0,2

O

(~

q)c).

/\~>.

~1\~

ConductionDeformation heat

ConductionDeformation heat

Frietional heat

\

////

O,~)

ConduotionConductionConvection

1'o

f0'8

0'6J::

~: 0'4

N0'2

o

O,l

Fig.

ql

//

/

O,~

Fig.

3

~~~

l ~~).

//

// / // / ee

~/ ~~e/0~) / c) .,,~+~'/' /0,4 '~\ ~S'

O~ / ~e/ *eeHr/1(y' 06, / s:e*

' O.. ~e~~Od)

' O.;9/

/Local reference deformation for central plane.

/tV~;

ll

ll//// ,~5~S~)

17

/ ll// ~S~~~)

// // // e~ ~:~S (;

7cS ~

l ~(~~ ~:\o

/v~'~(S'~;

/ //r~~S~)

~~~:o

Q~' /l cJ'~

Ol+1/c! 'Q\~:~~06 ;.

~O;e

~ ~'n~S .e;/ v eS:e;~

h~~5~)~~

Q91~>

4. Local reference deformation rate for central plane

Local deformation withboundary theory andvisioplastic investigation

90E+08

Heatflowbalancemethod

Fourier heat conductionFinite difference method

2.2. Modelfor the Calculation of the TemperatureField

in the Deformation ZoneDepending on the boundary conditions (kinematic

and forming), the stock is heated or cooled in the de-

formation zone. Theheat fiow balance methodwasused

to calculate the temperature field forming in the

deformation zone; a one-demensional heat flow wasassumed(Fig. 5). Aheat balance was calc~ilated for all

discrete elements inside the deformation zone. This

allowed to describe

1.the heat flow from and to the neighbouring elements

2. the deformation heat generated in one element, and

3.the temporal changeof enthalpy in one element.

For the boundary elements, an additional heat flow dueto conduction and friction with the rolls was taken into

account.

2.3. Calculation of the Temperature Field during DelayTime

Fourier's heat conduction equation, a partial differ-

ential equation of the parabolic type, was used for

calculating the temperature field during delay time. Inthe general case (temperature dependenceon time and

C 1995 ISIJ

Fig. 5. Calculation of temperature field.

Alpha [W/(m^2'K)]

ge: smoothinsert

te: turbulent insert

oq: without transverse flow

mq: with transverse flow

80E+08

70E+08

60E+03

50E+03

40E+03

80E+03

20E*a8

1oE+08

oE+03

)2]i

IT

~1("~/:

[sr ,• ,•,-

'~/

d:i.

1102

85 4010 20 25 8015

water volumeflow[m3/h]

Fig. 6. Heat transfer coefficient as a function of water volumeflow and cooler tube design.

all three coordinates) it iS:

45

2

a~ a2 a2e2

= 2C(~) p(8) ~, A(S)

ey2 ezS+ + .

ax

+eh(S) .[(~)2+(~)2+(~)2J+ ~7 ......(1)

aS

Assuming that the only heat flow is that in vertical

direction (one-dimensional case). Eq. (1) is simplified to

aS+

aA(~) .(eSa~ 2 2+W....(2)C(S) ' p(S) ' - =A(S) '

at ex2 aS ex

With the help of the boundary condition

eSoe ' (Sumgcb ) A(S) '

ex " "" ""(3)- SRand

and the difference method, the temperature during delay

time could be calculated for each element (Fig. 6).

The determination of the heat transfer coefficient in

the cooler tubes is muchmore complicated. Here, the

heat transfer coefficient is calculated as a function ofthe surface temperature of the material being cooled(Sob)' the volume throughput of the cooling agent (~),

ISIJ International, Vol.

the diameter ratio wire/cooler tube (d*/d*), the temper-ature of the cooling agent (SM), the relative speed be-

tween stock and water (VR), and, most important, thecooler tube design (CTD):

( .d*

SM, VR,CTD .. ...(4)

,oc=f~~ob, V,

d.

Since it has not beenpossible to mathematically describe

these influencing factors so far, empirical equations wereused which were determined for several types of cooler

tubes after extensive measurements(Fig. 6). Individual

inputs for the heat transfer coefficient are possible in the

simulation for both water and air cooling. This allows

to calculate the temperature curves of each element. Sec.

5contains several calculation examples.

3. Microstructural Model

With few exceptions, knownmicrostructural calcula-

tion models refer to the basis formulated by Sellars.6,7)

However, the methodused for measuring the indicidual

material parameters very strongly, which restricts the

ranges of validity and application. Suchmodels can be

zener-Hollomon-parameter

Z = 8* expQu'

R*TFonning degree at start of dynamic recrystallization

": * Zd'lek =:al * Do

Dynamicrecrystallized fraction

.]* e-d =

-exp[eek

2

X lco"

I*(s *c;$

,,c: * ceo" c D exp ~:~ s1

Dynamicrecrystallized grain Size

Dd dl * Zdi

35 (1 995), No. 9

used !)nly for flat rolling or groove rolling at a lowdeformation rate.4~ Io) In Ref. I l), an attempt wasmadeto use the kinetics of static or metadynamicrecrystalliza-

tion to correct the delay time between two deformationsteps in wire rolling in such a way that the mateiral

parameters obtained in torsion tests can be employedin

the simulation of the microstructure. Thedependenceofmicrostructural formation on the deformation rate wasnot clarified.

TheFreiberg "RodandWire" modelallows to expandthe range of validity so that rod and wire rolling in

high-speed mills can be analyzed. The dynamic andstatic recrystallization even of partially recrystallized

austenitic microstructures is taken into account by the

accumulation of the hardening degree.

Themodelstructures, working steps and investigation

methods including several simulation calculations weredescribed in detail and critically evaluated in.1~3) In

deviation from the usual test methods,4~lo) the ther-

modynamic and thermokinetic material parametersincluded in the set of equations according to Fig. 7weredetermined directly in rolling rather than in fundamentalforming tests. The investigations were carried out in afour-stand continuous mill mostly equivalent to in-

dustrial plants. This allowed to vary the technological

parameters over a relatively wide range.For the characterization of the microstructure during

rolling, the test plant was supplemented in such a waythat the newly formed microstructure could be "frozen"in different time phases and forming stages. The formeraustenite and ferrite crystallites (for ferritic steel grades)

*U

400

s~1

3OO

a) dynamicmodel

Timefor 500/0 static recrystallization

t0'5 := f :,,

'exp(f4

'

*Qst

* Z!;*ef *Df *R*T

Static recrystallized fration

X I -1*/.,

:~

-exp[h o

hs

t ~t0'5

Static recrystallized grain size

D., = g] * eg= * D*gl * Zg'

Grain growih

* -D~" - D.n = X* t expQr'

R*TEffective forming degree

8~if(j)=F(e ~

i_ .Materia!, t ) +8,e(1-i)' Do(

l)(i-1) '~(i_1)

'

b) static model

Fig. 7. Calculation formulation in hot forming.

for microstructural transforma-

1103

200

10

o

10

O,9

O~

*O]>(

O,S

05

0,4

0,3

O,

O;

fLl~950'C, Do~49um lr

T~~1 , 24MnVk,l

/Is l 110C

l l

i.. lIt

'f' t,

th

liq*~1 i

J ac,

/ '

//A Jrl:iJ

/1,0 loO(

lil /"\~,.~, -~

l'i'i'

l',

~Ch ~Xd

0,5 90t

/'\

/1

!//

l\ Dd O Z~

~l•~~__

~F1,II-,I~

o aocQ5 1,O 1,5 2omm25 2

=,,: (hl,2~ Yl a,

o I Il: mo: ~:

Edge

1100

loOo

~

goo

aoo

Core

80

Fm70

60

O50 o~O

30

20

10

10

s~

x 10 17

5

xFig. 8. Assignment of local microstructural and forming

parameters.

C 1995

N

ISIJ

ISIJ International, Vol.

were madevisible by etching the grain boundaries. Byassigning the local microstructural and forming param-eters (Fig. 8), all material parameters of the two sets

of equations (Fig. 7) were obtained. By this method,the material behaviour can be described for the sameprocesses as in industrial production. The extendedrange of validity provides for increased reliability andsignificance of the structural model. This allows to pre-dict the structural formation processes for the high-speedrolling of various steel grades, from C-Mnto low-alloyto high-alloy steels.

For the dynamic subsystem, Fig. 9shows the depen-dence of the microstructural parameters on the form-ing parameters and steel types. The tendency towardsrecrystallization decreases in the order C-Mnsteel~,

low-alloy steel~,steel alloyed with vanadium=>high-alloy steel. Extensive data on the interaction of thealloying and microalloying elements and their precipi-tation in the austenite are required for an explanationof these facts. The precipitation behaviour during hotrolling is especially difficult to describe. Several ar-ticlesl2,13) in this field give a satisfactory mathematicaldescription of certain precipitations on a theoretical basis

(thermodynamic equilibrium classical nucleation and

35 (1995), No. 9

nucleus growth theory applied to precipitations). It is

not possible, however, to combine these models with amicrostructural model in the sense of Fig. 7. Asuccessfulcombination requires that all microstructural formationprocesses can be exactly described by theory.14) Byextensive investigations, the influence of several micro-alloying elements on the structural formation processescould be described using a modified form of thefundamental relationships (Fig. 7).9,15,16) In our ownmodel, the influence of the alloying elements on softeningand hardening processes was taken into account in theequations by meansof a wide variation of the formingconditions. Figure 10 showed the austenite grain size

distribution in the rolling stock in the deformation zoneof a high-strength structural steel (vertical direction) asa function of temperature.

At present, there are only a few applicable theoretical

models for the material behaviour during phase trans-formation.9) For the transformation y=>0(, the places

and rate of formation and the growth of nuclei, and thusthe ferritic grain size, can be calculated on the basisof the classical nucleation and growth theory. 17,18)

However, empirical equations are widely used to cal-

culate the ferritic grain size as a function of the austenitic

43.5

32,5

8k 21,5

0,5

O

1000 s~ I . Do = 100 um

~ ~~]

::::1:::

850~

C-Mnsteel steellow-alloysteel alloyed

withvanadium

a) Start Of dynamic recrystallization.

high-alloysteel

l0,9

0.8

0,7

Xd 0,6

0.5

0,4

o,3

0,2

o, lo

~~

s

.~_

O = 1050'C; D 100um

'-1- C-Mnsteel

-(>-• Iow -alloy steel

-x- steel alloyed with vanadium

high-auoy steel_I

o 20,5 i.5ls

b) Recrystallization behaviour.

2,5

Dd[umj

l 150 9501050S('C)

c) Dynamicrecrystallized grain size.

-c- C-Mnsteel

-x- Iow-alloy steel

-~>- steel alloYed withvanadium

-~- high-alloy steelFig. 9.

Dynamicrecrystallization behaviour.

850

C 1995 ISIJ 1104

ISIJ International, Vol. 35 (1 995). No. 9

70

60

50

20

10

Ocoa)c;~~~~~Fro

c;c~l*,N.

oo~~~reiative distance from edge (2*X/H I)

eDe~l

ccC:~

950

i050h 1150oa)~'hcohc~l\.cet,)

oc~e)o*

750

850

temp.[•C]

~ 60-70

~ 50-60

~] 40-50

E~] 30-40

I 20-30

~ 10-20

[] 0-10

Fig. 10.

Austenitic grain size distribution in vertical

direction as a function of temperature.

microstructure and the cooling rate.6,9,19) Similarly toRef. 6), the following relationship was obtained for ahigh-strength structural steel:

D. =3.75 +0.18 • Dv+ I .4 •~-o.s .........(5)

4. Mechanical Properties

Therelationship betweenthe ferritic grain size D* andthe mechanical properties was established on the basis

of experimental data. Thefollowing correlations are valid

for the high-strength structural steel under investigation:

R*=33779+88088 D o 5 ..........(6)

R. = - 13. 17 + 1350.49 • D~0.5 ..........(7)

A=46.96 - 45.28 • D~0.5. .... ....

.(8)

Z=78.05 - 38. 19 • D~0.5.... ....

...(9)

With decreasing size of the ferrite grains, the strength

properties are improved and the toughness properties

are only slightly impaired.

For low-alloy and high-alloy steels as well as high-

carbon grades, whosetransformation structure consists

of pearlite, bainite and martensite, the austenitic micro-

structure strongly influences the occurrence, appearance,percentage and morphology of the individual structural

components.20)Auniform fine-grained austenitic micro-

structure promotes a transformation structure favour-able for mechanical processing, such as ferrite, pearlite

or bainite. An undesirable hardening structure, whichis generally connected with a coarse-grained austenitic

structure after hot rolling, can• be avoided by temperaturecontrol during or after hot forming. It is difficult todescribe the dependenceof the mechanical properties onthe microstructure for these steel grades.

For austenitic and ferritic steel grades, the final

substructure present at roomtemperature is established

in hot forming. A small grain size has to be achievedin hot forming for these grades as well. Strength andtoughness are improved by grain refinement. Thefollow-

ing relationship was found for a ferritic chromium-alloyed steel:

1105

R~=434.60 + 1988.45 • D~0.5. ......

...(10)

Z=81 .94 - 130.42 • D~0.5 ..........(1 1)

5. Simulation and Planning of ThermomechanicalRoll-

ing

The integrated model "Rod and Wire" allows bothprocess and material-oriented simulation and optimi-zation calculations. A plant assessment was reportedin Refs. 2, 3). In this article, results obtained for wirerolling of a high-strength carbon steel (St 355) and-for comparison-an austenitic stainless steel (X8CrNi-Til8.lO) will be reported. As an example, rolling shall

be performed on a continuous wire block on whichsemifinished product with a cross section of 150mmxl50mmis processed to wire with a diameter of 514mmin 23 or 25 passes. The last 10 passes take place in thewire block with approx. 0.7m distance between twostands. The following calculations refer to a final di-

ameter of 5.5mmand a final rolling speed of 50m/s.

The influence of the initial rolling temperature and the

deformation rate on the final microstructure was in-

vestigated on several occasions.2,3,21,22) These have aweakinfluence on grain refinement. Therefore, temper-ature control to achieve a fine-grained austenitic struc-

ture will mainly be discussed here.

The following variants will be analyzed:

Vl conventional rolling (no infiuence on rolling stock

enthalpy)

V2 thermomechanical rolling with close temperaturecontrol

Since the initial rolling temperature has only a slight

impact on the formation of the austenitic microstructure,microstructural and forming parameters are calculated

and represented only for the last 14 passes.Figure 11 shows the temperature curve in the last 14

passes for the conventional rolling of steel St 355. 950'C

was selected as initial temperature. The temperatureremained almost constant prior to the wire block. In the

wire block, there is a marked increase in temperaturedue to the heating from pass to pass; this is especially

C 1995 ISIJ

ISIJ International, Vol. 35 (1 995), No. 9

pronounced in the core in which the defonuation is

muchstronger than in the case. After the last pass, the

average temperature weighed for the volume elementsof the rolling stock section is approx. I OOO'C.Bymeansof an intermediate cooling comprising four intensive

Metallformungsinstitut BAF

(,

a,h5

~q,$~~'!'

~1

Temperature curve

cooler tubes, the feeding temperatue to the block can bereduced to 750'C (Fig. 12). After leaving the block, the

average temperature of the rolling stock again rises to

approx. 880'C. In the controlled cooling line, the averagetemperature is again reduced to approx. 750'C. For a

Steel quality St355 Numberofpasses : 14 Initial telnperature['C]: 950JOO

07s

oso

025

ooo

975

9so

925

9(X)

s7s

850

s2s

11

107

l05

l02

l

975

a' 950h5~$ 92S~q,$~ 900

~,!, 87S

8SO

825

800 800

U l

Edge

2Time [s]

Average

s

Core

6

l]OO

l07S

lOSO

l025

lOOO

Fig. Il.

Temperature curve, steel grade St 355, variant I .

Metallformungsinstitut BAFSteel quality St355

(,

q,h5~q;

~~a,

H

Temperaturecurveeel quality St355 Numberofpasses : 14 Initial temperature['C]: 950

ooo

950

900

850

800

7so

700

6so

OOo

5so

500

450

400

loo

950

900

8so

300

750

700

6SO

eoo

5so

SOO

4SO

400400

o I

Edge

2 3Time [s]

Average

6 7

Core

B

lOOO

400

Fig. 12.

Temperature curve, steel grade St 355, variant 2.

Metallformungsinstitut BAF

(,

a,LS

~OSL~,L)

~1

TemperaturecurveSteel quality X8CrNiTil8, 10 Numberof passes 14 Initial temperature['C]: 950

Jl

l05

l9So

90C

850

SOO

7SO

700

e50

eOO

550

500

450

400

loo

050

oeo

9so

900

8so

800

750

700

650

coO

S50

500

4so

400400

o l

Edge

2 3Time [s]

Everage

6 7

Core

a

l loo

i050

Ioeo

400Fig. 13.

Temperaturecurve, steel grade X8CrNiTil8. 10, variant 2.

C 1995 ISIJ 1106

ISIJ International, Vol.

high rolling speed (approx. 50m/s), this requires five

cooler tubes with a cooling intensity of approx. 30OOOW/(m2K). In a distance of 50mafter the cooling line,

the temperature decreased only insignificantly by further

1O'C. The temperature behaviour for X8CrNiTi18, IOis

similar to that of St 355. Dueto the increased contentof alloying elements, stronger heating (due to higherdeformation resistance) and a reduced cooling effect

(due to a lower temperature and heat conductivity) wereobserved for this steel grade (Fig. 13). For the sameforming and cooling conditions as for St 355, a final

temperature of approx. I OOO'Cand a temperature of860'C after controlled cooling were obtained. Theseare by more than IOOKabove the values for the high-strengh C-Mnsteel St 355.

Figure 14 showsthe changein the austenitic grain size

for both variants at extreme positions of the rolling stock(case and core). After the first pass, the microstructureof the C-Mnsteel wasnot recrystallized in the case area.In the core, the austenite grains had been reduced to

14,~m due to the muchhigher local deformation (Fig.

14a)). During rolling, the microstructure wascompletely

60 T,

50

~4O 1ooEE 30a,

C] 20

10

O

' ~~~s-:1~ :~•-:~

35 (1995), No. 9

softened in the first four passes. In variant I,in which

neither intermediate nor controlled cooling were used,strong grain growth was observed prior to and afterfeeding to the block (24.4 and i7.8 ,lm). If the tempera-ture of the stock is very fast reduced to approx. 750'C,fine grains cah be preserved by suppressing the graingrowth (V2). Onthe whole, the grain refining effect ofintermediate and controlled cooling is muchstronger invariant 2 than in the conventional variant I .

By thereduction of the final rolling temperature by approx.lOOK, the austenitic grain size of the steel is reduced by5-8 pm. The following Table I shows the simulationresults for St 355.

By close temperature control, markedly finer grainsand better strength can be obtained in high-speed wirerolling while the toughness values are only slightly

impaired.

A muchmore inert recrystallization behaviour wasobserved for steel grade X8CrNiTil8.10 due to therecrystallization inhibition exerted by the alloyingelements (Fig. 14b), see also Fig. 9). Due to the lowerforming degree and temperature, the case wascomplete-

~t,1 ,o h CD a,to coco

>

pcsition

o u,~- tQrl Q)~N clN clcl cl

a) St 355

50

50

E 40

~EE 30~,

O 20

10

O

' "0'1"~'e'l-" I Ie' I IOL ~ lC'I

o

~~

I

l

I

C~l

1:

,1, '$ L"

=

(,

>

,o

,:

r~ co Q) o,1 ,1clcl

,,,1 ~cl

u,cl

Locl

position

Fig. 14.

Changeof grain size in the last 14 passes.

n: afterpass number

v: beforeb) X8CrNiTi18. IO

Table 1.

VariantFinishing Temperature I s

temperature after rollingDy

('C) ('C) (pm)

D.

(pm)

R~

(MP)

R.

(MP)

A('/.)

Z("/.)

12

1OOO850

990

76017

97.2

5.8

666703

490549

3028.2

63.8

62.2

1107 C 1995 ISIJ

iSIJ International, Vol. 35

ly softened only after 10 to 11passes depending on the

temperature distribution in the stock. The critical

fonuing degree for dynamic recrystallization strongly

depends on the temperature. While dynamic recrys-tallization starts at a forming degree of 8=0.27 at adeformation temperature of ~u=1200'C, the minimumforming degree for dynamic recrystallization is e=2.33at Su=900'C. Below900'C, the microstructure does notrecrystallize even at the maximumforming degree pos-sible under the test conditions. At a low deformationrate (O. 1~).5 l/s), dynamicrecrystallization wasmarkedlyless pronouncedat a forming degree of 0.61 to 0.65 de-

pending on the temperature (1 OOO-1100'C).23) In com-parison with C-Mnand heat treatment grades,1'2,22)

these forming degrees required for starting dynamicrecrystallization are markedly higher. As was shownin,24) this wascaused by the strong inhibition of recrys-tallization by solved Cr and Ni; solved Cr played thedecisive role. This result is confirmed in extensive pub-lications.25,26)

The austenite grains are temperature resistant whenthe microstructure is completely recrystallized. If therolling temperature is decreased by approx. 100'C, thegrain size can only be reduced by approx. 1-2,lm.

Nomenclature

A: uniform elongation in tensile test

ai,a2,a3 : coefficients and exponentsC: heat capacity of material per unit voluem

cl'c2,c3,c4 : coefficients and exponentsdl'd2 : coefficients and exponents

D: austenitic grain size

D* : ferritic grain size

Dv: recrystallized grain size

Dw: austenitic grain size after grain growthel,e2 : coefficients and exponents

fl'f2,f3,f4,f5 : coefficients and exponentsgl,g2,93,94 : coefficients and exponents

h: Iocal thickness of rolling stockhl,h2 : coefficients and exponents

hA: thickness of rolling stock at outlet

hE: thickness of rolling stock at inlet

hfl : neutral point height

n : exponentQK~: activation energy for grain growth

Qst : activation energy for static recrystallization

Qw: activation energy for hot forming

R: gas constantR~: tensile strength

R* : yield strength

t : time available for grain growthtp : delay time

T, S: temperaturev: speed

(1 995). No. 9

X: recrystallized fraction

Z: reduction of area after fracture, in tensile test~/: intensity of heat source8: forming degree

~: deformation rate

p: density

A: heat conductivity~Umgeb: ambient temperature

SRa.c: case temperature of rolling stock

S: cooling rate

Indices

d: dynamicst : static

v : reference values

o : initial value

x, y, z : spatial coordinates

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C 1995 ISIJ 1108