Computational Exploration of Microstructural Evolution in

1. Introduction

Contemporary objectives for steel processing are increas-ingly complex and often contrasting i.e. obtaining a desiredproduct with optimum combination of properties such asstrength, toughness, weldability and formability at lowercost. An important step to achieve these objectives is to de-velop mathematical models for the determination of defor-mation and recrystallization behaviour during thermome-chanical processing (TMP) based on laboratory-scale hottorsion or compression tests. Computer simulations incor-porating these models are then developed to determine opti-mum process sequences to obtain fine grained steels withdesirable combination of micro constituents by controllingthe process parameters such as strain, strain rate, tempera-ture and cooling conditions in the strip and/or plate mill.However, application of such models to rod rolling requiresextra care as this process is characterized by continuousmulti-pass deformation (up to 31 passes) at high strain ratein the range of 0.4–3 000 s�1, at elevated temperatures inthe range 1 173–1 373 K, and very short interpass times ofthe order of 0.015–1.0 s. These processing conditions makeit virtually impossible to study experimentally the mi-crostructural evolution both on laboratory and industrialscales. Hence, numerical and computational exploration re-mains to be the most important way to gain an insight in to

the microstructure evolution during rod rolling. The knowl-edge of the in-process microstructural evolution is criticalfor both the optimization of the manufacturing scheduleand adjustment of properties of the as rolled product.1,2) Forexample, a fine austenite grain size is desirable at the end ofrolling to decrease its hardenability and to obtain a fine fer-rite�pearlite structure via controlled rolling and cooling toeliminate or reduce the necessity of post-rolling annealingtreatments such as annealing or spheroidization where re-quired and to improve the mechanical properties of the as-rolled products. Another example is reducing surface decar-burization of high carbon spring steels and bearing steels bycontrolling the rolling process parameters and acceleratedwater-cooling before they enter the STELMOR air-coolingprocess

In these situations, determination of high temperaturemicrostructural evolution through mathematical model be-comes imperative. Previous efforts3–5) to simulate micro-structural evolution for rod rolling of medium C–Mn steelshave concentrated mainly on calculating evolution of themean austenite grain size. However, the relative con-tribution of dynamic and metadynamic recrystallizationprocesses towards final microstructure has not been dis-cussed in these reports. In addition, the calculation of effec-tive true strains and strain rates in each deformation passhas not been detailed. In the present work, the focus is on

ISIJ International, Vol. 43 (2003), No. 9, pp. 1421–1430

1421 © 2003 ISIJ

Computational Exploration of Microstructural Evolution in aMedium C–Mn Steel and Applications to Rod Mill

P. A. MANOHAR, Kyuhwan LIM, A. D. ROLLETT and Youngseog LEE1)

Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA-15213,USA. 1) Plate and Rod Research Group, Technical Research Laboratories, POSCO, Pohang, P.O. Box 36, Korea.

(Received on January 27, 2003; accepted in final form on April 8, 2003 )

An ‘Expert System’ is proposed in this work to conduct computational exploration of the deformation andrestoration behaviour of a medium C–Mn steel under high strain rate conditions, at elevated temperaturesand complex strain paths that occur in rod rolling process. The expert system computes appropriate ther-momechanical parameters necessary for describing rod rolling process in detail and then utilizes these para-meters in mathematical models to determine microstructure evolution during a typical industrial-scale rodrolling process. Microstructure simulation in rod rolling is a challenging problem due to the fact that severalsoftening processes may operate sequentially or concurrently during each deformation step. Different soft-ening processes have very different impact on microstructure development and therefore it is important toinvestigate the particular combinations of processing conditions under which transition of operating soften-ing processes occurs. In the present work, the transition from dynamic to metadynamic recrystallization isstudied in detail based on the criteria of critical strain, austenite grain size and Zener–Hollomon parameterwhen the interpass (interdeformation) time is very short of the order of few milliseconds during the laterstages of rod rolling. Computational results are subsequently validated by comparing the program output toin-plant measured microstructure data. The proposed expert system is designed as an off-line simulationtool to examine and assess the various options for thermomechanical process optimization.

KEY WORDS: rod rolling process; microstructural evolution; mathematical modeling; thermomechanicalprocessing; recrystallization kinetics.

several fundamental aspects of microstructure developmentincluding static, dynamic and metadynamic recrystalliza-tion processes and their kinetics, how to resolve the mecha-nism transitions when they operate concurrently and finallytheir specific contribution to microstructure evolution incontinuous rod rolling process. It will be shown that the rel-evant concepts to determine the mechanism transitions asimplemented in the proposed expert system allow the cal-culation of the relative amounts of dynamically and meta-dynamically recrystallized material during any deformationpass as a function of known values of process variablessuch as strain, strain rate, temperature, interpass time andin-process and post-process cooling conditions. In addition,pass-by-pass strain, strain rate and temperature calculationprocedures are implemented as independent calculationsub-modules. Finally, the results from these sub-modulesare combined in the expert system along with the metallur-gical models to calculate microstructure evolution duringthe thermomechanical processing. Initial (i.e. as-reheated)microstructure, roll pass schedule and cooling condition arethe basic inputs to the system. Comparing the final predict-ed austenite grain size with that obtained in rod mill vali-dates the model applicable for medium C–Mn steels. A fur-ther validation was possible by comparing the predicted fer-rite grain size of the final product with that obtained via in-dustrial processing.

2. Development of Expert System for MicrostructuralEvolution in Rod Rolling Process

The computation in the expert system begins by compil-ing the output from strain, strain rate and temperature cal-culation sub-modules implemented previously by one of theauthors and co-workers6–9) in to data arrays. The mathemat-ical models incorporated in the expert system subsequentlycompute the microstructure evolution based on the comput-ed data for process parameters during each pass. The pro-gram then determines the evolution of austenite grain size,fraction recrystallized and recrystallization kinetics for agiven roll pass and cooling conditions. In-process graingrowth is calculated subsequently. This process is iterateduntil the manufacturing process is finished. At this stage,the final microstructural parameters are computed usingnon-isothermal grain growth procedure. Finally, expectedferrite grain size is also determined. In the following sec-tions, the pass-by-pass strain, strain rate and temperaturesub-modules are described, subsequently details of the met-allurgical model are given and finally, an outline of thewhole expert system is presented.

2.1. Thermomechanical Modeling of Rod RollingProcess

2.1.1 Strain at a Pass (Pass-by-pass Strain)Rod rolling process involves a change in cross-sectional

shape of the rolling stock through many sets of groovedrolls to obtain a final round shape of the rod from the origi-nal rectangular cross-section of the billet. The geometry ofthe roll grooves is non-rectangular (oval, round, diamond,square etc.) and therefore the workpiece undergoes com-plex strain and stress paths that cannot be simplified as ei-ther plane strain or plane stress. The average pass strains

are typically calculated by multiplying the area strains, (i.e.the natural logarithm of the ratio of the fractional reduc-tions in cross-sectional area through the rolling stands) bysome constant factors.4). However, a mathematical rationalefor the use of the constant factors has not been given.Another model10) for the calculation of pass strain andstrain rate in rod rolling is based on the assumption of planestrain deformation. In this case, the three-dimensional de-formation zone was subdivided into longitudinal strips ofequal width in the roll gap direction and each strip was ana-lyzed separately. No experimental verification was providedto support the assumption of plane strain deformation. Inthe present work, a model for calculating strain in rod andbar rolling proposed by one of the authors and coworkers7,8)

is utilized. The model has been verified experimentally forrod and bar rolling. The model is based on the elementarytheory of plasticity and the equivalent rectangle approxima-tion method. Strain in a pass is assumed to be homogenous-ly distributed across the stock. While the detailed calcula-tion procedure is given in the cited works, the followingmain results are utilized in the present work.

The pass strain is defined as the maximum effective aver-age strain at a given pass calculated according to the fol-lowing relation:

................(1)

Where e is the pass strain, and e1, e2, and e3 [��(e1�e2)in this case] are the plastic deformation components alongthe principal axes of deformation. These strain componentsare determined based on the dimensions of the rolling stockthrough following equations:

...............................(2)

...............................(3)

Where Wi and Wp are equivalent initial and final cross-sec-tional widths while Hi and Hp are equivalent initial and finalcross-sectional heights of the work piece.

2.1.2. Strain Rate at a Pass (Pass-by-pass Strain Rate)Analogous to drawing and forging processes, the strain

rate in rod rolling changes at various stages of deformation.The strain rate is the maximum at the entrance to the roll(or in its vicinity) and decreases along the roll bite, finallybecoming zero at the outlet. For this reason, it is necessaryto introduce an average strain rate for a given pass. The av-erage strain rate can be defined as the strain over a time in-terval taken for workpiece to pass through the roll gap.Hereafter the average strain rate is referred to as the strainrate. A critical question in the calculation of strain rate ishow to define the effective roll radius at a given pass, whichis a representative value of varying radius of roll groove. Aprocedure based on effective roll radius to calculate thepass-by-pass strain rate in rod rolling has been proposed ina previous publication.9) According to this model, the mean

ε2 � lnH

Hi

p

ε1 � lnW

Wi

p

εεε

εε

� � �2

31 1

2

2

1

2

1 2

/

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strain rate is calculated through the following relation:

....................................(4)

Where e is the average effective strain rate in a given passand tp is the time interval during which the stock resides inthe roll-bite. The tp is calculated according to the followingequation:

...............................(5)

Where L is the effective projected contact length of thegrooved roll with workpiece, N is the roll speed (rpm) andReff is the effective roll radius at a given pass.

2.1.3. Temperature Evolution in Rod and Bar RollingThe temperature of the workpiece during rolling depends

on various factors such as rolling speed, initial temperatureof the billet, the amount and nature of the plastic deforma-tion, the cross sectional shape of workpiece at each pass,cooling condition in the individual passes and distributionof cooling and equalization zone between stands (passes).To take care of the combined action of these parameters, amodel for predicting temperature evolution of workpieceduring rod and bar rolling can be formulated based on thefollowing assumptions: i) uniform initial temperature of thebillet; ii) no longitudinal temperature gradient (i.e., infinite-ly long rod); iii) uniform heat generation across the crosssection of workpiece due to plastic deformation in the rollgap; and iv) circular cross sectional shape at each pass.Under these assumptions, temperature variation within therod is governed by the one-dimensional axi-symmetric heattransfer equation.11) The solution method of the heat trans-fer equation using finite difference method with boundaryconditions is as described in Refs. 12) and 13). The valuesof conductivity and specific heat capacity of material havebeen taken to be a function of the temperature of the mater-ial and were obtained from the literature.14) To predict thetemperature variation of workpiece under the action ofwater-cooling in the cooling zone and equalization zone be-tween stands, the model proposed by Morales et al.15,16) hasbeen adopted. The model includes the influence of opera-tion parameters such as rod size, rolling speed, rod temper-ature and water flow-rate on the temperature distributionwithin the rod under the action of water-cooling and simu-lated the temperature evolution of rod and bar for many

cases. Both radiative and convective heat transfer modelswere incorporated in the thermal model to calculate stockcooling during rolling and water-cooling. The emissivity ofthe steel was assumed to be 0.8. During deformation in theroll gap, most of the mechanical energy is transformed intoheat. This deformation heating is determined for each ele-ment at each time step using a mean flow stress obtained byintegrating the relevant constitutive equation. It should bementioned here that frictional heat was ignored in compari-son to the heat due to deformation in the current work.

2.2. Modeling of Microstructure Evolution

As steel is deformed at high temperatures, several typesof softening processes occur in steel to reduce the internalenergy of the deformed metal. When the deformation strainis high enough, the deformed grains may be replaced bynew, strain free grains via a process termed recrystallization(RXN). When recrystallization occurs subsequent to defor-mation, it is termed static recrystallization (SRX). Undercertain circumstances, the recrystallization may occur con-currently with deformation, a process called dynamic re-crystallization (DRX). In some cases dynamic recrystalliza-tion may initiate through nucleation, but may not proceed tocompletion during deformation. In these cases, the recrys-tallization is completed after deformation by the growth ofdynamically nucleated grains. This is known as metady-namic or postdynamic recrystallization (MDRX). The con-ditions under which SRX, DRX and MDRX occur are de-termined by the combination of processing parameters.

2.2.1. RXN PhenomenaThe particular combinations of process parameters that

lead to different softening phenomena can be understoodfrom the schematic high temperature stress–strain (s–e) di-agrams for steels shown in Fig. 1. The stress–strain dia-grams of the type shown in Fig. 1 are obtained in varioustesting schemes such as uniaxial tension, uniaxial compres-sion, torsion, and plane strain compression. The strain andstress values obtained in each type of tests may be convert-ed to equivalent strain and equivalent stress and plotted asshown in Fig. 1, via a suitable yield criterion (e.g. vonMises) so that the flow behaviour obtained in differentkinds of tests could be compared on a common platform. Itmay noted from Fig. 1 that s increases as e increases in theinitial part of the curves through work hardening up to acritical strain, e c, beyond which DRX is initiated. The ma-

tL

NRpeff

�60

2π

εε

�tp


1423 © 2003 ISIJ

Fig. 1. Schematic equivalent stress–strain diagrams showing various high temperature softening phenomena in steels as afunction of process variables.

terial work hardens as strain increases further, but at a re-duced rate, owing to dynamic recovery and the onset ofDRX until e reaches another critical value, ep, peak strainwith a corresponding stress value, sp, peak stress. At thisstage stress falls as the strain is increased beyond ep be-cause the rate of work hardening is offset by the rate ofsoftening owing to the significant amount of DRX. Withfurther straining, material deforms under a steady stateregime denoted by s ss–e ss. DRX may not reach completionduring a deformation pass and the growth of dynamicallynucleated nuclei would continue during the interpass lead-ing to MDRX condition. When strain is less than e c, staticrecrystallization may be initiated during the interpass time.

2.2.2. Transition Conditions for Different RXN Phe-nomena

Mathematical models that describe the kinetics of thevarious recrystallization processes are given in Table 1.The different softening processes (SRX, DRX, MDRX) re-sult in different high temperature microstructures in steelsand therefore it is essential to determine which process(es)are active during a given deformation pass. One way to dealwith the problem of transition conditions that separate SRXand MDRX in strip rolling of steel was proposed by Sunand Hawbolt24) where authors suggested that two conditionsviz. e�e c and Z�Zlim must be met simultaneously forMDRX to occur, where Zlim is the limiting value of theZener–Hollomon parameter given according to:

Zlim�5�1015 exp(�0.0155d0) .................(6)

Where d0 is the austenite grain size prior to recrystalliza-tion. Such a model is empirically based and suggests arather straightforward relation between transition condi-tions for SRX/MDRX with initial grain size. Also, the tran-sition conditions for DRX/MDRX remain to be definedwith this approach while they are most relevant to the rodrolling process. Kinetics of concurrent and competingevents of strain accumulation and relaxation must decidethe transition conditions for SRX, DRX and MDRX andtherefore more detailed microstructure descriptors are re-quired to define the transition conditions between the differ-ent softening phenomena. In addition, the process condi-tions in strip rolling are quite different (strain rates slower,interpass times longer and temperature range wider in striprolling) compared to those in rod rolling and therefore thepreviously suggested transition conditions will not be ap-plicable to rod rolling. Therefore, an alternative approach isproposed in this work to resolve the DRX and MDRX tran-sition as described in the following section.

2.2.3. Peak Strain, Critical Strain and Recrystallized Vol-ume Fraction Model

In the current work, the kinetics of dynamic recrystal-lization described in terms of peak and critical strains wereutilized to resolve DRX / MDRX transition. The peak andcritical strains were calculated based on the following rela-tions22):

ep�6.97�10�4�Do0.3�Z 0.17 ..................(7)

e c�0.81�ep ...............................(8)


© 2003 ISIJ 1424

Table 1. Mathematical models describing the kinetics of relevant softening mechanisms.

Equation (7) includes the effect of initial austenite grainsize (controls diffusion path length), and temperature-com-pensated strain rate (Zener–Hollomon parameter) on strainaccumulation and relaxation, which in turn decide the criti-cal strain for the onset of DRX. In the strain range from e c

and ep, DRX will initiate, but perhaps will not lead to com-pletion when the interpass times are short. In such cases,the amount of fraction recrystallized dynamically is com-puted according to a version of JMAK kinetics given ac-cording to the following equation17):

.................(9)

2.2.4. Grain Growth ModelThe austenite grain growth under continuous cooling

conditions is calculated by using the additivity rule wherethe cooling thermal cycle was divided into isothermal timesteps5,25) through the following relation for MDRX grains4):

.........................................(10)

Where d ti is the length of time step i and Ti is the tempera-ture of step i.

Grain growth during the time that the stock cools fromfinish rolling temperature up to the g→a transformationstart temperature is of critical importance that determinesthe final ferrite grain size along with the cooling ratethrough the g→a transformation temperature range. Theferrite grain size (ag.s.) prediction model developed for hotstrip rolling26) is adopted here:

ag.s.�{Va�exp(50.7�Df0.024�51 000/Ar3)}

1/3 ....(11)

Where Va is the volume fraction of ferrite (determined ex-perimentally in this work), Df is the austenite grain size justprior to the onset of g→a transformation (mm), and Ar3 isg→a transformation start temperature (°C) under prevalentcooling conditions (1.5 K/s in the present case) for a givencomposition.

3. Applications to Rod Mill

A continuous rod rolling process of POSCO No. 3 rodmill is shown in Fig. 2. It consists of thirty one passes inall, however the last two passes are sizing passes and are ig-nored for rigorous analysis in the present study. It is evidentfrom Fig. 2 that several delay zones exist in the thermome-chanical processing sequence for example, between pass #5and #6; pass #11 and #12 (not shown in Fig. 2); pass #13

and #14 and pass #19 and #20 while two cooling zones areemployed between pass #27 and #28 and final cooling sub-sequent to pass #31 where the temperature is reduced fromfinish rolling temperature �1 243 K down to �1 103 Kusing high speed water cooling (�1 000 K/s). Further cool-ing of the rod occurs in STELMOR cooling line at a muchslower cooling rate of �1.5 K/s. The rolling speed increasesfrom 0.12 m/s at the first pass up to 110 m/s in the final passas the 160�160 mm square billet is reduced to �6.0 mmdiameter rod. Area reductions obtained in each pass variesin the range 17–27%, except for the final two passes whereit is around 5%. The last two passes (#30 and #31) are thefinal sizing passes and are ignored for microstructure mod-elling in this work.

4. Results

The flow chart for the expert system that simulates ther-momechanical processing for rod mill is given in Fig. 3.Initial (i.e. as-reheated) microstructure and rolling scheduleare the basic inputs to the system. The program then calcu-lates the deformation conditions such critical and peakstrains, and Zener–Hollomon parameter based on initialgrain size, strain, strain rate and temperature. The logicalconditions described in Sec. 2.2.3 along with relevant math-ematical models listed in Table 1 are used to determinewhich RXN mechanism operates for the calculated combi-nation of process parameters and to compute the evolutionof grain size, fraction recrystallized and recrystallization ki-netics for a given roll pass schedule and finally, expectedferrite grain size is determined using Eq. (11). The expertsystem is implemented on a PC workstation in Windowsenvironment using object oriented C��.

4.1. Output of the Expert System

Detailed microstructural evolution computed by the ex-pert system is given in Table 2. The data given in Table 2show that significant dynamic recrystallization followed byMDRX occurs in the roughing mill (pass #2–#10), whileremaining passes of the roughing mill (#11–#13) showMDRX as the main operating recrystallization mechanism.Intermediate finishing mill passes (#14–#19) are character-ized by either static or metadynamic recrystallizationprocess being more dominant. The MDRX process alsodominates in almost all passes of the finishing mill (#20–#27). The last two passes of the reduction and sizing mill(#28 and #29) are interesting where stain rate is very high(�2 000 s�1), interpass time very short (�9–12 ms), andrelatively low temperature (�1 243 K). In this case, criticalstrain is too high to initiate DRX in pass #28 so that SRXinitiates in the interpass time. However, the time available

D D t RTi i

i

f7

o7� � � � � �8 2 10 400 00025. exp( / )δ∑

F B

k

XDRXc

p

� ��

1 expε ε

ε


1425 © 2003 ISIJ

Fig. 2. Schematic diagram showing a typical industrial-scale rod rolling sequence studied in this work; RF: ReheatingFurnace, RM: Roughing Mill, IRM: Intermediate Roughing Mill, IFM: Intermediate Finishing Mill, NTM: Non-Twisting Mill, RSM: Reducing and Sizing Mill; #1 and #2 are water cooling zones. All dimensions are in mm.


© 2003 ISIJ 1426

Tab

le2.

Dyn

amic

mic

rost

ruct

ure

evol

utio

n du

ring

mul

ti-p

ass

rod

roll

ing.

Fig

.3.

Flo

w c

hart

for

the

exp

ert

syst

em t

o de

term

ine

mic

rost

ruc-

tura

l evo

luti

on in

rod

rol

ling

.

for recrystallization is so short that only about 36% of thevolume is recrystallized. This leads to a large amount of re-tained strain in the material so that the effective strain inpass #29 exceeds the critical strain despite a high value ofe c leading to DRX followed by MDRX in this pass. Theaustenite grain size gets refined from an initial value of�300 mm down to �3.3 mm after finish rolling. The austen-ite grains coarsen to a size of �15 mm during cooling fromfinish rolling temperature to the cooling stop temperature(CST), and subsequently during slower cooling from CSTto Ar3. This not surprising because the material studied is amedium C–Mn steel where the grain growth is not inhibitedby second phase particles or through any significant solutedrag effect. Also, the grain size is very fine at this stage,which means that the grain growth rate is expected to behigh according to the curvature driven grain growth theo-ry.27) This means that the advantage gained in refining theaustenite grain size through DRX and MDRX duringrolling is lost to an extent during the cooling segments.Evolution of mean austenite grain size and the correspond-ing strain rate as a function of rolling pass is shown in Fig.4. Significant increases in the mean austenite grain size dueto in-process grain growth during the TMP delays men-tioned in Sec. 3 are also evident in Fig. 4.

4.2. Validation of Expert System

The specimens obtained from POSCO No. 3 rod millwere sectioned, mounted, polished and etched in 4% Nitalin the usual way. The micrographs in Fig. 5(a) were takenwith a Philips SEM at 400X and 3000X to obtain the ap-propriate resolution for prior austenite grain size and ferritegrain size respectively. The images taken for measuringaustenite grain size were traced along ferrite grains precipi-


1427 © 2003 ISIJ

Fig. 5. (a) SEM micrograph of industrially processed steel, etchant: 4% Nital, Mag.: 400�; (b) prior austenite grainboundaries are traced to determine austenite grain size just before g→a transformation; (c) Histogram showingthe overall austenite grain size distribution. See text for the explanation of curve fitting parameters. m is the meanaustenite grain size.

Fig. 4. Predicted austenite grain size evolution and variation instrain rate as a function of rolling pass.

tated along prior austenite grain boundary to delineate prioraustenite grains. It should be mentioned here that some ex-perience and judgment is necessary in tracing the prioraustenite boundaries. Better accuracy in measurement maybe obtained from a fully martensitic microstructure by theuse of well-known metallographic etching techniques to re-veal more clearly the prior austenite grain boundaries.However, it is not possible to quench the rod in industrialprocessing to a fully martensitic microstructure prior tocoiling. Despite this limitation, the overall statistics of theaustenite grain size distribution as measured by this methodis shown in Fig. 5(c). It is evident from Fig. 5(c) that themeasured and normalized grain size distribution compareswell with the lognormal distribution that is expected underpost-processing normal grain growth regime. The distribu-tion of the measured austenite grain size is analyzed bynon-linear curve fitting method using the following expres-sion for the lognormal distribution:

........(12)

Where, f(x) is the probability density of the continuous,random, and independent variable x (i.e. area-equivalentaustenite grain diameter in this case), y0 and A are fittingcoefficients, w is skewness and xc is kurtosis of lognormal

distribution. Skewness represents a lack of symmetry in aprobability distribution while kurtosis is a measure of how“fat” a probability distribution’s tails are. The R2 value ofthe lognormal distribution curve fit shown in Fig. 5(c) isfairly close to 1, which means that the grain size measure-ment procedure described above is reasonable.

The average austenite grain size was subsequently deter-mined using the Scion-Image image analysis program tomeasure area of each grain on the traced image and areaequivalent diameter was calculated according to the proce-dure outlined in the relevant ASTM standard.28) Austenitemicrostructures are presented in Figs. 5(a) and 5(b) whileferrite microstructures are presented in Figs. 6(a) and 6(b).The predicted austenite grain size just before the onset ofg→a transformation is 15.2 mm while the measured prioraustenite grain size in industrially processed steel is14.4 mm. The transformed ferrite grain size is measured tobe 4.6 mm while the predicted ferrite grain size is 4.9 mm. Itis clear from this data that the predicted and experimentallymeasured mean austenite and ferrite grain size comparequite well, which validates the expert system that simulatesthe microstructural evolution in rod rolling process.

5. Discussion

The close agreement between the predicted austenitegrain size at the end of rolling and that obtained from in-

f x yA

wx

x

x

w( ) exp

ln

� �

�

0

2

22 2πc


© 2003 ISIJ 1428

Fig. 6. (a) SEM micrograph of industrially processed steel, etchant: 4% Nital, Mag.: 3 000�; (b) image processing to ex-tract ferrite grains from the microstructure shown in (a); (c) histogram showing the overall ferrite grain size distri-bution.

dustrially processed material is interesting. The mathemati-cal models used in this work to compute the microstructuralevolution had been determined in laboratory torsion testingunder strain rate conditions of up to 100 s�1 while industrialrod rolling involves strain rates as high as 3 000 s�1. Con-stitutive relations in high strain rate regime could be differ-ent compared to those determined in laboratory under thelow strain rate regime. This should have introduced certaininaccuracies in the computed microstructure. One possiblereason why this has not happened can be explained bystudying the parameters for the industrial process sequencesimulated here. It is clear from the data presented in Table 2that the first seventeen passes have a strain rate �100 s�1,which compares well with the strain rates used in laborato-ry studies. The austenite grain size reaches �8 mm at thisstage. Further processing of the material does not seem torefine the austenite grain size to any significant extent inthis material. It should be noted here that the steel composi-tion being studied is plain carbon steel that is characterizedby rapid recrystallization and grain growth kinetics in theabsence of any precipitate pinning or a strong solute dragcaused by solutes such as Mo and Nb. As a result, the re-finement of austenite grain size achieved during the laststages of processing is lost due to rapid grain growth via in-process and non-isothermal grain growth during cooling.For more complex compositions such as low alloy and mi-croalloyed steels, high strain rate constitutive relationswould be required to be incorporated in the expert system.

Based on the foregoing analysis, the major operatingmechanism as a function of austenite grain size and Zener–Hollomon parameter may be determined as shown in Fig.7. The three-dimensional plot shown in Fig. 7 provides fur-ther insight in to particular combinations of process and mi-crostructural variables for SRX, DRX and MDRX to occur.The points for MDRX in Fig. 7 are clustered, which indi-cates that MDRX is the dominant softening mechanismwhen the austenite grain size is relatively small (3–17 mm)and Zener–Hollomon parameter is in the range 5–70�1014.The DRX is dominant where the austenite grain size is inthe range 20–40 mm and the Zener–Hollomon parameter iscomparatively low in the range 0.02–0.5�1014. The SRXdominates when pass strain does not exceed the criticalstrain for a given pass, as expected. It should be mentionedhere that the data for the first pass is not included in Fig. 7as the initial austenite grain size in this case is very coarseas-reheated grain size �300 mm and would not lead tocomplete DRX because of the long diffusion distances in-volved.

It is also noteworthy that the expert system developed inthe current work predicts metadynamic recrystallization asthe predominant grain refinement softening mechanismwhich agrees well with previous studies20,29) based on labo-ratory simulation and industrial process data. Therefore thecurrent model may now be used to analyze the capabilitiesof rod rolling process when the critical process variablesare changed in the model. The data shown in Fig. 8(a)demonstrates that a 50% reduction is austenite grain sizeobtained by post deformation accelerated cooling wouldyield a 20% refinement in ferrite grain size. It is wellknown that further ferrite grain refinement is possible byincreasing the cooling rate through the g→a transforma-


1429 © 2003 ISIJ

Fig. 7. Operating recrystallization mechanism as a function ofaustenite grain size and Zener–Hollomon parameter. Key:Recrystallization Type 1�90% SRX; Type 2��90%SRX (i.e. partial SRX) Type 3�90% MDRX, Type4��90% MDRX (i.e. DRX�MDRX).

Fig. 8. (a) Predicted ferrite grain refinement as a function ofprior austenite grain size; and (b) austenite grain refine-ment as a function of finish rolling temperature.

tion range. On the other hand, reducing the finish rollingtemperature for existing cooling rates does not appear tohave significant influence on austenite grain size prior tothe g→a transformation (Fig. 8(b)). The main reason forthis behaviour is that the rapid grain growth kinetics inC–Mn steel during cooling segments offsets the advantagegained when the finish rolling temperature is reduced.Microalloy addition (e.g. Ti, Nb) to the steel compositionwould retard the post deformation grain growth significant-ly and thus it would be possible to retain most of theaustenite grain refinement advantage accrued due to DRXand MDRX processes.

6. Conclusions

(1) An expert system is proposed in this work to com-pute the microstructural evolution in rod rolling that in-volves high strain rate deformation and complex strainpaths. The predicted austenite microstructure at the end ofrolling and the ferrite grain size subsequent to transforma-tion correlate well with the data obtained from industriallyprocessed material thus validating the simulation proce-dure.

(2) Transition between dynamic recrystallization(DRX) and metadynamic recrystallization (MDRX) hasbeen resolved based on austenite grain size and Zener–Hollomon parameter. It is found that MDRX dominateswhen austenite grain size is comparatively fine (3–17 mm)and Zener–Hollomon parameter is relatively high (5–70�1014) compared to conditions for DRX (Do�20–40 mm,Z�0.02–0.5�1014).

(3) Two main techniques for austenite grain refinementin rod rolling appear to be the effective utilization of DRXand MDRX processes in the final passes of rod rolling andincreasing cooling rates subsequent to rolling and throughthe g→a transformation range. Both of these techniqueswill result in significant ferrite grain refinement. However,the reduction in finish rolling temperature per se appears tohave limited scope in this regard due to rapid grain growthkinetics during final cooling segments.

Acknowledgement

The authors thank POSCO, South Korea for the provi-sion of steel samples and information about typical wire

rod rolling schedule.

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Computational Exploration of Microstructural Evolution in