Process modeling of microalloyed steel for near net shape casting

S.V. Subramanian1, G.Zhu1, H. S. Zurob1, G. R. Purdy1, G.C. Weatherly1, J. Patel2, C.Klinkenberg2 & R. Kaspar3

1McMaster University, Hamilton, Canada, 2Niobium Products Company, GmbH, Germany,3Max Planck Institute for Eisenforschung, Dusseldorf, Germany

ABSTRACT

Strip casting is an emerging technology for flat products; it is based on the concept of near-netshape casting; it holds potential for substantial energy saving and reduction in environmentallyundesirable emission. In conventional thermo-mechanical processing, the pinning pressure due tothe effects of Nb and NbC on boundary mobility is used to advantage to retard staticrecrystallisation and thus aid strain accumulation during “pancaking of austenite”. The time-temperature-deformation schedule characteristic of thin slabs (30-50 mm) and strips are such thatit is not possible to take full advantage of the conventional approach to microalloyingtechnology.

Quantitative analysis of thin slab direct rolling (TSDR) shows that it is possible to obtain ultra-fine austenite grains (< 3 micron diameter) via dynamic recrystallization; this requires that acritical accumulated strain be exceeded. Recent research at McMaster University has shown thatstrain-induced precipitation at dislocation nodes is effective in retarding static softening byrecovery, especially at the short interpass times characteristic of thin slab processing. Theinhibition of static softening then permits the accumulation of the large driving forces requiredfor lower-temperature dynamic recrystallization.

The available information on the effects of niobium on the critical strain for dynamicrecrystallization generated by Lutz Meyer and coworkers relates to the total niobium content ofthe steel; this data-base has been used in a series of simulations of austenite grain sizedevelopment in multi-pass rolling schedules. Several of these have been validated byexperimental studies using the thermo-mechanical simulator WUMSI.

Even in the case of thicker strip (10-15 mm), the time-temperature-deformation schedule is toorapid to take advantage of the strain-induced precipitation of NbC. There is however anopportunity to utilize upstream processing: Previous research has shown that TiN can serve as aprecursor for the epitaxial precipitation of NbC. To take advantage of this mechanism, it isessential to obtain a fine dispersion of TiN particles. Quantitative modelling shows that this canbe done through the design of base chemistry, the control of solidification variables, and thecontrol of post-solidification cooling schedules. Each of these variables is used to increase thethermodynamic potential for the precipitation of TiN from austenite, thereby promoting a gooddispersion of TiN via strain-induced precipitation.

Introduction:

Solidification processing played a major part when the slab casting technology was integratedwith plate rolling. The energy consumption of slab cold charging (CCR) is 1400 KJ/kg, which isdecreased to 200KJ/kg by hot direct rolling (HDR) [ 1 ]. The integration of casting with therolling technology warranted basic research to gain a quantitative understanding of the influenceof the base chemistry, solidification processing and post-solidification cooling schedules of theslab in the caster on the precipitation behavior of microalloying elements during thermo-mechanical processing [2-3]. In rough rolling schedule, repeated static recrystallisation ispromoted in order to ensure a homogeneous austenite grain size of about 25 um diameter at thestart of finish rolling operation. The time-temperature-deformation schedule in finish rolling iscarried out in the temperature window where the strain induced precipitation of NbCN occurs atdislocation nodes generated by deformation. These precipitates are effective in preventing staticrecrystallisation in the inter-pass time between successive rolling passes In consequence, strainaccumulation occurs within the pan-caked austenite, thus increasing the density of heterogeneoussites for ferrite nucleation (Sv factor). Dutta1 and Sellars have applied successfully the diffusioncontrolled classical nucleation theory to predict the onset of strain induced precipitation ofniobium carbo-nitride during hot rolling of steel [4]. Quantitative modeling of interaction of thestrain induced precipitation with the static recrystallisation was developed to predict therecrystallisation limit (RLT) and recrystallisation stop temperature (RST). Controlled rolling iscarried out well below the temperature at which recrystallisation is fully retarded so thatsubstantial strain could be accumulated in austenite prior to transformation in order to increasethe nucleation density of ferrite.

The next step in the evolution of continuous casting was thin slab casting. With thin slab directrolling (TSDR), the slabs (30-80 mm) are thinner than conventional continuous cast rolling CCR(200-250 mm). Casting speeds are nearly five times faster, 3-6 m/min in TSDR compared with0.75 to 2 m/min in CCR. With TSDR processing, the slabs still hot from the caster are directcharged to a temperature equalization furnace, followed by rolling in a tandem mill consisting atrain of five or more rolling stands with facilities for water cooling in the last few passes. Thestarting austenite is relatively coarse in grain size, being in the range of 200-300 µm in diametercompared to 25-40 µm in CCR. Since the total strain is limited by the starting slab size, thermo-mechanical processing has to be redesigned for TSDR in order to achieve ultra-fine grain size inthe final product without the benefit of austenite conditioning from roughing. Detailed studieson the evolution of microstructure in thin slab rolling are lacking in microalloyed steels. Someinvestigations on microstructure development in V-N and Ti-V-N microalloyed steels during thinslab rolling process and on physical properties on strips rolled from thin slab casting have beenreported recently [5,6]. One objective of this paper is to analyze strain accumulation asinfluenced by solute and precipitation of microalloying elements in thermo-mechananical rolling,and to identify the critical process parameters in the base chemistry design and optimisation ofrolling schedule for grain size control in thin slab processing of microalloyed steel.

Significant progress has been made in the recent years in gaining a quantitative understanding ofthe complex interactions of solute and precipitation with recovery and recrystallisation whichcause static softening after a single pass deformation. The pioneering work of Dutta2 , Palmiereand Sellars [7] has considered the role of dislocation nodes in providing heterogeneous

nucleation sites for strain induced precipitation, and the dislocation core in enhancing thediffusion, which aids the growth and coalescence of the precipitates. The model has led to aquantitative understanding of the time evolution of nucleation, growth and coalescence of straininduced precipitates after single pass deformation. This model could be coupled withrecrystallisation models to predict the recrystallisation limit and recrystallisation stoptemperature. According to the earlier Sellars model [ 4 ], the recrystallisation is stopped onceultra-fine precipitates are effective in pinning the sub-grain boundary. In the recent work atMcMaster University, Zurob et al. [ 8 ] have explicitly considered the time evolution of straininduced precipitation and its interaction with recovery and recrystallisation processes. This workhas underscored the importance of recovery in static softening after single pass deformation asdistinct from earlier work, which tends to focus on precipitate interaction with recrystallisation.The recent advance in the quantitative understanding of the interaction of solute and precipitateswith the recovery and recrystallisation processes after single pass deformation is the fundamentalbuilding block to develop physically based models for strain accumulation in multi-pass rolling.Earlier work of Kaspar et al. has identified the need for complete redesigning of rolling schedulein thin slab processing in order to achieve grain size control [9]. Kaspar has demonstrated that itis feasible to obtain ultra- fine grains by dynamic / metadynamic recrystallisation by large straindeformation in low temperature window [10]. In the present work, the current understanding ofstatic softening is applied to the design of base chemistry and optimisation of rolling schedulesfor thin slab casting. The data-base generated by Lutz Meyer and coworkers [11,12] on criticalstrain for dynamic recrystallisation and static softening at strains approaching critical strain fordynamic recrystallisation in Nb microalloyed steel are used to develop predictive model fordynamic recrystallisation. The validation of modeling predictions was carried out byexperimental simulation of strip rolling schedule of slab materials of about 35 mm starting size,using the computer controlled, servo-hydraulic hot deformation simulator, WUMSI at the Max-Planck-Institut fur Eisenforschung, Dusseldorf.

Strip casting is an emerging technology for flat product based on the concept of near net shapecasting with potential for substantial cost saving [13]. The commercial process based on twinrolls is to go into production in North America to make strip with thickness ranging from 0.7 to2.1 mm and width 2000mm maximum at a typical casting speed of 80 m/min. The process isclaimed to deliver energy saving of 50% over thin slab casting plant and a decrease in greenhouse gas emissions by 40%. This technology will be initially applied to stainless steel and plaincarbon steels. Since the heat dissipation in the roll is a limiting factor, there is alternative processunder development in Europe to produce thicker strip in the range of 10-15 mm in steel [14]. Thetechnology is based on delivery of metal on to a moving water-cooled belt, where larger amountof heat abstraction can be achieved by increasing the cooling length of belt. The rapid coolingschedules in near net shape casting of even thicker strip warrant novel strategies to exploit thepotential benefits of microalloying additions.

Additional basic studies were carried out to increase the pinning pressure by epitaxial growth ofNbC on TiN particles dispersed by upstream solidification processing. The effectiveness of theseprecipitates in raising the recrystallisation limit temperature was confirmed by hot torsionsimulation [15]. This strategy has the advantage of obviating the need for strain inducedprecipitation by thermo-mechanical processing, which offers distinct advantage in near net shape

processing. The potential application of these results for near net shape casting will beexamined.

The approach:

Grain refinement of austenite by dynamic recrystallisationDerby [16] has analysed the dependence of grain size on stress during dynamic recrystallisationin a number of metals. The steady state grain size is interpreted as the dynamic balance betweenthe rate of formation of the deformation structure and the mean velocity of the recrystallisinggrain boundaries. The grain size for steady state dynamic recrystallisation is given in Ashby-Derby analysis [ 17 ] by

ε

δ&

12

kTbDKd B= (1)

where K, DB, k, ∗ ,b, T and &εare the material constant, grain boundary diffusion coefficient , Boltzmann constant, the grainboundary width, the Burgers vector, the temperature and strain rate respectively.

Hodgson [18] has reported that the rate of recrystallisation changes from being a strong functionof strain and temperature and a weak function of strain rate for static recrystallisation to beingonly a function of strain rate for metadynamic recrystallisation. The recrystallised grain size is afunction of the Zener-Hollomon parameter only for metadynamic recrystallisation as well asdynamic recrystallisation. However, in the case of static recrystallisation, the recrystallised grainsize is relatively little influenced by Zener-Hollomon parameter but is controlled by strain andinitial grain size. Hodgson [18] has analysed the available data-base from various sources andshowed that the dynamically (ddyn) and metadynamically (dmd) recrystallised grain size can besatisfactorily related to Zener-Hollomon parameter (Z), where Z = &ε exp ( Q/RT), with Qdef=300KJ/mol, as given by following equations.

27.04109.3 −×= Zddyn (2)

27.04108.6 −×= Zdmd (3)

In metadynamic recrystallisation, the nucleation of new grains occurs during deformation and thegrowth of the grains occurs subsequently. The larger the Z, the finer the dynamicallyrecrystallized grain size. Zhu, Gao and Subramanian [19 ] have analysed the data-base on criticalstrain for dynamic recrystallisation εc in microalloyed steel generated by Lutz-Meyer andcoworkers [ 11,12] and correlated the critical strain for dynamic recrystallisation εc with Zthrough the following expression:

96.0ln048.0 −= Zcε (4)Thus, the inter-relationships among εc, d and Z are established. The larger the Z, the larger thecritical strain for dynamic recrystallisation εc, and the finer the dynamically recrystallised grainsize, d. Even though there is a change in the mechanism of dynamic recrystallisation from thebulge nucleation theory to sub-grain rotation particularly at large strain-high strain rate

deformation process [20], the inter-relationship between dynamically recrystallised grain sizewith Z still holds good [ 19 ].

An objective of the present work is to identify processing conditions required to achieve largestrain accumulation in multi-pass rolling to overcome the large critical strain for dynamicrecrystallisation. In order to achieve this, the static softening in the interpass time should beminimised. Any static recrystallisation before dynamic recrystallisation will cause mixed grainsize, which is undesirable. Thus a quantitative understanding of the complex interactions ofsolute and precipitation with recovery and recrystallisation which cause static softening isessential to achieve large strain accumulation in order to produce homogeneous fine grain size bydynamic recrystallisation.

Physically based models for strain accumulation:

Effect of deformation on time evolution of precipitate size and density:Dutta2, Palmiere and Sellars model

Dutta2, Palmiere and Sellars[ 7 ] have developed a model, which gives a complete description ofkinetics of strain induced precipitation, i.e., the time evolution of precipitate volume fraction andsize. The model captures in essence the role dislocations in enhancing the nucleation, growth,and coarsening kinetics of strain induced precipitation. The presence of dislocations offersnumerous heterogeneous nucleation sites, and hence, the precipitate number density isapproximately four orders of magnitude greater for the deformed austenite compared with theundeformed austenite. In addition, the precipitation starts much earlier in the deformed steel, intimes almost three orders of magnitude quicker than for undeformed austenite. Coarsening isalso much faster in the deformed steel as is evident from the onset of the decrease in theprecipitate number density. The precipitate number density in the deformed austenite reaches amaximum very early and subsequently starts decreasing while the precipitate volume fraction isstill increasing. This is contrary to the results observed during precipitation in the undeformedaustenite, where the precipitate number density reaches a maximum when the precipitation isalmost complete (i.e. the precipitate volume percent is nearly 100). This is a result of enhancedcoarsening kinetics in the deformed material because of dislocation-assisted diffusion.Interestingly the mean precipitate size is larger in the undeformed steel even though the kineticsis slower in the undeformed steel. This is a consequence of lower activation energy forprecipitation on dislocations, which in turn means the nucleation rate is very high in thedeformed steel, leading to a very high precipitate number density even in the early stages ofaging. Consequently higher precipitate number density leads to smaller precipitate radius. Nbconcentration in the austenite matrix is depleted as more and more precipitation occurs. Nbdepletion in the matrix is more in undeformed matrix, which is consistent with higher precipitatedensity and larger diameter of precipitates compared to deformed austenite. A completedescription of the volume fraction and size evolution of the precipitates from the foregoingmodel can be coupled to recovery and recrystallisation processes to compute strain accumulationpass by pass in multi-pass rolling.

Interaction of strain induced precipitation with static softening:Zurob, Hutchinson, Brechet and Purdy’s model

A quantitative model has been developed at McMaster University by Zurob et al. [ 8 ] to describethe interaction of strain induced precipitation with static softening. The model considers theelementary descriptions of time evolution of strain induced precipitation [7], recovery [21] andrecrystallisation first and then couples the key interactions between precipitation and recovery,precipitation and recrystallisation, as well as recovery and recrystallisation. The model alsoincorporates both solute and precipitate interaction with recovery and recrystallisation processesexplicitly. The basic equations used in the quantitative modeling are summarised in appendix-1.

The time evolution of strain induced precipitation is captured in the model similar to that ofDutta2, Palmiere and Sellars [7]. The driving force for recovery and recrystallisation is the storedenergy of deformation. The interactions of both recrystallisation and recovery with straininduced precipitation are assumed to be very similar. The presence of precipitates and soluteaffect the mobility of structural defects by pinning and solute-drag effects. The progress ofrecovery will reduce the driving force available for the migration of recrystallisation boundariesand should slow down the recrystallisation process.

Recovery: The precipitation occurring at the nodes of the dislocation network pins thosesegments, which are unable to recover. When the number density of precipitates exceeds thenumber density of dislocation nodes, recovery processes are completely stopped. Eventually, thecoarsening of precipitates decreases the number density of precipitates and unpins thedislocations, causing the recovery to take place. Thus the static softening by recovery is timedependent just after single pass deformation.

Recrystallisation: The driving force for recrystallisation is taken as the stored energy ofdeformation less the retarding Zener drag term to capture the pinning effect of precipitates on therecrystallisation boundary. Since the stored energy from the dislocation density is subject totime-dependent recovery processes and hence the driving force for recrystallisation is also time-dependent. The effect of solute drag effect on the boundary mobility is captured using Cahn’streatment [22]. Since solute content in the matrix is dependent on the time evolution of straininduced precipitation, the mobility is also time-dependent.

The model predictions are compared with the experimental measurements [23] on precipitateparticle diameter (TEM), the softening fraction (double hit compression) and the recrystallisedfraction (optical metallography) as a function of time in a Nb- microalloyed steel at severaltemperatures. A comparison of the experimental with model predictions at 850°C is shown inFigure –1 and 2. The predicted time evolution of the particle diameters ( Figure-1) and thesoftening and recrystallisation fractions ( Figure-2) are in excellent agreement. The softeningfractions were evaluated using a rule of mixtures of the recrystallised and unrecrystallisedfractions coupled to a strengthening model which included contributions from dislocationhardening, precipitation strengthening, and solid solution hardening. The softening curveexhibits a hump between 1 and 100 seconds during which the softening fraction steadily rises toa maximum and then falls. This hump is due the interaction between recovery and precipitationand is not related to the recrystallisation process. The stored energy decreases from 0.5 to 0.46

MPa in the first 10 sec after which a plateau in the stored energy is observed. This decrease instored energy is a consequence of recovery processes and the plateau arises from the inhibitionof recovery by precipitate pinning. Coarsening of the precipitate distribution unpins thedislocation network and allows the recovery process to resume after 200 sec. During the periodwhen the recovery is inhibited, precipitation is the dominant microstructural change occurringand this hardens the material, giving rise to the hump. In the present case the Zener pressure dueto precipitates on boundaries only begins to outweigh the stored energy at long time, and thatonly after the stored energy has been substantially reduced from 0.5 MPa to 0.1 MPa throughrecovery.

Important process parameters for strain accumulation:

Retardation of recovery: Solute Nb is effective in interacting with dislocations, retarding thedislocation mobility associated with the recovery process, but strain induced precipitates ofNbCN at dislocation nodes are far more effective in pinning segments of dislocations and thusprevent the recovery process. The coarsening of precipitates is aided by dislocations, which willunpin dislocations causing recovery to occur. Once the dislocation is unpinned from theprecipitate, the lattice diffusion is expected to take over, which will slow down the growth andcoarsening kinetics. The coarsening of precipitates and unpinning of dislocations can be avoidedif the interpass time is small. But in multi-pass rolling new dislocation network is being formedwith each pass, which will increase the dislocation density and hence the stored energy. Unlessthere is adequate residual Nb, there may not be adequate precipitation to pin all the dislocations.In consequence, softening by recovery could occur. This underscores the importance of adequatesolute Nb for dynamic precipitation and also to restrict the number of passes and the interpass

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Softening FractionRecrystallized FractionSoftening data of Kang et al [17]Rex. data of Kang et al [17]Softening data of Kang et al [23]Rex. data of Kang et al [23]

Figure 1: The predicted particle size evolution is in goodagreement with the experimental data of Kang et al [23].The data is for a steel containing 0.03%Nb, 0.076% C.The steel is deformed 30% at 850oC.

Figure 2: The predicted softening and recrystallizedfractions are compared with the experimental data of Kanget al [23] at 850oC.

time. In other words, ensure that there is thermodynamic potential available for precipitation atall the dislocation nodes as the dislocation density is increased by multi-pass rolling.

The modeling results teach us that the recovery starts at very early stage before precipitationoccurs on dislocation nodes. Once precipitation occurs, the recovery is slowed down and once allthe dislocation nodes are pinned by dislocations, the recovery is stopped. This occurs within 1-10seconds depending on the degree of super-saturation for the precipitation. The coarsening ofprecipitates leading to unpinning of dislocations is diffusion driven. The onset of coarseningvaries with temperature. For example, the coarsening starts in about 10 seconds at 950 C,whereas it is about 100 seconds at 850C. Once recovery occurs, the total stored energy isprogressively decreased. However, the nucleation of precipitates at the fresh dislocation nodeswill tend to deplete solute niobium in the matrix, which is not desirable. Lowering of thetemperature window of rolling, decreasing the inter-pass time, and reducing the number ofpasses are three important factors to increase strain accumulation in multi-pass rolling. Kasparand coworkers have shown that dynamic recrystallisation nucleates preferentially in prior grainboundaries and dynamic recrystallisation is invariably accompanied by meta-dynamicrecrystallisation [ 24 ].

Retardation of recrystallisation

Recrystallisation and grain growth both involve grain boundary mobility. These processestypically start much later than recovery. Particle pinning and solute drag effect are well knownmechanisms that retard the boundary mobility. Adequate Nb must be present in solution ifboundary mobility is to be reduced through the solute drag effect; this requires excess soluteniobium in the matrix to counteract solute depletion by growing precipitates. Second phaseparticles can also act to exert pinning force on the boundary mobility. This raises the possibilityof increasing the pinning pressure through additional second phase particles such as TiN or Ti-V–N or Ti-NbCN.

The modeling results show that the pinning pressure due to strain induced precipitates is only afraction of the stored energy in the beginning of precipitation and hence ineffective in retardingthe boundary at this stage. However, the pinning pressure is effective in retarding the boundarymobility at longer time of holding when the stored energy is substantially decreased by recovery.Kaspar and coworkers have demonstrated by microstructural investigations that in the lowtemperature window ( 770C), the softening by recrystallisation was very limited (less than 10 %)even with the longest holding time [ 25 ]. The technological implication is that at short interpasstimes in the low temperature window, softening by recovery is significant.

Summary of critical process parameters:(i) Design of base chemistry: low interstitials ( C,N) , high solute Nb(ii) Ensure adequate fine precipitation of NbC to pin dislocation segments in order to arrest

the softening by recovery(iii) Ensure adequate solute Nb to retard the boundary mobility in recrystallisation(iv) Ensure adequate amount of second phase particles to exert large pinning pressure on the

boundary in order to retard recrystallization.

Model Validation

Design of base chemistryIn order to obtain high solute niobium during thermo-mechanical processing, the base chemistryis designed to low interstitials (C 0.03, and N 0.003), Ti of about 0.015 wt % to meet thestoichiometric requirement to tie up all the nitrogen as TiN. Thus the steel is designed to have alarge supersaturation for the precipitation of NbC in the low temperature window of rolling. Thebase chemistry of the steel is given in Table-1.

Table-1C Si Mn P S Al N Cr Cu Ni Nb Ti

HTP 0.03 0.16 1.49 0.013 0.001 0.024 0.005 0.27 0.25 0.16 0.086 0.011

Solidification processing modeling

Quantitative analysis of solute redistribution during dendritic solidification and post-solidification cooling at different node points from the slab surface was carried out for the abovechemistry. The solute redistribution over the interdendritic spacing was analysed using finitedifference method. The thermal history at each node point was given by finite element method.The results show that the interstitial solutes exhibit negligible microsegregation, suggesting thatthe diffusion of interstitial solutes, i.e. C and N are able to keep pace with the rate of advance ofthe solid–liquid interface. In contrast, the substitutional solutes give rise to significantmicrosegregation that persists to lower temperatures. However, the effect of lowering the carbonis to increase the temperature window in the delta phase field, where significant homogenisationof substitutional solute occurs. This is because the diffusion coefficients of Nb and Ti in the deltaferrite (BCC structure) are about 20 times greater than those in the austenite (FCC structure) atthe same temperature [2,3].

Design of rolling schedules for strain accumulation to achieve dynamic recrystallisation

Strip rolling was chosen for model validation because of the short interpass time and well-defined time-temperature-deformation schedule in multi-pass rolling. The initial mill trial wascarried out in a strip rolling mill designed for 7 passes. This schedule yielded a fine ferrite grainsize; however the dynamic recrystallisation occurred once in the fifth pass in accordance withmodel predictions. The design strategy for multi-pass rolling used in the current approachinvolves the promotion of dynamic recrystallisation twice within the seven passes. Thus dynamicrecrystallisation was first promoted at the end of the first two passes. The objective is to obtainan austenite grain size that is both fine and homogeneous as a starting grain size for subsequentprocessing. This step is intended to compensate for the elimination of the roughing schedule.

The final grain refinement is achieved by promoting dynamic recrystallisation in the final passunder large Z condition. Thus the deformation schedule in the last five passes was designed toaccumulate a large strain (greater than the critical strain for dynamic recrystallisation -corresponding to large Z) in the last pass. Recall that large Z is promoted by lowering thetemperature. A strain accumulation model based on the Lutz-Meyer data-base developed by Zhu,Gao and Subramanian is used to optimise the rolling schedule to achieve grain refinement ofaustenite by dynamic recrystallisation [26].

In order to achieve dynamic recrystallisation at the end of first two passes, large reductions wereimparted in the first two passes, but the pass reductions were kept well within the safe limit ofmill loading. This ensured a uniformity of starting austenite grain size before the final passsequence. The strain accumulation was kept below the critical strain for static recrystallisation,which was determined experimentally for the deformation conditions.The pass reductions in the last five passes are designed for progressive strain accumulationsufficient to overcome the critical strain for dynamic recrystallisation in the last pass. The passreductions were progressively decreased for shape control. The strain accumulation was keptbelow the critical strain for static recrystallisation, which is determined experimentally for thedeformation conditions. In the last pass, adequate strain is imparted to overcome the large criticalstrain for dynamic recrystallisation, which is a function of Z. The larger the Z, (i.e. the lower thetemperature) the larger is the critical strain for dynamic recrystallisation.

The details of the time-temperature- deformation schedule of the rolling schedule aresummarised in Table–2. The modeling prediction of strain accumulation pass by pass, is given inFigure-3. The data-base on the critical strain for static recrystallisation was generated onWUMSI from previous trials. Figure-4 shows the raw flow stress data along with temperatureplots. Figure-5 shows the corrected strengthening curve for the rolling schedule. Figure-6 showsthe typical microstructure of uniformly dispersed ferrite grain size of about 1.5 um obtained fromthis trial. Though the model predictions relate to dynamically recrystallised austenite grain size,it was difficult to delineate metallographically the prior austenite grain size in the low interstitialsteel and hence only the final ferrite grain size was measured. The grain size distribution offerrite from this trial resulting from grain refinement of austenite by dynamic recrystallisation attwo stages is relatively finer and more uniform compared to a previous mill trial, in whichdynamic recrystallisation was promoted once in the fifth pass, see Figure- 7.

Table 2 Current rolling schedule for strip rolling simulationPass

NumberTime (S) Thickness (mm) Reduction(%) Temperature (°C)

Start Start 37.12 Start Start1 0.00 23.53 36.61 8282 6.13 16.00 32.00 8123 10.53 12.07 24.54 7964 13.85 9.26 23.28 7815 16.40 7.78 16.00 7676 18.44 7.08 9.00 7527 20.17 5.95 16.00 735

Figure (3): Model prediction of strainaccumulation, pass by pass, leading todynamic recrystallization after the 2nd and7th passes.

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Figure (4): Raw flow stress data along with sampletemperature during the strip rolling simulation.

Figure (5): Corrected strengthening curve for the striprolling simulation.

Figure (6): Typical microstructure of the uniformly dispersed ferrite grain size obtained from the strip rollingsimulation.

Figure 7: Comparison of distributions of grain size between new (recent simulation in WUMSI, schedule K-T-35-5.9) and old (previous trail in Thyssen) rolling schedule

Role of microalloying elements in thick strip casting

Even in thicker strip with thickness in the range of 10-15 mm, the deformation schedule isinadequate to exploit the benefits of strain induced precipitation on strain accumulation.

However, the benefits of microalloying elements in precipitation strengthening, solid solutionstrengthening and transformation hardening from solute effects can be utilised. Thereforealternative strategies are required to exploit the benefits of microalloying technology in strainaccumulation. Strain induced precipitation at the dislocation nodes is effective retarding therecovery process. High solute niobium can be used to advantage to retard the recovery process.The pinning pressure of precipitates is effective in retarding the recrystallisation process. Thiscan be achieved if a large pinning pressure on boundary mobility can be ensured through a densedispersion of fine precipitates introduced in upstream processing of steel, using suitablecombination of microalloying elements. Mutual solubility of carbides and nitrides can beexploited for this purpose. Thermodynamic modeling capability is well advanced to provideguidelines for the selection of microalloying elements.

In a previous investigation [15] on a series of Ti-Nb low interstitial microalloyed steels, therecrystallisation limit temperature as determined by flow stress increase in hot torsionmeasurements was found to coincide with the equilibrium temperature for precipitation of mixedcarbides enriched in NbC in a precipitate of the type (TixNb1-x ) (C y N 1-y ), see Table-3. Theabsence of any undercooling associated with NbC precipitation had the net effect of raising therecrystallisation limit temperature. Sellars interpreted these results as follows: The effect of agood dispersion of TiN by upstream processing is to cause epitaxial growth of NbC on pre-existing TiN particles. The epitaxial growth obviated the nucleation step of NbC, whichotherwise would require undercooling even under strain induced condition. The epitaxial growthof NbC on TiN increases the pinning pressure on boundary mobility, retarding therecrystallisation, which could account for the observed increment in flow stress in hot torsionstudies. Figure - 8 shows a TEM picture of a NbC precipitate on a TiN particle, along withmicrochemistry analysis. The hot torsion plot and equibrium precipitation diagrams are alsoincluded in Figure-8. The stored energy calculated from dislocation density estimates from theflow stress measurement was consistent with the pinning pressure estimate from precipitates andthe maximum grain size. However, in order to achieve this increased pinning pressure from NbCat high temperature, it is essential to get a dense dispersion of fine TiN precipitates, which act assubstrates for epitaxial growth of NbC. The base chemistry design and control of solidificationprocessing are important factors to promote homogeneity of substitutional solutes (Ti, Nb and V)during dendritic solidification followed by post solidification homogenization in delta ferrite [26]. The objective is to promote homogeneous thermodynamic potential for precipitation of TiN inaustenite at high temperature. The strain induced precipitation of TiN could be promoted bydeformation in upstream processing. The mutual solubility of nitrides of Ti and V can be used toadvantage in the design of base chemistry. Figure- 9 is a schematic showing the beneficial effectof raising the recrystallisation limit temperature by epitaxial growth of NbC on pre-existing TiNon strain accumulation during hot rolling of thin slab or thicker strip. The experimentalinvestigation on Ti-V system showed that mixed nitrides of Ti-V occur in high temperature wellseparated from mixed carbides that occur at low temperature [27 ]. The process control requiredto get a uniform dispersion of TiN was considered as exacting in steel making in the past. It ishoped that the potential benefits of using microalloying elements in combination in near netshape processing technology will provide the impetus for further basic studies in this area.

Figure 8(a): Equilibrium fraction of TiC and NbC as afunction of temperature.

Figure 8(c): An example of epitaxial precipitation ofcomplex carbonitrides.

Figure 8(b): Effect of the epitaxial precipitation ofcomplex carbonitrides on the flow stress.

Figure 8(d): Chemical analysis of the precipitates shownin 8(c).

Table-3 : Compositions of the steels used by Subramanian et al. [15]

Conclusions:

(1) Ultra-fine grain size can be achieved in austenite by dynamic/metadynamic recrystallisationby strain accumulation sufficient to overcome a large critical strain for dynamicrecrystallisation. This can be achieved by promoting a large Z deformation condition.

(2) Multi-pass rolling can be used to advantage to accumulate large strain (pass by pass) bysuppressing static softening due to recovery and recrystallisation processes occurring in theinterpass time.

(3) Strain induced precipitation at dislocation nodes is effective in suppressing recovery bypinning dislocation segments. Subsequent recovery is associated with the unpinning ofdislocation nodes as the precipitates coarsen.

(4) The pinning pressures exerted by a large volume fraction of fine precipitates and the solutedrag effect are effective in retarding the static recrystallisation.

(5) A quantitative understanding of the relative contributions of solute, coherent and incoherentprecipitates on the retardation of recovery and recrystallisation processes is essential fordeveloping a physically based model for strain accumulation. In the absence of the same, anempirical model based on the available data-base on the effect of total niobium on the criticalstrain for dynamic recrystallisation and static softening at large strain due to Lutz Meyer etal. is used to predict strain accumulation in multi-pass rolling. Experimental simulation ofstrip rolling on thermo-mechanical simulator shows that it is feasible to obtain ultra-finegrains by strain accumulation in a low interstitial, high Nb steel in accordance with the modelprediction.

(6) The potential benefit of upstream precipitation control by alloy design and solidificationprocessing on grain size control of austenite in near net shape processing is demonstrated inTi-Nb microalloyed steel. Epitaxial growth of NbC on pre-existing TiN particles is shown toraise the recrystallisation limit temperature.

Figure 9: The effect of epitaxial growth of NbC on pre-existing TiN compared with strain inducedprecipitation of NbC on Tnr

Acknowledgements:The funding for the basic and applied aspects of the research by The Natural Sciences andEngineering Research Council of Canada through a Strategic Research Grant, Niobium ProductsCompany GmbH, Reference Metals Company Inc, U.S.A. and IPSCO, Canada are gratefullyacknowledged. Technical support by ThyssenKrupp Stahl, Germany, Stelco Inc, Canada andIPSCO, Canada, and LTV, U.S.A., is acknowledged with thanks. Research collaborations withProf. Mike Sellars of Sheffield university, Prof. John Jonas of McGill University, ProfessorEmeritus Lutz Meyer of Aachen University, Dr.Thomas Heller and Dr. Gunter Stich ofThyssenKrupp Stahl and Dr. Francisco Boratto of CSBM, Brazil are gratefully acknowledged.

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[17] Derby B. and Ashby M.F.: “On Dynamic Recrystallisation”, Scripta Metallurgica, Vol.21(1987), pp.879-884.[18] Hodgson P.D.: “The Metadynamic Recrystallisation of Steels”, THERMEC’97,International Conference on Thermo-mechanical Processing of Steels and Other Materials, Ed.by T. Chandra and T. Saki, The Minerals, Metals & Materials Society, (1997), pp.121-131.[19] G.Zhu et al. “ Studies on ultra-fine grains by dynamic recrystallisation in microalloyedsteels” Proc. of Int. Conf. on Thermo-mechanical processing of steel, May 24-26, 2000 , Inst forMaterials, U.K. publication, Vol-2, p. 466-475[20] Meyers, M. A., Nesterenko, V. F., LaSavia, J. C., and Xue, Q., 2001, Shear Localisation in

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Appendix 1:

The present appendix provides a brief summary of the recovery, recrystallisation and

precipitation modules used by Zurob et al. [8]. The key equations appear in Figure-10. The

three modules are coupled through the dislocation density ( ρ ), niobium concentration (CNb) as

well as the number (N) size (R) and volume fraction (Fv) of precipitates. Additional details on

the recrystallization, recovery and precipitation models are found in references [7, 8, 21]. For

the convenience of the reader, the symbols used are listed in Table-4.

Figure 10: Summary of the model used by Zurob et al. [8].

Table 4: A List of the symbols used in the model by Zurob et al. [8]Ac Area of a critical recrystallization nucleus.CNb Instantaneous concentration of Nb in solution (expressed as atom fraction).

EqNbC Equilibrium concentration of Nb in solution.PNbC Concentration of Nb in the precipitate.

Deff A weighted average of the bulk and pipe diffusion coefficients of Nb in austenite.Dpipe Nb diffusion coefficient through dislocations in austenite.dRdt|coarsening The rate of change of precipitate size due to pure coarsening [8].dRdt|growth The rate of change of precipitate size due to pure growth [8].E Young’s modulus.F Adjustable factor in nucleation equation.Fc Coarsening function. Fc is equal to 0 during pure growth and 1 during pure coarsening [8].Fv(t) Precipitate volume fraction.G(t) Net driving force for recrystallization.kB Boltzman’s constant.k Adjustable parameter used to calculate Nrex.M Taylor factor.M(t) Grain-boundary mobility in the presence of solute.Mpure Grain-boundary mobility of pure material.N(t), N Number of precipitate particles.Nc(t) Number of dislocation nodes.Nrex Number of recrystallization nuclei.Ntotal Peak number of precipitates.R(t), R Precipitate radius.Rn Radius of the critical precipitate nucleus.Sv The surface area per unit volume of an austenite grain.Ua Activation enthalpy of the operating recovery process.Va Activation volume of the operating recovery process.vd Debye Frequency.X Recrystallized fractionα Interaction parameter in Cahn’s solute-drag model [22].

rα Constant on the order of 0.15 (recovery equation).

nα Constant on the order of 1.05 (precipitate growth equation).

gbγ Grain-boundary energy.

nG∆ Activation energy for precipitation.

pσ Stress due to plastic deformation.