Numerical Modelling of Hot RollingMicrostructural evolution during plate rolling
J. Pyykkonen
Centre for Advanced Steel Research/Materials Engineering LaboratoryUniversity of Oulu
29.5.2011
J. Pyykkonen (CASR) University of Oulu 29.5.2011 1 / 27
Contents
1 Introduction
2 Proposed model & resultsHeat conductionRoll gapStatic recrystallisationRecrystallised grain sizeGrain growthComputational examples
3 Conclusions
J. Pyykkonen (CASR) University of Oulu 29.5.2011 2 / 27
Numerical Modelling of Hot Rolling
Introduction
This work is part of a larger FIMECC/Tekes-funded project(Development of hot and cold rolling processes by novel processmodelling methods - NoProMo).
The objective of the research is to developthermal-mechanical-microstructural model for optimizing plate rollingschedules in the case of titanium-microalloyed ulta-high-strength platesteel with the following composition: 0.15C, 0.30Si, 0.97Mn, 0.39Cr,0.032Al, 0.055Ni, 0.09Mo, 0.024Ti, 0.0052N and 0.0017B.
Reliable prediction of the plate temperature, roll force, torque andmicrostructure is essential for the proper set-up of sophisticatedthermo-mechanical treatment schedules of the plate mill.
In the development of ultra-high-strength plate steels, physicalsimulation and computer modelling are essential tools.
J. Pyykkonen (CASR) University of Oulu 29.5.2011 3 / 27
Numerical Modelling of Hot Rolling
Topics of interest:
Microstructureevolution
Temperaturebehaviour
Roll gap phenomena
Rolling models (IRTC, 2008)
J. Pyykkonen (CASR) University of Oulu 29.5.2011 4 / 27
Numerical Modelling of Hot Rolling
Microstructure control by TMCP(K. Nishioka and K. Ichikawa, Sci. Technol. Adv. Mater., 2012)
J. Pyykkonen (CASR) University of Oulu 29.5.2011 5 / 27
Numerical Modelling of Hot Rolling
Austenite grain refinement is based on:
1 Grain growth kinetics during slab reheating
2 Recrystallisation kinetics
3 Recrystallised grain size
4 Grain coarsening during the interpass time between deformations
Grain size after reheating Recrystallised grain size
J. Pyykkonen (CASR) University of Oulu 29.5.2011 6 / 27
Numerical Modelling of Hot Rolling
Proposed model - heat conduction
In order to predict thermal behaviour of a steel plate during rolling weneed to solve the governing heat conduction equation.
The conduction of heat due to temperature differences through acontinuum and temperature distribution through material isrepresented by the following equation.
A standard differential form of the conservation law for the heat:
∂ (ρcpT )
∂t= ∇ (k∇T ) + ST (1)
where T denotes the temperature, t is the time, cp is the specific heat,ρ is the density, k is the thermal conductivity of the given metal.
The evolution of latent heat due to solid-state phase transformations andchanges in heat due to internal work are included in term ST .
J. Pyykkonen (CASR) University of Oulu 29.5.2011 7 / 27
Numerical Modelling of Hot Rolling
The embedded Cash-Karp method
In order to use adaptive time-stepping an estimate of the localtruncation error of a single temporal integration step is required.
The explicit Cash-Karp method uses six function evaluations toproduce fourth- and fifth-order accurate solutions.
The error of the fourth order solution is the difference between thesetwo solutions.
The extended Butcher table for the Cash-Karp method.
0 01/5 1/5 03/10 3/40 9/40 03/5 3/10 -9/10 6/5 01 -11/54 5/2 -70/27 35/27 0
7/8 1631/55296 175/512 575/13824 44275/110592 253/4096 0(4th) 37/378 0 250/621 125/594 0 512/1771(5th) 2825/27648 0 18575/48384 13525/55296 277/14336 1/4
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Numerical Modelling of Hot Rolling
Adaptive time-stepping
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Numerical Modelling of Hot Rolling
Measured and predicted temperature behaviour
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Numerical Modelling of Hot Rolling
Proposed model - roll gap
A simplified inhomogeneous solution forthe roll pressure as the basis forsimulating roll force and torque([E. Orowan, Proc. Inst. Mech. Engrs.,1943], [I. Freshwater, Int. J. Mech.Sci., 1996]).
The local strain variation over platethickness direction in the roll gap isestimated by the relationship proposedby Moon & Lee, ISIJ International,2009.
Through-thickness temperaturedistribution in the roll gap is simulatedusing the Crank-Nicholson finitedifference method.
Contact geometry
Pressure distribution
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Numerical Modelling of Hot Rolling
Measured and predicted flow stress behaviour (P. Hautamaki)
Strain rate 3.5 [1/s]
J. Pyykkonen (CASR) University of Oulu 29.5.2011 12 / 27
Numerical Modelling of Hot Rolling
Proposed model - static recrystallisation
Using the time for 50% recrystallisation, t50, the recrystallised fractionX can be predicted as a function of time under isothermal conditions.The Kolmogorov-Johnson-Mehl-Avrami equation for metallurgicalprocesses such as static recrystallisation is often written in the formas given below.
The Kolmogorov-Johnson-Mehl-Avrami equation:
X = 1− exp
[ln (1− 0.5)
(t
t50
)n](2)
t50 = α1εα2Zα3dα4 exp
(QSRX
R · T
)(3)
where ε is the strain,Z is the Zener-Hollomon parameter, d is the grainsize, R is the gas constant, T is the temperature, QSRX is the activationenergy. Finally, material dependent constants are α1, α2, α3 and α4
J. Pyykkonen (CASR) University of Oulu 29.5.2011 13 / 27
Numerical Modelling of Hot Rolling
Proposed model - static recrystallisation
During hot rolling operations non-isothermal conditions prevail
This necessitates modification of the Avrami equation
Numerical solution can be achieved by means of numerical methodswhen the thermal program (T vs. t) is known(D. Martin, Comp. Mat. Sci., 2010)
SRX under non-isothermal conditions:
φ =ln (1− X )
ln (1− 0.5)=
[t
t50 (T )
]n
(4)
∂φ
∂t=
n
t
(t
t50 (T )
)n
(5)
X = 1− exp [ln (1− 0.5)φ] (6)
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Numerical Modelling of Hot Rolling
Recrystallisation kinetics (M. Somani)
Stress relaxationtests in a Gleeble1500
Process variables:strain, strainrate, temperature
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Numerical Modelling of Hot Rolling
Recrystallisation during the interpass timeThickness 100mm, ε = 0.2, ε = 1, T = 1050◦C, dγ = 60µmTime 20 s.
J. Pyykkonen (CASR) University of Oulu 29.5.2011 16 / 27
Numerical Modelling of Hot Rolling
Proposed model - recrystallised grain size
The size of the recrystallised grains is dependent on the strain, strainrate, temperature and initial grain size prior to deformation.With the aid of the fitted SRX model, the time for the completion ofSRX under different deformation conditions was predicted, and a newset of specimens was tested.
Grain size after recrystallisation (SRX):
dr = β1 + β2εβ3 εβ4dβ5 exp
(−Qd
RT
)(7)
Other simplified descriptions:
dr = β1εβ2dβ3 exp
(−Qd
RT
)(8)
dr = β1εβ2dβ3 (9)
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Numerical Modelling of Hot Rolling
Effect of deformation temperature and applied strain on measuredrecrystallised austenite grain size.
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Numerical Modelling of Hot Rolling
Effect of initial austenite grain size and strain on predictedrecrystallised austenite grain size.
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Reheating temperature:1150 ◦CDeformation temperature:1100 ◦CNo deformation
Area fraction
Micrograph and colour by value(grain diameter)
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Reheating temperature:1150 ◦CDeformation temperature:1100 ◦CStrain: 0.15, strain rate 5 1/s
Area fraction
Micrograph and colour by value(grain diameter)
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Reheating temperature:1150 ◦CDeformation temperature:1100 ◦CStrain: 0.30, strain rate 5 1/s
Area fraction
Micrograph and colour by value(grain diameter)
J. Pyykkonen (CASR) University of Oulu 29.5.2011 22 / 27
Numerical Modelling of Hot Rolling
Proposed model - grain growth
The grain boundary migration rate V is related to the driving pressurePG and retardation pressure PZ .
For simulating austenite grain growth the empirical relationshipproposed by Andersen and Grong (Acta Metall. Mater., 1995) is used
Grain coarsening:
V = M0 [PG − PZ ]1/n−1 (10)
dD
dt= M0 exp
(−Qapp
RT
) [1
D− f
k × r
](1/n−1)
(11)
Dlim = k × r
f(12)
where D is the average grain diameter, t is the time, T is the temperature,
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Numerical Modelling of Hot Rolling
Measured austenite grain coarsening after the completion ofrecrystallisation.
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Numerical Modelling of Hot Rolling
Computational examples
The experimental data presented was tied together in the form offitted sub-models describing restoration behaviour, recrystallised grainsize, grain coarsening and material behaviour under deformation.
Sample calculations using the microstructural model coupled with thetransient conduction of heat and roll gap quantities are presented inthe next slide.
Initial conditions:
Temperature: 1080 ◦CAustenite grain size: 100 µmTotal reduction in each case: 53 %
Predicted microstructure-time histories at the centre position of theplate using three different reduction schedules during plate rolling.
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Numerical Modelling of Hot Rolling
Simulation of the change in the austenite grain diameter using threedifferent reduction schedules.
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Numerical Modelling of Hot Rolling
Conclusions
1 Austenite conditioning and grain refinement is based on understandingand description of recrystallisation kinetics and grain size after thecompletion of static recrystallisation and grain coarsening.
2 For the Ti-microalloyed steel studied, recrystallised grain size isinsensitive to temperature and grain coarsening during the interpasstime is prevented → the importance of applied strain per rolling pass.
3 In order to minimize the austenite grain size during plate rolling, it ispreferable to increase the amount of strain towards the end of aroughing rolling schedule.
J. Pyykkonen (CASR) University of Oulu 29.5.2011 27 / 27
