New Models for Steels Microstructure Simulation under Hot Rolling and Accelerated Cooling (Presentation, SPNSʹ2013)

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New Models for Steels Microstructure Simulation New Models for Steels Microstructure Simulation under Hot Rolling and Accelerated Coolingunder Hot Rolling and Accelerated Cooling

Vasilyev A.A.Vasilyev A.A., Sokolov D.F., Sokolov S.F, Kolbasnikov N.G. , Sokolov D.F., Sokolov S.F, Kolbasnikov N.G.

ISPNSISPNSʹ́20132013Oulu, Finland; Oulu, Finland; June 19, 2013June 19, 2013

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■ A physically based approach for calculation of the effective activation energies of austenite microstructure evolution

processes developing in steels under hot rolling and accelerated cooling

■ Self-diffusion activation energy in a complexly alloyed austenite

■ New models for numerical simulation of the austenite grain growth, static recrystallization and its transformation under

continuous cooling

ObjectivesObjectives

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SelfSelf--DDiffusiiffusion Activation Energy on Activation Energy in Complexly Alloyed Austenitein Complexly Alloyed Austenite

→ the key GG parameter:

Austenite Grain Growth (GG) SGBD DQQ 0.5

SDQ Self-Diffusion Activation Energy

Austenite Static Recrystallization (SRX)

effGGQ

50

50

( ) 1 exp 0.693 ,

exp

; ;...;

n

SRX

SRX

SRX SRX C X Z

tF tt

Qt

RTQ Q y y y

→ the key SRX parameter: SRXQ

Ferrite Grain Nucleation/Growth

NN

N N C X Z

C X Z

QJRT

Q Q y y y

dR M Gdt

QM M T M

RT

Q Q y y y

/

/0/ / /

/ /

exp ,

; ;...;

,

exp ,

; ;...;

NQ

/Q

lim

0

1 1 ,

exp

( ; ;...; )

effGB

effeff eff GGGB GB GB

eff effGG GG C X Z

dDM

dt D D

QM M T MRT

Q Q y y y

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Experimental Data on QExperimental Data on QSD SD in Austenitic Alloysin Austenitic Alloys

References

[1] Gruzin P.L. Self-Diffusion in γ−Iron // MPhM Problems, 1952

[2] Gruzin P.L., Kornev Yu.V., Kurdiumov G.V. Carbon Effect on Self-Diffusion in γ−Iron // MPhM Problems, 1952

[3] Gruzin P.L., Noskov B.M., Shirokov V.I. Effect of Manganese on Self-Diffusion in γ−Iron // MPhM Problems, 1955

[4] Gruzin P.L. Chromium Effect on Self-Diffusion in γ−Iron // MPhM Problems, 1955

[5] Bokstein S.Z., Kazakov V.A., Kishkin S.T., Mirsky L.M. Investigation of Refractory Alloying Elements Effect on Self-Difusion in γ−Iron // Proceedings USSR Academy of Science, 1955

C Mn Si Ni Mo Cr Nb V Ti Alloy аt. % (site fractions)

QSD, J/mol

γ − Fe 0,19 − − − − − − − − 295500

С1 1,54 0,13 0,62 − − − − − − 247100

С2 2,10 0,11 0,18 − − − − − − 204600

С3 3,60 0,46 0,32 − − − − − − 175900

С4 4,97 0,14 0,32 − − − − − − 128900

Mn1 0,09 0,41 − 0,31 − − − − − 347355

Mn2 0,14 1,17 0,12 0,17 − − − − − 380835

Mn3 0,16 2,29 0,14 0,09 − − − − − 393390

Mn4 0,14 2,82 0,09 0,11 − − − − − 401760

Ni1 0,19 0,40 0,08 11,29 − − − − − 278721

Ni2 0,19 0,40 0,08 23,40 − − − − − 260307

Ni − Mo1 0,17 0,14 0,08 24,14 0,24 − − − − 284580

Ni − Mo2 0,17 0,14 0,08 24,28 1,07 − − − − 324338

Ni − Mo3 0,17 0,15 0,08 24,54 2,55 − − − − 401500

Nb1 0,08 0,15 0,07 23,21 − − 0,04 − − 311200

Nb2 0,004 0,16 0,07 23,27 − − 0,51 − − 372456

Nb3 0,002 0,16 0,07 23,36 − − 1,06 − − 399668

Ti1 0,16 0,43 0,07 23,44 − − − − 0,02 282906

Ti2 0,001 0,43 0,07 23,38 − − − − 1,75 385020

Cr1 0,79 0,24 0,36 − − 4,26 − − − 275100

Cr2 0,14 0,21 0,12 − − 8,43 − − − 340400

V1 0,16 0,16 0,10 23,74 − − − 2,27 − 231000

V2 0,16 0,16 0,10 23,67 − − − 5,43 − 204400

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QQSDSD Dependence on Austenite CompositionDependence on Austenite Composition

this equation allows performing high accuracy SDAE calculations with account of the effect of C and most practically important SAE:

X = Mn; Si; Ni; Cr; Mo; Nb; Ti; V_______________________________________________________________________________________

A.A. Vasilyev, N.G. Kolbasnikov, S.F. Sokolov and D.F. SokolovJ. Solid State Phys., 2011, Vol. 53, p. 2086

* *311691 278242 1 exp ( 3.94 ) [ / ], XpSD C X X

ХQ y q y J mol

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lim *

1 P

Z P

RDf

0.5GG SDQ Q

Grain Growth ModelingGrain Growth Modeling

01 1

**

lim

( ) ( )( ) exp exp ,( )

GG SD AE GG SD AEQ Y Q YdD t Mdt R RT D t D

−0.502.020.271.510.32Ni-Mo2

−0.494.00.261.040.21Ni-Mo1 [3]

−0.49−0.260.490.08Mo

[2]0.0480.49−0.041.880.05Nb-Mo

−−−0.0250.680.781080

−−−0.0090.30.038DQSK [1]

−−−0.0120.740.17A36

Ref.NbMoNiSiMnCSteel

−0.502.020.271.510.32Ni-Mo2

−0.494.00.261.040.21Ni-Mo1 [3]

−0.49−0.260.490.08Mo

[2]0.0480.49−0.041.880.05Nb-Mo

−−−0.0250.680.781080

−−−0.0090.30.038DQSK [1]

−−−0.0120.740.17A36

Ref.NbMoNiSiMnCSteel

[1] M. Militzer, A. Giumelli, E. Hawbolt // Metall. Mater. Trans. A, 1996, Vol. 27A, p. 3399

[2] K.A. Alogab, D.K. Matlock, J.G. Speer, H.J. Kleebe // ISIJ Int., 2007, Vol. 47, p. 307

[3] U. Sangho, M. Joonoh // ISIJ Int., 2004, Vol. 44, p. 1230

Chemical compositions of the steels [wt.%], for which the experimental data utilized in GG-model calibration

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Grain Growth Modeling ResultsGrain Growth Modeling Results

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The model provides good quantitative agreement with the experimeThe model provides good quantitative agreement with the experimental resultsntal results. .

This means that the proposed approach for the process activationThis means that the proposed approach for the process activation energy energy calculation based on its relationship with the selfcalculation based on its relationship with the self--diffusion activation energydiffusion activation energy

is correct.is correct.

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3

0

( ) 1 exp ( ) ( ) ( )

t

rexSRX rex GB rex ZX t N M G P d

Recrystallization

; ( 0) rex rex dN N d t

( ) ( ) rex dG t t

( ) ( ( ); ( ); ;...); ( )rex rexGB GB SD C Nb XM t M Q y t y t y T t

( ) ( ); ( )Z Z p pP t P N t R t

Recovery CNP precipitation

( )d t

( )d t ( )pN t

( )pN t

( )pR t/ ; , ( )ssNb V C NХ t

Modeling Static RecrystallizationModeling Static Recrystallization

Zurob H.S., Hutchison C.R., Brechet Y., Purdy G. // Acta Mater., 2002, Vol. 50, p. 3075

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SRX Modeling ResultsSRX Modeling Results

0,0240,181,080,21S20,0410,241,230,11S1

NbSiMnCChemical composition, wt/%Steel

0,0240,181,080,21S20,0410,241,230,11S1

NbSiMnCChemical composition, wt/%Steel

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Chemical composition, wt. %C Mn Si Mo Nb V Ti N

0,06 1,7 0,2 0,2 0,045 0,04 0,02 0,006

Chemical composition, wt. %C Mn Si Mo Nb V Ti N

0,06 1,7 0,2 0,2 0,045 0,04 0,02 0,006

Line-pipe steel Х90

The experimental data is obtained utilizing double-hit compression experiments performed with the help of Gleeble 3800 system.

The recrystallized fractions are evaluated by the “back extrapolation” method.

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Ferrite Transformation Model

Ferrite nucleation

First mode → ← Second mode

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2( ; ; ) ( ) exp exp ,( ; )

PF N kk AE k k

AE

QJ t T Y C N tRT RT G T Y

Nucleation rate:

0 01 1 23 2

10 1( ) ( ); ( ) 1 ( )

N t N t N t S td d a nucleation sites volume densities;

. ( )0 5N SD AEQ Q Y

;k kC

activation energy of lattice reconstructive transformation;

empirical parameters

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Ferrite growthMixed-mode model is used [1-3]:

*/ * 0 int

/0.5 ( )( ; ) exp ( );

SD AE

L AE C CQ YV T Y M x x

RT

int/

int

( ; )( ; )C CC AE

C AEC C

x xD T YV T YR x x

/ /

C LV V intCx

[1] B. Ya. Lyubov. Kinetic Theory of Phase Transformations (Metallurgiya, Moscow, 1969; Amerind, New Delhi, 1978)

[2] G.P. Krielaart, J. Sietsma, S. Zwaag // Mater. Sci. Eng. А, 1997, Vol. 237, p. 216

[3] A.A. Vasilyev, D. F. Sokolov, N.G. Kolbasnikov, S.F. Sokolov // Phys. Solid State, 2012, Vol. 54, p. 1565

Pearlite Transformation Model

Mixed-mode model is applied for pearlite growth rate calculation [3]:

*/ * 0 int

/0.5 ( )( ; ) exp ( );

SD AE

L AE C CQ YV T Y M x x

RT/

int/ 6.35 ( ; ) C CC AE

CC C

x xD T YVS x x

/ /C LV V

intCx

Vasilyev A. Carbon Diffusion Coefficient in Complexly Alloyed Austenite // Proc. MS&T’2007, Detroit, 2007, p. 537

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Austenite Transformation Model CalibrationAustenite Transformation Model Calibration

The model was calibrated on the basis of our own research results obtained with the help of the Gleeble 3800 system, as well as published data for 15 steels.

Steel С Mn Si Cr Ni Cu Mo Nb V Ti

S1 (X80) 0.08 1.47 0.20 – – – 0.19 0.042 0.064 0.010

S2 (Х90) 0.06 1.70 0.20 – – – 0.20 0.045 0.040 0.020

S3 (Х100) 0.04 1.90 0.25 0.10 0.45 0.20 0.31 0.050 0.020 0.020

S4 0.18 0.72 0.20 0.03 0.07 0.19 0.02 – 0.010 –

S5 0.22 0.46 0.26 0.98 0.18 0.27 0.05 – – –

S6 0.4 0.68 1.58 0.08 0.07 0.14 – – – –

S7 0.74 0.55 0.36 0.04 0.04 0.07 – – – –

S8 0.004 0.14 0.03 0.03 0.04 0.04 0.004 0.002 0.002 0.060

S9 0.06 0.17 0.01 0.02 0.03 0.06 0.004 0.002 0.001 0.001

S10 0.10 0.56 0.81 0.66 0.55 0.42 0.006 0.022 0.003 0.004

S11 0.10 0.56 0.55 0.21 0.13 0.12 0.12 0.022 0.065 0.004

S12 0.11 1.55 0.66 0.03 0.03 0.05 0.003 0.003 0.005 0.003

S13 0.13 0.40 0.02 0.04 0.04 0.06 0.004 0.002 0.002 0.001

S14 0.20 0.40 0.19 0.03 0.03 0.05 0.004 0.002 0.004 0.002

S15 0.23 1.31 0.21 0.03 0.03 0.05 0.007 0.003 0.005 0.003

The cooling rate and austenite grain size were varied in wide ranges (CR: 1÷200°С/s; Dγ: 20÷130 μm) to obtain the spectrum of practically important microstructures.

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Steel С Mn Si Nb Ti , d m

0.002 0.01 0.06 S1

0.0003 0.11 0.1

0.01 0.038

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S3 0.07 0.76 0.01 0.023 0.013 18

Modeling Results Modeling Results

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Modeling Results

Steel С Mn Si Cr , d m

S4 0.084 0.58 0.02 0.03 100

Steel С Mn Si Cr , d m

S8 0.18 0.72 0.2 0.19 20

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Modeling Results Modeling Results

Steel С Mn , d m

S11 0.45 0.49 20

Steel С Mn Si Cr Ni , d m

S10 0.4 0.68 1.58 0.08 0.07 74

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Modeling Results Modeling Results

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CR CR –– dependence of Austenite Deformation Effectdependence of Austenite Deformation Effect

The model describes experimentally observed CR – dependence of the austenite pre-deformation effect on the transformation kinetics caused by relaxation of the internal

stresses.

Deformation temperature: 850 °C

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Prediction of Structural Parameters Prediction of Structural Parameters

Ferrite grain size: Bainite block size:

1/3

PF2fd3N

1/3

BB P

B

2fd3N

2222

Developed SoftwareDeveloped Software

The program for simulation of separate austenite microstructure evolution processes:- Grain growth- Dynamic recrystallization- Static recrystallization- Flow stress curves

The program for simulation of the resultant austenite microstructure evolution under hot rolling due to interacted processes of:Grain growth + Dynamic recrystallization + Recovery + Static

recrystallization + CNP precipitation

with account of the effects of steel complex alloying.

The program for simulation of the austenite transformation with formation of:

Ferrite + Pearlite + Bainite + Martensite

with account of the effects of steel complex alloying.

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SummarySummary

New models for numerical simulation of the austenite grain growth, static recrystallization and its transformation under continuous cooling have been developed as a result of the work performed.

The models account for the effect of complex alloying by such elements as C; Mn; Si; Ni; Mo; Nb; Ti; and V with the help of suggested physically based approach for calculation of the effective activation energies of austenite microstructure evolution processes developing in steels under hot rolling and accelerated cooling.

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Thanks for your attentionThanks for your attention!!