simulation of ppprecipitation kinetics in c+n...

Chair of Materials Technology Institute of Materials

Simulation of precipitation p pkinetics in C+N Steels

Laís Mújicaa,b, Sebastian Webera,c, Werner Theisena

a) Ruhr-Universität Bochum, Lehrstuhl Werkstofftechnik b) Max-Planck Institut für Eisenforschung, Düsseldorf

c) Helmholtz-Zentrum Berlin

Thermo-Calc Anwendertreffen

Thermo-Calc Anwendertreffen – September 2009 - Laís Mújica 1

Aachen, September 2009


Outline

• Description to the system

• Nucleation of precipitates

• Diffusion calculations

• Conclusion



Description of the systemDescription of the system



Introduction

• Twinning induced plasticity

austenitic matrix

• Usually are Fe-Mn-C or Fe-Mn-Al-Si systems with low corrosion

i tresistance

• Use of carbon and nitrogen as interstitial to give strengthinterstitial to give strength

• Manganese, Chromium • TWIP steels exhibit exceptional pdeformability and strength



1500L

• TWIP, fully austenitic materialG

1200C]

A

F+A

material

• Find out the appropriate amount of each element

L+A

900ure

[° A

• Direct austenitic solidificationA+M23C6900

mper

at A+M23C6+M2(C,N)

A+σ

• Avoid N2 degassing

• Avoid precipitates

23 6

600

Tem A+σ

M23C6+M2(C,N) • Optimize chromium and manganese contents

3000 0.2 0.4 0.6 0.8 1.0

(C+N) [wt%]

12Cr-20Mn-CN C/N=0.75 P=1 bar TCALC TCFE5


(C+N) [wt%] TCALC -TCFE5


Composition

Content wt% Interstitials

F M C C N C+N C/NFe Mn Cr C N C+N C/N

bal. 20.0 12.0 0.24 0.32 0.56 0.75

bal. 25.0 12.0 0.30 0.40 0.70 0.75

bal. 30.0 12.0 0.30 0.40 0.70 0.75bal. 30.0 12.0 0.30 0.40 0.70 0.75

Ingot castingH i 50% T 1150°CHammering: ε= 50%, T= 1150°CSolution annealing: T= 1150°CQuenching in water



Material properties

1000 25Mn12CrCN 0°

600

800

30Mn12CrCN 0° 20Mn12CrCN 0°

Pa]

400

600

tres

s [M

P0

200St

0 20 40 60 80 100

Elongation [%]



• Optimum C/N ratio1600

Precipitates

L

L+A

G

Optimum C/N ratio

• Isopleths to verify the austenite field

1400

600

[°C]

A

L+Astability

• Total interstitial 1200

ature

[

A+M2(C,N) A+M23C6

content constant

• Tendency to form 800

1000

mper

a

A+M23C6+M2(C,N)

ycarbides and nitrides

600

800

Te

• Intercrystalline corrosion

0 1 2 3 4 5

012345 W(N)x10-3

(C)W



NucleationNucleation



• Chemical potential of the

FundamentalsChemical potential of the nucleus is controlled by the surrounding matrixBinary system Fe-Ni

• Change of chemical potentials are related to the tangent to the Gibbs gfree energy curve of the matrix

• Difference between tangent and G nucleusdefines the driving force of the transformation parallel tangent

Source: G. Inden. Notes



• Dependent not only on driving

Fundamentals• Dependent not only on driving

force but on the surface energy

C iti l di h l ti σπ 24 r

• Critical radius where nucleation is possible

GrrrG Δ+Δ 32 44)( πσπNucleusEmbryos

− σ2

VGrrrG Δ+=Δ3

4)( πσπ

r

Vcrit G

rΔ

=

34 • Heterogeneous nucleation: VGr Δ3

34π • Heterogeneous nucleation:

foreign bodies promote nucleation



Nucleation - Driving force

FCC (γ) M23C6 • ΔGV is calculated f

0,6

C6

DGM(M23C6)

Nucleation

from TCALC, where the matrix phase

0,4

ce M

23C

Nucleation thermodynamically

favored

active, the nucleant dormant and

0,2

ng fo

rc

No nucleation

dormant and the other phases suspended

0,0Driv

i

suspended

600 700 800 900 1000-0,2


Temperature [°C]


0 / 2

Nucleus critical radio

F G i σ = 0.4 J/m2

Vm = 6.35x10-6 m3/mol• From ΔGV is

estimated the critical radius10-9]

• Asymptotic behavior due to th i it t 10-10di

us [m

]

the proximity to driving force equal to 0

10-11

10

tical

rad

10 11

Crit

550 600 650 700 750 800 850 900 950

10-12

T t [°C]


Temperature [°C]


Nucleus composition0 68 0 175

• Nucleus composition is higher in Fe as 0,64

0,68

fr]

Cr Mn 0,174

0,175

gtemperature increases0,60

Mn)

[wt-f

r) [w

t-fr]

0,172

0,173

• Nucleus composition is higher in Mn

0,56

M23

C6,M

M23

C6,C

r

0 170

0,171

higher in Mn and Cr as temperature decreases

0,52 w(M

w(M

0,169

0,170

decreases600 700 800 900 1000

0,48

Temperature [°C]

0,168


p [ ]


Diffusion calculations



• DICTRA

Problem set-up• DICTRA

• Single cell calculations:

• FCC(γ) - M23C6

• 20Mn12Cr0.24C0.32N, Nucleus, Nr=5 nm ,

1atm

• Geometric grid

r=5 nm

• Circular geometry

SSOL4 MOB2Matrix, M • SSOL4-MOB2

• Isothermal conditions

Matrix, Mr=5 µm



Problem set-up

• For each temperature, the correspondent composition of the nucleus is incorporated as an input

• For all the calculations the nucleus radius of 5 nm is set as a parameter

• The matrix composition is the original of the substrate

I th l t i id f 0 8 d 20 i t • In the nucleus, a geometric grid f=0.8 and 20 points was used. In the matrix, a geometric grid f= 1.25 and 60 points was employed



M23C6 Growth

0,01

0,1• 850°CΔT 1 10 7

1E-4

1E-3

mol

-fr] ΔTmin= 1x10-7s

ΔTmax= 1x105 s

1E-6

1E-5

M23

C6) [

m

1E-8

1E-7

inn(

M

10-9 10-7 10-5 10-3 10-1 101 103 105 1071E-9

Time [s]


Time [s]


M23C6 Growth10-5

• Based on the composition, equilibrium is

10-5

850°Cequilibrium is reached up to 1x108s

10-6

ter [

m]

10-7

Dia

met

10-8

10-8 10-6 10-4 10-2 100 102 104 106 108

10 8

Ti [ ]


Time [s]


Elements diffusion



Carbon

• Carbon

T=0s T=1e2 s T=1e4 s T=1e6 sT 1 8

diffuses form the fcc matrix towards the

0,1T=1e8 s

ol-fr

]

carbide

x(C

) [m

o

0,01

x

10-9 10-8 10-7 10-6 10-5

Distance [m]



Nitrogen • Nitrogen content is diminished in 0 014 is diminished in the surroundings of th bid

0,012

0,014

the carbide.

• Concentration of N is increased in

0,008

0,010

ol-fr

]

N is increased in the outer part of the cell.

0,004

0,006

x(N

) [m

o

• Agreement with Ab initiocalculations on 0 000

0,002

x

T=0s T=1e2s T=1e4s T=1e6sT=1e8s calculations on

M23C6 destabilization by N

1E-9 1E-8 1E-7 1E-6 1E-5

0,000

Distance [m]

T 1e8s


by NDistance [m]


Chromium

• Chromium diffuses form the fcc matrix

0,5 T=0s T=1e2s T=1e4s T=1e8s

the fcc matrix towards the carbide

0,4

ol-fr

]

T=1e6s

• Outer part of M23C6 is Cr-rich0 2

0,3

(Cr)

[mo

rich

0,1

0,2x(

1E-9 1E-8 1E-7 1E-6 1E-5

,

Distance [m]


Distance [m]


Chromium

0,13

0,12l-fr]

0,11

(Cr)

[mo

0,10

T=0s T=1e-3s T=1e-2s T=1e-1s T=1s

x(

6E-9 8E-9 1E-8 1,2E-8 1,4E-8

Distance [m] Source: W. Theisen, H. Berns.


Ferritic materials


Manganese

• Manganese content is i d i h

0 19

0,20

increased in the surroundings of the carbide.

0 17

0,18

0,19

ol-fr

]

• Concentration of Mn is i d i th

0,16

0,17

(Mn)

[mo

increased in the outer part of the cell.0,14

0,15x( T=0s T=1e2s T=1e4s T=1e6sT 1e8s

1E-9 1E-8 1E-7 1E-6 1E-50,13

Distance [m]

T=1e8s


Distance [m]


Carbide growthKinetic analysisKinetic analysis



• Appropriate Appropriate criteria to construct the TTT diagrams from diagrams from the simulation results of 20M 12C ll20Mn12Cr alloy

• Comparison with experimental experimental data


Source: V. Gavriljuk, H. Berns. High Nitrogen Steels


i i Critical time – Linear intersection approach

Kinetics

-2

fr)]

log(mol-fr) Linear Fit of log(mol-fr) Linear Fit of log(mol-fr)

pp

-4

og(m

ol-

-6

l-fr)

[Lo

-8

Log(

mo

-8 -6 -4 -2 0 2 4 6 8-10

L

L (ti ) [L ( )]


Log(time) [Log(s)]


KineticsCritical time – 2nd derivative approachCritical time 2 derivative approach

-2)] log(mol-fr)Boltzmann of log(mol-fr)

-4

g(m

ol-fr

) Boltzmann of log(mol-fr)

-6

-fr) [

Log

-8

Log(

mol

-

-8 -6 -4 -2 0 2 4 6 8-10

L (ti ) [L ( )]

L


Log(time) [Log(s)]


Critical time – 2nd derivative approach

0,50

0,75 Derivative Y1

0,25

0,50

ol-fr

))m

e))2

0 25

0,00

(Log

(mo

(Log

(tim

-0,50

-0,25

d2 ( d(

-8 -6 -4 -2 0 2 4 6 8-0,75

Log(time) [Log(s)]


Log(time) [Log(s)]


1000Consolidated

intercept derivative

900

re [°

C]

800

pera

tuTe

m

100 101 102 103 104700


Critical time [s]


Conclusions• Assuming homogeneous nucleation of M23C6 in the austenitic

matrix Fe-20Mn-12Cr-0.24c-0.32N, it is thermodynamically

ffavored at temperatures over 900°C

• Assuming homogeneous nucleation of M23C6 in the austenitic Assuming homogeneous nucleation of M23C6 in the austenitic

matrix Fe-20Mn-12Cr-0.24c-0.32N, the critical temperature for

precipitation is 850°Cp p

• It is possible to construct TTT diagrams based on Dictra

calculations. The results can be more conservative than the

experimental ones constructed on the basis of changes of


macroscopic properties.


EXPERIMENTAL-CURRENT AND FURTHER WORK:

I th l h t t t t f l i A t T (700• Isothermal heat treatment of samples in Ar at Temp (700-900°C each 50°C) followed by water quenching

• Oxalic acid electrolytic etching – ASTM 262/98 –Susceptibility to Intergranular Attack in Austenitic Stainless Steels



Thank you very much for Thank you very much for your attentiony


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