IDENTIFICATION OF THERMAL BOUNDARY CONDITIONS …

20/11/06ROUX Guilhem-MichelDEN/SAC/DM2S/SEMT/LM2S

1

IDENTIFICATION OF THERMAL BOUNDARY CONDITIONS

AND THERMO-METALLURGICAL BEHAVIOUR OF X10CrMoVNb9-1 STEEL

-APPLICATION TO A « DISK-SPOT » WELDING EXPERIMENT

Guilhem-Michel ROUX1,2 , Olivier BLANCHOT3, René BILLARDON1

¹ LMT-Cachan

² CEA (DEN/DM2S/SEMT/LM2S), 3 CEA (DRT/UTIAC)

AKNOWLEDGEMENTS: AYRAULT D., KICHENIN J., BRACHET J.C., DE CARLAN Y.


2

OUTLINE

� INTRODUCTION

� MICROSTRUCTURAL CHANGES IN T91 STEELS

� SIMULATION OF THE

THERMO-METALLURGICAL BEHAVIOUR OF T91 STEELS

� IDENTIFICATION OF THERMAL BOUNDARY CONDITIONS

DURING A « DISK-SPOT » EXPERIMENT

� NUMERICAL SIMULATIONS OF THE DISK-SPOT

EXPERIMENT

� PERSPECTIVES


3

INTRODUCTION

� FRAMEWORK OF THIS STUDY

Design of Very High Temperature Reactors of the future using gas coolant

nominal temperature: 450°C => martensitic steel

Numerical welding simulation

Initial state after welding

(microstructure, distorsions, residual stresses, defects, …)

Failure assessment of welds


4

INTRODUCTION

� NUMERICAL SIMULATION OF TIG WELDING

� TIG torch model

(heat, plasma, metal deposit,…)

� Thermo-metallo-mechanical model

for materials

� Coupled heat-transfert, metallurgical

and mechanical analyses

(CAST3M welding finite element simulation

with an element deposit technique)


5

INTRODUCTION

� OBJECTIVES OF THIS PRESENTATION

TIG torchwithout filler material

Heat source

Identification/validation on a simple experiment

Thermo-metallo (mechanical) model for base material

Coupled heat transfert and

metallurgical analysis


6

MICROSTRUCTURAL CHANGES IN T91 STEELS

� CHEMICAL COMPOSITION: X10CrMoVNb 9-1

0.0040.0750.2010.0030.0060.0070.0020.0110.0540.9518.3050.130.2160.4050.099% wt

TiNbVAsSnPSAlCuMoCrNiSiMnC

� Fe-0.1wt%C/Cr EQUILIBRIUM PSEUDO BINARY DIAGRAM:

α ferrite and M23C6 carbides

γ austenite and M23C6 carbides

γ austenite

γ austenite and δ ferrite

γ austenite, δ ferrite and L

Liquid

8 %

Fe-0.1wt % C

A1

A3

Tm


7


� SOME EFFECTS OF ALLOYING ELEMENTS:

Chromium equivalent factor by Ezaki:

CrCrequivalentequivalent = %Cr + 6.%Si + 4.%Mo + 1.5.%W + 11.%V + 5.%Nb + 12.%AL += %Cr + 6.%Si + 4.%Mo + 1.5.%W + 11.%V + 5.%Nb + 12.%AL +

8.%Ti 8.%Ti –– 40.%C 40.%C –– 2.%Mn 2.%Mn –– 4.%Ni 4.%Ni –– 2.%Co 2.%Co –– 30.%N 30.%N -- %Cu%Cu

= 10.811 > 8 => Presence of δ-ferrite

� CARBIDES PRECIPITATION:

In majority : M23C6

Others : M2X

MX

M7C3

…

Number and surface evolution of particules in fonction of

temperature

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

790 810 830 850 870 890 910 930 950 970 990

Température (°C)

num

bers

of partic

ule

s b

y s

urface

(nbr/µm

²)

-0,1

0,1

0,3

0,5

0,7

0,9

1,1

1,3

1,5

surfa

cic

facto

r(%)

by numberby surface

[Duthilleul et al. 2003]

Phase change


8


� THERMAL COMPLEX LOADING INDUCED BY MULTIPASS WELDING:

multipass welding

time

AC1

AC3

Tm

time

AC1

AC3

Tm

Multi-austenitisation

Reheating of quenched martensite


9


� NON-EQUILIBRIUM TRANSFORMATIONS ON HEATING:

840

860

880

900

920

940

0,1 1 10 100 1000 10000

t(s)

Te

mp

era

ture

(°C

)

AC 3

AC 1

AC 5 0


50°C/s 0,1°C/s


10


16500 / 11000 /C h T C h•

° > > °

� NON-EQUILIBRIUM TRANSFORMATIONS ON COOLING:


Welding process:


11


� REHEATING OF QUENCHED MARTENSITE :

Microstructural change of quenched martensite

and carbide precipitation

=> modification of mechanical properties.

[Hong et al. 2001]

Martensite obtained by quenching

after austenisation at 1050°C

Tempered at 700°C Tempered at 750°C Tempered at 800°C


12

SIMULATION OF THE THERMO-METALLURGICAL BEHAVIOUR OF T91 STEELS

� CONSIDERED TRANSFORMATIONS :

� Tempered martensite (material initial state)→ austenite

� (Austenite ↔ δ ferrite)

� Solid ↔ liquid

� Austenite → quenched martensite

� (quenched martensite → tempered martensite)


13


( )CB

y T =CA

0

20

40

60

80

100

120

800 850 900 950 1000

temperature (°C)

au

ste

nit

e p

rop

ort

ion

(%

) dT/dt=0,1K/s

dT/dt=0,2K/s

dT/dt=0,5K/s

dT/dt=1K/s

dT/dt=5K/s

dT/dt=10K/s

dT/dt=50K/s

dT/dt=100K/s

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

840 850 860 870 880

Temperature (°C)

au

ste

nit

e p

rop

ort

ion

(%

)

� AUSTENITIC TRANSFORMATION ON HEATING:

� experimental evidence

T

εth

C

A

B

dilatometric curve

equilibrium curve

1

3

( ) ( , ) ( , ) expeq

ET y T y T C T T y T

RT

• • • = −

Zhu and Devletian extrapolation:


14


0

0 0( )m

eq eqy T = 1- exp(-(K (T - A )) )

� model

T

t

Aeq0

AC1

AC3[T(t)]eq

T(t)

y

T

10

T(t)

[T(t)]eq

Equilibrium transformation (J.M.A. law)

Non equilibrium transformation [Brachet 1998]

incubationincubation

growthgrowth

1( )n

eq

dy (T,t) E= Kexp - T y A (1- y )

dt RT(t)

γ

γ γ+

−


15


0

1( )

eq

t

it

dT dt

t T dT=∫

1

0

i sat

eq

Ct (T)= A(A -T)exp

T - A

� incubation law

Extension of additivity Scheil rule to heating:

T

t

Ti

Aeq0

AC1

∆tit

isothermalisothermal

AC1

ti

A1sat

T

T(t)

NonNon--isothermalisothermalincubation

Phenomenological model:

1( )

i

i i

t

t T

∆=∑


16


� identification

Inverse identification with Matlab©

(Aeq0, Ko and mo), (A, A1sat and C) and (K, W and n)

equilibrium incubation growth

First order Runge-Kutta scheme with ∆tstep=1°C:

0

10

20

30

40

50

60

70

80

90

100

800 850 900 950 1000

Temperature (°C)

au

ste

nit

e f

rac

tio

n (

%) Equilibre (Zhu&Devletian)

V=0,1°C/s (Experimental)

V=1°C/s (Experimental)

V=100°C/s (Expérimental)

Equilibre (Simulation)

V=0,1°C/s (Simulation)

V=1°C/s (Simulation)

V=100°C/s (Simulation)


17


m 0 m Sy (T)= y (1- exp(-K (M -T)))γ

� MARTENSITIC TRANSFORMATION :

Koistinen-Marburger model:

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 20 40 60 80 100 120 140

Ms - T (°C)

Ma

rte

ns

ite

fra

cti

on


18

IDENTIFICATION OF THERMAL BOUNDARY CONDITIONS DURING A « DISK-SPOT » EXPERIMENT

� DISK-SPOT SIMPLE TIG WELDING TEST :

8mmR=50mm

ThermocouplesDisplacement sensors

Ceramic supports

experimental set up at DRT/UTIAC

TIG torch

back

DEP1

DEP2

DEP3

DEP4DEP5

2.4 mm tungsten

electrode (with 2% TH)

12 or 16 mm

10 mm

30°


19


� TEMPERATURE RESULTS :

TC1 TC3TC2

TC4

TC6 TC5

0

200

400

600

800

1000

0 500 1000 1500 2000time (s)

tem

pera

ture

(°C

)

TC1

TC2

TC3

TC4

TC5

TC6

50 mm8 mm

Aeq0

MS


20


Vertical displacements

-0,12

-0,10

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,00E+00 1,00E+04 2,00E+04 3,00E+04

time (s)

dis

pla

ce

me

nt

(mm

)

DEP2

DEP3

DEP4

DEP5

DEP1

� DISPLACEMENT RESULTS :

DEP6

DEP7 DEP8

disk

DEP1DEP2DEP3

DEP4

DEP4

Radial displacements

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18

0 5000 10000 15000 20000 25000 30000 35000

time (s)

dis

pla

ce

me

nt

(mm

)

DEP6

DEP7

DEP8


21

2

2

r3

SP =Qe ro−

� BOUNDARIES CONDITIONS TO IDENTIFY :

� Heat source parameters

� Convection and radiation

Infinite Gaussian heat source:

Convection/radiation model:

( )v extq h T T= − −

Snord

Ssud

rmax

0 < r < rmax

h=h(T) on Snord and Ssud


Hypothesis:

Low uncertainties on ρ, Cp and λ


22

� IDENTIFICATION OF h(T) FOR LOW TEMPERATURES :

� Experiment

T0=800°C

Initial state

Oven heated disk

Air cooling

TC1(T) TC3(T)

TC5(T)TC6(T)

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300

time (s)

tem

pera

ture

(°C

) TC1 exp

TC3 exp

TC5 exp

TC6 exp



23

� Inverse identification

0

10

20

30

40

50

60

0 200 400 600 800

temperature (°C)

h (

W/m

²)

Results:

h(T)

[T(t)]exp vs [T(t)]sim



24

� Presentation of the new experimental protocol

Two different experiments with same h(T) => convex problem

Torch 1

16 mm

Temperatures for experiment 1 Q1, r1,

Q2,r2,

h(1400°C)

Q1, r1

Torch 2

12 mm

Temperatures for experiment 2

Q2, r2



0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400 1600

Temperature (°C)

h (

W/m

²)

Results:

Q1=865.65 W

r1=1.09E-03 m

Q2=816.42 W

r2=3.959E-03 m



25

� Comparaison between experimentations and simulations

Torch 1

0

200

400

600

800

1000

0 100 200 300time (s)

tem

pp

ratu

re (

°C)

TC1 exp

TC1 sim

TC2 exp

TC2 sim

TC4 exp

TC4 sim

TC5 exp

TC5 sim

TC6 exp

TC6 sim



26

Torch 2

0

200

400

600

800

1000

1200

0 100 200 300

time (s)

tem

pera

ture

(°C

)

TC1 exp

TC1 sim

TC2 exp

TC2 sim

TC4 exp

TC4 sim

TC5 exp

TC5 sim

TC6 exp

TC6 sim



27

0 0.005 0.01 0.015 0.020

50

100

150

200

25

30

35

40

45

h (W

/m²)

r1 (m)

cri

teri

on

(°C

)� Verification of the critererion’s convexity

In the {r1,h} plane In the {Q1,r2} plane

400600

8001000 0

0.01

0.02

30

40

50

60

70

80

90

r2 (m)

Q1 (W)

cri

teri

on

(°C

)



28

NUMERICAL SIMULATIONS OF THE DISK-SPOT EXPERIMENT

� CAST3M MESH

� THERMAL PROPERTIES

� thermal

conductivity

20

22

24

26

28

30

32

0 200 400 600 800 1000 1200 1400 1600

temperature (°C)

conductivity (W

/m/K

)

4 – node

linear element


29

300

400

500

600

700

800

900

1000

0 200 400 600 800 1000 1200 1400 1600

temperature

Cp

(J

/m3

)

� specific

heat

� specific mass

7000

7100

7200

7300

7400

7500

7600

7700

7800

0 200 400 600 800 1000 1200 1400 1600

temperature (°C)

Weig

ht

by v

olu

me (

Kg

/m3)



30

� SIMULATIONS FOR TORCH 1 DISK-SPOT EXPERIMENT

� Temperatures (at the end of heating)

t (s)

Q

0 75



31

� Phases

Austenite

Tempered martensite

t (s)

Q

0 75



32

Quenched martensite

Tempered martensite

t (s)

Q

0 75


300


33

� Comparison between experiment and simulation


Models to be improved:

• Austenite ↔ δ ferrite

• Solid ↔ liquid

• Grain growth

Fine grains

Larger grains


34

� Macrographies


Molten zone

δ-ferrite zone

ZAT 1ZAT 2

Base metal


35

PERSPECTIVES

� VALIDATION OF THERMO-METALLURGICAL MODEL

FOR NON CONSTANT ANISOTHERMAL LOADING

� γ GRAIN GROWTH MODEL

� THERMO-MECHANICAL BEHAVIOUR

� MULTIPASS SIMPLE TEST

DISK-CYCLE experiment:

T•

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