Club Cast3M 2010
Prediction of (residual stresses and) microstructural state
after multi-pass GTA-Welding
of X10CrMoVNb9-1 martensitic steel
Farah Hanna*,***, Guilhem Roux**
Olivier Asserin*, René Billardon***
* CEA, DEN, DM2S, SEMT, LTA, 91191 Gif sur Yvette, France.
** CEA, DRT, LITEN, DTBH, LCTA, 38054 Grenoble, France.
*** LMT-Cachan, ENS de Cachan/CNRS/UPMC (University Paris 6), 94235 Cachan, France.
Industrial background and motivations
-Thick forged components
assembled by multipass GTAWelding
- Martensitic steel X10CrMoVNb9-1
a possible candidate for
Very High Temperature Reactors
- Numerical simulation of welding process
MUSICA test case
Numerical simulation of
multi-pass GTAWelding
Initial state after welding
(microstructure, residual stresses,…)
2
X10CrMoVNb9-1 steel - Phase changes
Pseudo-binary equilibrium diagram
Continuous Cooling diagram
Fe-Cr à 0.1% wt C [Easterling, 1992]
"T91" [Duthilleul, 2003]
During heating (1st pass)
Base material (tempered martensite) → Austenite → δ Ferrite → Liquid
During cooling
Liquid → δ Ferrite → Austenite → Quenched martensite
[Roux 2007]
[Roux 2006]
[Hanna 2009]
During subsequent heating (2nd and following passes)
[Hanna 2010]
Quenched martensite → Tempered martensite → Austenite → …
3
Martensite tempering
Heat treatments
Tempered @ 500°C
for 6 min.
Tempered @ 500°C
for 1h
Martensite tempering → Carbides precipitation
Tempered @ 750°C
for 5h30
4
Measurement of carbides precipitation
Indirect measurement of carbides precipitation
through the percentage of free carbon in the matrix
by Thermo-Electric Power measurements (Seebeck effect)
Specimen
Hot junction
Sspecimen  Sref 
Cold junction
V (chemical composition)
T
5
Measurement of carbides precipitation
TEP measurements after different tempering heat treatments (TT , tT )
TEPQ = 10.78
TEPAR = 11.49
Precipitation evolution Tempering evolution
TEPQ = 10.78
TEPAR = 11.49
Definition of the
“tempering factor”
xT 
TEP  TEPQ
TEPAR  TEPQ
6
Modelling of martensite tempering
Fick law
J   D grad C
C
1D

 J  D
x
Conservation law
C
C
J
1D
 div J 


t
t
x
Isothermal case
r+h
x  Dt
Temperature dependence of the diffusion coefficient and generalisation

 H  
x   D0 exp  
 t
 RT  

1
n


x
 H  1 n
1
D0 exp  
x
n
 RT 
Proposed evolution law for tempering factor xT
xT 
 H  1 n
1
D 0 exp  
1  x T H T  TTTh 
 xT
n
 RT 


7
Identification of tempering model
xT 
 H  1n
1
D0 exp  
 xT 1  xT  H (T  TTTh )
n
 RT 
D0  2.41013
H  278.2 KJ/mol
n  3.61
•coherent with Cr bulk diffusion and carbides growth-coalescence
•not applicable to tempering at T < 475°C (with long holding times)
(secondary ageing, embrittlement)
8
Hardness vs. tempering factor
 x 1 
HVTM  HVQ   HVQ  HVAR  exp  T

x
 0 
HVAR  185
HVQ  513
x0  0.374
9
Modelling the thermo-metallurgical-mechanical behaviour
(Phase changes enthalpies)
Phase changes
Thermal
Standard anisothermal mechanical
behaviour for each phase
MODEL
Metallurgical
Mechanical
Multiphasic behavior
UMAT formalism integration
Lois Castem
CHAB_NOR_R
CHAB_NOR_X
CHAB_SINH_R
CHAB_SINH_X
explicit integration
10
Modelling the multiphasic behaviour
Two scale mixing mechanical law:
•Reuss approach
 11
 11
11(1)
•Voigt approach
[Goth 2002]
 11
  x(1)C(11)  x(2)C(21) 
11( 2)
11
 11(1)
 11( 2)
 11
  x(1)C(1)   x( 2)C( 2) 
•Hill & Berveiller-Zaoui type approach [Cailletaud, 87] [Pilvin, 90]
Intergranular accommodation variables
[Robert 2007] for welding
11
Modelling the multiphasic behaviour
•Hill & Berveiller-Zaoui type approach [Cailletaud, 87] [Pilvin, 90]
Intergranular accommodation variables
[Robert 2007] for welding
TRIP (Transformation Induced Plasticity):
[Hamata 1992]
[Roux 2007]
[Coret 2001]
12
Mechanical behaviour of each phase
Anisotropic elastoviscoplastic mechanical behaviour
Norton Law
Isotropic hardening
avec
Linear and non-linear Kinematic
hardening
avec
Tempering martensite (reception state)
essais de viscosité en phase martensitique revenue
700
800
600
600
T=20°C
T=400°C
400
500
T=500°C
T=20°C
T=400°C
400
F/So (MPa)
F/So (MPa)
essais de viscosité en phase martensitique revenue
T=500°C
T=700°C
300
T=900°C
T=1000°C
200
T=700°C
200
T=900°C
T=1000°C
0
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
-200
-400
100
-600
0
0
0.01
0.02
0.03
0.04
dL/Lo
0.05
0.06
0.07
0.08
-800
dL/Lo
13
Mechanical behaviour of each phase
Quenched martensite
essais de viscosité en phase martensitique trempée
essais de viscosité en phase martensitique trempée
1200
1500
1000
1000
T=20°C
T=200°C
500
F/So (MPa)
F/So (MPa)
800
600
T=20°C
400
T=300°C
T=400°C
0
-0.05
-0.04
-0.03
-0.02
T=200°C
-0.01
0
0.01
0.02
0.03
0.04
0.05
-500
T=300°C
T=400°C
200
-1000
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-1500
dL/Lo
dL/Lo
Tempering occurs for T> 400°C
Austenite
essais de viscosité en phase austénitique
essais de viscosité en phase austénitique
450
40
400
35
T=200°C
350
T=300°C
30
T=400°C
T=1000°C
T=500°C
T=600°C
250
T=700°C
T=800°C
200
T=900°C
T=1200°C
T=1300°C
20
T=1500°C
15
T=1000°C
150
T=1100°C
25
F/So (MPa)
F/S (MPa)
300
10
100
5
50
0
0
0
0.01
0.02
0.03
0.04
dL/Lo
0.05
0.06
0.07
0.08
0
0.01
No kinematic hardening
0.02
0.03
0.04
dL/Lo
0.05
0.06
0.07
0.08
14
Mixing tempered and quenched martensites
Experimental procedure
Model for quenched
+
tempered martensite
experiments at xt=0.6 (500°C)
+
essai à 300°C
1200
contrainte (MPa)
1000
800
linear evolution for simulations
600
400
•Tempering has a softening effect on elasticity and isotropic hardening
martensite
martensite revenue
50%-50%
MT=20%-MB=80%
200
•No dependance of temperature on mixing evolution
MT=80%-MB=20%
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
•Linear dependance of mechanical parameters with tempering state ([Inoue 85]
approach)
0.08
dL/Lo
15
Mixing austenite and quenched martensite
essai à 300°C
1200
1000
contrainte (MPa)
βeta model:
800
600
400
200
martensite
austénite
0
0
0.01
0.02
0.03
0.04 50%-50%
0.05
0.06
MT=20%-AU=80%
dL/Lo
MT=80%-AU=20%
Reuss approach:
0.08
Voigt approach:
essai à 300°C
essai à 300°C
1200
1200
1000
1000
martensite
800
austénite
50%-50%
MT=20%-AU=80%
MT=80%-AU=20%
600
400
200
contrainte (MPa)
contrainte (MPa)
0.07
martensite
800
austénite
50%-50%
MT=20%-AU=80%
MT=80%-AU=20%
600
400
200
0
0
0
0.01
0.02
0.03
0.04
dL/Lo
0.05
0.06
0.07
0.08
0
0.01
0.02
0.03
0.04
dL/Lo
0.05
0.06
0.07
0.08
16
Simulation of dilatometry tests
Free dilatometry curve:
TRIP experiments:
0.015
0.01
0.005
0MPa
100MPa
0
50MPa
0
200
400
600
800
1000
25MPa
1200
-25MPa
-0.005
-50MPa
100MPa
-0.01
17
Simulation of Satoh experiment
T
Coupling between hardening of
mother and daughter phases and
TRIP
[Petit-Grotabussiat 2000]
for 16MND5 alloy
modele serie
500
modele en B
400
modele parallele
300
contrainte (MPa)
Overestimation of
TRIP effect
600
experimental cycle n°1
200
100
0
-100 0
200
400
600
800
1000
1200
1400
-200
-300
-400
-500
No plasticity of quenched martensite phase
temperature (°C)
Very low influence of homogenization rule
18
Simulation of Disk Spot experiment
Experimental set-up : [Cavallo 1998] [Cano 1999]
torche TIG
R=50mm
capteurs de déplacement
8mm
thermocouples
Test at DEN/DM2S/SEMT/LTA
Inverse analysis identification of
heat source intensity and spatial
distribution
[Roux 2006]
19
Simulation of Disk Spot experiment
Prediction of
final metallurgical state:
δ -ferrite
Residual stresses on upper surface (X ray diffraction measurements):
450
450
experimental RX residual stresses
350
simulated residual stresses for Beta
model
250
simulated residual stresses for Reuss
approach
simulated residual stresses for Voigt
approach
150
50
-50
5
10
15
20
25
30
35
40
45
50
-150
Experimental residual stresses for
Beta model
simulated residual stresses for Beta
model
simulated residual stresses for Reuss
approach
simulated residual stresses forVoigt
approach
250
150
50
-50
5
10
15
20
25
30
35
40
45
50
-150
-250
-350
Tangential residual stresses (MPa)
Radial residual stresses (MPa)
350
-250
Distance from disk center (mm)
Radial shift (bad HAZ prediction?)
Distance from disk center (mm)
20
Simulation of Disk Spot experiment
Residual stresses on upper surface (X ray diffraction measurements):
500
500
Experimental residual stesses
400
simulated residual stresses for
Beta model
simulated residual stresses for
Reuss approach
simulated residual stresses for
Voigt approach
300
200
100
0
0
5
10
15
20
25
30
35
-100
-200
-300
40
45
50
Tangential residual stresses (MPa)
Radial residual stresses (MPa)
400
Experimental residual stresses
300
simulated residual stresses for
Beta model
simulated residual stresses for
Reuss approach
simulated residual stresses for
Voigt model
200
100
0
0
5
10
15
20
25
30
35
40
45
50
-100
-200
Distance from disk center (mm)
-300
Distance from disk center (mm)
Again overestimation of TRIP effect
Similar stress distribution with Beta model and Voigt Approach
21
Simulation of Disk Spot experiment
Residual stresses on half thickness (Neutron diffraction measurements):
800
600
400
simulated residual stresses for
Beta model
simulated residual stresses for
Reuss approach
300
simulated residual stresses for
Voigt approach
200
100
0
5
10
15
20
400
25
30
35
40
45
50
Tangential residual stresses (MPa)
Experimental residual stresses
Experimental residual stresses
500
simulated residual stresses for
Beta model
400
simulated residual stresses for
Reuss approach
300
simulated residual stresses for
Voigt approach
200
100
0
5
10
15
20
25
30
35
40
45
50
-200
Experimental residual stresses
-300
300
-200
600
-100
-100
Normal residual stresses (MPa)
Radial residual stresses (MPa)
700
500
Distance from disk center (mm)
Distance from disk center (mm)
simulated residual stresses for
Beta model
200
simulated residual stresses for
Reuss approach
simulated residual stresses for
Voigt approach
100
0
5
10
15
20
25
30
35
40
45
50
-100
-200
Distance from disk center (mm)
22
Multipass MUSICA experiment
Experimental set-up at DEN/DM2S/SEMT/LTA
TIG multipass welding
TC3
TC2
TC1
Temperature measurements
Inverse identification of heat source
for each pass [Hanna 2006]
23
Multipass MUSICA experiment
Quenched martensite
Prediction of final metallurgical
state:
Strong tempering effect
of previous passes
Without tempering
1
With tempering
vertical displacement (mm)
0.5
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Vertical distorsion
-0.5
w ith tempering
-1
w ithout tempering
-1.5
-2
-2.5
tim e (s)
24
Multipass MUSICA experiment
Residual stresses:
Sxx
Syy
With tempering
Without tempering
Szz
25
Conclusion & perspectives
•Differential model has been developed to model phase change
During cooling : - martensite transformation
During heating : - austenitization of quenched and tempered martensites
Not presented here - tempering of martensite
•This thermometallurgical model allows for the prediction of hardness profiles
through welds by simple post-processing of heat transfer analyses
•This thermometallurgical model has been coupled to elasto-viscoplastic
constitutive equations identified for each metallurgical phase
•A simple homogenization approach has been used associated to martensitic
transformation
•This model could be applied for bainitic transformation
(case of the 16MnD5 steel)
•This thermometallurgical mechanical model has been implemented in Cast3M and
validated in terms of residual stresses prediction for welding experiments
26