Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
Document: V7.22.101
HSNV101 - Thermo- plasticity and metallurgy
uncoupled in simple traction
Summary:
One treats the determination of the mechanical evolution of a cylindrical bar subjected to thermal evolutions
T T
() and metallurgical Z T () known and uniform (the metallurgical transformation is of bainitic type).
The elements used are axisymmetric elements and the relation of behavior is the plasticity of
von Mises with linear isotropic work hardening (for modeling B, one also takes account of plasticity
of transformation).
The yield stress and the slope of the traction diagram depend on the temperature and the composition
metallurgical.
The dilation coefficient depends on the metallurgical composition.
The metallurgical transformations take place with! p = 0 (it is in the sense that the test uncouples plasticity from
transformation of traditional plasticity).
The results provided by Code_Aster are very satisfactory with errors lower than 2%.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
2/8
1
Problem of reference
1.1 Geometry
Z
Radius: = 0.05 Mr. has.
Height: H = 0.2 Mr.
P
C
D
H
R
With
B
has
1.2
Properties of materials
T
6
E T
E
aust
aust
= 200000.10 Pa
=
+ saust
O
y
O
(T - T) let us note H (T) () ()
= E (T) - (T)
aust
= 0.3
= 400. 106 Pa
H aust = Haust
aust
O
O
O
+
(T - T)
=
- 6
-
15. 10
° C 1
saust =
6
-
0.5 10 Pa. ° C 1
H aust
6
fbm
O
= 1250 10 Pa
- 6
- 1
fbm
fbm
= 23.5 10 ° C
=
+ S fbm
O
aust
6
- 1
aust
y
O
(T - T) = 5 10 Pa.°C
- 3
fbm
= 2.52 10
= 530. 106 Pa
H fbm = H fbm
fbm
+
(O
T - T)
ref.
O
O
fbm
ref.
T
=
°
900 C
fbm
6
- 1
fbm
S
= 0.5 10 Pa.° C
H
6
O
= - 50 10 Pa
- 3
- 1
- 1
- 1
fbm
CP = 2.000.000 J.m ° C
= 9999.9 W.m ° C
= - 5.106 P a° -
C 1
m
K =
- 10
- 1
1. 10
Pa
* aust
=
characteristics relating to the austenitic phase
* fbm
=
characteristics relating to the phases ferritic, bainitic and martensitic
fbm
=
thermal dilation coefficient of the phases ferritic, bainitic and martensitic
aust
=
dilation coefficient of the austenitic phase
ref.
=
deformation of the phases ferritic, bainitic and martensitic at the temperature of reference,
fbm
austenite being regarded as not deformed at this temperature: translated the difference
of compactness enters the cubic crystallographic structures to centered faces (austenite) and
cubic centered (ferrite).
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
3/8
TRC to model a metallurgical evolution of bainitic type, on all the structure, of the form:
0.
if T1
1 = 60 S
T -
Z
1
fbm
=
if
1 T < 2
2 = 112 S
2 - 1
if T
1.
2
Law of plasticity of transformation: ! Pt
fbm
= K
F (Z fbm)!Z fbm
with F Z
()
(
)
fbm = Z fbm 2 - Z fbm
1.3
Boundary conditions and loadings
·
uZ = 0 on side AB (condition of symmetry).
p
O T
for T
p
p T
() =
1
O = 6.106 Pa
for T
·
360.106 Pa
traction imposed on the side CD,
1
1 = 60 S
.
·
T
T O
=
+ µt, µ = - 5°C.s-1 on all the structure.
1.4 Conditions
initial
T O = 900°C = Tref
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
4/8
2
Reference solution
2.1
Method of calculation used for the reference solution
Before transformation, elastic solution for T < 1.
(
T
()
T) = p
E
HT
O T
zz T () = zz T () + zz T () =
+
E
aust T - T O
(
)
aust
The yield stress is reached for '
O
1
=
= 47.06 S.
Po - saust × µ
Before transformation, elastoplastic thermo solution, '1 T1, 1 = 60 S.
(T) = p
E
HT
p ()
O T
zz T () = zz T () + zz T () + T
zz
E
T ()
HT
zz T
() =
T () = Z
E
zz
aust × aust T - T O
(
)
T () - aust + Saustµ T
(
)
p
y
zz T
() =
Haust
O
+ austµ T
During the transformation, élasto-metallurgical thermo solution, 1 < T < 2, 2 = 112 S.
(T) = 360.106 Pa
E
HT
Pt
p
zz (T)
= zz T () + zz T () + T
60
zz () + zz (
)
thzz T () = Zaust × aust T - To
(
) + Zfbm ×fbm T - To
(
) +Zfbm ×reffbm
p
()
zz T
() = K fbmF Zfbm Po1
After the transformation, elastoplastic thermo solution, 2 < T < 3, 3 = 176 S.
(T) =
6
E
HT
p
Pt
360 10 Pa
zz (T) = zz T () + zz T () + zz T () + zz 112
()
T () - fbm
(+ sfbmµt)
p
O
zz T
() =
H fbm + fbmµ
O
T
2.2
Results of reference
pzz, and zz for T = 47, 48, 64 and 114 seconds.
pzz for T = 60 and 176 seconds.
2.3 Bibliography
[1]
DONORE A.M. - WAECKEL F.: Influence structure transformations in the laws of
behavior elastoplastic Note HI-74/93/024.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
5/8
3 Modeling
With
3.1
Characteristics of modeling
y
C
D
N13
N11
N12
N9
N10
N7
N6
N8
N1
N3
N4
N2
N5
With
B
WITH = N4, B = N5, C = N13, D = N12.
3.2
Characteristics of the grid
A number of nodes: 13
A number of meshs and types: 2 meshs QUAD8, 6 meshs SEG3
3.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
META_THER
[U4.23.01]
THER_LINEAIRE
OPTION
META_ELGA_TEMP
[U4.23.05]
DEFI_MATERIAU
META_MECA_FO
[U4.23.01]
STAT_NON_LINE
COMP_INCR
RELATION
META_EP
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.01]
RECU_CHAMP
NOM_CHAM
VARI_ELNO_ELGA
[U4.62.01]
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
6/8
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
pzz T = 47 S
0
0
0
T = 47 S
0
0
0
T = 47 S
282. 106
282. 106
0
zz T = 47 S
4.1125 103
4.1125 103
0
pzz T = 48 S
3.2653 103
3.26537 103
0.011
T = 48 S
1
1
0
T = 48 S
288. 106
288. 106
0
zz T = 48 S
9.3469 104
9.34645 104
0.005
pzz T = 60 S
0.04
0.04
0
pzz T = 64 S
0.040
4.0 10-2
0
T = 64 S
0
0
0
T = 64 S
360. 106
360. 106
0
zz T = 64 S
3.4683 102
3.46908 102
0.023
pzz T = 114 S
0.04107
4.10688 102
+0.004
T = 114 S
1
1
0
T = 114 S
360. 106
360. 106
0
zz T = 114 S
0.03684
3.68407 102
0
pzz T = 176 S
0.06206
6.20680 102
0.000
4.2 Remarks
In this modeling:
Pt (
)
zz T, Z
= 0
4.3 Parameters
of execution
Version: 4.02.14
Machine: CRAY C90
Obstruction memory:
8 megawords
Time CPU To use:
109.3 seconds
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
7/8
5 Modeling
B
5.1
Characteristics of modeling
y
C
D
N13
N11
N12
N9
N10
N7
N6
N8
N1
N3
N4
N2
N5
With
B
WITH = N4, B = N5, C = N13, D = N12.
5.2
Characteristics of the grid
A number of nodes: 13
A number of meshs and types: 2 meshs QUAD8, 6 meshs SEG3
5.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
META_THER
[U4.23.01]
THER_LINEAIRE
OPTION
META_ELGA_TEMP
[U4.23.05]
DEFI_MATERIAU
META_MECA_FO
[U4.23.01]
META_PT
STAT_NON_LINE
COMP_INCR
RELATION
META_EP_PT
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.01]
RECU_CHAMP
NOM_CHAM
VARI_ELNO_ELGA
[U4.62.01]
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV101 - Thermo- plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B Page:
8/8
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
pzz T = 47 S
0
0
0
T = 47 S
0
0
0
T = 47 S
282. 106
282. 106
0
zz T = 47 S
4.1125 103
4.1125 103
0
pzz T = 48 S
3.2653 103
3.26535 103
0.011
T = 48 S
1
1
0
T = 48 S
288. 106
288. 106
0
zz T = 48 S
9.3469 104
9.34644 104
0.005
pzz T = 60 S
0.04
0.04
0
pzz T = 64 S
0.04
4.0 102
0
T = 64 S
0
0
0
T = 64 S
360. 106
359.99 106
0.004
zz T = 64 S
4.00085 102
4.000268 102
0.015
pzz T = 114 S
0.041071
4.10751 102
+0.004
T = 114 S
1
1
0
T = 114 S
360. 106
360.01 106
0.000
zz T = 114 S
0.072841
7.144112 102
1.915
pzz T = 176 S
0.06206
6.2066 102
0.000
6.2 Remarks
In this modeling, one takes into account the term due to the plasticity of transformation:
!Pt (T, Z) 0
when!
Z 0
6.3 Parameters
of execution
Version: 4.02.14
Machine: CRAY C90
Obstruction memory:
8 megawords
Time CPU To use:
114.11 seconds
7
Summary of the results
The results found with Code_Aster are very satisfactory, with percentages of error
lower than 0.025% except for the deformation at moment 114 S where the error reaches 2% for modeling
B.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Outline document