Code_Aster ®
Version
4.0
Titrate:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V7.22 booklet: Thermomechanical statics nonlinear of the voluminal structures
Document: V7.22.102
HSNV102 - Thermo- metal-worker-plasticity coupled in
simple traction
Summary:
One treats the determination of the mechanical evolution of a cylindrical bar subjected to evolutions thermics
T T
() and metallurgical Z T () known and uniform (the metallurgical transformation is of martensitic type).
The elements used are axisymmetric elements and the relation of behavior is plasticity of
von Mises with isotropic work hardening (for modeling B, one also takes account of the 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 couples the plasticity of
transformation of traditional plasticity).
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
2/8
1
Problem of reference
1.1 Geometry
Z
C
D
Radius: = 0.05 Mr. has.
H
Height: H = 0.2 Mr.
R
With
B
has
1.2
Properties of materials
T
6
E T
E
aust
aust
= 200 000.10 Pa
=
+ saust
O
y
O
(T - T) let us note H (T) () ()
= E (T) - (T)
aust
= 0.3
= 50. 106 Pa
Haust = Haust
aust
O
O
O
+
(T - T)
=
- 6
-
15. 10
° C 1
saust =
6
-
1.3 10 Pa.° C 1
Haust
fbm
O
= 0 Pa
- 6
- 1
fbm
fbm
= 23.5 10 ° C
=
+ S fbm
O
aust
6
- 1
aust
y
O
(T - T) = 1 10 Pa.°C
- 3
fbm
= 2.52 10
= 50. 106 Pa
H fbm = H fbm
fbm (
O
T - T)
ref.
O
O
+
fbm
fbm
6
- 1
fbm
S
= 1. 10 Pa.° C
Ho
= 0
- 3
- 1
- 1
- 1
fbm
CP = 2.000.000 J.m ° C
= 9999.9 W.m ° C
= - 6. 106
Pa ° -
C 1
F
B
m
K = 0 K
= K =
- 10
-
1. 10
Pa 1
Note:
The indices or exponents fbm relate to the parameters materials of the phases
ferrito-perlitic, bainitic and martensitic and the indices or exponents aust relate to
austenite.
TRC to model a metallurgical evolution of martensitic type of the form:
0.
if T
1
1 = 25 S
1
- E T (- 1) if
1 T < 2
2 = 40 S
= 0.03 = - 10°C.s-1
1.
if T 2
1.3
Boundary conditions and loadings
·
uZ = 0 on side AB (condition of symmetry).
· traction imposed on the side CD, (
p T) = p T
O
, Po = 15.106 Pa.
·
T
T O
=
+ µt, µ = 10°C.s1 on all the structure.
1.4 Conditions
initial
T O = 900°C.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
Before transformation, elastic thermo solution for T < 1 (not of transformation metallurgical
!Z = 0).
(T) = Po T
E
HT
T ()
zz T
() = zz T () + zz T () =
+
E
aust T - T O
(
)
aust
The yield stress is reached for
O
1
=
= 25 S.
Po - saust × K
During the transformation, solution thermo metal-worker-élasto-plastic, for 1 < T < 2 with
2 = 40 S.
(T) = Po T
E
HT
p ()
Pt
zz T
() = zz T () + zz T () + T + T ()
zz
zz
E
T ()
zz T
() =
E
HT
[
]
zz T
() = Zaust × aust T - To
(
) + Zfbm × fbm T - To
(
) + reffbm
T () - Z
aust T
() + Z
fbm
(
)
p
aust × y
fbm ×
T
() =
y T
()
Zaust × Haust T
() + Zfbm × H fbm T
()
Pt
K
K
T
() = K
(
) 2
m × Po × 1 -
- K
1 - Z
2 × ×
m × Po × T -
2 × ×
After transformation, elastoplastic thermo solution, for T > 2
(T) = Po T
E
HT
p
zz T
() = zz T () + zz T () + (T)
zz
2.2
Results of reference
, zz, p, to 24 S, 26 S, 40 S and 90 S.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
4/8
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_REFR
[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:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
5/8
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
p T = 24 S
0
0
-
T = 24 S
0
0
-
T = 24 S
360. 106
360. 106
0
zz T = 24 S
3.84 10-3
3.84 10-3
0
p T = 26 S
0.0372
3.7217 10-2
0.047
T = 26 S
1
1
0
T = 26 S
390. 106
390. 106
0
zz T = 26 S
3.428 10-2
3.4283 10-2
p T = 40 S
0.0625
6.2523 10-2
0.038
T = 40 S
1
1
0
T = 40 S
600. 106
600. 106
0
zz T = 40 S
0.06198
6.1977 10-2
0.068
p T = 90 S
0.0741
7.4146 10-2
0.062
T = 90 S
1
1
0
T = 90 S
1350. 106
1350. 106
0
zz T = 90 S
0.069844
6.9854 10-2
0.014
4.2 Remarks
In this modeling:
Pt T
(, Z) = 0
4.3 Parameters
of execution
Version: 4.00.06
Machine: CRAY C90
System: 8.0
UNICOS
Obstruction memory:
8 megawords
Time CPU To use:
42.47 seconds
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
6/8
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_REFR
[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:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
7/8
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
p T = 24 S
0
0
-
T = 24 S
0
0
-
T = 24 S
360. 106
360. 106
0
zz T = 24 S
3.84 10-3
3.84 10-3
0
p T = 26 S
0.0372
3.7217 10-2
0.047
T = 26 S
1
1
0
T = 26 S
390. 106
390.00 106
0.000
zz T = 26 S
0.051507
5.098 10-2
1.009
p T = 40 S
0.06252
6.2523 10-2
0.037
T = 40 S
1
1
0
T = 40 S
600. 106
600. 106
0
zz T = 40 S
0.10197
1.0093 10-1
1.018
p T = 90 S
0.07407
7.4145 10-2
0.062
T = 90 S
1
1
0
T = 90 S
1350. 106
1350. 106
0
zz T = 90 S
0.10984
1.08806 10-1
0.942
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: 4.00.06
Machine: CRAY C90
System: 8.0
UNICOS
Obstruction memory:
8 megawords
Time CPU To use:
94.44 seconds
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Code_Aster ®
Version
4.0
Titrate:
HSNV102 - Thermo- metal-worker-plasticity coupled in simple traction
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.102-B Page:
8/8
7
Summary of the results
Two modelings give very good approximations of the reference solution.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Outline document