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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
Organization (S):
EDF/IMA/MN
Manual 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 expansion factor
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 conventional plasticity).
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
1
Problem of reference
1.1 Geometry
Z
C
D
H
With
B
has
R
Radius: = 0.05 Mr. has.
Height: H = 0.2 Mr.
1.2
Properties of materials
(
)
()
() ()
() ()
(
)
(
)
E
S
T T
H T
T E T
E T
T
H
H
T T
S
H
S
T T
H
H
y
aust
oaust
aust
O
oaust
aust
oaust
aust
O
fbm
aust
oaust
aust
yfbm
ofbm
fbm
O
aust
ref.
ofbm
fbm
ofbm
fbm
=
=
+
-
=
-
=
=
=
+
-
=
=
=
=
=
+
-
=
=
=
=
+
-
-
-
-
-
-
-
°
°
°
°
200 000.10 AP
let us note
0.3
50. 10 AP
15. 10
C
1.3 10 AP. C
0 AP
23.5 10
C
1 10 AP. C
2.52 10
50. 10 AP
6
6
6
1
6
1
6
1
6
1
3
6
(
)
fbm
O
fbm
ofbm
fbm
F
B
m
T T
S
H
CP
K
K
K
-
=
=
=
=
=
=
=
=
°
°
°
-
°
-
-
-
-
-
-
-
1. 10 AP. C
0
2.000.000 J.m
C
9999.9 W.m
C
6. 10 AP C
0
1. 10
AP
6
1
3
1
- 1
1
6
1
10
1
Note:
Indices or exponents
fbm
relate to the parameters materials of the phases
ferrito-perlitic, bainitic and martensitic and indices or exponents
aust
relate to
austenite.
TRC to modelize a metallurgical evolution of martensitic type of the form:
0.
1
-
E
T
-
1
(
)
1.
if
T
1
if
1
T
<
2
if
T
2
1
=
25 S
2
=
40 S
=
0.03
=
-
10
°
C.S
-
1
1.3
Boundary conditions and loadings
·
U
Z
= 0 on side AB (condition of symmetry).
·
traction imposed on the side CD,
()
p T
p T
O
=
,
p
O
= 15.10
6
AP.
·
T
T
T
O
=
+ µ
,
µ
= 10°C.s
1
on all the structure.
1.4 Conditions
initial
T
O
= 900°C.
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Before transformation, elastic thermo solution for
T
<
1
(not of metallurgical transformation
!Z
=
0
).
T
()
=
p
O
T
zz
T
()
=
zz
E
T
()
+
zz
HT
T
()
=
T
()
E
+
aust
T
-
T
O
(
)
The yield stress is reached for
1
=
oaust
p
O
-
S
aust
×
K
=
25 S
.
During the transformation, solution thermo metal-worker-élasto-plastic, for
1
<
T
<
2
with
2
= 40 S.
T
()
=
p
O
T
zz
T
()
=
zz
E
T
()
+
zz
HT
T
()
+
zz
p
T
()
+
zzpt
T
()
zz
E
T
()
=
T
()
E
zz
HT
T
()
=
Z
aust
×
aust
T
-
T
O
(
)
+
Z
fbm
×
fbm
T
-
T
O
(
)
+
ref.
fbm
[
]
p
T
()
=
T
()
-
Z
aust
×
y
aust
T
()
+
Z
fbm
×
y T
()
fbm
(
)
Z
aust
×
H
aust
T
()
+
Z
fbm
×
H
fbm
T
()
Pt
T
()
=
K
m
×
p
O
×
1
-
K
2
× ×
-
K
m
×
p
O
×
T
-
K
2
× ×
1
-
Z
(
)
2
After transformation, elastoplastic thermo solution, for
T
>
2
T
()
=
p
O
T
zz
T
()
=
zz
E
T
()
+
zz
HT
T
()
+
zz
p
T
()
2.2
Results of reference
,
zz
,
p
,
to 24 S, 26 S, 40 S and 90 S.
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
3 Modeling
With
3.1
Characteristics of modeling
N1
N2
N3
N4
N5
N6
N7
N8
N9
N10
N11
N12
N13
With
B
C
D
y
WITH = N4, B = N5, C = N13, D = N12.
3.2
Characteristics of the mesh
A number of nodes: 13
A number of meshs and types: 2 meshs
QUAD8
, 6 meshs
SEG3
3.3 Functionalities
tested
Controls
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]
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
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. 10
6
360. 10
6
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. 10
6
390. 10
6
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. 10
6
600. 10
6
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. 10
6
1350. 10
6
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
Overall dimension memory:
8 megawords
Time CPU To use:
42.47 seconds
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
5 Modeling
B
5.1
Characteristics of modeling
N1
N2
N3
N4
N5
N6
N7
N8
N9
N10
N11
N12
N13
With
B
C
D
y
WITH = N4, B = N5, C = N13, D = N12.
5.2
Characteristics of the mesh
A number of nodes: 13
A number of meshs and types: 2 meshs
QUAD8
, 6 meshs
SEG3
5.3 Functionalities
tested
Controls
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]
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
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. 10
6
360. 10
6
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. 10
6
390.00 10
6
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. 10
6
600. 10
6
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. 10
6
1350. 10
6
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
Z
0
0
when
6.3 Parameters
of execution
Version: 4.00.06
Machine: CRAY C90
System: 8.0
UNICOS
Overall dimension memory:
8 megawords
Time CPU To use:
94.44 seconds
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
7
Summary of the results
Two modelings give very good approximations of the reference solution.