Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
1/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
Document: V7.22.104
HSNV104 - Thermo plasticity and metallurgy in
plane deformations with restoration
of work hardening
Summary:
One treats the determination of the mechanical evolution of a right-angled parallélipipède in plane deformations
subjected to evolutions thermics
T T
()
and metallurgical
Z T
()
known and
uniforms (the metallurgical transformation is of bainitic type).
The elements used are two-dimensional elements in plane deformations and the relation of behavior
is the plasticity of von Mises with linear isotropic work hardening. Account of the restoration is taken
of work hardening, but not of the plasticity of transformation.
The expansion factor
depends on the metallurgical composition.
The reference solution is obtained by the analytical resolution of the problem.
The results provided by Code_Aster are very satisfactory with errors lower than 0,8%.
Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
2/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
1
Problem of reference
1.1 Geometry
C
D
H
With
B
has
R
X
y
Width: = 0.05 Mr. has.
Height: H = 0.2 Mr.
1.2
Properties of materials
()
() ()
()
()
E
H T
T E T
E T
T
H
T
H
CP
fbm
oaust
ref.
aust
ref.
fbm
fbm
=
=
=
-
=
=
=
=
=
=
=
=
-
-
-
-
-
-
-
-
°
°
°
°
°
200000.10 AP
20.10
C
let us note
0.3
20.10
C
2.52 10
2000.10 AP
900 C
2000.10
AP
2000000 J.m
C
9999.9 W.m
C
6
6
1
6
1
3
6
6
3
1
- 1
1
*
aust
=
characteristics relating to the austenitic phase,
*
fbm
=
characteristics relating to the phases ferritic, bainitic and martensitic,
fbm
=
thermal expansion factor of the phases ferritic, bainitic and martensitic,
aust
=
expansion factor of the austenitic phase
ref.
fbm
=
deformation of the phases ferritic, bainitic and martensitic at the temperature of
reference, austenite being regarded as not deformed at this temperature:
translated the difference in compactness between the cubic crystallographic structures with
centered faces (austenite) and cubic centered (ferrite).
Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
3/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
TRC to modelize a metallurgical evolution of bainitic type, on all the structure, of the form:
Z
fbm
=
0.
T
-
1
2
-
1
1.
if
T
1
if
1
T
<
2
if
T
2
1
=
60 S
2
=
112s
Law of plasticity of transformation:
()
!
!
Pt
fbm
fbm
fbm
K
F Z
Z
=
with
F Z
fbm
()
=
Z
fbm
Z
-
Z
fbm
(
)
one thus does not take account of the plasticity of transformation one takes
K
fbm
= 0
Notations:
T
1
()
=
T
1
T
2
()
=
T
2
1.3
Boundary conditions and loadings
·
U
Y
= 0 on side AB;
U
X
= 0 in A.
·
T
T
T
O
=
+ µ
,
µ
= 5°C.s
1
on all the structure.
·
The loading on the structure is due to the phenomena of thermal dilation and
metallurgical constrained in direction Z by the condition of plane deformations.
1.4 Conditions
initial
T
O
=
900
°
C
=
T
ref.
Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
4/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Before transformation, elastic thermo solution until
T
1
such as in
T
1
:
zz
= -
E
HT
=
y
T
-
T
O
= -
yaust
E
+
has
= -
100
°
C
T
1
=
20s
thus for
T
T
1
zz
= -
E
T
-
T
O
(
)
Before transformation, and for
T
T
1
,
elastoplastic thermo solution such as:
zz
=
zz
HT
+
zz
p
+
E
=
0
zz
=
R
0
zz
p
+
y
from where
(1
R 0aust
+
1
E)
=
y
aust
R0aust
-
(T
-
T0) and
zz
p
=
p
=
-
R0aust
During the transformation, one is in elastic mode, one thus has an elastic thermo solution with
phase shift.
= -
E
(T
-
T
0
)
+
Z
ref.
fbm
+
zz
p
(
1
)
[
]
After the transformation, there is always an elastic thermo solution until
T
2
.
In
T
2
:
zz
=
R T, Z,
EFF
(
)
+
y
T, Z
(
)
Because of the restoration of work hardening and owing to the fact that one was in elastic mode during all
transformation: R = 0 before replastification.
One thus has in
T
2
:
zz
= -
E
(T
-
T
0
)
+
ref.
fbm
+
zz
p
(
1
)
[
]
=
yfbm
(T
-
T
0
)
= -
yfbm
+
E (
ref.
fbm
+
zz
p
(
1
)
[
]
E
(T
-
T
0
)
= -
624
°
C
T
2
125s
Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
5/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
For T < 276°C one has an elastoplastic thermo solution such as:
zz
=
HT
+
E
+
zz
p
(T)
zz
=
R
0
zzp
(T)
-
zz
p
(
1
)
[
]
+
y
from where
(1
R
0fbm
+
1
E)
=
yfbm
R
0fbm
-
(T
-
T
0
)
-
ref.
fbm
-
zz
p
(
1
)
2.2
Results of reference
zz
,
EFF
E
T
EFF
with
T
=
60s
zz
,
EFF
E
T
EFF
with
T
=
89s
zz
,
EFF
E
T
EFF
with
T
=
112s
zz
,
EFF
E
T
EFF
with
T
=
176s
2.3 Bibliography
[1]
DONORE A.M. - WAECKEL F. - Influence of structure transformations in the laws of
behavior elastoplastic Notes HI-74/93/024.
[2]
DONORE.A. Mr. - WAECKEL.F. - RAZAKANAIVO.A. - Doc. Aster [R4.04.02].
Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
6/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
3 Modeling
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_THER
[U4.23.01]
THER_LINEAIRE
OPTION
META_ELGA_TEMP
[U4.23.05]
DEFI_MATERIAU
META_MECA_FO
[U4.23.01]
META_RE
STAT_NON_LINE
COMP_INCR
RELATION
META_EP_RE
[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:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
7/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
4 Results
4.1 Values
tested
Identification
Reference
Aster
% difference
zz
T = 60s
4.0792E8
4.080E8
0.02%
EFF
T = 60s
3.9604E3
3.9599E3
0.02%
EFF
T = 60s
0.
0.
0.%
zz
T = 89s
7.0684E8
7.0152E8
0.752%
EFF
T = 89s
3.9604E3
3.9599E3
0.01%
EFF
T = 89s
0.
0.
0.%
zz
T = 112s
9.4392E8
9.44E8
0.008%
EFF
T = 112s
0.
0.
0.
EFF
T = 112s
0.
0.
0.
zz
T = 176s
12.101E8
12.102E8
0.012%
EFF
T = 176s
0.
0.
0.
EFF
T = 176s
5.068921E3
5.0688E3
0.002%
4.2 Remarks
In this modeling:
zz
Pt
T, Z
(
)
=
0
The error on
zz
at 89 seconds comes in fact from the error made on the numerical description of
metallurgical transformation which is, at this moment, from approximately 56%.
4.3 Parameters
of execution
Version: 4.02.14
Machine: CRAY C90
Overall dimension memory:
8 megawords
Time CPU To use:
188.88 seconds
Code_Aster
®
Version
4.0
Titrate:
HSNV104 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL, A. RAZAKANAIVO
Key:
V7.22.104-A
Page:
8/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
5
Summary of the results
The results found with Code_Aster are very satisfactory, with percentages of error
lower than 0.8%.