Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
1/10
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:V7.22.103
HSNV103 - Thermo plasticity and metallurgy
in plane deformations
Summary:
One treats the determination of the mechanical evolution of a right-angled parallépipède in subjected plane deformations
with evolutions thermics
T T
()
and metallurgical
Z T
()
known and uniform (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 (for modeling B, one also holds
count 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.
For modeling A (without plasticity of transformation), the reference solution is obtained by the resolution
analytical of the problem. For modeling B (with plasticity of transformation), the reference solution is
obtained by the numerical resolution of the problem by using axisymmetric elements for which one
impose the condition of plane deformations.
The results provided by Code_Aster are very satisfactory with errors lower than 0,5%.
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
2/10
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
S
T T
H T
T E T
E T
T
H
H
T T
S
H
S
T T
H
H
yaust
oaust
aust
O
oaust
aust
oaust
aust
O
fbm
aust
oaust
aust
yfbm
ofbm
fbm
O
aust
ref.
ofbm
fbm
O
fbm
=
=
+
-
=
-
=
=
=
+
-
=
=
=
=
=
+
-
=
=
=
=
-
-
-
-
-
-
-
°
°
°
°
200000.10 AP
let us note
0.3
400. 10 AP
15. 10
C
0.5 10 AP. C
1250 10 AP
23.5 10
C
5 10 AP. C
2.52 10
530. 10 AP
6
6
6
1
6
1
6
6
1
6
1
3
6
(
)
fbm
fbm
O
ref.
fbm
ofbm
fbm
fbm
T T
T
C
S
H
CP
K
+
-
=
°
=
=
=
=
=
=
°
-
°
°
-
°
-
-
-
-
-
-
-
900
1
0.5 10 AP. C
50 10 AP
2.000.000 J.m
C
9999.9 W.m
C
5 10 AP C
1. 10
AP
6
1
6
3
1
- 1
1
6
1
10
.
*
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
of compactness enters the cubic crystallographic structures to centered faces (austenite) and
cubic centered (ferrite).
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
3/10
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
T
T
T
T
fbm
=
-
-
<
=
=
0
1
1
2
1
1
1
2
2
1
2
.
.
if
if
if
60 S
112 S
Law of plasticity of transformation:
()
!
!
Pt
fbm
fbm
fbm
K
F Z
Z
=
with
()
(
)
F Z
Z
Z Z
fbm
fbm
fbm
=
-
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:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
4/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
2
Reference solution (for modeling A)
2.1
Method of calculation used for the reference solution
Before transformation, elastic thermo solution until
T
1
such as:
(
)
zz
HT
y
O
yo
zz
O
E
T T
E
S
C
T
S
T
T
E
T T
= -
=
-
= - + =
°
=
= -
-
76 92
15 38
1
1
,
,
thus for
Before transformation, and for
T
T
1
,
elastoplastic thermo solution such as:
()
(
)
()
(
)
(
)
zz
zz
zzp
y
zzp
y
O
zz
zzp
O
R
T
E
T T
E R T
E
T T
=
=
+
= -
-
-
+
= -
+
-
0
and
from where and
During the transformation, one remains in load as long as
!
HT
<
0
(
) ()
!
,
,
HT
O
ref.
T
T
T
T
C
T
T
S
fbm
=
=
-
-
+
-
-
=
°
=
=
0
2
538 82
72 23
1
2
2
for T > 538,82 °C
there is thus an elastoplastic thermo soution with phase shift:
()
()
(
)
[
]
()
()
(
)
(
)
zzp
y
O
ref.
zz
zzp
O
ref.
T Z
E
Z T T
Z
E R T Z
E
Z T T
Z
fbm
fbm
= -
-
-
+
+
= -
+
-
+
,
,
and
and for T < 538,82 °C
there is thus an elastic thermo soution with phase shift:
()
(
)
()
[
]
zz
O
ref.
zzp
E
Z T T
Z
T
fbm
= -
-
+
+
2
After the transformation, one replastifie when:
()
()
zz
zzp
y
R T Z
T Z
=
+
,
,
with
(
)
zz
zz
O
ref.
E
T T
fbm
=
+
-
+
=
0
that is to say
T
C
=
°
267 06
,
and one thus has for
T
<
267,06
°
C
(
)
[
]
()
()
()
()
zzp
ref.
O
y
zz
zzp
y
E
T T
T Z
R T Z
E
R T Z
T Z
fbm
=
-
-
-
-
+
=
+
,
,
,
,
and
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
5/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
2.2
Results of reference
, p,
xx
and
zz
with
T
=
16s
p,
xx
and
zz
with
T
=
60s
p
with
T
=
72s
, p,
and
zz
with
T
=
112s
,
xx
and
zz
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.
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
6/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
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_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]
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
7/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
xx
T = 16 S
2.4599 10
3
2.4599 10
3
0.001
T = 16 S
1
1
0
T = 16 S
360.13 10
6
360.13 10
6
0
p T = 16 S
7.9345 10
5
7.9345 10
5
0.001
xx
T = 60 S
1.0309 10
2
1.0309 10
2
0.003
p
T = 60 S
5.7213 10
3
5.7213 10
3
0.001
T = 60 S
265.73 10
6
265.73 10
6
0.001
p
T = 72 S
5.8420 10
3
5.8162 10
3
0.442
T = 112 S
0
0
0
T = 112 S
12.82 10
6
12.76 10
6
0.384
p T = 112 S
5.8421 10
3
5.8162 10
3
0.444
xx
T = 176 S
1.5886 10
2
1.5886 10
2
0.003
T = 176 S
1
1
0
T = 176 S
133.55 10
6
133.55 10
6
0.002
4.2 Remarks
In this modeling:
()
zzpt
T Z
,
=
0
The error on the plastic deformation cumulated at 72 seconds comes in fact from the error made on
numerical description of the metallurgical transformation which is, at this moment, from approximately 0,5%.
4.3 Parameters
of execution
Version: 4.02.14
Machine: CRAY C90
Overall dimension memory:
8 megawords
Time CPU To use:
194.69 seconds
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
8/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
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_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]
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
9/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
T = 60 S
265.73 10
6
265.73 10
6
0.001
p T = 60 S
5.7213 10
3
5.7213 10
3
0.001
yy
T = 89 S
1.0325 10
2
1.0326 10
2
0.012
p
T = 89 S
5.7213 10
3
5.7213 10
3
0.001
T = 89 S
13.545 10
6
13.5457 10
6
0.006
yy
T = 112 S
8.9197 10
3
8.9208 10
3
0.017
T = 112 S
101.39 10
6
101.345 10
6
0.044
p T = 112 S
5.7213 10
3
5.7213 10
3
0.001
yy
T = 176 S
1.5884 10
2
1.5889 10
2
0.03
p T = 176 S
9.3610 10
2
9.3610 10
2
0
T = 176 S
130.72 10
6
130.72 10
6
0
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
The reference solution is obtained by the numerical resolution of the problem with elements
axisymmetric for which one imposes the condition of plane deformations.
6.3 Parameters
of execution
Version: 4.02.14
Machine: CRAY C90
Overall dimension memory:
8 megawords
Time CPU To use:
202.42 seconds
Code_Aster
®
Version
4.0
Titrate:
HSNV103 - Thermo plasticity and metallurgy in plane deformations
Date:
01/12/98
Author (S):
F. WAECKEL
Key:
V7.22.103-B
Page:
10/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
7
Summary of the results
The results found with Code_Aster are very satisfactory, with percentages of error
lower than 0.5%.