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
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 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 expansion factor
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 conventional plasticity).
The results provided by Code_Aster are very satisfactory with errors lower than 2%.
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
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
HI-75/98/040/A
1
Problem of reference
1.1 Geometry
C
D
H
With
B
has
Z
R
P
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
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
m
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:
HSNV101 - Thermo plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B
Page:
3/8
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics
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
=
112 S
Law of plasticity of transformation:
()
!
!
Pt
fbm
fbm
fbm
K
F Z
Z
=
with
F Z
fbm
()
=
Z
fbm
2
-
Z
fbm
(
)
1.3
Boundary conditions and loadings
·
U
Z
= 0 on side AB (condition of symmetry).
·
traction imposed on the side CD,
p T
()
=
p
O
T
360 10
6
AP
for
T
1
for
T
1
p
O
=
6 10
6
AP
1
=
60 S
.
·
T
T
T
O
=
+ µ
,
µ
= - 5°C.s
- 1
on all the structure.
1.4 Conditions
initial
T
O
=
900
°
C
=
T
ref.
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
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 solution for
T
<
1
.
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
×
µ =
47.06 S.
Before transformation, elastoplastic thermo solution,
1
'
T
1
,
1
= 60 S.
T
()
=
p
O
T
zz
T
()
=
zz
E
T
()
+
zz
HT
T
()
+
zz
p
T
()
zz
E
T
()
=
T
()
E
zz
HT
T
()
=
Z
aust
×
aust
T
-
T
O
(
)
zz
p
T
()
=
T
()
-
yaust
+
S
aust
µ
T
(
)
H
oaust
+
aust
µ
T
During the transformation, élasto-metallurgical thermo solution,
1
<
T
<
2
,
2
= 112 S.
T
()
=
360 10
6
AP
zz
T
()
=
zz
E
T
()
+
zz
HT
T
()
+
zz
Pt
T
()
+
zz
p
60
()
zz
HT
T
()
=
Z
aust
×
aust
T
-
T
O
(
)
+
Z
fbm
×
fbm
T
-
T
O
(
)
+
Z
fbm
×
ref.
fbm
zz
p
T
()
=
K
fbm
F Z
fbm
()
P
O
1
After the transformation, elastoplastic thermo solution,
2
<
T
<
3
,
3
= 176 S.
T
()
=
360 10
6
AP
zz
T
()
=
zz
E
T
()
+
zz
HT
T
()
+
zz
p
T
()
+
zz
Pt
112
()
zz
p
T
()
=
T
()
-
ofbm
+
S
fbm
µ
T
(
)
H
ofbm
+
fbm
µ
T
2.2
Results of reference
zz
p
,
,
and
zz
for T = 47, 48, 64 and 114 seconds.
zz
p
for T = 60 and 176 seconds.
2.3 Bibliography
[1]
DONORE A.M. - WAECKEL F.: Influence structure transformations in the laws of
behavior elastoplastic Notes HI-74/93/024.
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
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_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:
HSNV101 - Thermo plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B
Page:
6/8
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
zz
p
T = 47 S
0
0
0
T = 47 S
0
0
0
T = 47 S
282. 10
6
282. 10
6
0
zz
T = 47 S
4.1125 10
3
4.1125 10
3
0
zz
p
T = 48 S
3.2653 10
3
3.26537 10
3
0.011
T = 48 S
1
1
0
T = 48 S
288. 10
6
288. 10
6
0
zz
T = 48 S
9.3469 10
4
9.34645 10
4
0.005
zz
p
T = 60 S
0.04
0.04
0
zz
p
T = 64 S
0.040
4.0 10
- 2
0
T = 64 S
0
0
0
T = 64 S
360. 10
6
360. 10
6
0
zz
T = 64 S
3.4683 10
2
3.46908 10
2
0.023
zz
p
T = 114 S
0.04107
4.10688 10
2
+0.004
T = 114 S
1
1
0
T = 114 S
360. 10
6
360. 10
6
0
zz
T = 114 S
0.03684
3.68407 10
2
0
zz
p
T = 176 S
0.06206
6.20680 10
2
0.000
4.2 Remarks
In this modeling:
zz
Pt
T, Z
(
)
=
0
4.3 Parameters
of execution
Version: 4.02.14
Machine: CRAY C90
Overall dimension memory:
8 megawords
Time CPU To use:
109.3 seconds
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
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_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:
HSNV101 - Thermo plasticity and metallurgy
Date:
01/12/98
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key:
V7.22.101-B
Page:
8/8
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
zz
p
T = 47 S
0
0
0
T = 47 S
0
0
0
T = 47 S
282. 10
6
282. 10
6
0
zz
T = 47 S
4.1125 10
3
4.1125 10
3
0
zz
p
T = 48 S
3.2653 10
3
3.26535 10
3
0.011
T = 48 S
1
1
0
T = 48 S
288. 10
6
288. 10
6
0
zz
T = 48 S
9.3469 10
4
9.34644 10
4
0.005
zz
p
T = 60 S
0.04
0.04
0
zz
p
T = 64 S
0.04
4.0 10
2
0
T = 64 S
0
0
0
T = 64 S
360. 10
6
359.99 10
6
0.004
zz
T = 64 S
4.00085 10
2
4.000268 10
2
0.015
zz
p
T = 114 S
0.041071
4.10751 10
2
+0.004
T = 114 S
1
1
0
T = 114 S
360. 10
6
360.01 10
6
0.000
zz
T = 114 S
0.072841
7.144112 10
2
1.915
zz
p
T = 176 S
0.06206
6.2066 10
2
0.000
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: 4.02.14
Machine: CRAY C90
Overall dimension 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.