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
Organization (S): EDF/IMA/MN
Handbook 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 dilation coefficient 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%.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
1
Problem of reference
1.1 Geometry
y
Width: = 0.05 Mr. has.
Height: H = 0.2 Mr.
C
D
H
R
X
With
B
has
1.2
Properties of materials
T
6
E T
E
aust
aust
= 200000.10 Pa
=
+ saust
O
y
O
(T - T) let us note H (T) () ()
= E (T) - (T)
aust
= 0.3
= 400. 106 Pa
H aust = H aust
aust
O
O
O
+
(T - T)
=
- 6
-
15. 10
° C 1
saust =
6
-
0.5 10 Pa.° C 1
H aust
6
fbm
O
= 1250 10 Pa
- 6
- 1
fbm
fbm
= 23.5 10 °C
=
+ S fbm
O
aust
6
- 1
aust
y
O
(T - T) = 5 10 Pa.°C
- 3
fbm
= 2.52 10
= 530. 106 Pa
H fbm = H fbm
fbm
+
(O
T - T)
ref.
O
O
fbm
ref.
T
=
°
900 C
fbm
6
- 1
fbm
S
= 0.5 10 Pa.°C
H
6
O
= - 50 10 Pa
- 3
- 1
- 1
- 1
fbm
.cp = 2.000.000 J.m °C
= 9999.9 W.m °C
= - 5.106 P a° -
C 1
fbm
K
=
- 10
- 1
1. 10
Pa
* aust
=
characteristics relating to the austenitic phase
* fbm
=
characteristics relating to the phases ferritic, bainitic and martensitic
fbm
=
thermal dilation coefficient of the phases ferritic, bainitic and martensitic
aust
=
dilation coefficient of the austenitic phase
ref.
=
deformation of the phases ferritic, bainitic and martensitic at the temperature of reference,
fbm
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).
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
TRC to model a metallurgical evolution of bainitic type, on all the structure, of the form:
0.
if T
1
1 = 60 S
T -
Z
1
if
1 T
fbm
=
< 2 2 =
112 S
2 -
1 if T
1
2
.
Law of plasticity of transformation: ! Pt
fbm
= K
F (Z fbm)!Z fbm
with F (Z) = Z (Z - Z
fbm
fbm
fbm)
Notations: T
(1) = T1
T
(2) = T2
1.3
Boundary conditions and loadings
·
uY = 0 on side AB; . uX = 0 in A.
·
T
T O
=
+ µt, µ = 5°C.s1 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 = Tref
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
2
Reference solution (for modeling A)
2.1
Method of calculation used for the reference solution
Before transformation, elastic thermo solution until T1 such as:
- O
HT
O
y
zz = -
E
= y T - T =
= 76, °
92 C
E + S
T1 = 15 38
, S
thus for T T1
O
zz = -
E (T - T)
Before transformation, and for T T1, elastoplastic thermo solution such as:
p
zz = 0
and zz =
R zz + y
- (T) -
O
E T - T
p
y
(
)
of
p
O
zz =
where and zz = - E
+
T - T
E + R T
(zz
)
()
(
During the transformation, one remains in load as long as!HT < 0
O
-
T -
+
T1 -
T
HT
() ref.
fbm
2
! = 0 T =
(
= 538 °
82 C
2 -)
,
T = t2 = 72,23s
for T > 538,82 °C
there is thus an elastoplastic thermo soution with phase shift:
-
O
y (T, Z) - E (Z) T - T
+ Z ref.
p
[() fbm]
p
O
zz =
and
= - E
+
Z T - T + Z
E + R (T, Z)
zz
(zz () () réffbm)
and for T < 538,82 °C
there is thus an elastic thermo soution with phase shift:
O
p
zz = - E (Z)
[(T-T) +Zréf +zz (T
fbm
2)]
After the transformation, one replastifie when:
p
zz = R (T, Z) zz + y (T, Z)
with
zz
O
zz =
+ (T - T) + ref. = 0
E
fbm
that is to say T = 267
°
06
,
C
and one thus has for T < 267,06°C
O
E - ref.
-
T - T
- y T, Z
p
[
fbm
(
)] ()
p
zz =
and
= R T, Z
+
T, Z
R (T, Z)
zz
() zz y ()
+ E
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
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 Note HI-74/93/024.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
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_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]
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
xx T = 16 S
2.4599 103
2.4599 103
0.001
T = 16 S
1
1
0
T = 16 S
360.13 106
360.13 106
0
p T = 16 S
7.9345 105
7.9345 105
0.001
xx T = 60 S
1.0309 102
1.0309 102
0.003
p T = 60 S
5.7213 103
5.7213 103
0.001
T = 60 S
265.73 106
265.73 106
0.001
p T = 72 S
5.8420 103
5.8162 103
0.442
T = 112 S
0
0
0
T = 112 S
12.82 106
12.76 106
0.384
p T = 112 S
5.8421 103
5.8162 103
0.444
xx T = 176 S
1.5886 102
1.5886 102
0.003
T = 176 S
1
1
0
T = 176 S
133.55 106
133.55 106
0.002
4.2 Remarks
In this modeling:
Pt
zz (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
Obstruction memory:
8 megawords
Time CPU To use:
194.69 seconds
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
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_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]
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
T = 60 S
265.73 106
265.73 106
0.001
p T = 60 S
5.7213 103
5.7213 103
0.001
yy T = 89 S
1.0325 102
1.0326 102
0.012
p T = 89 S
5.7213 103
5.7213 103
0.001
T = 89 S
13.545 106
13.5457 106
0.006
yy T = 112 S
8.9197 103
8.9208 103
0.017
T = 112 S
101.39 106
101.345 106
0.044
p T = 112 S
5.7213 103
5.7213 103
0.001
yy T = 176 S
1.5884 102
1.5889 102
0.03
p T = 176 S
9.3610 102
9.3610 102
0
T = 176 S
130.72 106
130.72 106
0
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
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
Obstruction memory:
8 megawords
Time CPU To use:
202.42 seconds
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
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
7
Summary of the results
The results found with Code_Aster are very satisfactory, with percentages of error
lower than 0.5%.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A
Outline document