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
Organization (S): EDF/IMA/MN
Handbook 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 dilation coefficient 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%.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A

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
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
- 6
- 1
E T
E
fbm
= 200000.10 Pa
= 20.10 ° C
let us note H (T)
() ()
= E (T) - (T)
aust
- 6
- 1
O = 20.10 °C
= 0.3
Haust =
6
-
2000.10 Pa
3
ref.
= 2.52 10
fbm
T ref. =
°
900 C
H fbm = 2000.106 Pa
CP =
-
2000000 J.m3
-
° C 1
= 9999.9 W.m
- 1
-
° C 1
* 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
fbm
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).
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A

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
TRC to model a metallurgical evolution of bainitic type, on all the structure, of the form:
0.

if T1
1 = 60 S
T -
Z
1
fbm
=
if


1 T < 2
2 = 112s
2 - 1

if T
1.
2

Law of plasticity of transformation: ! Pt
fbm
= K
F (Z fbm)!Z fbm
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) = 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:
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
2
Reference solution
2.1
Method of calculation used for the reference solution
Before transformation, elastic thermo solution until T1 such as in T1:
- aust

y
zz = - E HT = y
T - To =
= - 100°C
E + has
T1 = 20s
thus for T T1
zz = - E T - To
(
)
Before transformation, and for T T1, elastoplastic thermo solution such as:



HT
p
zz = zz + zz + = 0
E

p

zz = R0zz + y
aust
1
1
y
0
p
-
from where (
+) =
- (T - T) and zz = p =
R aust
E
aust
aust
0
R0
R0
During the transformation, one is in elastic mode, one thus has an elastic thermo solution with
phase shift.
= - E (T - T0) + Z
p
ref.
+ (
fbm
zz
1)
[
]
After the transformation, there is always an elastic thermo solution until t2.
In t2:
(
)
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 t2:
fbm + E (
+ p (

p
fbm
y
ref. fbm
zz
1)
[
]
zz = - E (T - T 0) + ref.
+ (
(T - T0) = -
fbm
zz
1)
[
] =y
E
(T - T0) = - 624°C
t2 125s
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A

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
For T < 276°C one has an elastoplastic thermo solution such as:


p
zz = HT + + (T)
E
zz

p
p
zz = R0 zz (T) - zz (1)


[
] +y
fbm
1
1

from where (
+) = y
- (T - T0) -
- p (
R fbm
E
fbm
ref. fbm
zz
1)
0
R0
2.2
Results of reference

EFF
EFF
zz,
and with T = 60s

EFF
EFF
zz,
and with T = 89s

EFF
EFF
zz,
and with T = 112s

EFF
EFF
zz,
and 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.
[2]
DONORE.A. Mr. - WAECKEL.F. - RAZAKANAIVO.A. - Doc. Aster [R4.04.02].
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A

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
3 Modeling
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]
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]
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A

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
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:
ptzz 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
Obstruction memory:
8 megawords
Time CPU To use:
188.88 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:
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
5
Summary of the results
The results found with Code_Aster are very satisfactory, with percentages of error
lower than 0.8%.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/98/040/A

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