Code_Aster
®
Version
7.4
Titrate:
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Date:
22/07/05
Author (S):
S. LECLERCQ, L. SALMONA
Key
:
V6.04.179-A
Page:
1/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/MMC, CS IF
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.179
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Summary:
The purpose of this test is to validate the law
LEMA_SEUIL
derived from the law from
LEMAITRE
conventional. In particular, us
we will delay on the activation of the specific threshold to this law. One thus carries out a creep test on one
geometry simple to know a cube here.
A modeling 3D with elements HEXA8 is currently available.
Code_Aster
®
Version
7.4
Titrate:
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Date:
22/07/05
Author (S):
S. LECLERCQ, L. SALMONA
Key
:
V6.04.179-A
Page:
2/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
Co-ordinates of the points:
WITH B C D E F G H
0. 1.
1. 0. 0.
1. 1. 0.
0. 0.
1. 1. 0.
0. 1. 1.
0. 0. 0. 0. - 1.
- 1.
- 1. - 1.
1.2
Material properties
Elastic properties:
E = 165000 MPa
= 0.3
Viscous properties:
Law of
LEMA_SEUIL
To = 14.143 10
- 13
MPa
- 1
.neutron
- 1
S = 0.0788 10
10
MPa
- 1
.s
- 1
1.3
Boundary conditions and loadings
Surface force:
F = 220 MPa
Irradiation:
Flow of irradiation: 1.85 10
15
neutrons.cm
2
.s
- 1
.
Imposed displacements:
Node a: DX=DY=DZ=0.
Node E: DX=DY=0.
Node D and node H: DX=0.
On the first increment of time the force passes from 0 to its maximum value 220 MPa linearly by
report/ratio at time for then being maintained constant over all the duration of the experiment.
X
With
B
D C
F
H
G
E
Z
y
Code_Aster
®
Version
7.4
Titrate:
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Date:
22/07/05
Author (S):
S. LECLERCQ, L. SALMONA
Key
:
V6.04.179-A
Page:
3/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The goal of the reference solution is analytically to calculate the value of the threshold from which
creep appears.
Some results of nonregression on displacements with the last pitch of time are added
to check the total rigidity of the system.
For the analytical calculation of the threshold one a:
As long as the structure remains elastic and because of the boundary conditions, the tensor of the stresses
is written:
·
For the first pitch of time ranging between 0 and 106 S
()
T
T
xx
4
10
2
.
2
-
=
, T in second and
xx
in MPa. The other components of the tensor are
null.
·
For the others not of time,
MPa
xx
220
=
However one a:
()
=
T
eq
U
S
D
0
1
Maybe as in this case
xx
eq
=
,
one obtains in an immediate way by solving D=1 the value of
time from which creep is declared: T
1
= 4.08181818 10
6
S
Thus for a time equal to T
1
, the viscous deformations are null and D is worth 1.
2.2
Results of reference
Variable interns V1 and V2 at the point A, B, C and E as well as the displacement of the points B to the last pitch of
time
2.3 References
bibliographical
[1]
P. BONNIERES: Integration of the viscoelastic relations in
STAT_NON_LINE
[R5.03.08] February 2001
Code_Aster
®
Version
7.4
Titrate:
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Date:
22/07/05
Author (S):
S. LECLERCQ, L. SALMONA
Key
:
V6.04.179-A
Page:
4/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
Elements 3D (HEXA8)
Only one element was modelized to represent the cube
Along axis Z:
1 layer of elements
Total thickness:
1
Limiting conditions:
Node A
Node E
Node D
Node H
DX=DY=DZ=0.
DX=DY=0.
DX=0.
DX=0.
pressure on face BCFG
F = 220. MPa
3.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and types: 1 HEXA8 and 1 QUAD4 (faces external skin).
3.3 Functionalities
tested
Controls
AFFE_CHAR_MECA DDL_IMPO
FORCE_FACE
GROUP_NO
GROUP_MA
“MECHANICAL” AFFE_MODELE “3D”
ALL
DEFI_MATERIAU LEMA_SEUIL_FO
CALC_ELEM “VARI_ELNO_ELGA”
“SIEF_ELNO_ELGA”
With
B
D C
F
H
G
E
X
y
Z
Code_Aster
®
Version
7.4
Titrate:
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Date:
22/07/05
Author (S):
S. LECLERCQ, L. SALMONA
Key
:
V6.04.179-A
Page:
5/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Localization Size
Reference
Aster %
difference
In V1
0.00000000
0.00000000 0%
V2
1.00000000
9.9999999949239
10
- 01
- 5.08
10
- 8
%
B V1
0.00000000
0.00000000 0%
V2
1.00000000
9.9999999949239
10
- 01
- 5.08
10
- 8
%
DX
/
7.8380536694423
10
- 2
/
DY
/
1.2984914071992
10
- 16
/
DZ
/
1.2984914071992
10
- 16
/
C V1 0.00000000
0.00000000 0%
V2
1.00000000
9.9999999949239
10
- 01
- 5.08
10
- 8
%
E V1
0.00000000
0.00000000 0%
V2
1.00000000
9.9999999949239
10
- 01
- 5.08
10
- 8
%
Code_Aster
®
Version
7.4
Titrate:
SSNV179 - Cubic under creep via the law
LEMA_SEUIL
Date:
22/07/05
Author (S):
S. LECLERCQ, L. SALMONA
Key
:
V6.04.179-A
Page:
6/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
5
Summary of the results
The objective of this case test is completely filled since activation of creep via the detection of
threshold is very precise (about 10
- 8
% of error). Of course, since it is about viscous phenomenon,
the discretization in time plays a very important part in particular in the surrounding of the activation of the threshold.
In this case test a very particular care was taken to surround time when the threshold is reached in way
specify to obtain satisfactory results.