Code_Aster ®
Version
7.3
Titrate:
SSNA113 - Eprouvette notched in viscoplasticity
Date
:

13/10/04
Author (S):
S. MICHEL-PONNELLE, A. PARROT Key
:
V6.01.113-A Page:
1/6

Organization (S): EDF-R & D/AMA, MMC
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.113

SSNA113 ­ Eprouvette notched in viscoplasticity

Summary:

This test models a notched sample into axisymmetric. The law of behavior used is the law
VISC_ISOT_TRAC. Two loading rates are simulated:



· slow:
-
T = 1000s
that is to say
3
1
& = 10
-
S


· rapid:
T = 0.001s
that is to say
3
1
& 10 -
=
S

The results (effort resulting and contraction from the ligament) are compared with the calculations carried out with the model
of viscous Rousselier (ROUSS_VISC) degenerated so that the evolution of porosity is negligible.

Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSNA113 - Eprouvette notched in viscoplasticity
Date
:

13/10/04
Author (S):
S. MICHEL-PONNELLE, A. PARROT Key
:
V6.01.113-A Page:
2/6

1
Problem of reference

1.1 Geometry

Ud
U
P8
P9
30
P2
4.8
P0
P1
3
5.4


The test-tube is axisymmetric, and only half of the test-tube is represented. Dimensions
are given in millimetres.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSNA113 - Eprouvette notched in viscoplasticity
Date
:

13/10/04
Author (S):
S. MICHEL-PONNELLE, A. PARROT Key
:
V6.01.113-A Page:
3/6

1.2
Properties of material

Isotropic elasticity
Young modulus: E =
MPa

215000

Poisson's ratio: = 0.3
Traction diagram
Traction diagram
1100
1000
900
has
)
P
M
800
T
E
(
700
T
R
has
in
N
C
O
600
500
400
0
0,2
0,4
0,6
0,8
1
deformation

Coefficient for viscous law

MPa

6176
0 =

VISC_SINH
13
0 =
10

483
3.31131121

m = 6.76


9
-
Coefficients of the model of Rousselier
f0 = 510
used to obtain the solution of
D = 0.0001
reference

MPa

1575
1 =


1.3
Boundary conditions and loadings

Because of symmetry, vertical displacements are blocked for side P0P1 is DY=0.
Side P8P9 is subjected to a displacement imposed Ud = 1 Misters.
The loading is imposed using 500 steps of time in T=1000s for the slow case and T=0.001s for
the fast case.

2
Reference solution

2.1
Results of reference

The reference solution is obtained by carrying out same calculation with the model of Rousselier in
viscous version (COMP_INCR = “ROUSS_VISC”, DEFORMATION = “PETIT_REAC”) of which them
parameters were selected in order to return the effect of negligible porosity.
One compares the contraction of the ligament, i.e. displacement following X of the P1 node like
resulting effort (REAC_NODA) on face P8P9. One is interested in 3 values of Ud displacement:
0.05mm, 0.5mm and 1mm.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSNA113 - Eprouvette notched in viscoplasticity
Date
:

13/10/04
Author (S):
S. MICHEL-PONNELLE, A. PARROT Key
:
V6.01.113-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

·
Modeling AXIS_SI

3.2
Characteristics of the grid

The grid is obtained by GIBI.




A number of nodes: 1440
A number of meshs: 445 QUAD8

3.3 Functionalities
tested

Commands
AFFE_MODELE AFFE
MODELISATION
AXIS_SI
DEFI_MATERIAU TRACTION


VISC_SINH


STAT_NON_LINE COMP_INCR
VMIS_ISOT_TRAC_V
DEFORMATION
SIMO_MIEHE

4
Results of modeling A

Fast speed

Identification displacement
Reference
Aster
% difference
U =0.05 mm
REAC_NODA on P8P9
3.43132 103
3.42727 103
- 0.12

Uy in P1
- 8.0411 10-3
- 8.09476 10-3
0.67
U =0.5 mm
REAC_NODA on P8P9
3.93495 103
3.92628 103
- 0.22

Uy in P1
- 4.06758 10-1
- 4.06649 10-1
- 0.03
U =1 mm
REAC_NODA on P8P9
3.17328 103
3.16438 103
- 0.28

Uy in P1
- 8.89457 10-1
- 8.89189 10-1
- 0.03

Slow speed

Identification displacement
Reference
Aster
% difference
U =0.05 mm
REAC_NODA on P8P9
2.86423 103
2.86076 103
- 0.12

Uy in P1
- 1.52635 10-2
- 1.52998 10-2
0.24
U =0.5 mm
REAC_NODA on P8P9
3.36223 103
3.35580 103
- 0.19

Uy in P1
- 4.19637 10-1
- 4.19497 10-1
- 0.03
U =1 mm
REAC_NODA on P8P9
2.73903 103
2.73204 103
- 0.26

Uy in P1
- 9.14404 10-1
- 9.14069 10-1
- 0.04
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSNA113 - Eprouvette notched in viscoplasticity
Date
:

13/10/04
Author (S):
S. MICHEL-PONNELLE, A. PARROT Key
:
V6.01.113-A Page:
5/6

5
Summary of the results

One obtains a good agreement of the results between the 2 models with lower deviations than 1%.
At the total level, one notes that to the maximum 4 iterations are necessary to obtain convergence.
On the level of the integration of the law of behavior, less than 10 iterations are necessary for
to obtain an accuracy of 10-9.

Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSNA113 - Eprouvette notched in viscoplasticity
Date
:

13/10/04
Author (S):
S. MICHEL-PONNELLE, A. PARROT Key
:
V6.01.113-A Page:
6/6

Intentionally white left page.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/04/005/A

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