Code_Aster ®
Version
5.0
Titrate:
SSNA108 - Modèles de Weibull and of Rice and Tracey


Date:
23/09/02
Author (S):
R. MASSON, Key P. BREBAN
:
V6.01.108-A Page:
1/4

Organization (S): EDF/MMC

Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.108

SSNA108 - Modèles de Weibull and of Rice and Tracey

Summary:

This test of nonlinear quasi-static mechanics makes it possible to validate the models of Weibull and Rice -
Tracey in 2D (command POST_ELEM) in the case of a notched axisymmetric test-tube subjected to one
simple tensile test.

The modeling of the test-tube is carried out with elements 2D (QUA8).
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNA108 - Modèles de Weibull and of Rice and Tracey


Date:
23/09/02
Author (S):
R. MASSON, Key P. BREBAN
:
V6.01.108-A Page:
2/4

1
Problem of reference

1.1 Geometry

A notched cylindrical test-tube is considered:

· diameter of the test-tube: 18 mm,
· radius of the notch: 5 Misters.

1.2
Properties of material

One adopts an elastoplastic law of behavior of Von Mises with isotropic work hardening
“TRACTION” whose traction diagram is given point by point:


0.0027 0.005 0.01 0.015 0.02 0.025 0.03 0.04 0.05 0.075 0.1

(MPa)
555.589.631 657.676.691 704.725.741 772 794

0.125
0.15 0.2.0.3.0.4 0.5.0.6.0.7 0.8 0.9
812.827.851 887.912.933 950.965.978 990

The deformations used in the relation of behavior are the linearized deformations.
Young modulus E amounts to 200 GPa while the Poisson's ratio is worth 0,3.

The coefficients of the model of Weibull used are as follows:

m = 8,
V = 100 m
µ,
0
= 2630MPa.
U

1.3
Boundary conditions and loadings

While referring to the figure [§3.1] boundary conditions are as follows:

· BC: following imposed displacement (Y),
· OA: displacements blocked according to (Y),
· OB: displacements blocked according to (X).

1.4 Conditions
initial

Null constraints and deformations.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNA108 - Modèles de Weibull and of Rice and Tracey


Date:
23/09/02
Author (S):
R. MASSON, Key P. BREBAN
:
V6.01.108-A Page:
3/4

2
Reference solution

2.1
Method of calculation

Numerical solution calculated by CASTEM2000 and Zébulon.

2.2
Sizes and results of reference

The constraint of Weibull (WEIBULL) as well as the rate of triaxiality (RICE_TRACEY) on different
meshs were calculated at various moments.

2.3
Uncertainties on the solution

Precision of the codes.

3 Modeling
With

3.1
Characteristics of the grid






10 mm





B

C



30 mm














O In R=2 mm
Y













X





5 m m

3.2
Characteristics of the grid

A number of nodes: 1219
A number of meshs and types: 320 (QUA8).

3.3 Functionalities
tested

Commands


DEFI_MATERIAU
WEIBULL
M
VOLU_REFE
SIGM_REFE
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_ISOT_TRAC
DEFORMATION
PETIT
CALC_ELEM
OPTION
EPSG_ELGA_DEPL
POST_ELEM
WEIBULL
COEF_MULT
OPTION
SIGM_ELGA
POST_ELEM
RICE_TRACEY
COEF_MULT
LOCAL
OUI
OPTION
SIGM_ELMOY

3.4
Sizes tested and results

The variation noted with the reference solution remains lower than 1%.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNA108 - Modèles de Weibull and of Rice and Tracey


Date:
23/09/02
Author (S):
R. MASSON, Key P. BREBAN
:
V6.01.108-A Page:
4/4

4
Summary of the results

The results obtained by Code_Aster are close to the reference solution since the variation with
reference solution is lower than 1%.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A

Outline document