Code_Aster
®
Version
5.0
Titrate:
SSNA108 - Models of Weibull and Rice and Tracey
Date:
23/09/02
Author (S):
R. MASSON, P. BREBAN
Key
:
V6.01.108-A
Page:
1/4
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A
Organization (S):
EDF/MMC
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.108
SSNA108 - Models of Weibull and 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 (control
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).
Code_Aster
®
Version
5.0
Titrate:
SSNA108 - Models of Weibull and Rice and Tracey
Date:
23/09/02
Author (S):
R. MASSON, P. BREBAN
Key
:
V6.01.108-A
Page:
2/4
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A
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
m
0
100
=
µ
,
U
MPa
=
2630
.
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 locked according to (Y),
·
OB: displacements locked according to (X).
1.4 Conditions
initial
Null stresses and deformations.
Code_Aster
®
Version
5.0
Titrate:
SSNA108 - Models of Weibull and Rice and Tracey
Date:
23/09/02
Author (S):
R. MASSON, P. BREBAN
Key
:
V6.01.108-A
Page:
3/4
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A
2
Reference solution
2.1
Method of calculation
Numerical solution calculated by CASTEM2000 and Zébulon.
2.2
Sizes and results of reference
The stress 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 mesh
10 mm
B
C
30 mm
O In R=2 mm
Y
X
5 mm
3.2
Characteristics of the mesh
A number of nodes: 1219
A number of meshs and types: 320 (QUA8).
3.3 Functionalities
tested
Controls
DEFI_MATERIAU
WEIBULL
M
VOLU_REFE
SIGM_REFE
STAT_NON_LINE
COMP_INCR
RELATION
DEFORMATION
VMIS_ISOT_TRAC
SMALL
CALC_ELEM
OPTION
EPSG_ELGA_DEPL
POST_ELEM
WEIBULL
COEF_MULT
OPTION
SIGM_ELGA
POST_ELEM
RICE_TRACEY
COEF_MULT
ROOM
OPTION
YES
SIGM_ELMOY
3.4
Sizes tested and results
The variation noted with the reference solution remains lower than 1%.
Code_Aster
®
Version
5.0
Titrate:
SSNA108 - Models of Weibull and Rice and Tracey
Date:
23/09/02
Author (S):
R. MASSON, P. BREBAN
Key
:
V6.01.108-A
Page:
4/4
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/02/009/A
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%.