Code_Aster
®
Version
5.0
Titrate:
SSNA103 - Chock of the parameters of the model of Weibull
Date:
13/09/01
Author (S):
R. MASSON, W. LEFEVRE, G. BARBER
Key
:
V6.01.103-A
Page:
1/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/01/046/A
Organization (S):
EDF/RNE/MTC
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.103
SSNA103 - Chock of the parameters of the model
of Weibull
Summary:
This test validates control RECA_WEIBULL allowing the identification of the parameters
m
and
U
model of
Weibull.
The identification is carried out using a data base made up of 45 tests, all carried out on
cylindrical test-tubes smooth at three different temperatures, - 150°C, - 100°C and 50°C. This base of
data is obtained by random hard copy of a sample representative of the statistical law of Weibull
agent with values of
m
and
U
fixed arbitrarily.
Code_Aster
®
Version
5.0
Titrate:
SSNA103 - Chock of the parameters of the model of Weibull
Date:
13/09/01
Author (S):
R. MASSON, W. LEFEVRE, G. BARBER
Key
:
V6.01.103-A
Page:
2/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/01/046/A
1
Problem of reference
1.1 Geometry
Each test is carried out on a smooth cylindrical test-tube. For obvious reasons of
symmetries, an axisymmetric modeling 2D of the quarter of the structure is sufficient.
1.2
Properties of material
One describes the behavior of material studied by an elastoplastic law of Von Mises with
linear isotropic work hardening, “VMIS_ISOT_LINE”. Deformations used in the relation of
behavior are the linearized deformations.
E
E
T
Y
The Poisson's ratio does not depend on the temperature,
= 0,3.
Code_Aster
®
Version
5.0
Titrate:
SSNA103 - Chock of the parameters of the model of Weibull
Date:
13/09/01
Author (S):
R. MASSON, W. LEFEVRE, G. BARBER
Key
:
V6.01.103-A
Page:
3/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/01/046/A
Values of the Young modulus E, the tangent module E
T
and of the elastic limit are given in
the following table:
Temperature [°C]
150
100
50
E [MPa]
200000 200000
200000
And [MPa]
2000 2000
2000
Y
[MPa]
750 700
650
1.3
Boundary conditions and loadings
By referring to the figure §1.1 the boundary conditions and loadings are as follows:
On segment BC (Y=L
0
), imposed displacement following direction OY:
T [°C]
Displacement (L
0
) with the rupture for a datum length L
0
of 203.5 mm
[mm]
The results for each temperature are classified by ascending order
- 50
10,68 28,78 30,31 31,66 32,53
33,90
34,38
35,82
36,69
37,09
37,37 37,49 38,45
39,77
44,39
- 100
20,57 21,68 23,32 24,37 24,66
25,59
25,84
27,51
28,44
29,30
29,68 30,16 30,18
30,20
30,95
- 150
11,33 14,70 14,79 14,90 18,62
18,87
19,00
19,37
19,61
20,07
21,19 22,79 23,28
24,17
24,41
On segment OA (Y=0) displacements locked according to direction OY.
On segment OB (X=0) displacements locked according to direction OX.
1.4 Conditions
initial
Null stresses and deformations.
Code_Aster
®
Version
5.0
Titrate:
SSNA103 - Chock of the parameters of the model of Weibull
Date:
13/09/01
Author (S):
R. MASSON, W. LEFEVRE, G. BARBER
Key
:
V6.01.103-A
Page:
4/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/01/046/A
2
Reference solution
2.1
Method of calculation
No calculation is necessary to obtain the reference solution. Values
m
and
U
(M and
SIGM_REFE in option WEIBULL of DEFI_MATERIAU) which one seeks to identify with
Code_Aster are known and make it possible to generate the base of the experimental data. Thus, them
strains with rupture are in the following way given:
For each couple
m
and
U
associated a temperature of test, a sample of 15 values of
forced of Weibull to the rupture were determined by random hard copy taking into account the law
following statistics:
-
-
=
m
U
W
W
F
P
exp
1
)
(
The stress of Weibull is defined by:
()
W
I
I m
I
I
m
V
V
=
0
The summation relates to volumes of matter
V
I
plasticized,
I
I
indicating the main stress
maximum in each one of these volumes (volume V
0
(VOLU_REFE in option WEIBULL of
DEFI_MATERIAU) is equal to (50
µ
m)
3
).
In the case of a stress in simple traction with the assumption of the small deformations,
stress of Weibull,
W
, expresses itself according to the strain with the rupture (L
0
)/L
0,
, according to:
W
T
T
Y m
E L L
L
E
E
V
V
=
-
+
-
0
0
0
1
One thus deduces from this expression and the preceding random hard copy the values of lengthenings with
rupture deferred in the table of [§1.3].
2.2
Sizes and results of reference
Reference variables of
m
and
U
used to create the bases of experimental tests are
the following ones:
Temperature [°C]
50
100
150
m
24 24
24
U
[MPa]
2800 2700
2600
2.3
Uncertainties on the solution
Uncertainty on the solution cannot be given in a precise way. It can be rather high.
Indeed, the values of reference can be found only if populations are considered
experimental made up of an infinite number of samples.
Code_Aster
®
Version
5.0
Titrate:
SSNA103 - Chock of the parameters of the model of Weibull
Date:
13/09/01
Author (S):
R. MASSON, W. LEFEVRE, G. BARBER
Key
:
V6.01.103-A
Page:
5/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/01/046/A
3 Modeling
With
3.1
Characteristics of the mesh
A number of nodes: 149
A number of meshs and types: 40 elements QUAD8
3.2 Functionalities
tested
Controls
DEFI_MATERIAU WEIBULL
M
VOLU_REFE
SIGM_REFE
STAT_NON_LINE COMP_INCR RELATION
DEFORMATION
VMIS_ISOT_LINE
SMALL
RECA_WEIBULL LIST_PARA
RESU
METHOD
CORR_PLAST
OPTION
SIGM_REFE
M
EVOL_NOLI
TEMPLE
COEF_MULT
MAXI_VRAI
NOT
SIGM_ELMOY
GROUP_MA: CB
GROUP_MA: BO
GROUP_MA: OA
Code_Aster
®
Version
5.0
Titrate:
SSNA103 - Chock of the parameters of the model of Weibull
Date:
13/09/01
Author (S):
R. MASSON, W. LEFEVRE, G. BARBER
Key
:
V6.01.103-A
Page:
6/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-26/01/046/A
3.3
Sizes tested and results
Identification of one
m
commun run at the three experimental bases and of one
U
by base.
Temperature [°C]
Reference
Code_Aster
m
U
[MPa]
m
U
[MPa]
50 24 2800
26,7
2536
100 24 2700 26,7 2428
150 24 2600 26,7 2372
3.4 Remarks
Although the variation enters the values of (
m
,
U
) obtained with RECA_WEIBULL and their values of
reference remains considerable, it is in conformity with the result sought taking into account the number
relatively weak of samples used for retiming (15 per temperature). To obtain them
values of reference it would be necessary considerably to increase the number of samples per temperature
(N>1000). The noted variation remains however reasonable (about 10%). In addition,
growth of
U
according to the temperature is respected
3.5 Parameters
of execution
Version: 5.4
Machine: SGI - ORIGIN 20 00 - R12000
Overall dimension memory: 16 Mo
Time CPU To use: 23s
4
Summary of the results
The results obtained by Code_Aster show that the automatic procedure of chock of
parameters of the models of Weibull functions and gives coherent results with the results
theoretical waited.