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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
1/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
Organization (S):
EDF-R & D/MMC, CS













Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
Document: V7.14.100



EPICU01 - Validation of the control
POST_K_BETA




Summary:

This test validates the operation of the control
POST_K_BETA
who calculates the factors of intensity of
stresses with the two points of defects, using the stresses with the nodes resulting from the mechanical resolution.
This test breaks up into two type of modeling:
·
Axisymmetric EPICU01a: modeling,
·
EPICU01b: modeling 3D.
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
2/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
1
Problem of reference
1.1 Geometry
The studied geometry is that of a section of tank bimetal, limited to 45° in azimuth.





















1.1.1 Defect
considered
In the method K
, the defect is not modelized in the mesh. The mesh makes it possible to calculate
stresses with the nodes. A postprocessing is then applied to calculate the factor of intensity
stresses by the method
starting from the stresses with the nodes (the method is detailed in
[R7.02.10]).
For this test, the defect considered is elliptic and of longitudinal orientation. Its dimensions are them
following (see figure which follows):
·
depth:prof_def = 6mm
·
width: 2b = 60mm
·
shift in the coating: decaf = ­ 0,2mm
R
Er
Er
Z
Er
1994 mm
7.5 mm
200 mm
200 mm
45°
Base metal
Coating
Center
the tank
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
3/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
Center tank
Initial defect
Defect considered
in calculation
prof_def
- decaf
Coating
Base metal
2b
ray_int
ep_rev
2a
ep_mdb
1.2
Material properties
For calculation in thermics:
Two properties are indicated, it acts of:
·
LAMBDA: thermal conductivity isotropic function of the temperature, expressed in W.m
­
1
.K
- 1
,
·
BETA: voluminal enthalpy according to the temperature, expressed in J.m
­ 3
.
For the coating:
Temperature (°C)
Lambda
0 14.7
20 14.7
50 15.2
100 15.8
150 16.7
200 17.2
250 18
300 18.6
350 19.3
Temperature (°C)
BETA
0 0.000000.E+00
50 1.102100.E+08
100 3.013300.E+08
150 5.014300.E+08
200 7.081300.E+08
250 9.188800.E+08
300 1.132910.E+09
350 1.348980.E+09
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
4/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
For the base metal:
Temperature (°C)
Lambda
0 37.7
20 37.7
50 38.6
100 39.9
150 40.5
200 40.5
250 40.2
300 39.5
350 38.7
Temperature (°C)
BETA
0 0.000000.E+00
50 1.061900.E+08
100 2.903300.E+08
150 4.829100.E+08
200 6.832800.E+08
250 8.921600.E+08
300 1.109440.E+09
350 1.335060.E+09
For calculation in mechanics:
Four parameters are indicated, it acts of:
·
E:
modulus Young, expressed out of AP,
·
naked = 0.3
Poisson's ratio,
·
ALPHA:
isotropic thermal expansion factor, expressed in °C,
·
TEMP_DEF_ALPHA = 20: value of the temperature to which values of the coefficient of
thermal dilation ALPHA were determined, expressed in
°C.
For the coating:
Temperature (°C)
E
0 1.985E+11
20 1.97E+11
50 1.95E+11
100 1.915E+11
150 1.875E+11
200 1.84E+11
250.1.8E+11
300 1.765E+11
350 1.72E+11
Modeling has
Modeling B
Temperature (°C)
ALPHA
Temperature (°C)
ALPHA
0 1.756E-05
20 1.764E-05
20 1.64E-05
50 1.7787E-05
50 1.654E-05
100 1.8019E-05
100 1.68E-05
150 1.8225E-05
150 1.704E-05
200 1.8575E-05
200 1.72E-05
250 1.8568E-05
250 1.75E-05
300 1.8768E-05
300 1.777E-05
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
5/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
For the base metal:
Temperature (°C)
E
0 2.05E+11
20 2.04E+11
50 2.03E+11
100 2e+11
150 1.97E+11
200 1.93E+11
250 1.89E+11
300 1.85E+11
350.1.8E+11
Modeling has
Modeling B
Temperature (°C)
ALPHA
Temperature (°C)
ALPHA
0 1.2878E-05
20 1.3002E-05
20 1.122E-05
50 1.3198E-05
50 1.145E-05
100 1.3521E-05
100 1.179E-05
150 1.382E-05
150 1.214E-05
200 1.4102E-05
200 1.247E-05
250 1.4382E-05
250 1.278E-05
300 1.4682E-05
300 1.308E-05

1.3
Boundary conditions and loadings
The boundary conditions imposed are those of an axisymmetric system.
Two types of loadings are applied:
·
heat exchange in internal skin,
·
fluid pressure in internal skin.


2
Reference solution
2.1
Results of reference
The results of reference are those resulting from a similar calculation carried out starting from code CUVE1D.

2.2
Uncertainty on the solution
2%
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
6/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
3 Modeling
With
3.1
Characteristics of modeling
2D, axisymetic (SEG3, QUAD8)

3.2
Characteristics of the mesh
A number of nodes: 63
A number of elements: 12

3.3 Functionalities
tested
Controls
MECA_STATIQUE
INTE_MAIL_2D DEFI_SEGMENT
POST_K_BETA FISSURES



K1D
DEPTH
WIDTH
ORIENTATION

TABL_MECA_REV
TABL_MECA_MDB
TABL_THER
5 mm
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
7/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
4
Results of modeling A
4.1 Values
tested
Below, the comparison of the Aster results compared to the results of reference resulting from the code
of calculation CUVE1D:

Type of value
Moment
Reference Aster
% difference
K1_REV
0
1.5298E+07
1.5198E+07
0
KCP_REV 0
1.8239E+07
1.8239E+0.7 0
TEMPPF_REV
0
287
287
0
K1_MDB
0
1.53234E+07
1.5234E+07
0
KCP_MDB 0
2.03147E+07
2.03147E+07 0
TEMPFF_MDB
0
287
287
0
K1_REV
3871
9.4963E+06
9.4963E+06
0
KCP_REV 3871
2.70057E+07
2.70057E+07 0
TEMPPF_REV
3871
84.93
84.93
0
K1_MDB
3871
4.3231E+06
4.3231E+06
0
KCP_MDB 3871
2.9587E+06
2.9587E+06 0
TEMPFF_MDB
3871
86.09
86.09
0
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
8/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
5 Modeling
B
5.1
Characteristics of modeling
3D (SEG3, QUAD8, HEXA20)

5.2
Characteristics of the mesh
A number of nodes: 480
A number of elements: 2559

5.3 Functionalities
tested
Controls
MECA_STATIQUE
INTE_MAIL_3D DEFI_SEGMENT
POST_K_BETA FISSURES



K1D
DEPTH
WIDTH
ORIENTATION

TABL_MECA_REV
TABL_MECA_MDB
TABL_THER
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
9/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
6
Results of modeling B
6.1 Values
tested
Below, the comparison of the Aster results compared to the results of reference resulting from the code
of calculation CUVE1D:

Type of value
Moment
Reference Aster
% difference
K1_REV
3871
9.419E+06
9.517E+06
1.04
KCP_REV 3871
25.563E+06
25.503E+06 0.23
TEMPPF_REV
3871
84.84
84.92
0.10
K1_MDB
3871
3.578E+06
3.604E+06
0.74
KCP_MDB 3871
26.363E+06
26.197E+06 0.63
TEMPFF_MDB
3871
86.02
86.08
0.07
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Code_Aster
®
Version
6.3
Titrate:
EPICU01 - Validation of the control
POST_K_BETA
Date:
07/01/04
Author (S):
A. DAHL, A. BOYER
Key
:
V7.14.100-A
Page:
10/10
Manual of Validation
V7.14 booklet: Thermomechanical linear statics of the voluminal systems
HT-26/03/023/A
7
Summary of the results
This case test validates the control
POST_K_BETA
for the two types of modeling.