Code_Aster
®
Version
3
Titrate:
HPLV102 - Calculation of G thermo elastic in infinite medium
Date:
21/05/96
Author (S):
G. DEBRUYNE, E. SCREWS
Key:
V7.03.102-A
Page:
1/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
V7.03.102 document
HPLV102 - Calculation of G thermo elastic in medium
infinite for a circular fissure
Summary
It is about a test of breaking process into thermomechanical for an axisymmetric problem. One
consider a circular fissure plunged in a presumedly infinite medium. One imposes a uniform temperature on
lips of the fissure. This test makes it possible to calculate the rate of refund of energy G.
The interest of the test is the stability of G according to various crowns and the comparison with an analytical solution.
This test contains a modeling into axisymmetric.
The variations of the calculation of G on various crowns compared to the reference solution do not exceed
1,5%.
Code_Aster
®
Version
3
Titrate:
HPLV102 - Calculation of G thermo elastic in infinite medium
Date:
21/05/96
Author (S):
G. DEBRUYNE, E. SCREWS
Key:
V7.03.102-A
Page:
2/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
1
Problem of reference
1.1 Geometry
B
C
O
Y
With
X
AB: grnm2
OC: grnm1
A: N3
OA: grn03
BC: grn05
It is about a circular fissure of radius OA = 5.
The presumedly infinite medium is modelized by a sphere of radius OB = 600.
1.2
Material properties
Thermal conductivity:
= 1.
Thermal expansion factor:
= 10
- 6
/°C
Young modulus:
E = 2.10
5
MPa
Poisson's ratio:
= 0.3
1.3
Boundary conditions and loadings
·
Mechanics: Imposed Déplacment
(GROUP_NO: grnm1 DX: 0.)
(GROUP_NO: grnm2 DY: 0.)
·
Thermics
:
TEMP_IMPO
(GROUP_NO: grno3 TEMP: 0. )
(GROUP_NO: grno5 TEMP: - 1.)
(NODE: N3 TEMP: - 1.)
Code_Aster
®
Version
3
Titrate:
HPLV102 - Calculation of G thermo elastic in infinite medium
Date:
21/05/96
Author (S):
G. DEBRUYNE, E. SCREWS
Key:
V7.03.102-A
Page:
3/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution results from OLESIAK and SNEDDON [bib1]:
O
Y
Z
X
has
T
0
= constant = -- 1
The expression of the rate of refund of energy is as follows:
(
)
(
)
G
E
K
K
E
T
has
= -
=
-
1
1
2
12
1
0
with
that is to say:
(
)
(
)
G
E T has
=
-
-
1
1
2
2
2
02
2.2
Result of reference
The result of reference is thus: G = 5.9115 10
- 7
J/m
2
2.3 Reference
bibliographical
[1]
Uniform Temperature one has Penny-Shaped Crack (OLESIAK and SNEDDON (1959)), begun again
in Handbook off stress-intensity, factors of G.C. SIH.
Code_Aster
®
Version
3
Titrate:
HPLV102 - Calculation of G thermo elastic in infinite medium
Date:
21/05/96
Author (S):
G. DEBRUYNE, E. SCREWS
Key:
V7.03.102-A
Page:
4/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
3 Modeling
With
3.1
Characteristics of modeling
It is about a modeling into axisymmetric:
3.2
Characteristics of the mesh
A number of nodes: 832
A number of meshs and types: 323
TRIA6
, 42
QUAD8
, 59
SEG3
Crown 1:
Rinf=1.
Rsup=4.
Crown 2:
Rinf=0.5
Rsup=4.5
Crown 3:
Rinf=1.5
Rsup=3.5
Crown 4:
Rinf=1.
Rsup=4.5
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
THERMICS
AXIS
[U4.22.01]
AFFE_MODELE
MECHANICS
AXIS
[U4.22.01]
THER_LINEAIRE
[U4.33.02]
MECA_STATIQUE
[U4.31.01]
CALC_THETA
THETA_2D
[U4.63.02]
CALC_G_THETA
OPTION
CALC_G
[U4.63.03]
Code_Aster
®
Version
3
Titrate:
HPLV102 - Calculation of G thermo elastic in infinite medium
Date:
21/05/96
Author (S):
G. DEBRUYNE, E. SCREWS
Key:
V7.03.102-A
Page:
5/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
4
Results of modeling A
4.1 Values
tested
The values tested are those of the rate of refund of energy G on the various crowns
of integration:
Identification
Reference
Aster
% difference
% Tolerance
Crown 1 G
1.4778 10
- 6
1.4586 10
- 6
1.30
1.50
Crown 2 G
1.4778 10
- 6
1.4574 10
- 6
1.38
1.50
Crown 3 G
1.4778 10
- 6
1.4583 10
- 6
1.32
1.50
Crown 4 G
1.4778 10
- 6
1.4573 10
- 6
1.38
1.50
4.2 Notice
The value of reference is G = 5.945 10
- 7
J/m
2
It is given per unit of area of extension of the fissure, therefore for A = 5 and taking into account
symmetry of the mesh, it is necessary to compare the result of Aster with:
G
G
has
Aster
ref.
=
×
2
= 1.4778 10
- 6
, because G
in Aster to a surface of extension of 1 radian corresponds.
4.3 Parameters
of execution
Version: 3.1
Machine: CRAY C98
System:
UNICOS
Overall dimension memory:
8 MW
Time CPU To use:
6 seconds
Code_Aster
®
Version
3
Titrate:
HPLV102 - Calculation of G thermo elastic in infinite medium
Date:
21/05/96
Author (S):
G. DEBRUYNE, E. SCREWS
Key:
V7.03.102-A
Page:
6/6
Manual of Validation
V7.03 booklet: Thermomechanical stationary linear of the voluminal systems
HI-75/96/032/A
5
Summary of the results
Invariance of the result compared to the crowns. Correct thermal term.