Code_Aster
®
Version
7.1
Titrate:
HSNA120 - Propagation in a network of fissures
Date:
02/06/04
Author (S):
Mr. SEYEDI, S. TAHERI
Key
:
V7.23.120-A
Page:
1/6
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
V7.23.120 document
HSNA120 - Propagation in a network of fissures
in fatigue thermomechanical
Summary:
This axisymmetric test makes it possible to preserve a methodology of simulation of the propagation in a network
fatigue cracks thermomechanical. It is a question of a method of mending of meshes automatic to follow
the projection of fissures and a strategy of propagation in a network. The whole of the method is
programmed in PYTHON in the command file.
The test comprises the modeling of the propagation of four parallel fissures in the thickness of a tube
subjected to a variation in temperature on its internal skin and a monotonous axial stress.
Code_Aster
®
Version
7.1
Titrate:
HSNA120 - Propagation in a network of fissures
Date:
02/06/04
Author (S):
Mr. SEYEDI, S. TAHERI
Key
:
V7.23.120-A
Page:
2/6
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
The studied problem consists being studied of the propagation of a network of four parallel fissures of
lengths and of arbitrary distances in the thickness of a tube subjected to a variation in temperature
on its internal skin. [Figure 1.1-a] the geometry of the model studied as well as the loadings shows
and boundary conditions considered. The distances between the fissures and their lengths are
data in the tables [Table 1.1-1] and [Table 1.1-2].
Appear 1.1-a: the geometry and the boundary conditions of the model
Fissure
F1 F2 F3 F4
Length (mm)
0,68 0,70 0,08 0,69
Table 1.1-1: The initial length of the fissures and their distances
Fissure d12
d23
d34
Outdistance (mm)
2,89 2,06 0,61
Table 1.1-2: The distance enters the fissures
127 mm
Code_Aster
®
Version
7.1
Titrate:
HSNA120 - Propagation in a network of fissures
Date:
02/06/04
Author (S):
Mr. SEYEDI, S. TAHERI
Key
:
V7.23.120-A
Page:
3/6
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
HT-66/04/005/A
1.2
Material properties
The material is elastic linear isotropic. Mechanical properties and thermal of material
are:
Young modulus
E = 2,1E5 MPa
Poisson's ratio
= 0,3
Thermal coefficient of conductivity
= 0,014 W/mm/°C
Voluminal farmhouse
= 8th-6 kg/mm
3
Specific heat
CP = 450 J/kg/°C
Thermal expansion factor
= 1,5E5 mm/°C
1.3
Boundary conditions and loadings
Mechanics:
Imposed displacements: embedding of the lower part.
Condition of contact between the lips of the fissures:
Conditions of unilateral contact without friction with pairing node-breakage (master-slave)
are considered to ensure nonthe penetration of the lips of fissures the moment of their closing.
Mean stress:
A mean stress of 60 MPa is applied to the higher edge of the model.
Thermal loading:
The loading applied to constant amplitude is imposed on the internal skin of the tube
)
2
(
2
0
ft
Cos
T
T
T
+
=
where
0
T
= 70°C,
T
= 100°C and
F
= 0,1 Hz.
CHART [num_calc] =AFFE_CHAR_MECA (MODELE=MOD_G [num_calc],
TEMP_CALCULEE = TEMPT [num_calc],
);
Code_Aster
®
Version
7.1
Titrate:
HSNA120 - Propagation in a network of fissures
Date:
02/06/04
Author (S):
Mr. SEYEDI, S. TAHERI
Key
:
V7.23.120-A
Page:
4/6
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
HT-66/04/005/A
2
Reference solution
One does not have an analytical solution for the calculation of the propagation of a network of fissures in
tire thermomechanical. Consequently, this case test is a case test of nonregression. The reference
is consisted results resulting from version 7.0 of Code_Aster.
2.1
Method of calculation of reference
Methodology used to deal with the problem of propagation of two-dimensional fissures in
fatigue relates to a calculation 2D plane or axisymmetric which takes into account a radial or axial cut
studied tube. This methodology allows the analysis of the propagation of the fissures in the thickness.
The present study consists in testing a numerical procedure of simulation of the propagation of
fissures in 2D or axisymmetric [bib1]. It is about a method based on automatic mending of meshes
to simulate the propagation of the fissures and a strategy of propagation in a network of fissures
in fatigue thermal.
The procedure of mending of meshes is led with GMSH which launches out automatically after each pitch
of propagation of the fissures to remake the mesh during calculation. Strategy of propagation of
network of fissures is controlled by increments over the lengths of the fissures. The kinetics of
propagation of the fatigue cracks can be described by a law of propagation in fatigue of the type
Paris. Within the framework of this modeling, a law of propagation of Paris modified (Peeled and Al
[bib2]) which takes into account the effect of the threshold of nonpropagation, the report/ratio of load and tenacity
material, is used.
By considering a theoretical increment length for all the fissures of the network, one finds
fissure which needs the minimum of a number of cycles to be propagated by considering the amplitude of
stress intensity factor manpower and the law of propagation. By applying this number of cycles to
structure, one finds the propagation of each fissure.
2.2
Results of reference
For three stages of propagation, the amplitude of stress intensity factor manpower
(
)
EFF
K
for
the dominant fissure and the number of cycles of the stage are compared with the values of reference. These
values are:
Stage 1:
(
)
EFF
K
= 0.0513,
NR
stage
= 212900
Stage 2:
(
)
EFF
K
= 0.0550,
NR
stage
= 178574
Stage 3:
(
)
EFF
K
= 0.0613,
NR
stage
= 135107
Code_Aster
®
Version
7.1
Titrate:
HSNA120 - Propagation in a network of fissures
Date:
02/06/04
Author (S):
Mr. SEYEDI, S. TAHERI
Key
:
V7.23.120-A
Page:
5/6
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
HT-66/04/005/A
3 References
bibliographical
[1]
Mr. SEYEDI: (2002) “Simulation of the propagation of a thermal network of faience manufacturing by
Code_Aster “, notes intern EDF R & D, HT-64/02/004/A.
[2]
J. PEELED, G. BAUDIN, and Mr. ROBERT: (1977) “Measurement and calculation of threshold of cracking
after overload “, Aerospace Search, vol. 3, pp. 191-201.
[3]
H. YAAKOUB AGA: (1996) “Fault tolerance initial: application to a cast iron G.S.
in fatigue “, Thesis of doctorate. University Paris 6.
4 Modeling
With
4.1
Characteristics of modeling
Modeling considers a tube runs which contains four fissures leading to its skin
intern. An axisymmetric model with the following geometrical characteristics was considered.
H = 60 mm
W = 9,23 mm
4.2
Characteristics of the mesh
The mesh was created by taking 3 main blocks. The block medium contains the fissures, it is him
even made up of 5 blocks.
A number of nodes: 15650
A number of meshs: 8147
SEG3: 456
TRIA6: 7685
Appear 4.2-a: Mesh finite elements and details of the fissures (initial situation)
Code_Aster
®
Version
7.1
Titrate:
HSNA120 - Propagation in a network of fissures
Date:
02/06/04
Author (S):
Mr. SEYEDI, S. TAHERI
Key
:
V7.23.120-A
Page:
6/6
Manual of Validation
V7.23 booklet: Thermomechanical nonlinear statics of the surface structures
HT-66/04/005/A
4.3
The law of propagation
The propagation of the fatigue cracks follows a law of the Paris type. Within the framework of fatigue to large
a number of cycles, the threshold of nonpropagation of fissure, the report/ratio of load and the tenacity of
material can influence the propagation velocity of the fissures. In this case, the law of
propagation of the fissures can be written as an amended law of Paris (Peeled and Al (1977) [bib2] and
Yaacoub Aga and Al (1998) [bib3]).
N
EFF
K
C
dN
da
=
with
)
(
)
(
max
R
G
K
K
K
R
G
K
K
HT
IC
HT
EFF
-
-
=
,
R
m
R
R
G
R
-
-
= 11
)
(
and
max
min
K
K
R
=
where
max
K
and
min
K
are factors of intensity of the stresses maximum and minimum
respectively,
HT
K
the threshold of nonpropagation,
R
the report/ratio of load and
IC
K
the tenacity of
material. The coefficients used are as follows:
C
= 9,34 10
- 4
N
= 2,6
R
m
= 0,37
HT
K
= 4 MPa.m
0.5
IC
K
= 66 MPa.m
0.5
5
Results of modeling A
5.1 Values
tested
The values tested are the amplitude of effective stress intensity factor and the number of
cycles applied.
Identification Reference Aster
% difference
Stage 1:
EFF
K
5.1300 E-2
5.131615 E-2
0.031
Stage 1: NR
2.1290 E+5
2.129012 E+5
5.6 E-4
Stage 2:
EFF
K
5.5000 E-2
5.496820 E-2
0.058
Stage 2: NR
1.7887 E+5
1.785738 E+5
1.0 E-4
Stage 3:
EFF
K
6.130 E-2
6.130244 E-2
0.004
Stage 3: NR
1.35107 E+5
1.351072 E+5
1.66 E-4