SSLV116- Fissure circular in medium 3d with idiot[...]

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Titre : SSLV116 - Fissure circulaire en milieu 3D avec con[...]
Responsable : GÉNIAUT Samuel
Date : 31/10/2014 Page : 1/12
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SSLV116- Fissure circular in medium 3d with initial
stresses.
Summary:
The purpose of this test is to validate the computation of the stress intensity factors (SIFs) along the crack of a
crack 3d, in the frame of elasticity in the presence of initial stresses.
This test brings into play a cube embedded on all its sides, presenting a plane central circular crack. It is
subjected to an initial stress field due to the application of a thermal field.
This test contains 2 modelizations:
• Modelization a: the crack is with a grid (FEM);
• Modelization B (present in the file of validation): the crack is not with a grid, it is represented by levelsets (X-FEM)
For two modelizations, SIFs are evaluated by the commands POST_K1_K2_K3 and CALC_G.
The numerical values are compared with the values obtained in the case of the thermal loading are equivalent.
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
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1
Reference problem
1.1
Geometry
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Figure 1.1 - Geometry of the case test.
The crack is to circulairE (penny shaped ace) of radius a=2m in the plane OXY . The with
dimensions one of the cube is length L=10a . Thus, it is considered that the crack is in an infinite
medium.
1.2
Material properties
The material is isotropic elastic the properties are:
E=200000 MPa
ν=0,3
α=0,00001 K −1
1.3
Boundary conditions and loadings
The outsides of volume are embedded.
Taking into account symmetries, only half of the structure is modelled: half space such as Y 0 .
Symmetry conditions are thus applied to the face in Y =0 : on this face, following displacement Y is
blocked.
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Figure 1.2: Symmetry condition
The structure, of uniform temperature 250 ° C initially, is subjected to a field of variable temperature in
space, according to Z. the structure cooled, but is clamped of any share. So stresses of opening are
created on the crack.
Figure below presents the profile of temperature imposed.
Figure 1.3 - Field of temperature imposed.
With the application of this field of temperature, stresses are create (closed crack). These stresses
are then extracted and can constitute a stress field initial for the computation of the stress intensity
factors.
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Reference solution
The reference solution is determined by computation of the factors of intensity of the stresses directly
starting from the thermal loading.
The validation is made starting from the maximum of the local energy release rate (in each node of
the face of crack) and of the stresses intensity factor room to 90 ° of crack.
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Modelization A
3.1
Characteristics of modelization
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In this model, the crack is with a grid (case FEM). The mesh comprises a core surrounding the cracktip. It is the same mesh as for the case test sslv154a.
Figure 3.1: radiant mesh
Figure 3.2: mesh of structure
3.2
Characteristics of the mesh
Number of nodes: 9967
Number of meshes and type: 864 PENTA15 and 1568 HEXA20
The characteristic length of an element close to the bottom to crack is of
0,12 m .
The middles nodes of the edges of the elements touching the crack-tip are has moved with the quarter
of these edges.
3.3
Results
Three integration contours of the field theta for the command CALC_G are used:
•
Crown 1: RINF=0,12 m and RSUP=0,528 m .
•
Crown 2: RINF_2=0,5 RINF and RSUP_2=0,5RSUP
•
Crown 3: RINF_2=1,5 RINF and RSUP_2=1,5 RSUP
A smoothing of the type is chosen LEGENDRE.
The parameter ABS_CURV_MAXI of the operator POST_K1_K2_K3 is selected so as to retain 5 nodes
on the segment of extrapolation.
K I is tested only at point such as ω=90° .
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Computation
option
POST_K1_K2_K3
Case
considered
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Crown
K1 (90 °)
1
2
( MPa.m )
638,76e6
Initial stress
638,76e6
1,919e6
Gauss points
Initial stress
Nodes
Gauss points
CALC_K_G
Max G (J/m ²)
Thermal
Thermal
CALC_G
:
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Initial stress
Nodes
1
1,92e6
2
1,954e6
3
1,934e6
1
1,92e6
2
1,954e6
3
1,934e6
1
1,943e6
679,3,36e6
2
1,952e6
677,11e6
3
1,944e6
688,62e6
1
1,943e6
679,3,36e6
2
1,952e6
677,11e6
3
1,944e6
688,62e6
Table 1- Results of modelization FEM.
It is noted whereas the results are:
•
In conformity with the references to 2% for G and 8% K1. Let us note that the reference
POST_K1_K2_K3 announcement an uncertainty of 9% for its result, about the variation noted with
CALC_K_G
•
Different from 0.1 to 1% for G between the options CALC_G and CALC_K_G,
•
Identical that the initial stress is considered with the nodes or the Gauss points
•
Independent of the crown with 2% pres for G of CALC_G, 0.5% for G of CALC_K_G and 2% for
K1.
3.4
Quantities tested
One tests many quantities here, in order to control the thermal reference and the initial state.
Identificatio
n
Computation
option
Notice
Type of reference
Value of
reference
%
Tolera
nce
max (Gref )
CALC_G,
thermal
couronne1
«NON
REGRESSION»
1.91937 106
1%
CALC_K_G,
thermal
couronne1
«ANOTHER
ASTER»
1.91937 106
1%
CALC_G,
Couronne1
1.91937 106
1%
initial
stress
initial stress
Gauss
«ANOTHER
ASTER»
CALC_G,
Couronne2
1.92013 106
2%
initial
initial stress
«ANOTHER
ASTER»
max (Girref )
max (Gini )
max (Gini2)
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max (Gini3)
max (Gini4 )
max (Gini5 )
max (Gini6 )
max (Girini )
max (Girini2)
max (Girini3)
max (Girini4 )
max (Girini5)
max (Girini6 )
Kref ( 90° )
stress
Gauss
CALC_G,
Couronne3
stress
initial
stress initial
Gauss
CALC_G,
Couronne1
initial
stress
initial stress
Noeud
CALC_G,
Couronne2
initial
stress
initial stress
Noeud
CALC_G,
Couronne3
initial
stress
initial stress
Noeud
CALC_K_G,
Couronne1
initial
stress
initial stress
Gauss
CALC_K_G,
Couronne2
initial
stress
initial stress
Gauss
CALC_K_G,
Couronne3
initial
stress
initial stress
Gauss
CALC_K_G,
Couronne1
initial
stress
initial stress
Noeud
CALC_K_G,
Couronne2
initial
stress
initial stress
Noeud
CALC_K_G,
Couronne3
initial
stress
initial stress
Noeud
POST_K1_K2_K3
Thermal
Kini ( 90 ° )
POST_K1_K2_K3
Initial
stress
Girini
K I ( 90° )
CALC_K_G,
Contrainte
initial
Girini2
K I ( 90° )
CALC_K_G,
Contrainte
initial
Girini3
K I ( 90° )
CALC_K_G,
Contrainte
initial
Girini4
K I ( 90° )
CALC_K_G,
Contrainte
Couronne1,
initial stress
Gauss
Couronne2
initial stress
Gauss
Couronne3
initial stress
Gauss
Couronne1
initial stress
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«ANOTHER
ASTER»
1.92013 106
1%
«ANOTHER
ASTER»
1.91937 106
1%
«ANOTHER
ASTER»
1.92013 106
2%
«ANOTHER
ASTER»
1.92013 106
1%
«ANOTHER
ASTER»
1.92013 106
1.5 %
«ANOTHER
ASTER»
1.95458 106
1.5 %
«ANOTHER
ASTER»
1.93471106
1.5 %
«ANOTHER
ASTER»
1.92013 106
1.5 %
«ANOTHER
ASTER»
1.95458 106
1.5 %
«ANOTHER
ASTER»
1.93471 106
1.5 %
«ANOTHER
ASTER»
6.387673 108
5%
«ANOTHER
ASTER»
6.387673 108
5%
«ANOTHER
ASTER»
6.387673 108
10%
«ANOTHER
ASTER»
6.387673 108
10%
«ANOTHER
ASTER»
6.387673 108
10%
«ANOTHER
ASTER»
6.387673 108
10%
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initial
Noeud
Girini5
K I ( 90 ° )
CALC_K_G,
Contrainte
initial
Couronne2
Girini6
K I ( 90 ° )
CALC_K_G,
Contrainte
initial
initial stress
Noeud
Couronne2
initial stress
Noeud
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«ANOTHER
ASTER»
6.387673 108
10%
«ANOTHER
ASTER»
6.387673 108
10%
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Modelization B
4.1
Characteristics of modelization
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In this model, the crack is not with a grid (case X-FEM).
It is the same mesh as for the case test sslv154b.
In order to obtain better a accuracy on the results, the free initial mesh was refined on the level of
crack-tip using the command MACR_ADAP_MAIL.
Figure 4.1: mesh of structure refined
4.2
Characteristics of the mesh
Number of nodes: 1146
Number of meshes and type: 64573 TETRA4
The characteristic length of an element close to the bottom to crack is of
4.3
0,07 m .
Results
Three integration contours of the field theta for the command CALC_G are used:
•
Crown 1: RINF=0,12 m and RSUP=0,528 m .
•
Crown 2: RINF_2=0,5 RINF and RSUP_2=0,5RSUP
•
Crown 3: RINF_2=1,5 RINF and RSUP_2=1,5 RSUP
A smoothing of the type is chosen LEGENDRE.
The parameter ABS_CURV_MAXI of the operator POST_K1_K2_K3 is selected so as to retain 5 nodes
on the segment of extrapolation.
K I is tested only at point such as ω=90° .
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Computation
option
POST_K1_K2_K3
Case considered
Crown
CALC_K_G
Max G (J/m ²)
K1 (90 °)
Initial stress
612e6
Initial stress
1
2
( MPa.m )
639, E6
Initial stress
:
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Thermal
Thermal
CALC_G
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2,06e6
1
2,03e6
2
1,95e6
3
2,06e6
1
1,92e6
677e6
2
1,94e6
661e6
3
2,07e6
688e6
Table 1- Results of modelization FEM.
It is noted whereas the results are:
•
In conformity with the references to 6% for G and 8% for K1. Let us note that the reference
POST_K1_K2_K3 present a variation of 4% between the thermal case and the case with initial
stresses
•
Different from 5% maximum for G between the options CALC_G and CALC_K_G,
•
Independent of the crown with 5% pres for G of CALC_G, 7% for G of CALC_K_G and 4% for K1.
4.4
Quantities tested
As for modelization A, one tests the value max of energy release rates and the stresses intensity
factor for an angle of 90 °, for 3 crowns, in the computation cases thermal and initial state.
However, in X-FEM, the stresses can be given only to the nodes, which limits the number of tests.
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One tests many quantities here, in order to control the thermal reference and the initial state.
Identificatio
n
Computation
option
Notice
Type of reference
Value of
reference
%
Toler
ance
max (Gref )
CALC_G,
thermal
couronne1
«NON
REGRESSION»
2.06919 106
1%
max (Gini )
CALC_G,
Couronne1
«ANOTHER ASTER»
2.06919 106
2%
Couronne2
«ANOTHER ASTER»
2.06919 106
6%
Couronne3
«ANOTHER ASTER»
2.06919 106
2%
Couronne1
«ANOTHER ASTER»
2.06919 106
7%
Couronne2
«ANOTHER ASTER»
2.06919 106
7%
Couronne3
«ANOTHER ASTER»
2.06919 106
3%
CALC_K_G,
Couronne1
«ANOTHER ASTER»
1.92013 106
1.5 %
initial
stress
initial stress
Noeud
CALC_K_G,
Couronne2
«ANOTHER ASTER»
1.95458 106
1.5 %
initial
stress
initial stress
Noeud
CALC_K_G,
Couronne3
«ANOTHER ASTER»
1.93471 106
1.5 %
initial
stress
initial stress
Noeud
«NON
REGRESSION»
6.397943 108
1%
initial
stress
max (Gini2)
CALC_G,
initial
stress
max (Gini3)
CALC_G,
initial
stress
max (Girini )
CALC_K_G,
initial
stress
max (Girini2)
CALC_K_G,
initial
stress
max (Girini3)
CALC_K_G,
initial
stress
max (Girini4 )
max (Girini5)
max (Girini6 )
Kref ( 90° )
POST_K1_K2_K
3
Thermal
Girini
K I ( 90° )
CALC_K_G,
Contrainte
initial
Couronne1,
«ANOTHER ASTER»
6.397943 108
7%
Girini2
K I ( 90° )
CALC_K_G,
Contrainte
initial
Couronne2
«ANOTHER ASTER»
6.397943 108
5%
Girini3
K I ( 90° )
CALC_K_G,
Contrainte
initial
«ANOTHER ASTER»
6.397943 108
8%
initial stress
Gauss
Couronne3
initial stress
Gauss
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Summary of results
This test validates the computation of the stress intensity factors of a crack 3d in the presence of initial
state.
The case of crack with a grid gives better satisfaction than case X-FEM, with less dependence on the
crown in particular.

SSLV116- Fissure circular in medium 3d with idiot[...]

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