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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
1/12
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
Organization (S):
EDF-R & D/AMA, CS IF
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear of the plane systems
V7.02.310 document
HPLP310 - Biblio_35 Fissures radial intern in one
thick cylinder under pressure and loading
thermics
Summary:
This test results from the validation independent of version 3 in breaking process.
It is about a two-dimensional test in statics in which one modelizes nonthe linearity of contact due to
refermeture partial of the fissure.
The behavior of the structure is thermoelastic linear isotropic.
The case test includes/understands only one plane modeling 2D for which one studies the influence of the load factor
mechanics
.
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
2/12
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
has
X
y
With
B
C
D
E
r2
r1
Cross-section of a thick tube presenting one
internal radial fissure
Report/ratio of the radii
B = r2/r1 = 2 (r1=1 mm, r2= 2 mm)
Depth of the fissure
has/(r2-r1) = 0,05
1.2
Properties of material
The material is thermoelastic linear isotropic standard.
Young modulus
E = 1000 MPa
Poisson's ratio
= 0,3
Linear expansion factor
T = 1E-6
Yield stress
0 = 1 MPa (being used to define the initial stress field created
by the process of autofrettage on the assumption of one
former behavior of elastoplastic type of Von Mises)
1.3
Boundary conditions and loadings
Boundary conditions (for a half-part in the area y
0)
Blocking UY = 0 on segment AB and the ligament OF (symmetry).
Linear relation UX (A) + UX (E) = 0 (to lock the horizontal adjustment)
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
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V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
Loadings
Loading n° 1: radial traction
rr (r2) =
0 on the external face; this produced mechanical loading
the same KI as an internal pressure acting simultaneously on the internal radius
r1 and on the lips of the fissure, without taking into account of nonthe linearity of
contact.
Loading n° 2: thermal loading are equivalent to an autofrettage defined as follows:
(
)
(
)
2
1
1
1
1
1
1
0
1
ln
ln
ln
1
2
3
4
R
R
T
T
R
R
R
R
R
T
T
T
T
R
E
T
T
T
=
·
-
-
=
·
-
·
+
=
In these formulas,
indicate the maximum radius of the area having undergone
autofrettage, T1 the temperature with the radius r1 and T
the temperature with the radius R =
in the thick tube not fissured. In the application noted here, one takes
= r2, which
corresponds to the autofrettage of the totality of the section of the thick tube, and one
does not take into account nonthe linearity of contact. One awaits one K negative for
positive temperatures (setting in compression of the tube not fissured).
Loading n° 3: linear combination loading n° 2 +
* loading n° 1,
(
T!) indicating
the mechanical load factor; one takes here into account nonthe linearity of
contact, which supposes an incremental application of the mechanical load.
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
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V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation by finite elements with code ABAQUS. Nonthe linearity of contact is modelized with aid
one-way elements GAP. The factor of intensity of the stresses is calculated from
the integral J.
2.2
Results of reference
Adimensional factor of intensity of the stresses according to the mechanical factor of loading,
in the case of loading n° 3
Notation:
F
K
has
L
IT
=
/
0
linear factor of intensity adimensional (obtained by combination
linear of the effects of autofrettage and mechanical loading, in
stopped feature)
F
K
has
NR
IN
=
/
0
nonlinear factor of intensity adimensional (obtained while holding
count nonlinearity of contact, in full feature).
(
)
K
EJ
I
2
2
1
= -
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
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V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
Empirical formula of the factor of intensity of the stresses under external radial voltage
()
W
R
R
K
P
has
C
B
C
B
B
has
W
and
B
C
has
W
has
W
C
has
W
has
W
I
= -
=
·
+
-
<
=
-
+
= -
+
+
2
1
0
1
0 2
2
1
0 5
2
2
0 5
2
1 1
0 01
0 8
1 5
3 0
2.397 2 705
0 884
0.244 1 447
0 809
ln
ln
,
,
,
,
,
,
,
,
,
,
,
,
,
Empirical formula of the factor of intensity of the stresses in autofrettage in full section
()
K
C has
C
B
B
has
W
and
B
C
has
W
has
W
has
W
has
W
C
has
W
has
W
Ia
=
·
+
+
<
=
-
+
-
+
=
-
+
-
0
1
2
0 75
4
2
1
0 05
0 15
1 5
0 25
2
0 05
1 8
1
0 01
0 8
1 5
3 0
30.221 57 714
29 954
2 444
1
51.522.111 027
63 244
ln
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
+
-
0 15
1 5
0 25
3 631
1
,
,
,
,
has
W
has
W
2.3 References
bibliographical
[1]
H. Mr. SHU, J. SMALL and G. BEZINE: Radial stress intensity factors for aces in thick walled
cylinders. I. Symmetrical aces II. Combination off autofrettage and internal presses.
Engng.Fract.Mechs., 49, n°4, 611-629, 1994.
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
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Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
The model consists of quadrangles with 8 nodes and triangles with 6 nodes.
It comprises 4877 nodes and 1598 elements.
3.2
Characteristics of the mesh
Use of procedure FISS 2d_V1.
The topological parameters concerning refinement around the bottom of fissure are:
·
nc = 4 (a number of crowns)
·
NS = 8 (a number of sectors)
·
nbcour = 1 (a number of crowns of déraffinement)
Y
X
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Version
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
7/12
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
Zoom of the fissured area
Zoom of the area fissured with “block of contact”
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
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V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
3.3
Functionalities tested
The rate of refund of energy G is calculated by the method THETA for the 4 following crowns:
·
Crown 0: Rinf = 0,0025 mm Rsup = 0,005 mm
·
Crown 1: Rinf = 0,005 mm Rsup = 0,0075 mm
·
Crown 2: Rinf = 0,0075 mm Rsup = 0,01 mm
·
Crown 3: Rinf = 0,005 mm Rsup = 0,03 mm
Controls
AFFE_CHAR_MECA CONTACT
NORMAL
STAT_NON_LINE COMP_ELAS
ELAS
NEWTON
RUBBER BAND
DEFI_FOND_FISS MELTS
GROUP_NO
NORMAL
CALC_THETA THETA_2D
GROUP_NO
CALC_G_THETA_T SYME_CHAR
SYME
OPTION
CALC_K_G
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Version
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
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Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
KI, loading n°1, crown 0, neglected contact
1,1482
1,12884
-
1,69
KI, loading n°1, crown 1, neglected contact
1,1482
1,12883
-
1,69
KI, loading n°1, crown 2, neglected contact
1,1482
1,12886
-
1,69
KI, loading n°1, crown 3, neglected contact
1,1482
1,12885
-
1,69
Identification Reference
Aster %
difference
KI, loading n°2, crown 0, neglected contact
-
0,41237
-
0,3847839
-
6,69
KI, loading n°2, crown 1, neglected contact
-
0,41237
-
0,3878
-
6,69
KI, loading n°2, crown 2, neglected contact
-
0,41237
-
0,3847897
-
6,69
KI, loading n°2, crown 3, neglected contact
-
0,41237
-
0,384786
-
6,69
Identification Reference
Aster %
difference
KI, loading n°3, contact,
= 0,33, crown 0
1,2075E-3 1,2688
10
3
5,078
KI, loading n°3, contact,
= 0,335, crown 0 3,0187E-3 3,0589E-3
1,332
KI, loading n°3, contact,
= 0,34, crown 0
5,4336E-3 5,4177E-3
-
0,293
KI, loading n°3, contact,
= 0,345, crown 0 8,5865E-3 8,2570E-3
-
3,837
KI, loading n°3, contact,
= 0,35, crown 0
1,2075E-2 1,1620E-2
-
3,767
KI, loading n°3, contact,
= 0,36, crown 0
2,1757E-2 2,15976E-2
-
0,73
KI, loading n°3, contact,
= 0,40, crown 0
6,6478E-2 6,67511E-2 0,41
Code_Aster
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Version
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
10/12
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
Identification Reference
Aster %
difference
KI, loading n°3, contact,
= 0,33, crown 1
1,2075E-3 1,19085E-3
-
1,19
KI, loading n°3, contact,
= 0,335, crown 1 3,0187E-3 3,03577E-3 0,565
KI, loading n°3, contact,
= 0,34, crown 1
5,4336E-3 5,4136E-3
0,368
KI, loading n°3, contact,
= 0,345, crown 1 8,5865E-3 8,2570E-3
-
3,838
KI, loading n°3, contact,
= 0,35, crown 1
1,2075E-2 1,1621E-2
-
3,761
KI, loading n°3, contact,
= 0,36, crown 1
2,1757E-2 2,15975E-2
-
0,73
KI, loading n°3, contact,
= 0,40, crown 1
6,6478E-2 6,67506E-2 0,41
Identification Reference
Aster %
difference
KI, loading n°3, contact,
= 0,33, crown 2
1,2075E-3 1,1604E-3
-
3,902
KI, loading n°3, contact,
= 0,335, crown 2 3,0187E-3 3,03287E-3 0,469
KI, loading n°3, contact,
= 0,34, crown 2
5,4336E-3 5,4131E-3
-
0,376
KI, loading n°3, contact,
= 0,345, crown
2
8,5865E-3 8,2572E-3
-
3,635
KI, loading n°3, contact,
= 0,35, crown 2
1,2075E-2 1,1621E-2
-
3,76
KI, loading n°3, contact,
= 0,36, crown 2
2,1757E-2 2,1598E-2
-
0,73
KI, loading n°3, contact,
= 0,40, crown 2
6,6478E-2 6,67529E-2 0,41
Identification Reference
Aster %
difference
KI, loading n°3, contact,
= 0,335, crown 3 3,0187E-3 2,7419E-3
-
9,169
KI, loading n°3, contact,
= 0,34, crown 3
5,4336E-3 5,4252E-3
-
0,154
KI, loading n°3, contact,
= 0,345, crown 3 8,5865E-3 8,2570E-3
-
3,837
KI, loading n°3, contact,
= 0,35, crown 3
1,2075E-3 1,1614E-2
-
3,81
KI, loading n°3, contact,
= 0,36, crown 3
2,1757E-2 2,1598E-2
0,73
KI, loading n°3, contact,
= 0,40, crown 3
6,6478E-2 6,67525E-2 0,41
Identification Reference
Aster %
difference
0
0,3410 0,3410
0
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Version
6.3
Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
11/12
Manual of Validation
V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
4.2 Remarks
The tables below give the rate of refund of energy G for two values of the coefficient
who correspond to nonthe separation of the lip of the fissure. (There is separation of the lip for
> 0,32).
Identification
Reference
G ASTER
G, loading n°3, contact,
= 0,30, crown 0
0
-
8,7941 10
-
16
G, loading n°3, contact,
= 0,30, crown 1
0
4,4308 10
-
15
G, loading n°3, contact,
= 0,30, crown 2
0
3,3312 10
-
15
G, loading n°3, contact,
= 0,30, crown 3
0
4,4794 10
-
13
Identification
Reference
G ASTER
G, loading n°3, contact,
= 0,32, crown 0
0
-
1,17E-14
G, loading n°3, contact,
= 0,32, crown 1
0
-
3,26E-16
G, loading n°3, contact,
= 0,32, crown 2
0
-
1,02E-15
G, loading n°3, contact,
= 0,32, crown 3
0 4,23E-13
4.3 Parameters
of execution
Version: 6.03
Machine: CRAY C90
Overall dimension memory:
16 MW
Time CPU To use: 136 seconds
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Version
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Titrate:
HPLP310 - Biblio_35 Fissures radial intern in a thick cylinder
Date:
22/11/02
Author (S):
S. GRANET, I. CORMEAU, B. KURTH
Key
:
V7.02.310-A
Page:
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V7.02 booklet: Thermomechanical stationary linear
HT-66/02/001/A
5
Summary of the results
The calculation of G is correct in all the cases, including for a completely closed fissure.