Code_Aster
®
Version
4.0
Titrate:
SZLZ107 Criteria of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A
Page:
1/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V9.01 booklet: Tire
Document: V9.01.107
SZLZ107 - Criteria of fatigue of CROSSLAND and
DANG VAN-PAPADOPOULOS
Summary:
The purpose of this test is calculation of the criteria of CROSSLAND and DANG VAN-PAPADOPOULOS.
Starting from a periodic and radial multiaxial loading, one calculates the value of the criterion of CROSSLAND, then
value of the criterion of DANG VAN-PAPADOPOULOS.
The loading being radial the values of the two criteria must be identical.
This test results from the thesis of I. PAPADOPOULOS “Tires polycyclic metals: a new approach”
and corresponds to a test of Gough-Pollard [bib1].
Results provided by the operator
POST_FATIGUE
[U4.67.01] are completely satisfactory.
Code_Aster
®
Version
4.0
Titrate:
SZLZ107 Criteria of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A
Page:
2/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
1
Problem of reference
The analysis consists in determining the criterion of CROSSLAND and the criterion of DANG
VAN-PAPADOPOULOS in a point of a structure subjected to a periodic multiaxial loading
radial.
Criterion of CROSSLAND:
has
P
+
- < =
has
B
max
0
where
has
T
T
T
T
T
T
T
T
T T
Max Max S T
S T
Max Max
S
S
S
S
S
S
S
P
Max
trace
D
D
=
-
=
+
+
+
+
+
=
=
=
=
-
=
1
2
1
2
1
2
2
2
2
1
3
3
3
0
0
1
0
0
0
11
2
22
2
33
2
12
2
13
2
23
2
0
0
0
0
0
0
1
0
1
~ () ~ ()
(~
~
~
~
~
~)
~
(
())
(
) (
)
max
amplitude of cission
with
diverter of the tensor of the stresses
maximum hydrostatic pressure
has
and
B
with
0
= limit of endurance in alternate pure shearing
D
0
= limit of endurance in alternate pure traction and compression
The criterion is:
Rcrit
P
has
=
+
-
has
B
max
If
Rcrit
is negative or null, there is no damage. If
Rcrit
it is positive is succeptible y to have
too bad.
Criterion of DANG VAN-PAPADOPOULOS:
K
P
*
max
+
- < =
has
B
0
where
K
R
*
=
2
where
R
radius of the smallest sphere circumscribed with the way of loading in
the space of the diverters of stresses
~
S
R
Max
S T
C
S T
C
C
C
Min max
S T
C
S T
C
P
Max
trace
D
D
T T
C K
T T
T T
=
-
-
-
-
=
=
=
-
=
0
0
0
0
0
0
0
1
3
3
3
(~ ()
*):(~ ()
*)
(~ ()
):(~ ()
)
(
())
(
) (
)
max
*
* =
where
is the center of the hypersphère
maximum hydrostatic pressure
has
and
B
with
0
= limit of endurance in alternate pure shearing
D
0
= limit of endurance in alternate pure traction and compression
Code_Aster
®
Version
4.0
Titrate:
SZLZ107 Criteria of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A
Page:
3/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
The criterion is:
Rcrit
K
P
=
+
-
*
max
has
B
If
Rcrit
is negative or null, there is no damage. If
Rcrit
it is positive is succeptible y to have
too bad.
1.1
Material properties
0
= limit of endurance in alternate pure shearing = 352. MPa
D
0
= limit of endurance in alternate pure traction and compression = 540.97 MPa
1.2
History of the loading
T
1.
2.
3.
xx
(T)
411.
0.
411.
xy
(T)
205.
0.
205.
yy
(T) =
zz
(T) =
xz
(T) =
yz
(T)
0.
0.
0.
The loading is considered periodic.
2
Reference solution
2.1
Method of calculation used for the reference solution
The results of reference result from the thesis of I. PAPADOPOULOS [bib1]. For the criterion of
CROSSLAND, one can also obtain them manually.
The loading being radial the two criteria must provide the same results.
2.2
Results of Reference
For the criterion of CROSSLAND, one tests the value of the amplitude of cission, the value of the pressure
hydrostatic maximum and the value of the criterion:
has
P
Rcrit
=
=
=
313.579 MPa
137. MPa
8.281
max
For the criterion of DANG VAN-PAPADOPOULOS, one tests the value of the radius of the smallest sphere
circumscribed with the loading, the value of the maximum hydrostatic pressure and the value of the criterion:
K
P
Rcrit
*
max
=
=
=
313.579 MPa
137. MPa
8.281
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibiographic
[1]
Thesis of I. PAPADOPOULOS “Tires polycyclic metals: a new approach”
(1987) ENPC.
Code_Aster
®
Version
4.0
Titrate:
SZLZ107 Criteria of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A
Page:
4/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
3 Modeling
3.1 Functionalities
tested
Order
Key word
Operand
Key
[U4.67.01]
POST_FATIGUE
HISTORY
SIGM_XX
SIGM_YY
SIGM_ZZ
SIGM_XY
SIGM_XZ
SIGM_YZ
CRITERION
“CROSSLAND”
“PAPADOPOULOS”
MATER
INFORMATION
DEFI_MATERIAU
TIRE
D0
[U4.23.01]
TAU0
Code_Aster
®
Version
4.0
Titrate:
SZLZ107 Criteria of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A
Page:
5/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
4
Results of modeling
4.1 Values
tested
Identification
Reference
Aster
% difference
Criterion of CROSSLAND
PRES_HYDRO_MAX (Pmax)
137.
137.
0.
AMPLI_CISSION (
has
)
313.579
313.579
0.
Criterion (Rcrit)
8.281
8.2809
0.001
Criterion of DANG VAN-PAPADOPOULOS
PRES_HYDRO_MAX (Pmax)
137.
137.
0.
RAYON_SPHERE (K *
)
313.579
313.579
0.
Criterion (Rcrit)
8.281
8.2809
0.001
4.2 Parameters
of execution
Version: 3.06.18
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
2.54 seconds
Code_Aster
®
Version
4.0
Titrate:
SZLZ107 Criteria of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A
Page:
6/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
5
Summary of the results
Results provided by
Code_Aster
coincide perfectly with the values of reference.