Code_Aster ®
Version
4.0
Titrate:
SZLZ107 Critères of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V9.01 booklet: Tire
Document: V9.01.107
SZLZ107 - Critères 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 “polycyclic Fatigue of metals: a new approach”
and corresponds to a test of Gough-Pollard [bib1].
The results provided by operator POST_FATIGUE [U4.67.01] are completely satisfactory.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ107 Critères of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A Page:
2/6
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
- B
max
< =
has
P
0
= 1
~
~
2
2
2
2
2
2
(1) - (0) = 1
1 (~ ~ ~
~
~
~
11 + 22 + 33 + 2 12 + 2 13 +
has
Max Max S T
S T
Max Max
S
S
S
S
S
2s)
2
23
0 t0T
0 T1 T
2
0 t0T
0 T1 T
2
= amplitude of cission
with S
~ deviative of the tensor of the constraints
where
1
Pmax = Max (trace
()) = maximum hydrostatic pressure
0 tT 3
has =
D
D
0
0
(0 -
) (
)
and
B =
3
3
0
with 0 = limit of endurance in alternate pure shearing
d0 = limit of endurance in alternate pure traction and compression
The criterion is: Rcrit = + has P
-
has
B
max
If Rcrit is negative or null, there is no damage. If Rcrit is positive it is succeptible y to have
too bad.
Criterion of DANG VAN-PAPADOPOULOS:
K * + has P
- B < =
max
0
*
where K
R
=
where R radius of the smallest sphere circumscribed with the way of loading in
2
the space of the diverters of constraints ~
S
R = Max (s~ (T) - C *):(s~ (T) - C *)
where C * is the center of the hypersphère
0 tT
C * = Min Max (s~ (T) - C):(s~ (T) - C)
CK
0 tT
1
P
max = Max (
trace ()) = maximum hydrostatic pressure
0 tT 3
D
D
has =
0
0
(
0 -
) (
)
and
B = 0
3
3
with 0 = limit of endurance in alternate pure shearing
d0 = limit of endurance in alternate pure traction and compression
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ107 Critères of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A Page:
3/6
*
The criterion is: Rcrit = K + has Pmax - B
If Rcrit is negative or null, there is no damage. If Rcrit is positive it is succeptible y to have
too bad.
1.1
Material properties
0 = limit of endurance in alternate pure shearing = 352. MPa
d0 = 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 Référence
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:
= 313.579 MPa
= 137. MPa
=
has
P
Rcrit
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 * = 313.579 MPa
P
= 137. MPa
Rcrit =
max
8.281
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibiographic
[1]
Thesis of I. PAPADOPOULOS “polycyclic Fatigue of metals: a new approach”
(1987) ENPC.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ107 Critères of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A Page:
4/6
3 Modeling
3.1 Functionalities
tested
Order
Key word
Operand
Key
[U4.67.01]
POST_FATIGUE
HISTOIRE
SIGM_XX
SIGM_YY
SIGM_ZZ
SIGM_XY
SIGM_XZ
SIGM_YZ
CRITERE
“CROSSLAND”
“PAPADOPOULOS”
MATER
INFO
DEFI_MATERIAU
FATIGUE
D0
[U4.23.01]
TAU0
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ107 Critères of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A Page:
5/6
4
Results of modeling
4.1 Values
tested
Identification
Reference
Aster
% difference
Criterion of CROSSLAND
PRES_HYDRO_MAX (Pmax)
137.
137.
0.
AMPLI_CISSION (A)
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
Obstruction memory:
8 MW
Time CPU To use:
2.54 seconds
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ107 Critères of fatigue CROSSLAND and PAPADOPOULOS
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.107-A Page:
6/6
5
Summary of the results
The results provided by Code_Aster coincide perfectly with the values of reference.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A