Code_Aster ®
Version
4.0
Titrate:
SZLZ108 Dommage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V9.01 booklet: Tire
Document: V9.01.108
SZLZ108 - Dommage by the methods of TAHERI
(“TAHERI_MANSON” and “TAHERI_MIXTE”)
Summary:
The purpose of this test is calculation of the damage starting from a history of purely uniaxial loading in
deformations by methods “TAHERI_MANSON” or “TAHERI_MIXTE”.
The methods of Taheri apply only to loadings in deformations and do not allow
contrary to the method of Manson-Coffin to hold account about appearance of the cycles of constraints.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ108 Dommage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A Page:
2/6
1
Problem of reference
The analysis consists in determining the damage undergone by a structure subjected to a history of
loading in deformations. One uses the method of Rainflow to determine the number of cycles
elementary and it half amplitude of each cycle.
For the loadings considered, the method of Rainflow determines 5 cycles of half amplitude:
1
2
3
4
5
= 0 2
. 5,
= 0 2
. 5,
= 0 7
. 5,
= 0 2
. 5 and
= 17
. 5.
2
2
2
2
2
Then one calculates the damage undergone by the structure by the method of TAHERI_MANSON and the method
TAHERI_MIXTE.
As long as the amplitude of deformations of the various cycles applied to the structure remains increasing
1 2
…
N
, the methods of TAHERI_MANSON and TAHERI_MIXTE are identical to
2
2
2
method of MANSON_COFFIN (calculation of the number of cycles to the rupture, Nrupt, by interpolation on
the curve of Manson-Coffin and calculation of the damage by 1 NR
).
rupt
I
i-1
On the other hand if a cycle I presents a half amplitude
lower than
, methods of
2
2
Taheri differ from the method of Manson-Coffin.
·
I
The method of “TAHERI_MANSON” consists in determining an amplitude of constraint
with
2
I
to leave
and
2
max (maximum value of the half amplitude of deformation met before
cycle I).
With this intention, the user must provide a tablecloth
,
2
2
max under the operand
TAHERI_NAPPE.
*
I
I
From
, one determines a half amplitude of deformations
using a function
2
2
introduced under operand TAHERI_FONC. The value of the elementary damage of cycle I, is
* I
determined by interpolation of
on the curve of Manson_Coffin.
2
· For method “TAHERI_MIXTE”, one proceeds in the same way for the determination of the half
I
amplitude of constraint
, then one determines the value of the elementary damage of cycle I
2
I
by interpolation of
on the curve of Wöhler.
2
This method thus requires the data of the curves of Wöhler and Manson_Coffin.
One determines the total damage by linear office plurality of the elementary damage.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ108 Dommage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A Page:
3/6
1.1
Material properties
For the calculation of the damage of “TAHERI_MANSON”, one needs the curve of Manson_Coffin, one
tablecloth allowing to calculate
from
and
2
2
max and of a function allowing to calculate
*
from
. The tablecloth (cyclic curve of work hardening with pre-work hardening) is introduced
2
2
under operand TAHERI_NAPPE and the function (cyclic curve of work hardening) under the operand
TAHERI_FONC. The curve of Manson_Coffin as for it is introduced into DEFI_MATERIAU
[U4.23.01].
For the calculation of the damage of “TAHERI_MIXTE”, one needs the curve of Manson_Coffin, of
curve of Wöhler and a tablecloth (cyclic curve of work hardening with pre-work hardening) allowing
to calculate
from
and
2
2
max. the tablecloth is introduced under operand TAHERI_NAPPE.
curve of Manson_Coffin and the curve of Wöhler is introduced into DEFI_MATERIAU.
Curve of Manson_Coffin
Curve of Wöhler
Nrupt
200.000.
200.000.
2
2.
200.
2
Tablecloth of Taheri (curves of cyclic work hardening with pre-work hardening)
max = 1.
max = 0.5
525.
2
2
25.
550.
50.
10.
2
10.
2
Function of Taheri (cyclic curve of work hardening)
2
10.
1000.
2
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ108 Dommage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A Page:
4/6
1.2
History of the loading
T
0.
1.
2.
3.
4.
5.
6.
(T)
0.
3.5
3.
3.5
3.
3.5
1.
7.
8.
9.
2.5
0.
0.5
2
Reference solution
2.1
Method of calculation used for the reference solution
The history of loading being very simple, the results of reference can be obtained
manually by applying the algorithms presented in the reference document [R7.04.01].
2.2
Results of Référence
Calculation of the elementary damage by the method of TAHERI_MANSON:
Cycle
1
Too bad
:
5.7142857E-6
Cycle
2
Too bad
:
5.7142857E-6
Cycle
3
Too bad
:
8.E-6
Cycle
4
Too bad
:
6.6666667E-6
Cycle
5
Too bad
:
4.E-5
calculation of the total damage by linear office plurality of Miner:
Too bad: 6.6095E-5
Calculation of the elementary damage by the method of TAHERI_MIXTE:
Cycle
1
Too bad
:
5.7142857E-6
Cycle
2
Too bad
:
5.7142857E-6
Cycle
3
Too bad
:
8.E-6
Cycle
4
Too bad
:
6.6666667E-6
Cycle
5
Too bad
:
4.E-5
calculation of the total damage by linear office plurality of Miner:
Too bad: 6.6095E-5
2.3
Uncertainty on the solution
Analytical solution.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ108 Dommage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A Page:
5/6
3 Modeling
3.1 Functionalities
tested
Order
Key word
Operand
Key
[U4.67.01]
POST_FATIGUE
HISTOIRE
EPSI
COMPTAGE
“RAINFLOW”
DOMMAGE
“TAHERI_MANSON”
“TAHERI_MIXTE”
TAHERI_NAPPE
TAHERI_FONC
MATER
CUMUL
“LINEAIRE”
INFO
2
DEFI_MATERIAU
FATIGUE
WOHLER
[U4.23.01]
MANSON_COFFIN
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SZLZ108 Dommage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A Page:
6/6
4
Results of modeling
4.1 Values
tested
Identification
Reference
Aster
% difference
Method “TAHERI_MANSON”
Cycle 1 DAMAGE
5.7142857E6
5.7142857E6
0.
Cycle 2 DAMAGE
5.7142857E6
5.7142857E6
0.
Cycle 3 DAMAGE
8.E6
7.9999999E6
0.
Cycle 4 DAMAGE
6.6666667E6
6.6666666E6
0.
Cycle 5 DAMAGE
4.E5
3.9999999E6
0.
DOMM_CUMU
6.6095E5
6.6095238E5
0.
Method “TAHERI_MIXTE”
Cycle 1 DAMAGE
5.7142857E6
5.7142857E6
0.
Cycle 2 DAMAGE
5.7142857E6
5.7142857E6
0.
Cycle 3 DAMAGE
8.E6
7.9999999E6
0.
Cycle 4 DAMAGE
6.6666667E6
6.6666666E6
0.
Cycle 5 DAMAGE
4.E5
3.9999999E6
0.
DOMM_CUMU
6.6095E5
6.6095238E5
0.
4.2 Parameters
of execution
Version: 3.06.18
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
2.42 seconds
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