Code_Aster
®
Version
4.0
Titrate:
SZLZ108 Damage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-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: V9.01.108
SZLZ108 - Damage 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 the 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-Whetstone sheath to hold account about appearance of the cycles of stresses.
Code_Aster
®
Version
4.0
Titrate:
SZLZ108 Damage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-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 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
2
0 25
2
0 25 2
0 75
2
0 25
2
1 75
=
=
=
=
=
.
,
.
,
.
,
.
.
and
.
Then one calculates the damage undergone by the structure by the method of
TAHERI_MANSON
and method
of
TAHERI_MIXTE
.
As long as the amplitude of deformations of the various cycles applied to the structure remains increasing
1
2
2
2
2
…
N
, methods of
TAHERI_MANSON
and
TAHERI_MIXTE
are identical to
method of
MANSON_COFFIN
(calculation of the number of cycles to the rupture,
NR
rupt
, by interpolation on
the curve of Manson-Whetstone sheath and calculation of the damage by
1 NR
rupt
).
On the other hand if a cycle
I
present a half amplitude
I
2
lower than
I
-
1
2
, methods of
Taheri differ from the method of Manson-Whetstone sheath.
·
Method of
“TAHERI_MANSON”
consist in determining an amplitude of stress
I
2
with
to leave
I
2
and
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
.
From
I
2
, one determines a half amplitude of deformations
I
*
2
using a function
introduced under the operand
TAHERI_FONC
. The value of the elementary damage of the cycle
I
, is
determined by interpolation of
I
*
2
on the curve of Manson_Coffin.
·
For the method
“TAHERI_MIXTE”
, one proceeds in the same way for the determination of the half
amplitude of stress
I
2
, then one determines the value of the elementary damage of the cycle
I
by interpolation of
I
2
on the curve of Wöhler.
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.
Code_Aster
®
Version
4.0
Titrate:
SZLZ108 Damage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A
Page:
3/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
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
2
from
2
and
max
and of a function allowing to calculate
*
2
from
2
. The tablecloth (cyclic curve of work hardening with pre-work hardening) is introduced
under the 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
2
from
2
and
max
. The tablecloth is introduced under the operand
TAHERI_NAPPE
.
curve of Manson_Coffin and the curve of Wöhler is introduced into
DEFI_MATERIAU
.
200.000.
2.
2
NR
rupt
Curve of Manson_Coffin
200.000.
200.
2
Curve of Wöhler
25.
10.
max
= 0.5
Tablecloth of Taheri (curves of cyclic work hardening with pre-work hardening)
525.
2
2
10.
2
2
550.
50.
max
= 1.
10.
1000.
Function of Taheri (cyclic curve of work hardening)
2
2
Code_Aster
®
Version
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Titrate:
SZLZ108 Damage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A
Page:
4/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
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 Reference
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 To mine:
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 To mine:
Too bad: 6.6095E-5
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
4.0
Titrate:
SZLZ108 Damage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A
Page:
5/6
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
EPSI
COUNTING
“RAINFLOW”
TOO BAD
“TAHERI_MANSON”
“TAHERI_MIXTE”
TAHERI_NAPPE
TAHERI_FONC
MATER
OFFICE PLURALITY
“LINEAR”
INFORMATION
2
DEFI_MATERIAU
TIRE
WOHLER
[U4.23.01]
MANSON_COFFIN
Code_Aster
®
Version
4.0
Titrate:
SZLZ108 Damage by the methods of TAHERI
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.108-A
Page:
6/6
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
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
Overall dimension memory:
8 MW
Time CPU To use:
2.42 seconds
5
Summary of the results
Results provided by
Code_Aster
coincide perfectly with the values of reference.