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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
1/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V9.01 booklet: Tire
Document: V9.01.100
SZLZ100 - Tire on an eccentric cycle
Summary:
The purpose of this test is calculation of the damage starting from a history of loading in stresses, then of a history
of loading in deformations.
Starting from a simple history of loading defined by
DEFI_FONCTION
[U4.21.02], the cycles are extracted
elementary by the method of counting of cycles of the RCCM [R7.04.01], then one calculates the damage
elementary associated each cycle, by interpolation on the curve of Wöhler of material (if history of
loading in stresses and by interpolation on the curve of Manson-Whetstone sheath of material) (if history of
loading in deformations).
The curve of Wöhler is defined by
DEFI_FONCTION
[U4.21.02]. The interpolation is of logarithmic curve type on
the number of cycles to the rupture NR and on the alternate stress Salt.
The curve of Manson-Whetstone sheath is also defined by
DEFI_FONCTION
.
To finish, one determines the total damage undergone by the part by cumulating all the elementary damage by
linear rule To mine.
In this test, one also checks the taking into account of the value of the mean stress on the calculation of
elementary damage by the method of Wöhler. The first calculation is carried out without correction, a second
with a correction To stack and the third with a correction of Goodman.
On this simple example, the extraction of the elementary cycles and the calculation of the damage can be made
manually, by applying the algorithms presented in the reference document [R7.04.01].
Results provided by the operator
POST_FATIGUE
[U4.67.01] are of this fact very satisfactory.
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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
2/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
1
Problem of reference
1.1 Geometry
The analysis consists in determining the damage undergone by a part in a point to which one provides the history
of loading.
To test the calculation of the damage by the method of Wöhler, one considers the history of loading in
stresses and one extracts the elementary cycles by a method of counting of cycles, which is in
this test method of the RCCM. Then one calculates the elementary damage due to each elementary cycle,
by interpolation on the curve of Wöhler of material.
The curve of Wöhler is founie in the form of a function point by point, which gives the value of
a number of cycles to the rupture according to the alternate stress
Salt
=
2
.
The interpolation is of logarithmic curve type on the X-coordinate and the ordinate and one authorize to prolong
linearly this function on the right and on the left.
Three different calls to the operator
POST_FATIGUE
[U4.67.01] allow to take account or not of
the mean stress of each elementary cycle.
The adopted correction is that of the diagram of Haigh, either according to the line of Goodman or according to
the parabola To stack [R7.04.01].
One determines the total damage by the linear rule of office plurality To mine.
To test the calculation of the damage by the method of Manson-Whetstone sheath, one considers the history of
loading in deformations and one extracts the elementary cycles by a method of counting of
cycles, which is in this test the method of the RCCM. Then one calculates the elementary damage due to
each elementary cycle, by interpolation on the curve of Manson-Whetstone sheath of material.
The curve of Manson-Whetstone sheath is provided in the form of a function point by point, which gives the value
number of cycles to the rupture according to
2
.
One determines the total damage by the linear rule of office plurality To mine.
1.2
Material properties
The curve of Wöhler of the material, which gives the value of the number of cycles to the rupture according to
the alternate stress is point by point defined by:
Salt
138.
152.
165.
180.
200.
250.
295.
305.
NR
1000000.
500000.
200000.
100000.
50000.
20000.
12000.
10000.
340.
430.
540.
690.
930.
1210.
1590.
2210.
2900.
5000.
2000.
1000.
500.
200.
100.
50.
20.
10.
Known = limit with the rupture of material = 850.
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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
3/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
History of the loading
T
0.
1.
2.
3.
4.
(T)
50.
600.
50.
­ 500.
50.
The curve of Manson-Whetstone sheath of the material, which gives the value of the number of cycles to the rupture in
function of
2
is point by point defined by:
2
138.
152.
165.
180.
200.
250.
295.
305.
NR
1000000.
500000.
200000.
100000.
50000.
20000.
12000.
10000.
340.
430.
540.
690.
930.
1210.
1590.
2210.
2900.
5000.
2000.
1000.
500.
200.
100.
50.
20.
10.
History of the loading
T
0.
1.
2.
3.
4.
(T)
50.
600.
50.
­ 500.
50.
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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
4/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
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
The counting of the elementary cycles by method RCCM leads to:
Nb_Cycl = 2
Cycle 1
Vale_Min:
- 500.
Vale_Max:
600.
Cycle 2
Vale_Min:
50.
Vale_Max:
50.
·
First call to
POST_FATIGUE
:
calculation of the elementary damage by the method of Wöhler without correction of HAIGH:
Cycle 1
Too bad:
1.053257E3
Cycle 2
Too bad:
0.
calculation of the total damage by linear office plurality To mine:
Too bad: 1.053257E3
·
Second call to
POST_FATIGUE
:
calculation of the elementary damage by the method of Manson-Whetstone sheath:
Cycle 1
Too bad:
1.053257E3
Cycle 2
Too bad:
0.
calculation of the total damage by linear office plurality To mine:
Too bad: 1.053257E3
·
Third call to
POST_FATIGUE
:
calculation of the elementary damage by the method of Wöhler with correction To stack:
Cycle 1
Too bad:
1.063631E3
Cycle 2
Too bad:
0.
calculation of the total damage by linear office plurality To mine:
Too bad: 1.063631E3
·
Fourth call to
POST_FATIGUE
:
calculation of the elementary damage by the method of Wöhler with correction of Goodman:
Cycle 1
Too bad:
1.250219E3
Cycle 2
Too bad:
0.
calculation of the total damage by linear office plurality To mine:
Too bad: 1.250219E3
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Estimate of fatigue to great numbers of cycles. Document [R7.04.01].
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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
5/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
3 Modeling
With
3.1 Functionalities
tested
Order
POST_FATIGUE
[U4.67.01].
Key word
Operand
HISTORY
SIGM:
COUNTING:
“RCCM”
TOO BAD:
“WOHLER”
MATER:
CORR_SIGM_MOYE:
“TO STACK”
“GOODMAN”
OFFICE PLURALITY:
“LINEAR”
INFORMATION:
2
HISTORY
EPSI:
COUNTING:
“RCCM”
TOO BAD:
“MANSON_COFFIN”
MATER:
OFFICE PLURALITY:
“LINEAR”
INFORMATION:
2
Key word
Operand
Keys
DEFI_MATERIAU
TIRE
WOHLER:
[U4.23.01]
KNOWN:
TIRE
'MANSON_COFFIN:
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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
6/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
NB_CYCL
2.
2.
0.
Cycle 1 VALE_MIN
­ 500.
­ 500.
0
VALE_MAX
600.
600.
0.
Cycle 2 VALE_MIN
50.
50.
0.
VALE_MAX
50.
50.
0.
First call to
POST_FATIGUE
:
Calculation of the damage:
Wöhler without correction
Cycle 1 DAMAGE
1.053257E3
1.053257E3
0.
Cycle 2 DAMAGE
0.
1.686747E7
1.69E7
DOMM_CUMU
1.053257E3
1.053425E3
0.016
Second call to
POST_FATIGUE
:
Calculation of the damage:
Manson-whetstone sheath
Cycle 1 DAMAGE
1.053257E3
1.053257E3
0.
Cycle 2 DAMAGE
0.
1.686747E7
1.69E7
DOMM_CUMU
1.053257E3
1.053425E3
0.016
Third call to
POST_FATIGUE
:
Calculation of the damage:
Wöhler correction To stack
Cycle 1 DAMAGE
1.063631E3
1.063631E3
0.
Cycle 2 DAMAGE
0.
1.686747E7
1.69E7
DOMM_CUMU
1.063631E3
1.063800E3
0.016
Fourth call to
POST_FATIGUE
:
Calculation of the damage:
Wöhler Goodman correction
Cycle 1 DAMAGE
1.250219E3
1.250219E3
0.
Cycle 2 DAMAGE
0.
1.686747E7
1.69E7
DOMM_CUMU
1.250219E3
1.250388E3
0.013
4.2 Parameters
of execution
Version: 3.06.18
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
3.4265 seconds
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Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
7/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
5
Summary of the results
This test is very simple and makes it possible to determine the values of reference manually, while applying
algorithms described in the reference document [R7.04.01].
So results of
Code_Aster
coincide perfectly with the values of reference.
background image
Code_Aster
®
Version
4.0
Titrate:
SZLZ100 Tires on an eccentric cycle
Date:
19/01/98
Author (S):
A. Mr. DONORE
Key:
V9.01.100-A
Page:
8/8
Manual of Validation
V9.01 booklet: Tire
HI-75/96/038 - Ind A
Intentionally white left page.