Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
1/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V9.01 booklet: Tire
Document:
V
V
9
9
.
.
0
0
1
1
.
.
1
1
0
0
5
5
SZLZ105 - Counting of cycles by RAINFLOW
and calculation of the damage
Summary:
Transitory linear elastic problem quasi-static in mechanics of the structures.
Calculation of the final damage in an element subjected to a cyclic loading, with an elastic behavior
linear.
A modeling in plane stresses and a modeling in 3D.
This test validates the method of counting of cycles (RAINFLOW) established in the operator
CALC_FATIGUE
[U4.67.01] as well as the method of calculation of the damage in imposed stress (curve of Wöhler) or
imposed deformation (curve of Manson-Whetstone sheath). The reference solution is an analytical solution.
It also validates the calculation of the stresses and equivalent deformations using the options
EQUI_ELGA_SIGM
,
EQUI_ELNO_SIGM
,
EQUI_ELGA_EPSI
,
EQUI_ELNO_EPSI
, EQUI_ELGA_EPME and
EQUI_ELNO_EPME.
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
2/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
1
2
3
4
y
X
F (T)
1.2
Material properties
Linear elasticity: E = 1. MPa
= 0.3
1000.
Curve of Wöhler
Curve of Manson-Whetstone sheath
10.
NR (cycles)
NR (cycles)
10.
2 (
MPa
)
1000.
2
1.3
Boundary conditions and loadings
·
Locked on face 1-4 following X - node 1 locked according to Y.
·
In unit simple traction on the face 2-3.
·
Loading F (T) in teeth of saw (according to the Article of Downing and Socie 1982) [bib1].
- 3
1
2
3
4
1 2
3 4 5 6 7
8
T
F (T)
1.4 Conditions
initial
Null stresses and deformations.
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
3/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution
·
calculation of the stresses and deformations. For a loading in simple traction, one obtains a state
of homogeneous stress uniaxial in any point:
=
=
0 0
0 0 0
0 0 0
0 0
0
0
0 0
and
the equivalent sizes are thus
VMIS
TRESCA
VMIS SG
=
=
=
,
_
and
INVA
INVA
SG
_
_
,
* sign
2
2
2
3
2
3
2
3
=
-
=
-
+
·
then manual calculation of the cycles by the method of RAINFLOW, as well as amplitudes of
loading
2
2
or
cycles
/2
INVA
- 2
2
/
1
2
3
4
1.
0.5
1.
3.5
0.8667
0.433315
0.8667
3.03335
·
finally carryforward of these values on the curves of Wöhler or Manson-Whetstone sheath to estimate it
unit damage with each cycle
I
, that is to say
NR
I
I
= 1
(
NR
I
being the number of cycles with rupture for
a given amplitude), as well as the cumulated damage
D
I
I
=
(linear rule of office plurality of
TO MINE).
Note:
One will use as equivalent stress
VMIS SG
_
=
and like equivalent deformation
INVA
SG
-
=
-
+
2
2
3
2
3
* sign
.
2.2
Results of reference
·
Being given the values of the parameters of loading used, one obtains simply in end
loading (increment 8)
= -
= -
=
=
3
3
0 9
2 6
2
.
.
.
.
_
INVA
.
·
For the calculation of the damage, one obtains:
D
D
Wöhler
I
I
Manson
I
I
=
=
=
=
-
=
-
=
4 813310
4 67 10
3
1
4
3
1
4
.
.
2.3 References
bibliographical
[1]
DOWNING and SOCIE, 1982. “Simple Rainflow counting algorithms”. Int. J.
Tire,
January 1982 (p. 31).
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
4/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling in plane stresses:
y
X
4
3
2
1
F/2
F/2
- 3
1
2
3
4
T (S)
1 2 3 4 5 6 7 8
F (NR)
3.2
Characteristics of the mesh
1 mesh QUAD4.
Square
width = 1
thickness = 1
3.3 Functionalities
tested
Order Mot-clé
factor
Key word
simple
Key argument
CALC_FATIGUE
OPTION
“DOMA_ELNO_SIGM”
“DOMA_ELNO_EPSI”
[U4.67.02]
HISTORY
EQUI_GD
“VMIS_SG”
“INVA_2SG”
HISTORY
RESULT
TOO BAD
“WOHLER”
“MANSON_COFFIN”
MATER
CALC_ELEM
OPTION
“EQUI_ELGA_SIGM”
[U4.61.02]
“EQUI_ELNO_SIGM”
“EQUI_ELGA_EPSI”
“EQUI_ELNO_EPSI”
DEFI_MATERIAU TIRES WOHLER
[U4.23.01]
MANSON_COFFIN
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
5/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
in all nodes at the end of the loading in
stress or in deformation
Wöhler damage
4.8133 10
3
4.813315
10
3
0.0003
Damage Manson-Whetstone sheath
4.6705 10
3
4.67048
10
3
- 0.0003
- 3.
- 3.
0.
VMIS
3. 3.
0.
TRESCA
3. 3.
0.
VMIS SG
_
- 3.
- 3.
0.
- 3.
- 3.
0.
0.9 0.9
0.
INVA
_2
2.6 2.6
0.
INVA
SG
_2
- 2.6
- 2.6
0.
4.2 Remarks
Fast test in CPU.
4.3 Parameters
of execution
Version: 5.02.10
Machine: SGI - Origin 2000
Overall dimension memory:
128 Mo
Time CPU To use: 4.84 seconds
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
6/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
Modeling in 3D:
y
X
6
8
7
F/4
F/4
1
5
F/4
2
4
F/4
3
5.2
Characteristics of the mesh
1 mesh HEXA8.
cubic of width = 1
5.3 Functionalities
tested
Order Mot-clé
factor
Key word
simple
Key argument
CALC_FATIGUE
OPTION
“DOMA_ELNO_SIGM”
“DOMA_ELNO_EPSI”
[U4.67.02]
“DOMA_ELNO_EPME”
HISTORY
EQUI_GD
“VMIS_SG”
“INVA_2SG”
HISTORY
RESULT
TOO BAD
“WOHLER”
“MANSON_COFFIN”
MATER
CALC_ELEM
OPTION
“EQUI_ELGA_SIGM”
[U4.61.02]
“EQUI_ELNO_SIGM”
“EQUI_ELGA_EPSI”
“EQUI_ELNO_EPSI”
“EQUI_ELGA_EPME”
“EQUI_ELNO_EPME”
DEFI_MATERIAU TIRES WOHLER
[U4.23.01]
MANSON_COFFIN
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
7/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
in all nodes at the end of the loading
Wöhler damage
4.8133 10
3
4.813315
10
3
0.
Damage Manson-Whetstone sheath
4.6705 10
3
4.67048
10
3
0.
- 3.
- 3.
0.
VMIS
3. 3.
0.
TRESCA
3. 3.
0.
VMIS SG
_
- 3.
- 3.
0.
- 3.
- 3.
0.
0.9 0.9
0.
INVA
_2
2.6 2.6
0.
INVA
SG
_2
- 2.6
- 2.6
0.
(
)
- HT
INVA_2
2.6 2.6
0.
(
)
- HT
INVA
SG
_2
- 2.6
- 2.6
0.
6.2 Remarks
Same results and reference that in plane stresses.
6.3 Parameters
of execution
Version: 5.02.10
Machine: SGI - Origin 2000
Overall dimension memory:
128 Mo
Time CPU To use: 5.34 seconds
Code_Aster
®
Version
5.2
Titrate:
SZLZ105 Counting of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, P. SCHOENBERGER
Key
:
V9.01.105-C
Page:
8/8
Manual of Validation
V9.01 booklet: Tire
HI-75/01/010/A
7
Summary of the results
This test validates the method and the calculation of the damage of Wöhler and Manson-Whetstone sheath.
The results of Code_Aster are identical to those obtained analytically.