Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V9.01 booklet: Tire
Document: V9.01.105
SZLZ105 - Comptage 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 constraints and a modeling in 3D.
This test validates the method of counting of cycles (RAINFLOW) established in operator CALC_FATIGUE
[U4.67.01] as well as the method of calculation of the damage in imposed constraint (curve of Wöhler) or
imposed deformation (curve of Manson-Coffin). The reference solution is an analytical solution.
It also validates the calculation of the constraints 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.
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
2/8
1
Problem of reference
1.1 Geometry
y
4
3
F (T)
1
2
X
1.2
Material properties
Linear elasticity: E = 1. MPa = 0.3
NR (cycles)
NR (cycles)
1000.
1000.
10.
2 (MPa)
10.
2
Curve of Wöhler
Curve of Manson-Coffin
1.3
Boundary conditions and loadings
·
Blocked on face 1-4 following X - node 1 blocked according to Y.
·
In unit simple traction on the face 2-3.
·
Loading F (T) in teeth of saw (according to Article de Downing and Socie 1982) [bib1].
F (T)
4
3
2
1
T
1 2
3 4 5 6 7
8
- 3
1.4 Conditions
initial
Null constraints and deformations.
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution
·
calculation of the constraints and deformations. For a loading in simple traction, one obtains a state
of homogeneous constraint uniaxial in any point:
0 0
0 0
= 0 0 0
and
= 0
0
0 0 0
0 0
= =
VMIS
TRESCA,
the equivalent sizes are thus
=
VMIS_SG
2
=
-
INVA_
,
2
3
and
2
+
2
=
-
INVA_2SG
* sign
3
3
·
then manual calculation of the cycles by the method of RAINFLOW, as well as amplitudes of
loading
or
2
2
cycles
/2
INVA-2/2
1
1.
0.8667
2
0.5
0.433315
3
1.
0.8667
4
3.5
3.03335
·
finally carryforward of these values on the curves of Wöhler or Manson-Coffin to estimate it
1
unit damage with each cycle I, is Dui =
(NR
NR
I being the number of cycles with rupture for
I
a given amplitude), as well as the damage cumulated D = Dui (linear rule of office plurality of
I
MINER).
Note:
One will use as equivalent constraint
=
VMIS_SG
and like equivalent deformation
2
+
2
-
= -
INVA
SG
* sign
.
3
3
2
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
INVA 2
.
_
.
·
For the calculation of the damage, one obtains:
4
D
=
-
4 8133
.
10 3 = Of
Wöhler
I
i=1
4
D
=
-
4 6
. 7 10 3
= Of
Manson
I
i=1
2.3 References
bibliographical
[1]
DOWNING and SOCIE, 1982. “Simple Rainflow counting algorithms”. Int. J.
Tire,
January 1982 (p. 31).
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
4/8
3 Modeling
With
3.1
Characteristics of modeling
Modeling in plane constraints:
y
F (NR)
4
F/2
3
4
3
2
1
T (S)
1 2 3 4 5 6 7 8
1
2
- 3
X
F/2
3.2
Characteristics of the grid
1 mesh QUAD4.
Square
width = 1
thickness = 1
3.3 Functionalities
tested
Order Mot-clé Key word
Key argument
factor
simple
CALC_FATIGUE
OPTION
“DOMA_ELNO_SIGM” [U4.67.02]
“DOMA_ELNO_EPSI”
HISTOIRE
EQUI_GD
“VMIS_SG”
“INVA_2SG”
HISTOIRE
RESULTAT
DOMMAGE
“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
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
5/8
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
in all nodes at the end of the loading in
constraint or in deformation
Wöhler damage
4.8133 103 4.813315
103
0.0003
Damage Manson-Whetstone sheath
4.6705 103 4.67048
103
- 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.
2.6 2.6
0.
INVA_2
INVA_2SG
- 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
Obstruction memory:
128 Mo
Time CPU To use: 4.84 seconds
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
6/8
5 Modeling
B
5.1
Characteristics of modeling
Modeling in 3D:
y
1
2
F/4
5
6
F/4
3
4
F/4
X
7
8
F/4
5.2
Characteristics of the grid
1 mesh HEXA8.
cubic of width = 1
5.3 Functionalities
tested
Order Mot-clé Key word
Key argument
factor
simple
CALC_FATIGUE
OPTION
“DOMA_ELNO_SIGM” [U4.67.02]
“DOMA_ELNO_EPSI”
“DOMA_ELNO_EPME”
HISTOIRE
EQUI_GD
“VMIS_SG”
“INVA_2SG”
HISTOIRE
RESULTAT
DOMMAGE
“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
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
7/8
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 103 4.813315
103
0.
Damage Manson-Whetstone sheath
4.6705 103 4.67048
103
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.
2.6 2.6
0.
INVA_2
INVA_2SG
- 2.6
- 2.6
0.
(- HT) INVA_2
2.6 2.6
0.
(- HT) INVA_2SG
- 2.6
- 2.6
0.
6.2 Remarks
Same results and reference that in plane constraints.
6.3 Parameters
of execution
Version: 5.02.10
Machine: SGI - Origin 2000
Obstruction memory:
128 Mo
Time CPU To use: 5.34 seconds
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Code_Aster ®
Version
5.2
Titrate:
SZLZ105 Comptage of cycles by RAINFLOW and calculation of the damage
Date:
28/10/99
Author (S):
A. Mr. DONORE, Key P. SCHOENBERGER
:
V9.01.105-C Page:
8/8
7
Summary of the results
This test validates the method and the calculation of the damage of Wöhler and Manson-Coffin.
The results of Code_Aster are identical to those obtained analytically.
Handbook of Validation
V9.01 booklet: Tire
HI-75/01/010/A
Outline document