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