Microsoft Word - V901106a. Doc.

Code_Aster

Version

4.0

Titrate:

SZLZ106 Tires under random stress

Date:

19/01/98

Author (S):

A. Mr. DONORE

Key:

V9.01.106-A

Page:

1/6

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: V9.01.106

SZLZ106 - Tire under random stress

Summary:

The purpose of this test is calculation of the damage starting from a random stress which is characterized by its
spectral moments.

From the spectral moments of the random loading one determines the average damage undergone by the structure
[R7.04.02].

With this intention one has two methods of counting of cycles of stresses:

method of counting of the peaks of stresses,

method of the goings beyond of a given level.

One tests also various possibilities of introduction the curve of Wöhler as well as the taking into account of
elastoplastic coefficient of concentration Ke.

The results of reference of this test are the values provided by software POSTDAM developed by
Department REME (EDF-DER-EP).

Results provided by the operator

POST_FATI_ALEA

[U4.67.05] are completely identical to those provided by

software POSTDAM.

Code_Aster

Version

4.0

Titrate:

SZLZ106 Tires under random stress

Date:

19/01/98

Author (S):

A. Mr. DONORE

Key:

V9.01.106-A

Page:

2/6

Manual of Validation

V9.01 booklet: Tire

HI-75/96/038 - Ind A

Problem of reference

The analysis consists in determining the average damage undergone by a part subjected to a loading
random.

Loading of the random type is entirely characterized by the values of the spectral moments
of command 0, 2 and 4:

and

who are introduced under the key words

MOMENT_SPEC_0

MOMENT_SPEC_2

and

MOMENT_SPEC_4

For the calculation of the damage it is necessary to choose a method of counting among the two available ones in

Code_Aster

method of counting of the peaks of stresses,

method of counting of going beyond of a given level.

It is necessary moreover introduce the curve of Wöhler of the material which can be defined in three forms
distinct mathematics:

function point by point, which gives the value of the number of cycles to the rupture, according to
the alternate stress S

alt

analytical form of Basquin: D = A S

alt

analytical form “current area”

alt

= alternate stress = 1/2 (E

/E)

= LOG

alt

)

has

D =

1./

if S

alt

³ = S

if not

where E

= Young Modulus associated with the curve with fatigue with material,

E = Young Modulus used to determine the stresses,
constants of the material a0, a1, a2 and a3,
and S

limit of endurance of material.

Moreover, one can possibly take account of an elastoplastic coefficient of concentration Ke,
defined by:

(

)

(

)

(

)

(

)

N m

m S

= + -

where

is the acceptable maximum stress,

and

two constants depending on material.

In this test, for a single given random loading, one determines the average damage in ten
distinct configurations, according to the shape of the curve of Wöhler and the method of counting of cycles.

Code_Aster

Version

4.0

Titrate:

SZLZ106 Tires under random stress

Date:

19/01/98

Author (S):

A. Mr. DONORE

Key:

V9.01.106-A

Page:

3/6

Manual of Validation

V9.01 booklet: Tire

HI-75/96/038 - Ind A

1.1

Material properties for the study of fatigue

The properties of material relate to the data of a curve of Wöhler making it possible to determine it
a number of cycles to the rupture for a level of loading given.

1.1.1 Curve of Wöhler in analytical form Basquin

Configuration 1

With

1.0017309939 E14

4.065

Configuration 2

With

32. E13

1.1.2 Curve of Wöhler in form “current area”

Parameters of definition of configuration 3:

EC.

SSL

11.495

0.25

0.07

220000.

200000.

Parameters of definition of configuration 4:

EC.

SSL

11.495

0.25

0.07

220000.

200000.

Moreover, one takes one account an elastoplastic coefficient of concentration Ke defined by
parameters for this configuration.

60.

0.6

1.4

1.1.3 Curve of Wöhler in form function point by point (configuration 5)

alt

25.

30.

35.

40.

3.125E+11

976562.5E+4

1.E+8

32000.

12860.09

5949.899

3051.76

alt

45.

50.

55.

60.

65.

70.

75.

1693.51

1000.0

620.921

401.8779

269.329

185.934

131.6869

alt

80.

85.

90.

95.

100.

105.

110.

95.3674

70.4296

52.9221

40.3861

31.25

24.4852

19.40379

alt

115.

120.

125.

130.

135.

140.

145.

15.5368

12.55869

10.23999

8.41653

6.96917

5.81045

4.8754

alt

150.

155.

160.

165

170.

175.

180.

4.11523

3.49294

2.98023

2.55523

2.20093

1.90397

1.65382

alt

185.

190.

195.

200.

1.44209

1.26207

1.10835

0.976562

1.2

History of the loading

The random loading is entirely characterized by the values of the spectral moments:

182.5984664

96098024.76

6.346193569E+13

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Version

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Titrate:

SZLZ106 Tires under random stress

Date:

19/01/98

Author (S):

A. Mr. DONORE

Key:

V9.01.106-A

Page:

4/6

Manual of Validation

V9.01 booklet: Tire

HI-75/96/038 - Ind A

Reference solution

2.1

Method of calculation used for the reference solution

The values of reference mentioned in this document are the values provided by the software
POSTDAM developed by Department REME.

2.2

Results of Reference

Configuration 1

Configuration 2

Method of counting

Level

PEAK

Level

PEAK

Average damage

3.851827E7

3.853037E7

3.129527E3

3.129848E3

Configuration 3

Configuration 4

Method of counting

Level

PEAK

Level

PEAK

Average damage

2.298920E3

2.299282E3

2.298920E3

2.299282E3

Configuration 5

Method of counting

Level

PEAK

Average damage

3.129531E3

3.129903E3

2.3 Functionalities

tested

Order

Key word

Operand

Keys

POST_FATI_ALEA

MOMENT_SPEC_0:

[U4.67.05]

MOMENT_SPEC_2:
MOMENT_SPEC_4:
COUNTING:

“LEVEL”

COUNTING:

“PEAK”

TOO BAD:

“WOHLER”

MATER:
CORR_KE:

“RCCM”

DURATION:

DEFI_MATERIAU

TIRE

WOHLER:

[U4.23.01]

TIRE

A_BASQUIN:
BETA_BASQUIN:

TIRE

A0:
A1:
A2:
A3:
SSL:
E_REFE:
N_KE_RCCM:
M_KE_RCCM:
SM_KE_RCCM

ELAS

E:
NAKED:

Code_Aster

Version

4.0

Titrate:

SZLZ106 Tires under random stress

Date:

19/01/98

Author (S):

A. Mr. DONORE

Key:

V9.01.106-A

Page:

5/6

Manual of Validation

V9.01 booklet: Tire

HI-75/96/038 - Ind A

Results of modeling A

3.1 Values

tested

Configuration 1:

Method going beyond of level

Configuration 1:

Method peaks of stresses

Reference

Aster

difference

Reference

Aster

difference

Too bad
means

3.851827E7

3.8517772E7

0.001

3.853037E7

3.8529874E7

0.001

Configuration 2:

Method going beyond of level

Configuration 2:

Method peaks of stresses

Reference

Aster

difference

Reference

Aster

difference

Too bad
means

3.129527E3

3.1294844E3

0.001

3.129848E3

3.1298563E3

0.001

Configuration 3:

Method going beyond of level

Configuration 3:

Method peaks of stresses

Reference

Aster

difference

Reference

Aster

difference

Too bad
means

2.298920E3

2.2988724E3

0.002

2.299282E3

2.2992316E3

0.002

Configuration 4:

Method going beyond of level

Configuration 4:

Method peaks of stresses

Reference

Aster

difference

Reference

Aster

difference

Too bad
means

2.298920E3

2.2988724E3

0.002

2.299282E3

2.2992316E3

0.002

Configuration 5:

Method going beyond of level

Configuration 5:

Method peaks of stresses

Reference

Aster

difference

Reference

Aster

difference

Too bad
means

3.129531E3

3.1294837E3

0.002

3.129903E3

3.1298556E3

0.002

3.2 Parameters

of execution

Version: 3.06.18
Machine: CRAY C90
Overall dimension memory:

8Mw

Time CPU To use:

5.017 seconds