SZLZ111 - Damage of Lemaître-Sermage in postprocessing POST

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

1/8

Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

Organization (S):

EDF-R & D/AMA

Manual of Validation
V9.01 booklet: Tire
Document: V9.01.111

SZLZ111 - Damage of Lemaître-Sermage
in postprocessing POST_FATIGUE

Summary:

The purpose of this test is calculation of the damage of Lemaître-Sermage “

LEMAITRE

“starting from a history of

unspecified multiaxial loading and of the history of the cumulated plastic deformation.

One calculates the damage starting from the data of the tensor of the stresses and the plastic deformation
cumulated in every moment T

(provided by the user). Moreover, one calculates the cumulated damage.

The characteristics material E (Young modulus),

(Poisson's ratio) and S (parameter of material)

must depend on the temperature T. The aforementioned must thus be provided by the user at the same moments as
(T) and p (T).

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

2/8

Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

Problem of reference

The damage is calculated,

()

, starting from the data of the tensor of the stresses,

()

, and of

cumulated plastic deformation,

()

(

)

(

)

(

)

if not

is the equivalent stress of von Mises

is the hydrostatic stress

represent the threshold of damage

is a characteristic materials (MPa)

is a characteristic materials

The cumulated damage is also calculated:

()

1.1 Properties

materials

Temp (°C)

E (MPa)

S (MPa)

0. 2.E+5 0. 7.

20. 2.E+5 0. 7.
40. 2.E+5 0. 7.

= 0.02

1.1.1 Modeling

With

In this modeling, one checks the calculation of the damage of Lemaître-Sermage compared to
reference solution given in [V9.01.109]. Values of the exponent

and of

the expression of the damage of generalized Lemaître are worth:

= 1.0 and

= 7.0

1.1.2 Modeling

In this second modeling, one checks the calculation of the damage of Lemaître-Sermage per report/ratio
with an analytical solution obtained by applying the algorithms presented in the document of
reference [R7.04.01]. Values of the exponent

and of

in the expression of the damage of

Generalized Lemaître are worth:

= 1.003 and

= 7.0

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

3/8

Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

1.2

History of the loading

T 43.11

100.

1000.

10000.

20000. 21000. 22000. 22200. 22400.

(T)

300. 300. 300. 300. 300. 300. 300. 300. 300.

(T) =

0. 0. 0. 0. 0.

0. 0.

(T) =

0. 0. 0. 0. 0.

0. 0.

(T) =

0. 0. 0. 0. 0.

0. 0.

(T) =

0. 0. 0. 0. 0.

0. 0.

(T)

0. 0. 0. 0. 0.

0. 0.

Temp

20.

20. 20. 20. 20. 20. 20.

p (T) (cumulated Plastic deformation)

43.11 0.019996

100. 0.046384

1000. 0.46384

10000. 4.6384
20000. 9.2768
21000. 9.74064
22000. 10.20448
22200. 10.297248
22400. 10.390016

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

4/8

Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

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

2.2.1 Modeling

With

T D (T)

(Damage)

43.11 0.

100. 0.000848907

1000. 0.014474925

10000. 0.178374238
20000. 0.524693005
21000. 0.602827469
22000. 0.73829052
22200. 0.792149807
22400. 0.967604351

The value of the cumulated damage is: 3.819263222

2.2.2 Modeling

The results of reference for the case test number 2 are obtained using the Excel spreadsheet in
which the expression of the damage of Lemaître-Sermage was established according to a diagram of integration
numerical identical to that used in routine POST_FATIGUE of Code_Aster.

One initially checks that uncertainty on the results obtained for the value

= 1.0 via

Microsoft Excel is acceptable:

Too bad

(Excel calculation)

Too bad

(reference solution)

Difference

0,0000000000 0,0000000000

0,00000%

0,0008489062 0,0008489070

- 0,00010%

0,0144749268 0,0144749250

0,00001%

0,1783742841 0,1783742380

0,00003%

0,5246932887 0,5246930050

0,00005%

0,6028278917 0,6028274690

0,00007%

0,7382915411 0,7382905200

0,00014%

0,7921514337 0,7921498070

0,00021%

0,9676720845 0,9676043510

0,00700%

In the second time, one generates a reference solution for a value of

= 1.003:

D (T) (Damage Excel solution)

43.11 0.0

100. 0.004742198

1000. 0.083020455

10000. 1.809947268
20000. 2.003578566
21000. 0.083020455
22000. 0.178700399
22200. 0.199207053
22400. 0.220252827

The value of the cumulated damage is: 4.582469221

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

5/8

Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

2.3

Uncertainty on the solution

2.3.1 Modeling

With

Analytical solution.

2.3.2 Modeling

Analytical solution.

2.4 References

bibiographic

[1]

A. Mr. DONORE: Estimate of the fatigue life to great numbers of cycles and in
oligocyclic fatigue. Note [R7.04.01] Index B.

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

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Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

3 Modeling

With

3.1 Functionalities

tested

Order

POST_FATIGUE HISTORY

SIGM_XX

SIGM_YY

SIGM_ZZ

SIGM_XY

SIGM_XZ

SIGM_YZ

EPSP

TEMP

TOO BAD

“LEMAITRE”

MATER

“LINEAR” OFFICE PLURALITY

INFORMATION

DEFI_MATERIAU

ELAS_FO

NAKED

DOMMA_LEMAITRE

EPSP_SEUIL

EXP_S

Results of modeling A

Identification Reference

Aster %

difference

Point 1 Damage

0,00000

Point 2 Damage

0.000848907

0.000849061

- 0,01814

Point 3 Damage

0.014474925

0.014474926

- 0,00001

Point 4 Damage

0.178374238

0.178374284

- 0,00003

Point 5 Damage

0.524693005

0.5246932887

- 0,00005

Point 6 Damage

0.602827469

0.602827891

- 0,00007

Point 7 Damage

0.73829052

0.73829154

- 0,00014

Point 8 Damage

0.792149807

0.79215143

- 0,00020

Point 9 Damage

0.967604351

0.96767208

- 0,00700

DOMM_CUMU 3.819263

3.8193343

- 0,00187

Code_Aster

Version

7.3

Titrate:

SZLZ111 - Damage of Lemaître-Sermage with option POST_FATIGUE

Date:

02/06/04

Author (S):

F. MEISSONNIER

Key

V9.01.111-A

Page:

7/8

Manual of Validation

V9.01 booklet: Tire HT-66/04/005/A

5 Modeling

5.1 Functionalities

tested

Order

POST_FATIGUE HISTORY

SIGM_XX

SIGM_YY

SIGM_ZZ

SIGM_XY

SIGM_XZ

SIGM_YZ

EPSP

TEMP

TOO BAD

“LEMAITRE”

MATER

“LINEAR” OFFICE PLURALITY

INFORMATION

DEFI_MATERIAU

ELAS_FO

NAKED

DOMMA_LEMAITRE

EPSP_SEUIL

EXP_S

Results of modeling B

Identification Reference

Aster %

difference

Point 1 Damage

0,0000000000

0,00000

Point 2 Damage

0,0008401910

0,0008401914

0,00005

Point 3 Damage

0,0143249000

0,0143248741

- 0,00018

Point 4 Damage

0,1762380000

0,1762381211

0,00007

Point 5 Damage

0,5133290000

0,5133285359

- 0,00009

Point 6 Damage

0,5863320000

0,5863316643

- 0,00006

Point 7 Damage

0,7028150000

0,7028154063

0,00006

Point 8 Damage

0,7412430000

0,7412431087

0,00001

Point 9 Damage

0,7967720000

0,7967724320

0,00005

DOMM_CUMU 3,5318900000

3,5318943339

0,00012