Code_Aster ®
Version
7.3
Titrate:
SZLZ111 - Dommage de Lemaītre-Sermage with option POST_FATIGUE Date:
02/06/04
Author (S):
F. MEISSONNIER Key
:
V9.01.111-A Page:
1/8

Organization (S): EDF-R & D/AMA

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

SZLZ111 - Dommage de Lemaītre-Sermage
in postprocessing POST_FATIGUE

Summary:

The purpose of this test is calculation of the damage of Lemaītre-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 constraints and the plastic deformation
cumulated in every moment Ti (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. That-Ci must thus be provided by the user at the same moments as
(T) and p (T).
Handbook of Validation
V9.01 booklet: Tire HT-66/04/005/A

Code_Aster ®
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SZLZ111 - Dommage de Lemaītre-Sermage with option POST_FATIGUE Date:
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1
Problem of reference

One calculates the damage, D (T), starting from the data of the tensor of the constraints, (T), and of
cumulated plastic deformation, p (T).


S

1

D & =
1 (+) 2
+ 3
1
eq
(1 - 2) 2

H p

if
&
p > p

(
D
1 - D) 2s 3ES
2ES



D = 0
if not

eq is the equivalent constraint of von Mises
H is the hydrostatic constraint
Pd represents the threshold of damage
S is a characteristic materials (MPa)
S is a characteristic materials

NR
The cumulated damage is also calculated: D = D (Ti).
i=1

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.

Pd = 0.02

1.1.1 Modeling
With

In this modeling, one checks the calculation of the damage of Lemaītre-Sermage compared to
reference solution given in [V9.01.109]. Values of the exhibitor S and S in
the expression of the damage of generalized Lemaītre are worth:

S = 1.0 and S = 7.0

1.1.2 Modeling
B

In this second modeling, one checks the calculation of the damage of Lemaītre-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 exhibitor S and S in the expression of the damage of
Generalized Lemaītre are worth:

S = 1.003 and S = 7.0
Handbook of Validation
V9.01 booklet: Tire HT-66/04/005/A

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1.2
History of the loading

T 43.11
100.
1000.
10000.
20000. 21000. 22000. 22200. 22400.
xx (T)
300. 300. 300. 300. 300. 300. 300. 300. 300.
yy (T) =
0. 0. 0. 0. 0.
0.
0.
0. 0.
zz (T) =
0. 0. 0. 0. 0.
0.
0.
0. 0.
xy (T) =
0. 0. 0. 0. 0.
0.
0.
0. 0.
xz (T) =
0. 0. 0. 0. 0.
0.
0.
0. 0.
yz (T)
0. 0. 0. 0. 0.
0.
0.
0. 0.
Temp
20.
20.
20.
20. 20. 20. 20. 20. 20.

T
p (T) (plastic Déformation cumulated)
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
Handbook of Validation
V9.01 booklet: Tire HT-66/04/005/A

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2
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 Référence

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
B
The results of reference for the case test number 2 are obtained using the Excel spreadsheet in
which the expression of the damage of Lemaītre-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 S = 1.0 via
Microsoft Excel is acceptable:

Too bad
Too bad
(Excel calculation)
(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 S = 1.003:

T
D (T) (Dommage ­ 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
Handbook of Validation
V9.01 booklet: Tire HT-66/04/005/A

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2.3
Uncertainty on the solution

2.3.1 Modeling
With

Analytical solution.

2.3.2 Modeling
B

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.
Handbook of Validation
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Code_Aster ®
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SZLZ111 - Dommage de Lemaītre-Sermage with option POST_FATIGUE Date:
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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


DOMMAGE
“LEMAITRE”



MATER




“LINEAR” OFFICE PLURALITY



INFO


DEFI_MATERIAU ELAS_FO
E




NAKED



DOMMA_LEMAITRE
S



EPSP_SEUIL


EXP_S



4
Results of modeling A

Identification Reference
Aster %
difference
Point 1 Damage
0.
0.
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

Handbook of Validation
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5 Modeling
B

5.1 Functionalities
tested

Order



POST_FATIGUE HISTORY
SIGM_XX



SIGM_YY


SIGM_ZZ


SIGM_XY


SIGM_XZ


SIGM_YZ


EPSP


TEMP


DOMMAGE
“LEMAITRE”



MATER




“LINEAR” OFFICE PLURALITY



INFO


DEFI_MATERIAU ELAS_FO
E




NAKED



DOMMA_LEMAITRE
S



EPSP_SEUIL


EXP_S



6
Results of modeling B

Identification Reference
Aster %
difference
Point 1 Damage
0,0000000000
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

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

Code_Aster ®
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Titrate:
SZLZ111 - Dommage de Lemaītre-Sermage with option POST_FATIGUE Date:
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7
Summary of the results

The results provided by Code_Aster coincide with the values of reference.

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

Outline document