Code_Aster ®
Version
3
Titrate:
SZLZ109 Dommage de Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V9.01 booklet: Tire
Document: V9.01.109
SZLZ109 - Dommage de Lemaitre
in postprocessing
Summary:
The purpose of this test is calculation of the damage of “LEMAITRE” starting from a history of multiaxial loading
unspecified and of the history of the cumulated plastic deformation.
The damage is calculated
(
D T) starting from the data of the tensor of the constraints (T) and the formation
figure cumulated (
p T) in every moment Ti (provided by the user). Moreover, one calculates the total damage
NR
D = (
D Ti).
i=1
The characteristics material E (Young modulus), (Poisson's ratio) and S (parameter of material)
must depend on the temperature T (T

(T) must thus be provided by the user at the same moments as
(T) and
(
p T)).
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A

Code_Aster ®
Version
3
Titrate:
SZLZ109 Dommage de Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A Page:
2/6
1
Problem of reference
The damage is calculated
(
D T) starting from the data of the tensor of the constraints (T) and of
cumulated plastic deformation (
p T).

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



(
if
1 -) 2
eq
H
p
p
Pd
D



ES
3
2ES


>
D =


0 if not
eq is the equivalent constraint of von Mises
H forced hydrostatic
Pd threshold of damage
S characteristic material (MPa)
NR
One also calculates the total damage D = (
D Ti).
i=1
1.1
Material properties
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
1.2
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) =
xy (T) =
xz (T) =
yz (T)
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
HI-75/96/068 - Ind A

Code_Aster ®
Version
3
Titrate:
SZLZ109 Dommage de Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A Page:
3/6
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
T
p (T) (plastic Déformation cumulated)
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
2.3
Uncertainty on the solution
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
V9.01 booklet: Tire
HI-75/96/068 - Ind A

Code_Aster ®
Version
3
Titrate:
SZLZ109 Dommage de Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A Page:
4/6
3 Modeling
3.1 Functionalities
tested
Order
Key word
Operand
Key
POST_FATIGUE
HISTOIRE
SIGM_XX
[U4.67.01]
SIGM_YY
SIGM_ZZ
SIGM_XY
SIGM_XZ
SIGM_YZ
EPSP
TEMP
DOMMAGE
“LEMAITRE”
MATER
CUMUL
“LINEAIRE”
INFO
DEFI_MATERIAU
ELAS_FO
E
[U4.23.01]
NAKED
DOMMA_LEMAITRE
S
EPSP_SEUIL
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A

Code_Aster ®
Version
3
Titrate:
SZLZ109 Dommage de Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A Page:
5/6
4
Results of modeling
4.1 Values
tested
Identification
Reference
Aster
% difference
Point 1 Damage
0.
0.
0.
Point 2 Damage
0.000848907
0.000849061
0.
Point 3 Damage
0.014474925
0.014474926
0.
Point 4 Damage
0.178374238
0.178374284
0.
Point 5 Damage
0.524693005
0.5246932887
0.
Point 6 Damage
0.602827469
0.602827891
0.
Point 7 Damage
0.73829052
0.73829154
0.
Point 8 Damage
0.792149807
0.79215143
0.
Point 9 Damage
0.967604351
0.96767208
0.007
DOMM_CUMU
3.819263
3.8193343
0.002
4.2 Parameters
of execution
Version: 3.06.19
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
2.44 seconds
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A

Code_Aster ®
Version
3
Titrate:
SZLZ109 Dommage de Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A Page:
6/6
5
Summary of the results
The results provided by Code_Aster coincide with the values of reference.
Handbook of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A