Code_Aster
®
Version
3
Titrate:
SZLZ109 Damage of Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A
Page:
1/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V9.01 booklet: Tire
Document: V9.01.109
SZLZ109 - Damage of 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 stresses
()
T
and of the formation
figure cumulated
()
p T
in every moment
T
I
(provided by the user). Moreover, one calculates the total damage
()
D
D T
I
I
NR
=
=
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
).
Code_Aster
®
Version
3
Titrate:
SZLZ109 Damage of Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A
Page:
2/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
1
Problem of reference
The damage is calculated
()
D T
starting from the data of the tensor of the stresses
()
T
and of
cumulated plastic deformation
()
p T
.
(
)
(
)
(
)
D
D
ES
ES
p
p
p
D
eq
H
D
= -
+
+
-
>
=
1
1
1
3
1
3
2
1 2
0
2
2
2
if
if not
eq
is the equivalent stress of von Mises
H
hydrostatic stress
p
D
threshold of damage
S
characteristic material (MPa)
The total damage is also calculated
()
D
D T
I
I
NR
=
=
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.
p
D
= 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) (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
3
Titrate:
SZLZ109 Damage of Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A
Page:
3/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
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 Reference
T
p (T) (cumulated Plastic deformation)
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.
Code_Aster
®
Version
3
Titrate:
SZLZ109 Damage of Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A
Page:
4/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
3 Modeling
3.1 Functionalities
tested
Order
Key word
Operand
Key
POST_FATIGUE
HISTORY
SIGM_XX
[U4.67.01]
SIGM_YY
SIGM_ZZ
SIGM_XY
SIGM_XZ
SIGM_YZ
EPSP
TEMP
TOO BAD
“LEMAITRE”
MATER
OFFICE PLURALITY
“LINEAR”
INFORMATION
DEFI_MATERIAU
ELAS_FO
E
[U4.23.01]
NAKED
DOMMA_LEMAITRE
S
EPSP_SEUIL
Code_Aster
®
Version
3
Titrate:
SZLZ109 Damage of Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A
Page:
5/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
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
Overall dimension memory:
8 MW
Time CPU To use:
2.44 seconds
Code_Aster
®
Version
3
Titrate:
SZLZ109 Damage of Lemaitre
Date:
24/08/99
Author (S):
A. Mr. DONORE
Key:
V9.01.109-A
Page:
6/6
Manual of Validation
V9.01 booklet: Tire
HI-75/96/068 - Ind A
5
Summary of the results
Results provided by
Code_Aster
coincide with the values of reference.