Code_Aster
®
Version
7.2
Titrate:
SZLZ110 - Damage of Lemaître-Sermage with option CALC_ELEM
Date:
02/06/04
Author (S):
F. MEISSONNIER
Key
:
V9.01.110-A
Page:
1/6
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: V9.01.110
SZLZ110 - Damage of generalized Lemaître
in postprocessing CALC_ELEM
Summary:
The purpose of this test is calculation of the damage of generalized Lemaître “
LEMAIT_S
“starting from the data of the tensor
stresses and plastic deformation cumulated at every moment T
I
(provided by the user).
The cumulated damage is also calculated.
The characteristics material E (Young modulus),
(Poisson's ratio), S and p
D
(parameters of material)
can depend on the temperature, which must thus be provided by the user at the same moments as them
constants and plastic deformation.
Code_Aster
®
Version
7.2
Titrate:
SZLZ110 - Damage of Lemaître-Sermage with option CALC_ELEM
Date:
02/06/04
Author (S):
F. MEISSONNIER
Key
:
V9.01.110-A
Page:
2/6
Manual of Validation
V9.01 booklet: Tire HT-66/04/005/A
1
Problem of reference
The damage is calculated
()
T
D
starting from the data of the tensor of the stresses
()
T
and of
cumulated plastic deformation
()
T
p
exit of a calculation in thermomechanics. The kinetics
of damage is given by:
(
)
(
)
(
)
=
>
-
+
+
-
=
if not
if
0
2
1
2
3
1
3
1
1
1
2
2
2
D
p
p
p
ES
ES
D
D
D
S
H
eq
S
&
&
eq
is the equivalent stress of von Mises
H
is the hydrostatic stress
D
p
represent the threshold of damage
S
is a characteristic of the material (MPa)
S
is a characteristic of material
The total damage is also calculated
()
=
=
NR
I
I
T
D
D
1
.
1.1 Properties
materials
S
Temp (°C)
E (MPa)
S (MPa)
P
D
Case 1
Case 2
0. 143006.0E+6
0.33
7.0 1.005E-6
0.8
1.003
20. 143006.0E+6
0.33
7.0 1.005E-6
0.8
1.003
40. 143006.0E+6
0.33
7.0 1.005E-6
0.8
1.003
Two values of the exponent
S
are successively used for the validation of the developments
in CALC_ELEM.
1.2 Loading
The loading corresponds to a tensile test at constant temperature and speed of deformation
imposed. It is defined in the paragraph [§2.2].
Code_Aster
®
Version
7.2
Titrate:
SZLZ110 - Damage of Lemaître-Sermage with option CALC_ELEM
Date:
02/06/04
Author (S):
F. MEISSONNIER
Key
:
V9.01.110-A
Page:
3/6
Manual of Validation
V9.01 booklet: Tire HT-66/04/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is generated starting from option POST_FATIGUE. Adopted methodology
consist in defining a history of loading in stresses and to recover the evolution of
cumulated plastic deformation associated starting from a tensile test 3D in thermo viscoplasticity.
History of loading
()
T
and
()
T
p
is then used in a calculation POST_FATIGUE with
parameters materials presented at the paragraph [§1.1] to define a reference solution.
2.2
Results of Reference
The result of reference of the damage of Lemaître is obtained for a tensile test to deformation
imposed and on constant temperature. The state of stresses and cumulated plastic deformation resulting
of this test are as follows:
Time [S]
Stress
Sxx (T) [AP]
Cumulated plastic deformation
P (T)
50
7.15030E+06 0.000000E+00
100
1.43006E+07 0.000000E+00
150
2.14509E+07 0.000000E+00
200
2.86012E+07 0.000000E+00
250
3.57515E+07 0.000000E+00
300
4.29018E+07 0.000000E+00
350
5.00521E+07 0.000000E+00
400
5.72024E+07 0.000000E+00
450
6.43527E+07 0.000000E+00
500
7.15030E+07 0.000000E+00
550
7.86533E+07 0.000000E+00
600
8.58036E+07 0.000000E+00
650
9.29539E+07 0.000000E+00
700
1.00091E+08 9.547120E-08
750
1.06433E+08 5.747160E-06
800
1.10614E+08 2.650910E-05
850
1.12888E+08 6.060610E-05
900
1.14130E+08 1.019250E-04
950
1.14913E+08 1.464460E-04
1000
1.15508E+08 1.922890E-04
This history of loading is then used with operator POST_FATIGUE option LEMAIT_S
to estimate the damage according to time with the properties materials defined in the paragraph
[§1.1]. The temperature is supposed to be constant and equalizes to 20 °C. One finds, according to the value of
parameter
S
used, following damage:
Code_Aster
®
Version
7.2
Titrate:
SZLZ110 - Damage of Lemaître-Sermage with option CALC_ELEM
Date:
02/06/04
Author (S):
F. MEISSONNIER
Key
:
V9.01.110-A
Page:
6/6
Manual of Validation
V9.01 booklet: Tire HT-66/04/005/A
4
Results of modeling
4.1 Values
tested
One tests the values of sizes DOM_LEM and D_CUMULE.
Identification Reference
Aster %
difference
S = 0.8
S = 1.003
S = 0.8
S = 1.003
S = 0.8
S = 1.003
Point 1 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 2 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 3 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 4 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 5 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 6 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 7 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 8 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 9 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 10 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 11 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 12 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 13 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 14 Damage
0,0000000 0,0000000 0,0000000 0,0000000
0,00000%
0,00000%
Point 15 Damage
0,0054373 0,0319264 0,0054373 0,0319262 - 0,00059% - 0,00077%
Point 16 Damage
0,0275450 0,1903340 0,0275449 0,1903330 - 0,00041% - 0,00051%
Point 17 Damage
0,0675939 1,0000000 0,0675938 1,0000000 - 0,00021%
0,00000%
Point 18 Damage
0,1215430 1,0000000 0,1215426 1,0000000 - 0,00036%
0,00000%
Point 19 Damage
0,1873180 1,0000000 0,1873169 1,0000000 - 0,00058%
0,00000%
Point 20 Damage
0,2662020 1,0000000 0,2662008 1,0000000 - 0,00046%
0,00000%
D_CUMULE 0,6756392
4,2222604 0,6756362 4,2222592
0,00045%
- 0,00003%
5
Summary of the results
The results provided by Code_Aster coincide with the values of reference.
