Code_Aster ®
Version
7.2
Titrate:
SZLZ110 - Dommage de Lemaître-Sermage with option CALC_ELEM
Date:
02/06/04
Author (S):
F. MEISSONNIER Key
:
V9.01.110-A Page:
1/6

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

Handbook of Validation
V9.01 booklet: Tire
Document: V9.01.110

SZLZ110 - Dommage de Lemaître generalized
in postprocessing CALC_ELEM

Summary:

The purpose of this test is calculation of the damage of Lemaître generalized “LEMAIT_S” starting from the data of the tensor
constraints and plastic deformation cumulated at every moment Ti (provided by the user).

The cumulated damage is also calculated.

The characteristics material E (Young modulus), (Poisson's ratio), S and Pd (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.
Handbook of Validation
V9.01 booklet: Tire HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SZLZ110 - Dommage de Lemaître-Sermage with option CALC_ELEM
Date:
02/06/04
Author (S):
F. MEISSONNIER Key
:
V9.01.110-A Page:
2/6

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) resulting from a calculation in thermomechanics. The kinetics
of damage is given by:


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

is the equivalent constraint of von Mises
eq
is the hydrostatic constraint
H
p represents the threshold of damage
D
S is a characteristic of the material (MPa)
S is a characteristic of material

NR
One also calculates the total damage D = D (T.
I)
i=1

1.1 Properties
materials

Temp (°C)
E (MPa)

S (MPa)
Pd
S
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 exhibitor 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].

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

Code_Aster ®
Version
7.2
Titrate:
SZLZ110 - Dommage de Lemaître-Sermage with option CALC_ELEM
Date:
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Author (S):
F. MEISSONNIER Key
:
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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 constraints and to recover the evolution of
cumulated plastic deformation associated starting from a tensile test 3D in thermo viscoplasticity.

The history of loading (T) and p (T) 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 Référence

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:

Constraint
Cumulated plastic deformation
Time [S]
Sxx (T) [Pa]
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:
Handbook of Validation
V9.01 booklet: Tire HT-66/04/005/A

Code_Aster ®
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Titrate:
SZLZ110 - Dommage de Lemaître-Sermage with option CALC_ELEM
Date:
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Author (S):
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:
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Damage (reference)
Time [S]
Case s=0.8
Case s=1.003
50
0.00000E+00 0.00000E+00
100 0.00000E+00
0.00000E+00
150 0.00000E+00
0.00000E+00
200 0.00000E+00
0.00000E+00
250 0.00000E+00
0.00000E+00
300 0.00000E+00
0.00000E+00
350 0.00000E+00
0.00000E+00
400 0.00000E+00
0.00000E+00
450 0.00000E+00
0.00000E+00
500 0.00000E+00
0.00000E+00
550 0.00000E+00
0.00000E+00
600 0.00000E+00
0.00000E+00
650 0.00000E+00
0.00000E+00
700 0.00000E+00
0.00000E+00
750 5.43732E-03
3.19264E-02
800 2.75450E-02
1.90334E-01
850 6.75939E-02
1.00000E+00
900 1.21543E-01
1.00000E+00
950 1.87318E-01
1.00000E+00
1000 2.66202E-01 1.00000E+00
Cumulated damage
6.75640E-01
4.22226E+00

2.3
Uncertainty on the solution

Numerically generated solution.

2.4 References
bibliographical

[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 HT-66/04/005/A

Code_Aster ®
Version
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Titrate:
SZLZ110 - Dommage de Lemaître-Sermage with option CALC_ELEM
Date:
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Author (S):
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:
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3 Modeling

3.1 Functionalities
tested

Order



CALC_ELEM
OPTION
ENDO_ELGA




ENDO_ELNO_ELGA


DEFI_MATERIAU ELAS_FO
E




NAKED




RHO




TEMP_DEF_ALPHA




ALPHA



DOMMA_LEMAITRE
S



EPSP_SEUIL


EXP_S



THER_FO
LAMBDA




RHO_CP



LEMAITRE_FO
NR



UN_SUR_K




UN_SUR_M



CIN2_CHAB_FO
R_0


R_I

B



C1


C2

K



W



G1

G2




A_I

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

Code_Aster ®
Version
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Titrate:
SZLZ110 - Dommage de Lemaître-Sermage with option CALC_ELEM
Date:
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Author (S):
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:
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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.

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

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