Code_Aster
®
Version
8.1
Titrate:
SSNV183 Creep test with the model
VENDOCHAB
Date:
01/09/05
Author (S):
O. DIARD
Key
:
V6.04.183-A
Page:
1/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/MMC
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.183
SSNV183 - Creep test with the model
VENDOCHAB
Summary:
The model
VENDOCHAB
, a formulation suggested by Chaboche begins again. It is about a coupled formulation
who covers a élasto-viscoplastic law with multiplicative isotropic work hardening and kinetics
of isotropic damage. This law was initially developed to predict the lifespan and cracking
vanes of the turbojets and more generally to envisage the time of ruin of the structures requested with
high temperatures.
This test of nonlinear quasi-static mechanics makes it possible to validate the model
VENDOCHAB
in 3D in the case
of a test-tube subjected to an isothermal uniaxial creep test. Stress and strain states
are homogeneous in the test-tube. This test validates the explicit integration of this model. Equations of this
coupled formulation are described in the booklet of reference [R5.03.15].
The modeling of the test-tube is carried out with an element 3D with 8 nodes (HEXA8).
Code_Aster
®
Version
8.1
Titrate:
SSNV183 Creep test with the model
VENDOCHAB
Date:
01/09/05
Author (S):
O. DIARD
Key
:
V6.04.183-A
Page:
2/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
The geometry is selected voluntarily simple, to translate a stress and strain state
homogeneous, as it is the case in uniaxial creep. It is here about an element of volume represented by
a cube on side 3 Misters modeling is voluminal and creep is done with imposed stress.
1.2
Properties of material
The characteristics are as follows:
Key word ELAS:
YOUNG = 150000.0 MPa
NAKED = 0.30
Key word VENDOCHAB:
S_VP = 0.,
SEDVP1 = 0.,
SEDVP2 = 0.,
N_VP = 12.,
M_VP = 9.,
K_VP = 2110.,
A_D = 3191.,
R_D = 6.3,
K_D = 14.
1.3
Boundary conditions and loadings
DZ = 0 on the lower side (Z==0)
DY = 0 on the left side (Y==0)
DX = 0 on the side postpones (X==0)
Pressure of 200 MPa imposed on the upper surface, such as:
P = 0 with T = 0s
P = 200 MPa with T = 0.1s
P = 200 MPa until T = 2.5 10
6
S
This corresponds to a uniaxial creep test under a constant loading of 200 MPa.
1.4 Conditions
initial
Null stresses and deformations.
Code_Aster
®
Version
8.1
Titrate:
SSNV183 Creep test with the model
VENDOCHAB
Date:
01/09/05
Author (S):
O. DIARD
Key
:
V6.04.183-A
Page:
3/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation
Analytical solution for the variable of damage D:
()
(
)
K
R
T
With
K
T
D
+
+
-
-
=
1
1
0
1
1
1
0
0,05
0,1
0,15
0,2
0,25
0,3
0,00E+00 5,00E+05 1,00E+06 1,50E+06 2,00E+06 2,50E+06 3,00E+06
Time (S)
Damage D
Analytical solution for the variable of isotropic work hardening viscoplastic, R, in the case of a threshold
Y
no one:
()
(
)
(
)
NR
M
M
K
NR
K
R
NR
R
T
With
K
K
With
NR
K
M
NR
M
T
R
+
+
-
+
-
+
-
-
-
+
+
=
1
1
0
0
0
)
1
(
1
1
1
0
0,001
0,002
0,003
0,004
0,005
0,006
0,007
0,008
0,00E+00 5,00E+05 1,00E+06 1,50E+06 2,00E+06 2,50E+06 3,00E+06
Time (S)
Varaible of E
C
isotropic steeping
(
R
)
Code_Aster
®
Version
8.1
Titrate:
SSNV183 Creep test with the model
VENDOCHAB
Date:
01/09/05
Author (S):
O. DIARD
Key
:
V6.04.183-A
Page:
4/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
In the preceding expressions, D is the variable of damage corresponding to the variable
intern VARI_9 and R are the variable of multiplicative viscoplastic work hardening corresponding to
internal variable VARI_8.
There is also the correspondence following, by reports/ratios with the parameters of the key word
VENDOCHAB
:
NR = N_VP
M = M_VP
K = K_VP
WITH = A_D
R= R_D
K = K_D
2.2
Sizes and results of reference
Evolution of the variable of damage, D, according to time. One tests this value with different
moments:
Moment Reference
Aster
% difference
520000 1.52596E-02
1.52081E-02 - 0.34
1000000 3.30676E-02
3.29962E-02 - 0.22
2000000 9.9465369E-02
9.92747E-02 - 0.19
2250000 1.37520763E-01
1.37173E-01 - 0.25
2500000 2.66018229E-01
2.62867E-01 - 1.18
Evolution of the variable of isotropic work hardening viscoplastic, R, according to time. One tests this
value at various moments:
Moment Reference
Aster
% difference
520000 2.300147E-03
2.29431E-03 - 0.25
1000000 3.179469E-03
3.17481E-03 - 0.15
2000000 4.95103E-03
4.94641E-03 - 0.09
2250000 5.592847E-03
5.58683E-03 - 0.11
2500000 6.99749E-03
6.97181E-03 - 0.37
The variation observed on D for T = 2.5 10
6
S is due to the very strong not linearity of the evolution of the variable
of damage.
2.3
Uncertainties on the solution
Precision of the codes
Code_Aster
®
Version
8.1
Titrate:
SSNV183 Creep test with the model
VENDOCHAB
Date:
01/09/05
Author (S):
O. DIARD
Key
:
V6.04.183-A
Page:
5/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
The discretization in time is rather fine:
(JUSQU_A = 2, A NUMBER = 10),
(JUSQU_A = 2., A NUMBER = 10),
(JUSQU_A = 20., A NUMBER = 10),
(JUSQU_A = 200., A NUMBER = 10),
(JUSQU_A = 2000., A NUMBER = 10),
(JUSQU_A = 20000., A NUMBER = 10),
(JUSQU_A = 200000., A NUMBER = 10),
(JUSQU_A = 1000000., A NUMBER = 30),
(JUSQU_A = 1600000., A NUMBER = 30),
(JUSQU_A = 1700000., A NUMBER = 40),
(JUSQU_A = 1800000., A NUMBER = 40),
(JUSQU_A = 1900000., A NUMBER = 40),
(JUSQU_A = 2000000., A NUMBER = 40),
(JUSQU_A = 2100000., A NUMBER = 40),
(JUSQU_A = 2200000., A NUMBER = 40),
(JUSQU_A = 2300000., A NUMBER = 40),
(JUSQU_A = 2400000., A NUMBER = 40),
(JUSQU_A = 2500000., A NUMBER = 40),
3.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs: 1 (HEXA8)
3.3 Functionalities
tested
Controls
DEFI_MATERIAU VENDOCHAB
STAT_NON_LINE COMP_INCR RELATION
VENDOCHAB
DEFORMATION
SMALL
NEWTON
STAMP
=
“ELASTIC”
CONVERGENCE
RESO_INTE
=
“RUNGE_KUTTA_2”
3.4
Sizes tested and results
Evolution of the variable of damage, D, according to time. One tests this value with different
moments:
Moment Reference
Aster
% difference
520000 1.52596E-02
1.52081E-02 - 0.34
1000000 3.30676E-02
3.29962E-02 - 0.22
2000000 9.9465369E-02
9.92747E-02 - 0.19
2250000 1.37520763E-01
1.37173E-01 - 0.25
2500000 2.66018229E-01
2.62867E-01 - 1.18
Code_Aster
®
Version
8.1
Titrate:
SSNV183 Creep test with the model
VENDOCHAB
Date:
01/09/05
Author (S):
O. DIARD
Key
:
V6.04.183-A
Page:
6/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Evolution of the variable of isotropic work hardening viscoplastic, R, according to time. One tests this
value at various moments:
Moment Reference
Aster
% difference
520000 2.300147E-03
2.29431E-03 - 0.25
1000000 3.179469E-03
3.17481E-03 - 0.15
2000000 4.95103E-03
4.94641E-03 - 0.09
2250000 5.592847E-03
5.58683E-03 - 0.11
2500000 6.99749E-03
6.97181E-03 - 0.37
3.5 Remarks
The variation observed on D for T = 2.5 10
6
S is due to the very strong not linearity of the evolution of the variable
of damage.
4
Summary of the results
The results obtained with Code_Aster are close to the analytical solution of reference since
the variation with the reference solution is lower than 1.2% and generally lower than 0.4% before
strong non-linearity leading to the final rupture.