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®
Version
7.4
Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.172
Viscoplastic SSNV172 Comportements
single-crystal
Summary:
This test makes it possible to validate the single-crystal behaviors in a uniaxial situation. Geometry
treated is a cube, the stress and strain state is homogeneous. In order to test the laws as well as possible of
behavior, independently of the definition of the systems of slip, one uses a system here of
particular slip, nonphysical, which represents a slip in only one direction. This allows
to compare two of the single-crystal viscoplastic behaviors, (with kinematic work hardening defined by
a variable of recall) to the macroscopic viscoplastic behaviors of Chaboche. For the others
behaviors one checks only nonthe regression of the results.
All these tests are carried out in only one modeling.
Code_Aster
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Version
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Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
One defines an element MA1, containing the P1 nodes, P2, P3, P4, P5, P6, P7 and P8.
1.2
Material properties
Elastic behavior with:
Young modulus:
MPa
E 145200
=
Poisson's ratio:
3
.
0
=
The first calculation (reference)
Behavior VISC_CIN1_CHAB
CIN1_CHAB=_F (R_0=75.5 MPa
R_I=85.27 MPa
B=19.34,
C_I=10.0 MPa
K=1.0,
W=0.0,
G_0=36.68,
A_I=1.0,),
LEMAITRE=_F (N=10.0,
UN_SUR_K=0.025 Mpa
- 1
UN_SUR_M=0.0,),
The second calculation: single-crystal, with system of UNIAXIAL slip
The behavior of the monocrystal is defined by:
Type of flow: ECOU_PLAS1 whose parameters are:
MPa
K
N
MPa
C
40
,
10
,
10
=
=
=
X
Y
Z
P1
P1
P2
P3
P4
P5
P6
P7
P8
Code_Aster
®
Version
7.4
Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Isotropic type of work hardening: ECRO_ISOT1 whose parameters are:
MPa
R
5
.
75
0
=
34
.
19
=
B
MPa
Q
77
.
9
=
0
=
H
Kinematic type of work hardening: ECRO_CINE1 whose parameters are:
68
.
36
=
D
The family of the systems of slip is: UNIAXIAL
The parameters used here, into uniaxial, correspond to those used for VISC_CIN1_CHAB, in
noticing simply that
0
R
R
Q
I
-
=
.
The third calculation:
The behavior of the monocrystal is defined by:
Type of flow: ECOU_VISC2 whose parameters are:
0
10
10
40
10
10
=
=
=
=
=
has
D
MPa
C
MPa
K
N
Isotropic type of work hardening: ECRO_ISOT2 whose parameters are:
5
.
75
0
=
R
34
.
19
1
=
B
0
2
=
B
77
.
9
1
=
Q
0
2
=
Q
0
=
H
Kinematic type of work hardening: ECRO_CINE2 whose parameters are:
68
.
36
=
D
10
10
=
M
0
=
m
0
=
C
The family of the systems of slip is: UNIAXIAL
There still, the parameters used here, into uniaxial, correspond to those used for
VISC_CIN1_CHAB, by noticing simply that Q=R_I-R_0.
The fourth calculation:
The behavior of the monocrystal is identical to that of the second calculation (the difference comes from
resolution: implicit in this case, and clarifies in the second calculation).
The fifth calculation:
The behavior of the monocrystal is this multiple time. Moreover its orientation compared to
total reference mark of definition of the co-ordinates is defined by an angle of 30 degrees around Z.
Code_Aster
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Version
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Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
For the family of systems of BASAL slip, the laws are:
Type of flow: ECOU_PLAS1 whose parameters are:
MPa
K
N
MPa
C
40
,
10
,
10
=
=
=
Isotropic type of work hardening: ECRO_ISOT1 whose parameters are:
MPa
R
5
.
75
0
=
34
.
19
=
B
MPa
Q
77
.
9
=
0
=
H
Kinematic type of work hardening: ECRO_CINE1 whose parameters are:
68
.
36
=
D
For the family of systems of PRISMATIC slip, the behavior of the monocrystal is
defined by:
Type of flow: ECOU_VISC2 whose parameters are:
0
10
10
40
10
10
=
=
=
=
=
has
D
MPa
C
MPa
K
N
Isotropic type of work hardening: ECRO_ISOT2 whose parameters are:
5
.
75
0
=
R
34
.
19
1
=
B
0
2
=
B
77
.
9
1
=
Q
0
2
=
Q
0
=
H
Kinematic type of work hardening: ECRO_CINE2 whose parameters are:
68
.
36
=
D
10
10
=
M
0
=
m
0
=
C
For the family of systems of slip CUBIQUE1, the behavior of the monocrystal is defined
by:
Type of flow: ECOU_VISC3 whose parameters are:
1
10
10
40
0
=
=
=
=
V
MPa
K
µ
Code_Aster
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Version
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Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
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Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Isotropic type of work hardening: ECRO_ISOT1 whose parameters are:
5
.
75
0
=
R
34
.
19
=
B
77
.
9
=
Q
0
=
H
Kinematic type of work hardening: ECRO_CINE2 whose parameters are:
68
.
36
=
D
10
=
M
5
.
1
=
m
1
=
C
For the family of systems of slip STIRRING, the behavior of the monocrystal is defined
by:
Type of flow: ECOU_VISC3 whose parameters are:
1
10
10
40
0
=
=
=
=
V
MPa
K
µ
Isotropic type of work hardening: ECRO_ISOT2 whose parameters are:
5
.
75
0
=
R
34
.
19
1
=
B
0
2
=
B
77
.
9
1
=
Q
0
2
=
Q
0
=
H
Kinematic type of work hardening: ECRO_CINE1 whose parameters are:
68
.
36
=
D
1.3
Boundary conditions and loadings
·
P4 node
:
0
=
= DY
DX
·
P8 node
:
0
=
=
=
DZ
DY
DX
·
Nodes P2 and P6
:
0
=
DX
·
Nodes P1, P3, P5 and P7
:
25
=
FX
The loading is increasing of
0
=
FX
with
755
.
0
*
25
=
FX
NR, in an increment, which leads to one
uniaxial state of stresses of 75.5 MPa (limit of linearity)
The loading believes then until
955
.
0
*
25
=
FX
NR in
100
increments.
Code_Aster
®
Version
7.4
Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
6/8
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
The first calculation (behavior VISC_CIN1_CHAB) is used as reference. Values obtained with
last increment are (in any point of the mesh):
Stress SIXX
- 9.55E+01
Total deflection
EPXX
- 6.7594E-04
Plastic deformation EPXX
- 1.823E-05
The second, third and the fourth calculations will be validated by comparison with this result. On the other hand,
the fifth calculation does not have a value of reference. The tests are thus of not-regression.
3 Modeling
With
3.1
Characteristics of the mesh
A number of nodes: 8.
Modeling 3D: 1 element of quadratic volume:
HEXA8
.
The structure contains only one grain, the stress and strain state is homogeneous.
The second, third and the fourth calculations will be validated by comparison with this result.
The second and the third calculations use an explicit integration (RUNGE_KUTTA).
The fourth calculation uses an implicit integration.
The fifth calculation uses an implicit integration, the selected orientation is
)
0
,
0
,
30
(
.
4
Results of modeling A
4.1 Functionalities
tested
Controls Options
DEFI_MATERIAU ECOU_VISC1
ECOU_VISC2
ECOU_VISC3
ECRO_ISOT1
ECRO_ISOT2
ECRO_CINE1
ECRO_CINE2
DEFI_COMPOR MONOCRYSTAL FAMI_SYST_GLIS
STAT_NON_LINE COMP_INCR
RELATION=' MONOCRISTAL'
COMPOR
RESO_INTE
Code_Aster
®
Version
7.4
Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
4.2 Values
tested
The second calculation (clarifies, ECOU_VISC1, ECRO_ISOT1, ECRO_CINE1)
Identification Reference
Aster %
difference
xx
SIEF_ELGA
- 95.5 - 95.5
0
xx
of
EPSI_ELGA_DEPL
- 6.7594E-04
- 6.7575E-04 0.03
xx
EPSP_ELGA
- 1.823E-05 - 1.804E-05
1.04
The third calculation (clarifies, ECOU_VISC2, ECRO_ISOT2, ECRO_CINE2)
Identification Reference
Aster %
difference
xx
SIEF_ELGA
- 95.5 - 95.5
0
xx
EPSI_ELGA_DEPL
- 6.7594E-04 - 6.7575E-04
0.03
xx
EPSP_ELGA
- 1.823E-05 - 1.804E-05
1.04
The fourth calculation (implicit, ECOU_VISC1, ECRO_ISOT1, ECRO_CINE21)
Identification Reference
Aster %
difference
xx
SIEF_ELGA
- 95.5 - 95.5
0
xx
EPSI_ELGA_DEPL
- 6.7594E-04
- 6.7624E-04 0.04
xx
EPSP_ELGA
- 1.823E-05 - 1.8528E-05
1.6
The fifth calculation (implicit, all behaviors, 4 families of systems of slip)
Test of nonregression
Identification Reference
Aster %
difference
xx
SIEF_ELGA
- 95.5 - 95.5
0
xx
EPSI_ELGA_DEPL
- 6.7571E-04 - 6.7571E-04
0
Code_Aster
®
Version
7.4
Titrate:
SSNV172 single-crystal viscoplastic Comportements
Date
:
02/11/05
Author (S):
J.M. PROIX, T. KANIT
Key
:
V6.04.172-A
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
5
Summary of the results
The results obtained are in concord with the reference solution. The noted difference
(1.6% to the maximum) comes from the different numerical diagrams, sensitive to the discretization
temporal.