Code_Aster
®
Version
5.0
Titrate:
HSNV105 Plates in traction-shearing élasto-viscoplasticity
Date:
17/12/01
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key
:
V7.22.105-A
Page:
1/6
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/01/010/A
Organization (S):
EDF/MTI/MN
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
Document: V7.22.105
HSNV105 - Plate in traction-shearing:
élasto-viscoplasticity with metallurgy
Summary:
This test of nonlinear quasi-static mechanics consists in charging in traction-shearing a square plate.
It is largely inspired by tests SSNP14 [V6.03.104] and SSNP15 [V6.03.105] from guide VPCS. The relation
of behavior which one validates here is a élasto-viscoplastic relation of behavior which one introduced
in Code_Aster for the mechanical analyzes taking of account metallurgy. It is an isotropic law of
Norton-Hoff type with an additive work hardening which can be restored.
The temperature and the metallurgical state are constant, one thus considers neither plasticity of transformation nor
metallurgical restoration of work hardening. One does not consider either viscous restoration of
work hardening.
The plate is modelized by a voluminal element (HEXA8).
The results obtained by Code_Aster are very close to the analytical solution of reference
(variation < 0.04%).
Code_Aster
®
Version
5.0
Titrate:
HSNV105 Plates in traction-shearing élasto-viscoplasticity
Date:
17/12/01
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key
:
V7.22.105-A
Page:
2/6
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
Square plate
D
D
D
D
D
C
D
B
With
y
X
1.2
Material properties
Isotropic elasticity
E = 195.000 MPa
= 0.3
Relation of comprise élasto-viscoplastic.
= 600 MPa.s
N
N = 3.5
C
= 0. MPa
C = 0. (not of viscous restoration of work hardening)
m =20.
1.3
Boundary conditions and loadings
In a: U
X
= U
y
= 0
On side AB: U
X
= 0
One uniformly imposes on the structure a temperature T = 750°C
and the TRC is such as the metallurgical state corresponding to this temperature is 100% ferritic.
Loading:
Way OA below of T = 0 to T = 10 S then hold of A until T = 60 S
With
0
93.1
D
(MPa)
D
(MPa)
151.2
Code_Aster
®
Version
5.0
Titrate:
HSNV105 Plates in traction-shearing élasto-viscoplasticity
Date:
17/12/01
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key
:
V7.22.105-A
Page:
3/6
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Being given the nature of the stresses, the solution (forced
, deformations
and deformation
figure cumulated
p
) is homogeneous. In a point of the way of loading OA, one obtains:
xx
D
xy
D
eq
D
D
=
=
=
+
2
2
3
The elastic strain is worth:
E xx
D
E xy
D
E yy
E xx
E
E
=
=
+
=
1
1
The viscoplastic deformation is worth:
if
with
where
if
eq
C
xx
vp
D
eq
xy
vp
D
eq
yy
vp
xx
vp
eq
C N
eq
C
xx
vp
xy
vp
yy
vp
R
p
p
p
R
R
R p
p
- -
>
=
=
=
=
- -
=
=
=
=
=
0
3
2
1
2
0
0
0
0
0
:
&
&
&
&
&
&
:
&
&
&
&
Lastly, the total deflection is:
xx
E xx
vp xx
xy
E xy
vp xy
yy
E yy
vp yy
=
+
=
+
=
+
The reference solution is obtained by using a program written in FORTRAN which carries out one
resolution step by step of the problem with an implicit diagram of discretization.
2.2
Results of reference
One will be interested in the values of the stresses and the deformations at point A of the way of loading
at the moment T = 10 S and T = 60 S
Code_Aster
®
Version
5.0
Titrate:
HSNV105 Plates in traction-shearing élasto-viscoplasticity
Date:
17/12/01
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key
:
V7.22.105-A
Page:
4/6
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Z
X
y
N07
N05
N06
N08
N03
N01
N02
N04
The loading and the boundary conditions are modelized by:
DDL_IMPO: (NODE: N04, DX: 0., DY:0.)
DDL_IMPO: (NODE: N08, DX: 0., DY:0., DZ:0.)
DDL_IMPO: (NODE: N02, DX: 0.)
DDL_IMPO: (NODE: N06, DX: 0.)
FORCE_NODALE: (NODE: (N01 N03 N05 N07), FX:
-
1
4
D
T
()
, FY:
-
1
4
D
T
()
)
FORCE_NODALE: (NODE: (N03 N04 N07 N08), FX:
-
1
4
D
T
()
)
FORCE_NODALE: (NODE: (N02 N04 N06 N08), FY:
1
4
D
T
()
)
FORCE_NODALE: (NODE: (N01 N02 N05 N06), FX:
1
4
D
T
()
)
One imposes moreover one uniform temperature on the structure being worth at any moment: T = 750°C with aid
of the operator
AFFE_CHAM_NO
.
3.2
Characteristics of the mesh
A number of nodes:
8
A number of meshs and type:
1 HEXA8
3.3 Functionalities
tested
Controls
DEFI_MATERIAU META_THER
THER_LINEAIRE OPTION
META_ELGA_TEMP
DEFI_MATERIAU META_VISC_FO
ETA
NR
C
M
AFFE_CHAR_MECA FORCE_NODALE NODE
STAT_NON_LINE COMP_INCR
RELATION
META_EVP
CALC_ELEM OPTION EPSI_ELNO_DEPL
Code_Aster
®
Version
5.0
Titrate:
HSNV105 Plates in traction-shearing élasto-viscoplasticity
Date:
17/12/01
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key
:
V7.22.105-A
Page:
5/6
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Variables Moments
(S) Reference
Aster %
difference
xx
10 2.4333E2
2.4337E2
0.018%
yy
10 1.2011E2
1.2014E2 0.018%
xy
10 2.2379E2
2.2383E2
0.019%
xx
30 5.2103E2
5.2118E2
0.029%
yy
30 2.5896E2
2.5903E2 0.029%
xy
30 4.8027E2
4.8041E2
0.029%
xx
60 5.9557E2
5.9576E2
0.032%
yy
60 2.9624E2
2.9633E2 0.032%
xy
60 5.4912E2
5.4929E2
0.032%
4.2 Parameters
of execution
Version: 5.07.02
Machine: SGI ORIGINI 2000 - R12000
Overall dimension memory:
300 Mo
Time CPU To use:
70 seconds
Code_Aster
®
Version
5.0
Titrate:
HSNV105 Plates in traction-shearing élasto-viscoplasticity
Date:
17/12/01
Author (S):
A. RAZAKANAIVO, F. WAECKEL
Key
:
V7.22.105-A
Page:
6/6
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HI-75/01/010/A
5
Summary of the results
The results obtained with Code_Aster are close to those of the reference solution
(variations < 0.05%)