Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
1/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
Organization (S):
EDF-R & D/AMA, Delta CAD
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.501
SSNV501 Emboutissage of a sheet by one
hemispherical punch (test of Wagonner)
Summary:
This test represents a calculation of stamping of a sheet by a rigid hemispherical punch in the presence of
great plastic deformations. This test is very much used in the simulation of working sheet.
The analyzed results are the vertical displacement of the punch according to the imposed force. They are
compared with a numerical reference solution.
Three axisymmetric modelings are carried out. The contact blank/punch and blank/die are of the type
node-mesh.
· Modeling a: the coefficient of friction, contact blank/punch and blank/matrix is null.
· Modeling b: the coefficient of friction, contact blank/punch and blank/matrix is equal to 0.15.
· Modeling C: modeling similar to modeling A with a finer mesh for the blank.
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
2/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
1
Problem of reference
1.1 Geometry
Axis of symmetry
Stamp
Blank (sheet)
R1
X
Punch
R2
Y
L
E
R1 = 50.8 mm
R2 = 6.35 mm (Radius of input)
L = 59.18 mm
E = 1. mm
p
With
1.2
Properties of material
Blank:
· E = 69004. NR/mm ˛
Young modulus
· = 0.3
Poisson's ratio
·
(
)
216
.
0
4
0
10
589
p
+
=
-
Law of work hardening
Punch, die
· E = 10
7
NR/mm ˛
Young modulus
· = 0.3
Poisson's ratio
Areas of contact: punch/blank, die/blank
· µ = 0.15
Coefficient of friction
1.3
Boundary conditions and loadings
C.L. :
· the matrix is embedded
· the periphery of the blank is embedded
Loading: pressure p = 12.33N/mm ˛ => force of stamping of 100 kN
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
3/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The method of calculation used to simulate the behavior in the area of contact is presented in
detail in the references [bib1] and [bib2].
2.2
Results of reference
Loading
(KN)
Displacement
µ=0, (mm)
Displacement
µ=0.15 (mm)
10 10.6 10.6
20 15.4 15.4
30 20.0 20.0
40 24.7 23.8
50 28.2 27.1
60 33.0 30.8
70 37.4 35.2
75 44.0 36.5
80
38.3
90
50.0
Displacements are extracted from [1].
2.3
Uncertainties on the solution
<5% graphic results
2.4 References
bibliographical
[1]
P. CHABRAND, F. DUBOIS, J.C. GELIN: “Modelling drawbeads in sheet metal forming”, Int.
J. Mechanics, flight 38 n°1 p 99-77 (1996)
[2]
R. WAGONER, E. NAKAMACHI and J.K. LEE: With benchmark test for sheet metal forming
analysis. Technical RepT. No ERC/NSM-S-90-22, Ohio State University (1988)
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
4/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
3 Modeling
With
3.1
Characteristics of modeling
Areas of contact
- DC1/C2F
- A2B/A1E
Points:
- A1 and A2 are geometrically confused
- C1 and C2 are geometrically confused
- A1, C1
with the blank
- A2
with the punch
- C2
with the radius entered/matrix
Solid meshs
- Blank
. 2 elements in the thickness
. 14 elements according to the radius
- Punch
. 20 elements on AE
- Matrix
. 6 elements on CF
6
Y
R
A1
A2
B
C2
C1
D
F
E
Surfaces slaves
Surfaces Masters
Solid: Modeling AXIS (QUAD4)
Contact: CONTACT (SEG2)
G
Boundary conditions
- dimensioned GF, C2G, BC1: DX=0, DY=0.
- dimensioned DA1, A2H: DX=0.
H
p=12.334N/mm ˛
Punch
Stamp
To avoid the rigid movements of body, one forces that displacements DY of the A1 points
(pertaining to the blank) and A2 (pertaining to the punch) are identical.
3.2
Characteristics of the mesh
A number of nodes: 182
A number of meshs: 131 QUAD4, 12 TRIA3 and 84 SEG2
Code_Aster
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Version
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Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
5/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
3.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING = “AXIS”
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA CONTACT
APPARIEMENT=' MAIT_ESCL',
RECHERCHE=' NOEUD_BOUCLE',
METHODE=' CONTRAINTE',
STAT_NON_LINE
COMP_INCR
RELATION = “VMIS_ISOT_TRAC”
DEFORMATION = “SIMO_MIEHE”
4
Results of modeling A
4.1 Values
tested
Identification
(Displacement)
Loading
(x10
3
NR)
Reference
Aster %
difference
DX (N87)
10.
10.6
9.98 - 5.88
DX (N87)
20.
15.4
15.09 - 2.01
DX (N87)
30.
20.0
19.34 - 3.28
DX (N87)
40.
24.7
23.60 - 4.47
DX (N87)
50.
28.2
27.62 - 2.04
DX (N87)
60.
33.0
32.01 - 3.01
DX (N87)
70.
37.4
37.10 - 0.80
DX (N87)
75.
44.0
40.71 - 7.47
4.2 Remarks
· The law of behavior of material constituting sheet is given linearized under-form.
· Calculation does not converge any more beyond 75% of the total load.
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
6/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
5 Modeling
B
5.1
Characteristics of modeling
Areas of contact
- DC1/C2F
- A2B/A1E
Points:
- A1 and A2 are geometrically confused
- C1 and C2 are geometrically confused
- A1, C1
with the blank
- A2
with the punch
- C2
with the radius entered/matrix
Solid meshs
- Blank
. 2 elements in the thickness
. 14 elements according to the radius
- Punch
. 20 elements on AE
- Matrix
. 6 elements on CF
6
Y
R
A1
A2
B
C2
C1
D
F
E
Surfaces slaves
Surfaces Masters
Solid: Modeling AXIS (QUAD4)
Contact: CONTACT (SEG2)
G
Boundary conditions
- dimensioned GF, C2G, BC1: DX=0, DY=0.
- dimensioned DA1, A2H: DX=0.
H
p=12.334N/mm ˛
Punch
Stamp
To avoid the rigid movements of body, one forces that displacements DY of the A1 points
(pertaining to the blank) and A2 (pertaining to the punch) are identical.
5.2
Characteristics of the mesh
A number of nodes: 182
A number of meshs: 131 QUAD4, 12 TRIA3 and 84 SEG2
5.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING = “AXIS”
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA CONTACT
APPARIEMENT=' MAIT_ESCL',
RECHERCHE=' NOEUD_BOUCLE',
METHODE=' LAGRANGIEN',
FROTTEMENT=' COULOMB',
COULOMB=0.15
STAT_NON_LINE
COMP_INCR
RELATION = “VMIS_ISOT_TRAC”
DEFORMATION = “SIMO_MIEHE”
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
7/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
6
Results of modeling B
6.1 Values
tested
Identification
(Displacement)
Loading
(x10
4
NR)
Reference
Aster %
difference
DX (N87)
0.3
5.00
4.84
- 3.14
DX (N87)
0.6
7.00
7.39
5.60
6.2 Remarks
· The law of behavior of material constituting sheet is given in linearized form.
· Calculations were carried out up to 6% of the loading, they can continue without
problem up to 78% of the total load, beyond calculation does not converge any more.
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
8/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
7 Modeling
C
7.1
Characteristics of modeling
Areas of contact
- DC1/C2F
- A2B/A1E
Points:
- A1 and A2 are geometrically confused
- C1 and C2 are geometrically confused
- A1, C1
with the blank
- A2
with the punch
- C2
with the radius entered/matrix
Solid meshs
- Blank
. 2 elements in the thickness
. 30 elements according to the radius
- Punch
. 20 elements on AE
- Radius entered/matrix
. 6 elements on CF
6
Y
R
A1
A2
B
C2
C1
D
F
E
Surfaces slaves
Surfaces Masters
Solid: Modeling AXIS (QUAD4)
Contact: CONTACT (SEG2)
G
Boundary conditions
- dimensioned GF, C2G, BC1: DX=0, DY=0.
- dimensioned DA1, A2H: DX=0.
H
p=12.334N/mm ˛
Punch
Stamp
To avoid the rigid movements of body, one forces that displacements DY of the A1 points
(pertaining to the blank) and A2 (pertaining to the punch) are identical.
7.2
Characteristics of the mesh
A number of nodes: 230
A number of meshs: 291 meshs (163 QUAD4, 12 TRIA3 and 116 SEG2)
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
9/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
7.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING = “AXIS”
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA CONTACT
APPARIEMENT=' MAIT_ESCL',
RECHERCHE=' NOEUD_BOUCLE',
METHODE=' CONTINUE',
MODL_AXIS = “YES”,
STAT_NON_LINE
COMP_INCR
RELATION = “VMIS_ISOT_TRAC”
DEFORMATION = “SIMO_MIEHE”
8
Results of modeling C
8.1 Values
tested
Identification
(Displacement)
Loading
(x10
4
NR)
Reference
Aster
% difference
DX (N87)
1.
10.6
8.35
- 21.18
DX (N87)
2.
15.4
14.07
- 8.66
DX (N87)
3.
20.0
18.58
- 7.11
DX (N87)
4.
24.7
22.69
- 8.13
DX (N87)
5.
28.2
26.74
- 5.20
DX (N87)
6.
33.0
31.01
- 6.03
DX (N87)
7.
37.4
36.05
- 3.62
DX (N87)
7.5
44.0
39.72
- 9.71
8.2 Remarks
· The law of behavior of material constituting sheet is given linearized under-form.
· Calculation does not converge any more beyond 75% of the total load.
Code_Aster
®
Version
8.2
Titrate:
SSNV501 Emboutissage of a sheet by a hemispherical punch
Date:
15/02/06
Author (S):
Mr. ABBAS, F. LEBOUVIER
Key
:
V6.04.501-A
Page:
10/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
9
Summary of the results
On the figure below we present, for modeling A, the deformation of the blank, the position of
the matrix and of the punch for a loading of 75kN.
One notes a variation compared to the references [bib1] and [bib2]. For a loading reaching 75%
total specified in these references, we have:
· for A, 7,5% of error on displacement,
· for C, 9,7% of error on displacement.
For modeling B (with friction), the error with 75% of the load given by the references [bib1]
and [bib2] is 6%.