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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
Organization (S): EDF-R & D/AMA, Delta CAD
Handbook 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 grid for the blank.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
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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
:
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1
Problem of reference
1.1 Geometry
Y
L
Stamp
Blank (sheet)
R2
X
With
E
Axis of symmetry
R1 = 50.8 mm
Punch
R2 = 6.35 mm (Rayon of input)
L = 59.18 mm
R1
E = 1. mm
p
1.2
Properties of material
Blank:
· E = 69004. NR/mm ²
Young modulus
· = 0.3
Poisson's ratio
.
0
· =
(- 4
589 10
p
+
Law of work hardening
0
) 216
Punch, die
· E = 107 NR/mm ²
Young modulus
· = 0.3
Poisson's ratio
Zones 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 ² => force of stamping of 100 kN
Handbook of Validation
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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:
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2
Reference solution
2.1
Method of calculation used for the reference solution
The method of calculation used to simulate the behavior in the zone of contact is presented in
detail in the references [bib1] and [bib2].
2.2
Results of reference
Loading Displacement
Displacement
(KN)
µ=0, (mm)
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)
Handbook of Validation
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HT-62/06/005/A
Code_Aster ®
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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
:
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3 Modeling
With
3.1
Characteristics of modeling
Solid: Modeling AXIS (QUAD4)
Solid meshs
Contact: CONTACT (SEG2)
- Blank
. 2 elements in the thickness
Stamp
. 14 elements according to the radius
Y
- Punch
Surfaces slaves
G
. 20 elements on AE
F
- Matrix
6
. 6 elements on CF
D
C2
A1
C1
A2
Zones of contact
B
R - DC1/C2F
- A2B/A1E
Surfaces Masters
Points:
Punch
- A1 and A2 are geometrically confused
- C1 and C2 are geometrically confused
- A1, C1 with the blank
- A2 with the punch
E
H
- C2 with the radius entered/matrix
Boundary conditions
p=12.334N/mm ²
- dimensioned GF, C2G, BC1: DX=0, DY=0.
- dimensioned DA1, A2H: DX=0.
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 grid
A number of nodes: 182
A number of meshs: 131 QUAD4, 12 TRIA3 and 84 SEG2
Handbook of Validation
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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
:
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3.3 Functionalities
tested
Commands 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
Loading
Reference
Aster %
difference
(Displacement)
(x103 NR)
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.
Handbook of Validation
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Code_Aster ®
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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
:
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5 Modeling
B
5.1
Characteristics of modeling
Solid: Modeling AXIS (QUAD4)
Solid meshs
Contact: CONTACT (SEG2)
- Blank
. 2 elements in the thickness
Stamp
. 14 elements according to the radius
Y
- Punch
Surfaces slaves
G
. 20 elements on AE
F
- Matrix
6
. 6 elements on CF
D
C2
A1
C1
A2
Zones of contact
B
R - DC1/C2F
- A2B/A1E
Surfaces Masters
Points:
Punch
- A1 and A2 are geometrically confused
- C1 and C2 are geometrically confused
- A1, C1 with the blank
- A2 with the punch
E
H
- C2 with the radius entered/matrix
Boundary conditions
p=12.334N/mm ²
- dimensioned GF, C2G, BC1: DX=0, DY=0.
- dimensioned DA1, A2H: DX=0.
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 grid
A number of nodes: 182
A number of meshs: 131 QUAD4, 12 TRIA3 and 84 SEG2
5.3 Functionalities
tested
Commands 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”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
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:
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6
Results of modeling B
6.1 Values
tested
Identification
Loading
Reference
Aster %
difference
(Displacement)
(x104 NR)
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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
Code_Aster ®
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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
:
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7 Modeling
C
7.1
Characteristics of modeling
Solid: Modeling AXIS (QUAD4)
Solid meshs
Contact: CONTACT (SEG2)
- Blank
. 2 elements in the thickness
Stamp
. 30 elements according to the radius
Y
- Punch
Surfaces slaves
G
. 20 elements on AE
F
- Radius entered/matrix
6
. 6 elements on CF
D
C2
A1
C1
A2
Zones of contact
B
R - DC1/C2F
- A2B/A1E
Surfaces Masters
Points:
Punch
- A1 and A2 are geometrically confused
- C1 and C2 are geometrically confused
- A1, C1 with the blank
- A2 with the punch
E
H
- C2 with the radius entered/matrix
Boundary conditions
p=12.334N/mm ²
- dimensioned GF, C2G, BC1: DX=0, DY=0.
- dimensioned DA1, A2H: DX=0.
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 grid
A number of nodes: 230
A number of meshs: 291 meshs (163 QUAD4, 12 TRIA3 and 116 SEG2)
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
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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
:
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7.3 Functionalities
tested
Commands 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
Loading
Reference
Aster
% difference
(Displacement)
(x104 NR)
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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
Code_Aster ®
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:
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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%.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
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