ESAFORM 2014
The 17th annual conference
on Material Forming
May 7-9, 2014
Dipoli Congress Centre
Espoo Finland
J.I.V. Sena1, L. Duchêne2, A.M. Habraken2,3, R.A.F.
Valente1, R. J. Alves de Sousa1
1GRIDS Research Group, TEMA Research Unity, Department of
Mechanical Engineering, University of Aveiro, Portugal.
2Department ArGEnCo, division MS2F, Universitie de Liège, Belgium.
3Research Director of the Fonds de la Recherche Scientique-FNRS
May, 2014
Numerical Simulation of a Conical Shape Made
by Single Point Incremental Forming
Adaptive Remeshing technique with solid-shell
elements
Aveiro, Portugal Liège, Belgium
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Contents
1. Introduction
2. SPIF Numerical simulation
3. Adaptive Remeshing
4. Benchmark: Conical shape component
Solid-Shell Element: RESS (Reduced Enhanced Solid-Shell)
5. Final Considerations
1
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Intr
oduction
� Tool guided by numerical control system, forming tool deforms
a clamped sheet into its desired shape
� High deformations occur close to the current location of the
tool.
� Single point incremental forming (SPIF) sheet forming
process adapted for rapid prototyping. Neither dies nor punches
to form a complex shape.
2
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Num
erical sim
ula
tion
� PROBLEM:
- Moving contact between the tool and the sheet
- The nonlinearities
� First Adaptive SPIF Remeshing : only for Shell finite elements*.
� Now : extension to 8 nodes 3D finite elements= RESS
(Reduced Enhanced Solid-Shell).
� RESS + Remeshing ADVANTAGES :
- Use a 3D constitutive law
- Prediction of the sheet thickness
- Decrease the CPU time
3
*see Cedric Lequesne et al., Numisheet 2008, Switzerland, September 1 - 5, 2008.
Work Scope
Refined mesh
near the tool
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Adaptive R
em
eshin
g• Selection of a neighborhood around the position of the tool center.
• Mesh dynamically refined on the tool vicinity
• Proximity condition :
D² ≤ α (L²+R²)
- D: minimum distance between the tool center and the four nodes of the
contact element
- L: length of the longest diagonal of the element
- R: radius of the tool
- α: coefficient adjusting the size of the neighborhood chosen by the user
4
Refinement / Unrefinement Criterion
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Additional Unrefinement Criterion
v ii
i 1,4
X H ( , )X=
= ξ η∑
c vd = X -X
maxd d≤
• Computation of the initial
relative position:
−Hi: interpolation function
−Xi: nodes positions of the coarse
element
−Xc: Current position of the node
−dmax: maximal admissible distance
chosen by the user
• Computation of the distance
• Unrefinement criterion
5
Adaptive R
em
eshin
g• To avoid losing geometric accuracy, if the mesh distortion significant keep
the refined mesh elements
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pk
n nk kJ pj
pj min
jn n
k kJ pj
p pj min
CZZ+
R R if R >R
1 CZ+
R R
Z if R R
=
≤
∑
∑
• j: the index of the new integration
point
• k: the index of the integration
point of another element in the
sphere
• p: is the index of the closest
integration point
• Zi: stress or state variables
components at the integration
point j
• Rkj: distance between the
integration point k and j
Interpolation of state variables and stress
• C: coefficient defined by the user
• n: degree of interpolation
• d: highest diagonal of the element
• D: highest diagonal of the structure
1
min
With :
R 1.5d
R 0.0001D
=
=
6
Adaptive R
em
eshin
g
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ELEMB
ELEMENT SUBROUTINE
Integration points loop
NO
Element’s
loop
STEP LOOP
LAMIN2
41Check the
convergence
iteratively
5
Converge ?
23
ELEMB2
PRINTPER
ECRVAR
PRIDON
YES
YESREMESHING ? ADAPT_REMESH
NO
Interpolates the stress and
state variable of coarse elements deactivated
NO
INTERPOL_ELEM
YES
Has remeshing
elements ?
6
7
8
Write in output files
INITIAL MESH (First Step)
MESH WITH REMESHING (Next Steps)
9
Generation of the new elements
Interpolation of the stress
and state variables for new
elements
INTERPOL_ELEM
7
Adaptive R
em
eshin
g
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Benchm
ark
Conical shape simulation
– Setup description:
– Material : Aluminium alloy AA7075-O
– thickness: 1.6 mm
– spherical tool radius: 6.33 mm
– Vertical step-down of 0.5 mm (90 contours)
8
– Benchmark proposal from NUMISHEET 2014 conference:
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Material
– Material : An aluminium alloy AA7075-O
– The constitutive law: Hill ( but Isotropic behaviour law)
– Parameters:
Young modulus: E1 = E2 = E3 = 72000 MPa
Poisson ratio: ν1 =ν2 = ν3 = 0.33
Coulomb modulus: G1 = G2 = G3 = 27067.669 MPa
– Hardening Swift law: σeq =K (ε0 + εpl)n with K= 335.1 MPa,
ε0= 0.004,
n= 0.157
9
Benchm
ark
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Solid
-Shell
Ele
ment RESS (Reduced Enhanced Solid Shell)*
*See in Alves de Sousa R.J. et al. (2007), I. J. P., Vol. 23, pp. 490-515. 10
� Solid-Shell Element specially designed for metal forming applications
� Implemented in LAGAMINE code
� Integration scheme (a) advantages:
- Reduced integration in plane
- Arbitrary number of integration points in one single layer in
thickness direction
� Combination Enhanced Assumed Strain of Simo and Rifai (1990)
� Stabilization technique
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MeshesB
enchm
ark
− Reference mesh without remeshing 5828 elements (RESS+CFI3D)
− One element in thickness direction
− 3 types of Elements :
− 8 node solid-shell finite element RESS with 5IP
− Contact element CFI3D with 4IP
− Symmetric and rotational boundary conditions (BINDS elements)
Rotational BC (BINDS elements)
Tool direction
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Meshes (continuation)B
en
ch
ma
rk
− Coarse mesh with adaptive remeshing, 410 elements (RESS+CFI3D)
− One element in thickness direction
− 3 types of Elements :
− 8 node solid-shell finite element RESS with 5IP
− Contact element CFI3D with 4IP
− Binds elements
− Adaptive remeshing parameters used: n=1,2,3,4; α=1.0; d=0.1mm12
Rotational BC (BINDS elements)
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Shape and thickness in a cross-section
13
Nu
me
ric
al
resu
lts
• Numerical shape at the middle section of the pie mesh to avoid
boundary condition effect
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Radius [mm]
Dep
th [
mm
]
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
Th
ick
ness
[m
m]
Bottom and Top (n=1) Bottom and Top (n=2)
Bottom and Top (n=3) Bottom and Top (n=4)
Bottom and Top (Reference mesh) Thickness n=1
Thickness n=2 Thickness n=3
Thickness n=4 Thickness Reference mesh
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0
5000
10000
15000
20000
25000
30000
35000
40000
0
0,1
0,2
0,3
0,4
0,5
0,6
0 1 2 3 4 5
CP
U t
ime
(s
)
Sh
ap
e e
rro
r [m
m]
Nº of nodes per edge (n)
d=0.1mm RD d=0.1mm TD CPU time d=0.1
Comparisons between time performance
• n=0 indicates the reference mesh (initial refined mesh)
• The shape accuracy for different levels of refinement is analysed in
different directions, transverse direction (TD) and rolling direction (RD)
• The refinement level which has a good agreement between the CPU
time and accuracy in both directions is n=214
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Num
erical re
sults
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Numerical vs Experimental
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Th
ick
ne
ss
[m
m]
De
pth
[m
m]
Radius [mm]
Shape prediction (n=2) Bottom layer Experimental shape RD
Experimental thickness RD Thickness prediction (n=2)
• The accuracy of shape and thickness obtained with adaptive remeshing
is acceptable
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Num
erical re
sults
Major and minor plastic strain
16
-0,05
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0 20 40 60 80
Majo
r p
lasti
c s
train
Radius [mm]
Experimental Major plastic strain RD Major plastic strain (n=2)
-0,05
-0,03
-0,01
0,01
0,03
0,05
0,07
0,09
0 20 40 60 80
Min
or
pla
sti
c s
train
Radius [mm]
Experimental Minor plastic strain RD Minor plastic strain (n=2)
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Evolution of force predictionN
um
erical re
sults
17
– N = 1 � 4 different levels of refinement
– Analytical force by Aerens* (team of Duflou KUL)
*See in Aerens R. et al. (2010), I. J. A.M. T., Vol. 46, pp. 969-982.
Analytical force
0
500
1000
1500
2000
2500
3000
3500
4000
0 20 40 60 80 100 120 140 160 180
Time
Ax
ial
Fo
rce (
Fz)
Fz Reference Fz n=1 Fz n=2 Fz n=3 Fz n=4 Experimental
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Fin
al C
onsid
era
tions
18
• 3D analysis of single point incremental forming process.
• This adaptive remeshing method induces CPU time reduction due to the
decrease of the number of elements of the mesh
• Interest of 3D finite elements,
• more accurate thickness computation
• full 3D constitutive laws
� all components of the stress field necessary for damage approach.
Thank you for your attention
Aveiro, Portugal Liège, Belgium
ACKNOWLEDGMENTS
• The authors would like to gratefully acknowledge the support given by
Portuguese Science Foundation (FCT) under the grant SFRH/BD/71269/2010 (J. I.
V. Sena).
• As Research director, A.M. Habraken would like to thank the Fund for Scientific
Research (F.R.S - FNRS, Belgium) for its support.