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.