Mechanisms in Incremental Mechanisms in Incremental Sheet FormingSheet Forming

W. C. Emmens, CORUS RD&TA.H. van den Boogaard, University of Twente

The Netherlands

© W. C. Emmens 2008 - w.c.emmens@utwente.nl

Seminar NSF08, Helsinki, Finland, 29-30 oct 2008

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What this is all about

In incremental forming large strains can be obtained, well beyond the classic FLC.

WHY?Figure: Shim, Park; 2001

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Enhanced formability

Questions to be asked:

• Observing plane-strain deformation in ISF, why is the process not limited by the instabilities that normally limit plane-strain stamping?

• What mechanism does finally limit the process?

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Process limits

AA 5154

(Hosford 1999)

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What is ISF?Incremental forming: A variety of forming processes all characterized by the fact that at any time only a small part of the product is actually deforming. This zone of local deformation is moving over the entire part by some means, mostly mechanical.

Or in brief:A progression of localized deformation. (K.J.)

(Mason 1984)

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What is ISF?

Source: DTU, Kopenhagen, Denmark

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What is ISF?

Characteristics of incremental forming:

• The deformation is localized into a small zone

• In that zone special conditions exist that raise the formability

⇒ How and Why?

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Next:

Forming/stabilizing mechanisms in ISF:

Continuous mechanisms:• 1 Shear• 2 Contact stress

Intermittent mechanisms:• 3 Bending-Under-Tension• 4 Cyclic effects

Other mechanisms:• 5 Hydrostatic stress

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1. Shear - principle

• Which type of shear? Not all are easy detectable!

• Distinguish between intermediate strain state and final strain state

A B C

in-plane shear through-thickness shear out-of-plane shear

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1. Shear - principle

-1.6 1.6-1.6

1.6

A shear stress reduces the yield stress in tension and raises the necking limit.

τ = 0 τ <> 0

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1. Shear - principle

A shear stress reduces the yield stress in tension and raises the necking limit.

pure tension pure shear

0.0 0.1 0.2 0.3 0.4 0.5 0.6

τ / σ f

0

1

2

3

4

5

ε z,neck / n

σ y / σ f

(data from Tekkaya 2006)

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1. Shear - historyDemonstrated by Hoogenboom (TUE), 2002Observed as occurring in ISF:- Sawada (Tokyo Un.) 2001, FEM- Bambach (RWTH) 2003, FEM- Eyckens (KUL) 2007+, FEM, exp.

Proposed as mechanism in ISF:- Allwood/Jackson (Cambridge), 2007+, FEM, exp.

Analysis: - Tekkaya (IUL) 2006, analytical - Eyckens (KUL) 2008, M-K

Investigated by Allwood c.s. “paddle forming”- Obtained high level of uniform elongation

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1. Shear - effects

effect on FLC, M-K analysis

(Eyckens 2008)Direction of shear

A B

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2. Contact stress - principle

A surface stress in compression reduces the yield stress in tension and raises the necking limit.

-1.6 1.6-1.6

1.6

σ3 = 0 σ3 < 0

contact stress

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Observed as occurring in ISF: - Bambach (RWTH) 2003, FEM ( hydrostatic stress)- Eyckens (Leuven) 2008, FEM

Proposed as mechanism in ISF:- Huang (US) 2008

Analysis:- Gotoh (Japan) 1995, anal. - Smith, Matin (US) 2003, 2005, anal. - Banabic (Cluj) 2008, M-K

Experimental investigation:- Taraldsen (Oslo) 1956, 1964, 1972, 600% (Cu-rod) - Rijken (HO) 1965, 100% (steel strip)- Olejnik (Warsaw) 1987, 590% (steel bar)

2. Contact stress - history

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2. Contact stress - effects

(Smith 2003, weakened in 2005)

γ = σ3 / σ1

Smith model

Gotoh model

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2. Contact stress - effects

0.0 0.1 0.2 0.3 0.4 0.5 0.6− σ 3 / σ 1

1

2

3

45678normalized necking limit

Smithn = 0.2

Smithn = 1.0

GotohBanabicAA3104

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specimen

set of tworotating rolls

2. Contact stress - testing

σn = 1-10% σy

forming is concentrated in the

contact zone: incremental forming

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2. Contact stress - results

(Taraldsen 1964, OFHC copper)

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2. Contact stress - results

measured stress-strain curves for steel (Taraldsen 1964)a, b = different steel grades

true stress engineering stress

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1/2. Shear & Contact stress

Both affect the stress state.

Both reduce the yield stress in tension. ⇒ localize the deformation

Both increase the formability to a certain level.⇒ additional stabilizing effect

Both depend on yield- and hardening-behaviour of the material.

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3. BUT - principle

R

t

w

X

YZ

F, TT

ee b

.tσ

e = t/2Rb

relation between tension force per unit width T and stretching strain e in BUT, assuming constant bending radius R

reduces tension force, creates stable deformation

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3. BUT - principle

0 50 100 1500

2

4

6

8

10

12

14maximum strain (%)

water jet ISFspinning

material thickness (µ m)

Results from can shaping experiments (1999-2002) using incremental techniques (Emmens 2004)

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Bending-under-tension: textbooksObserved as occurring in ISF:- Sawada (Tokyo Univ.) 2001, FEM

Proposed as mechanism in ISF:- Emmens (Corus) 2004, exp.

Investigations (using repetitive bending):- Benedyk (IIT) 1971, 2002, exp. 26 - 140% (var. mat) (mat. characterization)- Jongenburger/Mols (TUD) 1972, exp. 30 - 110% (var. mat.) (tension-levelling)- Hadoush (UT) 2007, FEM 200% (steel)- Emmens (UT) 2007+, exp. 430% (steel) (incremental forming)

3. BUT - history

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3. BUT - testing

specimen

set of threerotating rolls

only material actually being bent will deform ⇒ forming is

concentrated in the 6 bending zones: incremental forming

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3. BUT - results

0 50 100 150 200 250

elongation (mm)

0.0

0.5

1.0

1.5

2.0true length strain

normal tensile test

series 1series 2series 3

100

eng. strain (%)

50

150 200

300

500 400

600

dashed line= theory

(Emmens 2008)

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3. BUT - results

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4true strain

0

100

200

300

400

500

600true stress (MPa)

Ludwik-Nadai curve

(Emmens 2008)

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3. Bending-Under-tension

Does NOT affect the stress state: part of the sheet is in compression.

Reduces the yield force in tension and creates stable elongation to a certain strain increment.⇒ localizes the deformation⇒ additional stabilizing effect

Independent of yield- and hardening-behaviour or level of straining. (except Bauschinger effect)

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Summary so far

Shear and contact stress:- reduction of yield stress in tension due to change of the strain state;- capable of creating higher levels of deformation to an absolute level;

Bending-under-tension:- reduces yield force in tension due to simultaneous bending;- capable of creating higher levels of deformation to a relative level;

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Situation in ISF

PUNCHPUNCH

zt

R

position at last contour

zone of localized deformation

stretchedwall

SB

B

S = shearB = BUT = contact stress

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4. Cyclic effects - principle

Strong cyclic effects in ISF.

Repeated bending / unbending.

(Eyckens 2007)

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4. Cyclic effects - history

Cyclic effects in ISF:

- Emphasized by Bambach (RWTH) 2003

- Analysed using M-K theory by Eyckens (KUL) 2007, Van Bael (KUL) 2007

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4. Cyclic effects - results

(Van Bael 2007)

limit for straight strain path

limits in serrated straining

M-K analysis

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4. Cyclic effects - summary

Non-straight strain path (serrated yielding) can create enhanced formability.

Effects caused by non-isotropic hardening.

Note: bending-under-tension also implies cyclic effects

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5. Hydrostatic stress

Contact stress: σ3<0postpones necking

Compressive hydrostatic stress: σ1+σ2+σ3<0suppresses damage development

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5. Hydrostatic stress

Observed in ISF: - Hirt and Bambach (RWTH), 2002, 2003, FEM- Silva, 2008, analytically

sheared elements !(Bambach 2003)

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5. Hydrostatic stress

Effect of compressive hydrostatic stress:

Slows down damage development but does not suppress instabilities.

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Summary of mechanismsLocalize deformation due to local reduction of stretching force by:- Shear- Bending-under-tension- Contact stress

Stabilizing effects by:- Shear and Contact Stress (postpones necking)- Bending-under-tension (stable deformation)- Cyclic straining (postpones necking)

} experimental evidence it can create large uniform straining

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But …

ISF can be done with a high pressure water jet(Emmens, Iseki, Jurisevic)

- no tool, no tool contact- no friction- no contact pressure- no shear ?

ISF can be done on plastics (Frantzen 2008)

- fundamentally different plastic behaviour(yield stress depends on hydrostatic pressure)- material independent mechanisms?

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And …

2D operations (adapted tensile tests) differ from 3D operations:- no constraints from the surrounding material (back stresses)- max. strain much larger than in 3D ISF

Open questions: - are stabilizing mechanisms really necessary?- what is the effect of the actual moving of the zone of localized deformation?- what is the effect of the constraints caused by the surroundng material?

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Conclusions• Several mechanisms are known that can localize the forming and lift the formability, and are related to some aspect of Incremental Sheet Forming.

• At any moment more mechanisms may be at work simultaneously.

• It is not fully clear yet if and if so to what extent these mechanisms operate in a specific ISF operation.

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CopyrightThis presentation contains material copied from other publications, that is subjected to copyright by the respective authors or publishers. The original sources are:

•Sheet 2: M.S. Shim, J.J. Park; The formability of aluminium sheet in incremental forming; Journal of Materials Processing Technology 113 (2001) 654-658 •Sheet 4: Hosford, W.F., Duncan, J.L., 1999. Sheet Metal forming: A Review. JOM, 51 (11), pp. 39-44. •Sheet 5: B Mason, E. Appleton; Sheet metal forming for small batches using sacificial tooling; Proc. 3rd Int. Conf. on Rotary Metalworking, Kyoto, Japan, 1984, pp 495-51 •Sheet 6: Copyright DTU, Denmark•Sheet 13: P. Eyckens, A. Van Bael, P. Van Houtte; An extended Marciniak-Kuczinski forming limit model to assess the influence of through-thickness shear on formability; Proc. Numisheet 2008, Sept 1-5 2008, Interlaken, Switzerland, pp 193-198 •Sheet 16: Smith, L.M., Averill, R.C., Lucas, J.P., Stoughton, T.B., Matin, P.H., 2005. Influence of transverse normal stress on sheet metal formability. Int. J. of Plasticity 10 (2005) pp. 1567-1583•Sheet 19,20: Taraldsen, A., 1964. Stabilized tensile testing (i.e. without local necking). Materialprűfung, vol 6 (1964), nr. 6, pp 189-195.•Sheet 31: P.Eyckens, S. He, A. Van Bael, P. Van Houtte, J. Duflou; Forming Limit Predictions for the Serrated Strain Paths in Single Point Incremental Forming; Proceedings Numiform 07, june 17-21 2007, Portugal, AIP CP908, pp 141-146 •Sheet 33: A. Van Bael, P. Eyckens, S. He, C. Bouffioux, C. Henrard, A.M. Habraken, J. Duflou. P. Van Houtte; Forming Limit Prediction for Single-Point Incremental Sheet Metal Forming; Proceedings 10th ESAFORM, Zaragoza, Spain, April 18-20 2007, AIP CP907, pp 309-31 •Sheet 36: M. Bambach, G. Hirt, S. Junk; Modelling and Experimental Evaluation of the Incremental CNC Sheet Metal Forming Process; Proceedings 7th COMPLAS, Barcelona, Spain, April 7-10 2003

All other material is Copyright W.C. Emmens