FINITE ELEMENT PREDICTIONS FOR A COLD SHEET METAL FORMING PROCESS

USING TETRAHEDRAL MINI-ELEMENTS

Min-Cheol Lee, Sang-Hyun Sim, Jae-Gun Eom, and Man-Soo Joun 1

Department of Mechanical Engineering,

Gyeongsang National University

Jinju, Republic of Korea 1 Contact Author

Wan-Jin Chung*

Product Design and Manufacturing Engineering,

Seoul National University of Science and Technology

Seoul, Republic of Korea * Presenter

Sheet Forging

• Recently, industrial applications of sheet forging are increasing.

• The overall shape is made by sheet metal forming process ( stretching, drawing)

• In partial areas, forging is applied to get the detail shape which cannot be obtained by

conventional sheet metal forming process.

• Sharp corner, the drastic change of thickness can be achieved by using bulk metal forming

processes.

• Sheet forging is accompanied by three dimensional stress and deformation unlike

conventional sheet metal forming.

By Toyojima manufacturing co.

Background

• Sheet forging has the characteristics of both sheet metal forming and bulk

metal forming

• Simulation programs for specific process have been successfully used in

sheet metal forming and bulk metal forming

• However, the dedicated simulation programs for specific process show

limitations in simulation of sheet forging

• Thus, an appropriate simulation code for sheet forging is required.

Sheet

metal

forming

Bulk

metal

forming

Sheet forging

Elements for sheet forging simulation

• Shell element

– Widely used in most sheet metal forming simulation due to numerical efficiency

– Owing to geometrical and mechanical assumption, it shows distinctive limitations

when applied to plastic deformation in thickness direction.

– Cannot give reasonable answer to problems with sharp corner or drastic thickness

change even if the special shell element considering thickness stress is used

• Solid-shell element

– Express thickness stress nicely in the case that thickness change is moderate.

– However, still show limitations in sharp corner or drastic thickness change.

• Solid element

– No limitations in sharp corner or drastic thickness change due to no assumption in

geometrical and mechanical behavior

– Numerically inefficient due to the large number of element due to multi-layer mesh

systems to consider the bending in thickness direction.

– Use of bad quality elements with large aspect ratio due to small mesh size in

thickness direction may deteriorate the accuracy of the solution.

Sheet forging simulation using bulk metal forming simulator

• For successful simulation around the region with sharp corner or

drastic thickness change, bulk metal forming simulator should have

– Automatic mesh remeshing capability

– Solid element with good accuracy

• In this study, we used the bulk metal forming simulator, AFDEX 3D

with intelligent remeshing and MINI tetrahedral element.

• Bulk metal forming simulator should be also accurate in sheet metal

forming simulation for successful sheet forging simulation.

– Inherent boundary conditions in sheet metal forming should be treated

properly.

– accuracy by solid element should be competitive to the one by shell

element.

Adaptive remeshing - Considering contact boundary

contact boundary

Before remeshing After remeshing

Adaptive remeshing - Considering contact boundary

MINI Tetrahedral Element in AFDEX 3D

2

1 3

4

G

degree of pressure

degree of velocity

Developed by Arnold, Brezzi and Fortin.

Velocities and hydrostatic pressure are unknowns at real nodes

Velocities at the bubble node are condenced in the final equations

MINI tetrahedral element shows almost same accuracy in deformation

and stress distribution compared to hexahedral element.

Bend

ing p

rocess

Siz

ing p

rocess

Finite Element Ana. Des. 2009

Accuracy – Cold forging, rotor pole

Purpose

• In this study, conventional sheet metal forming is simulated by bulk metal

forming simulator using a multi-layer finite element mesh system.

– The accuracy of bulk metal forming simulator with linear tetrahedral MINI-

element is investigated.

– The influence of number of layers in a multi-layer finite element mesh system

on solutions of sheet metal forming simulations is also investigated.

Problem Definition

48

43

die

70

74

170

170

punch

blank

binder

die

punch

x

yz

x

⊙ Square-cup Deep Drawing Process

○ Blank : 150×150×0.78 mm

○ Flow Stress : 0.259566(0.007 ) MPa

workpiece

die

punch

binder

⊙ Quarter Mesh Model

○ NUMISHEET93 Benchmark Test

○ Binder Force : 19.6 kN, Binder is fixed away from die by 0.98 mm

○ Treatment of friction : the law of constant shear friction, with a shear factor of 0.02

○ No. of steps : 1,000

x

z

C B

A

DY

DX

Initial

blank

O

⊙ Definitions of Measured Draw-in

⊙ Finite element mesh system for the blank

Double-layer

Single-layer

To investigate the influence of he number of layers

⊙ Evolution of Deformed Shape and Effective Strain

100%

75%

50%

25%

0%

⊙ Final deformed shape and effective strain

Double-layer Single-layer

Comparison between Single-layer and Double-layer

x

z

C B

A

DY

DX

Initial

blank

O

DX, DY(mm) DD(mm)

Experiment results 27.95 15.36

Tetrahedral, Single-layer 27.61 13.85

Tetrahedral, Double-layer 26.50 13.15

Solid-shell (Xu et al.) 27.17 14.79

MTLFRM (shell) 28.90 16.20

LS-DYNA3D (shell) 30.03 16.43

PAM-STAMP (shell) 28.43 15.46

Comparison of the predictions with the

experimental results and other predictions by simulation.

⊙ Comparison of Draw-in

DX and DY were predicted well by both layers.

The difference in DD is mainly due to rigid-plastic assumption.

Distance from center(mm)

Th

ickn

ess

str

ain

0 20 40 60 80-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Experiment

Solid-shell (Xu et al.)

Tetrahedral, Single-layer

Tetrahedral, Double-layer

⊙ Comparison of Thickness Strain along OA line

Nice prediction of thickness strain in flange area

Double Peaks around punch corner observed in experiment

can be predicted by double-layer

The difference in the punch head is mainly due to rigid plastic assumption

# Elements 28185

# Nodes 9643

# Elements 13828

# Nodes 4790

(a) Deformation

# Elements 28185

# Nodes 9643

# Elements 13828

# Nodes 4790

(b) Effective strain

⊙ COMPARISON OF DEFORMATION AND EFFECTIVE STRAIN

BETWEEN FINE MESH AND COARSE MESH

DX, DY(mm) DD(mm)

Coarse Mesh 27.61 13.85

Fine Mesh 27.19 13.69

A sheet metal forming was simulated by bulk metal forming simulation program. A three-dimensional rigid-plastic finite element method with linear tetrahedral

MINI-elements was employed.

Multi-layer tetrahedral mesh systems were considered to represent bending deformation,

which is important in sheet metal forming.

Single- and double-layer mesh systems were investigated.

The application to the NUMISHEET93 benchmark. The resulting predictions were compared with experimental results and other predictions

found in the literature, and good agreement was noted.

The number of layers has little influence on the overall deformed shape.

The number of layers shows a non-negligible influence on plastic deformation near punch

corners with bending behavior.

The deformation around near-rigid region shows some deviations from experiment due to

rigid-plastic assumption.

The comparison indicates the feasibility of applying conventional bulk metal forming

simulators (with a little modification) to sheet metal forming process.

Conclusion

Thank you for your attention !