Plane Strain Extrusion – Slip-line Field Solution vs. FEM Solution

Nanshu LuES 246 Plasticity ProjectJan. 11, 2006

Outline

Metal Forming – Extrusion Slip-line Field Solution Unsymmetrical Extrusion FEM Solution Conclusions

Metal Forming – Extrusion

Extrusion: Metal forming process whereby the workpiece is placed in a chamber with an opening and is forced to escape through the opening, usually being pushed out by a mandrel.

Extrusion (a) and an assortment of extrudates (b)

Metal Forming, Betzalel Avitzur, Lehigh University

Slip-line Field SolutionABC

11 0

22 0 0

12

45 00

p kp k p k

CDE

11 1 1

22 1 1

12

sin 302

15 sin 302

3cos302

kp k p

kp k p

kk

0 1

1

22 1

22

2 24 12

13

12 3 2

12 23 2

p k p k const

p k

kp k

P H k H

11 2

22 2

12

sin 2sin 2

cos 2

p kp kk

Fan CAD

Hill R. (1948)

A

B

CD

EF

Gx 2

x 1H

Unsymmetrical Extrusion

2D dr

D

b cb c

Green A.P. (1955)

Fractional Reduction Eccentricity

Unsymmetrical Extrusion

Rough container walls

Smooth container walls

1 11.33log2 12pk r

1

11r

rr

2

11r

rr

1 2 1 212

p p p r p p

10.13 1 1.33log2 1p r rk r

FEM Solution – Modeling Skills Part:

Billet – 2D deformable shell Ram – 2D analytical rigid body

Property Material – steel

Elastic – 2000GPa, v=0.3 Plastic – Yield Stress = 400MPa, perfectly plastic

Material Orientation – local coordinate system Assembly

Billet – punch contact

Stress- Strai n Curve

0

50

100

150

200

250

300

350

400

450

0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6Strai n ε

Stre

ss σ

(MP

a)

400y MPa

FEM Solution – Modeling Skills Step

“Move ram” after initial step Maximum number of increments = 1000 Initial Increment = 0.0001 Minimum time increment = 1e-6 Nonlinear geometry

Output request History output – reaction force on the ram reference

point DOF monitor – monitor the horizontal displacement of

the ram reference point

FEM Solution – Modeling Skills Interaction

Frictionless surface-to-surface contact between billet and the ram at initial step

Load Boundary Condition

Symmetric boundary condition Displacement constraints Imposed displacement to the ram (=0.05m)

FEM Solution – Modeling Skills Mesh

Structured CPE4R elements Global seed size 0.002m

Job Monitor

FEM Solution – Deformed Shape

FEM Solution – Animation

FEM Solution – Reaction Force History

FEM Solution – P~H RelationH (m) 0 0.2 0.4 0.6 0.8 1

P/k 0.0000 0.6187 1.237

3 1.8560 2.4747 3.0933

Pmax (N) 0 75.6 154.2 217.9 308.4 377.5

Cal-P/k 0.0000 0.6547 1.335

4 1.8871 2.6708 3.2692

Extrusi on Force ~ Bi l l et Wi dth Rel ati on

0. 0000

0. 5000

1. 0000

1. 5000

2. 0000

2. 5000

3. 0000

3. 5000

0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1H (m)

P/k

123 2

H

400y MPa

14 0.13 1 1.33log1

H r rr

r=0.5,

FEM Solution – P~k Relationσy (MPa) 360 380 400 420 440

P/(2H) (MPa) 321.6 339.4 357.3 375.2 393.0 Pmax (N) 68.8 72.2 75.6 78.9 82.2

Cal-P/(2H) 344 361 378 394.5 411

Extrusi on Force ~ Yei l d Stress Rel ati on

320. 0

330. 0

340. 0

350. 0

360. 0

370. 0

380. 0

390. 0

400. 0

410. 0

420. 0

360 370 380 390 400 410 420 430 440Yi el d Stress (MPa)

P/(2

H)(M

Pa)

13 2

k

H=0.2m

FEM Solution – Unsymmetrical Extrusion

ε 0 0.2 0.4 0.6Δp/k 0.0000 0.0300 0.1300 0.2950 P (N) 204.8 206.6 211.3 218.6

Cal- Δp/k 0.0000 0.0390 0.1407 0.2988

I ncrease i n extrusi on pressure due to eccent r i ci ty

0. 0000

0. 0500

0. 1000

0. 1500

0. 2000

0. 2500

0. 3000

0. 3500

0. 4000

0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6Eccent r i ci t y ε

Δp/

k

r=0.8

Conclusion

Slip-line field method gives good solutions for metal-forming process

ABAQUS/CAE v6.5 is able to calculate perfectly-plastic material

Adaptive meshing is needed to simulate metal-forming process accurately

Thermal contact interaction should be included further

Acknowledgement

Joost Vlassak Jennifer Furstenau Xuanhe Zhao