1. Plane Strain Extrusion – Slip-line Field Solution vs. FEM Solution
Nanshu Lu
ES 246 Plasticity Project
Jan. 11, 2006

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

3. 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

4. Slip-line Field Solution
Hill R. (1948) A B C D E F G x2 x1 H
Fan CAD

5. Unsymmetrical Extrusion
Green A.P. (1955)
Fractional Reduction
Eccentricity

6. Unsymmetrical Extrusion
Rough container walls
Smooth container walls

7. 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

8. FEM Solution – Modeling Skills
Step
“Move ram” after initial step
Maximum number of increments = 1000
Initial Increment =
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

9. 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)

10. FEM Solution – Modeling Skills
Mesh
Structured CPE4R elements
Global seed size 0.002m
Job
Monitor

11. FEM Solution – Deformed Shape

12. FEM Solution – Animation

13. FEM Solution – Reaction Force History

14. FEM Solution – P~H Relation
H (m)
0.2
0.4
0.6
0.8 1
P/k
0.0000
0.6187
1.2373
1.8560
2.4747
3.0933
Pmax (N)
75.6
154.2
217.9
308.4
377.5
Cal-P/k
0.6547
1.3354
1.8871
2.6708
3.2692
r=0.5,

15. FEM Solution – P~k Relation
σy (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
H=0.2m

16. FEM Solution – Unsymmetrical Extrusionε
0.2
0.4
0.6
Δp/k
0.0000
0.0300
0.1300
0.2950
P (N)
204.8
206.6
211.3
218.6
Cal- Δp/k
0.0390
0.1407
0.2988
r=0.8

17. 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

18. Acknowledgement Thank You ^_^ Joost Vlassak Jennifer Furstenau
Xuanhe Zhao
Thank You ^_^