Plane Strain Extrusion – Slip-line Field Solution vs. FEM Solution Nanshu Lu ES 246 Plasticity Project Jan. 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 Solution Hill R. (1948) A B C D E F G x2 x1 H Fan CAD

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

Unsymmetrical Extrusion Rough container walls Smooth container walls

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

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 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,

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

FEM Solution – Unsymmetrical Extrusion ε 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

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 Thank You ^_^ Joost Vlassak Jennifer Furstenau Xuanhe Zhao Thank You ^_^