Slide 1

Plane Strain Extrusion Slip-line Field Solution vs. FEM Solution Nanshu Lu ES 246 Plasticity Project Jan. 11, 2006 Slide 2 Outline Metal Forming Extrusion Slip-line Field Solution Unsymmetrical Extrusion FEM Solution Conclusions Slide 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 Slide 4 Slip-line Field Solution Fan CAD Hill R. (1948) A B C D EF G x2x2 x1x1 H Slide 5 Unsymmetrical Extrusion Green A.P. (1955) Fractional Reduction Eccentricity Slide 6 Unsymmetrical Extrusion Rough container walls Smooth container walls Slide 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 Slide 8 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 Slide 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) Slide 10 FEM Solution Modeling Skills Mesh Structured CPE4R elements Global seed size 0.002m Job Monitor Slide 11 FEM Solution Deformed Shape Slide 12 FEM Solution Animation Slide 13 FEM Solution Reaction Force History Slide 14 FEM Solution P~H Relation H (m)00.20.40.60.81 P/k0.00000.61871.23731.85602.47473.0933 Pmax (N)075.6154.2217.9308.4377.5 Cal-P/k0.00000.65471.33541.88712.67083.2692 r=0.5, Slide 15 FEM Solution P~k Relation y (MPa)360380400420440 P/(2H) (MPa)321.6339.4357.3375.2393.0 Pmax (N)68.872.275.678.982.2 Cal-P/(2H)344361378394.5411 H=0.2m Slide 16 FEM Solution Unsymmetrical Extrusion 00.20.40.6 p/k0.00000.03000.13000.2950 P (N)204.8206.6211.3218.6 Cal- p/k0.00000.03900.14070.2988 r=0.8 Slide 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 Slide 18 Acknowledgement Joost Vlassak Jennifer Furstenau Xuanhe Zhao