Computational Modelling of Metal Forming Operations: A Finite Element Approach

This paper introduces an all-inclusive computational modeling (based on finite element method (FEM)) of complicated metal-forming operations, in this case, through cold extrusion of lead billet into an intricate die profile, to fashion E and X-shaped structures. The study is a combination of theoretical modeling using upper bound plasticity theory and experimental validation and finite element simulation to forecast the forming loads, strain distributions and flow patterns of the material in the case of extrusion process. An upper bound was formulated and its development facilitated the computation of governing equations of the energy dissipated by internal deformation, frictional dissipations at tool-workpiece interfaces, and shear deformational regions through a kinematically admissible velocity field. It involved experimental studies which were where plain carbon steels were used as tooling and lead billets were subjected to different lubrication conditions such as no lubrication, red oil, brake oil and mustard oil. The generated FEM model has effectively forecasted the extrusion forces as 92 MN, 70 MN, 67 MN and 75 MN under respective lubrication conditions and they are matched very well with experimental values of 88.5 MN, 66.0 MN, 65.0 MN and 69.5 MN respectively and the extrusion force prediction fall within 2-5% accuracy. Analysis showed that, with brake oil which had the highest viscosity, formed the lowest loads and extrusion pressure thus lowering the maximum pressure which was 281.59 kN/m2 (unlubricated) to 206.82 kN/m2. Proper strain calculation produced a value of 1.03 in agreement with strain contours using FEM method, and strain rates were averagely 16.54 s 1. This confirmed computational model illustrates how FEM can be used to streamline the die design, offer the capability of predicting the process parameters and minimize the element of trial-and-error process that are costly within industry in processes governed by metal formings.