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This paper focuses from the fundamentals of finite element flow formulation to the main aspects of computer implementation and modelling of three-dimensional bulk forming processes. Fundamental research and development is based on a comprehensive analysis of a wide range of theoretical and computational subjects such as selection of elements, solution procedures, contact algorithms, and meshing and remeshing procedures. We also focus on elastic analysis of tooling and a simple algorithm is proposed for transferring the load across the die–workpiece contact interface.The overall study is supported by several specially designed, cold forming experimental parts that were manufactured under laboratory-controlled conditions. Comparisons between theoretical predictions and experimental results comprise a wide range of topics such as material flow, geometry, forming load and strain distribution.

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This paper draws from the fundamentals of the finite element flow formulation to obtain aspects of computer implementation and modelling of industrial forging processes. Emphasis is given to a wide range of theoretical and numerical subjects such as selection of elements, solution procedures, contact algorithms, elastic analysis of tooling and interaction between two-and threedimensional finite element models. New algorithms are proposed for the elastic analysis of tooling and for transferring history-dependent scalar and tensorial quantities from axisymmetric into full three-dimensional mesh systems.The overall presentation is illustrated with the numerical modelling of two cold forging operations. Theoretical predictions obtained from the closed-die forging of a spider part (with predominantly complex three-dimensional material flow) are validated against experimental measurements obtained from laboratory-controlled manufacturing conditions. Assessment is provided in terms of material flow, geometrical profile, effective strain distribution and forging load. The latter is employed for illustrating the proposed methodology for performing the elastic analysis of tooling.The usefulness and efficiency of the algorithm for combining two-and three-dimensional finite element models is demonstrated by the numerical modelling of a typical multistage forging sequence utilized in the production of a Phillips-head screw.

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