A simplified method called “Pseudo Inverse Approach” (PIA) has been developed for axi-symmetrical cold forging modelling. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without classical contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, which leads to a very fast and robust plastic integration procedure. Numerical tests have shown that the Pseudo Inverse Approach is very fast compared to the incremental approach. In this paper, the PIA will be used in an optimization loop for the preliminary preform design in multi-stage forging processes. The optimization problem is to minimize the effective strain variation in the final part and the maximum forging force during the forging process. The numerical results of the optimization method using the PIA are compared to those using the classical incremental approaches to show the efficiency and limitations of the PIA.
The simplified method called Inverse Approach (I.A.) has been developed by Batoz, Guo et al.[1] for the sheet forming modelling. They are less accurate but much faster than classical incremental approaches. The main aim of the present work is to study the feasibility of the I.A. for the axi-symmetric forging process modelling. In contrast to the classical incremental methods, the I.A. exploits the known shape of the final part and executes the calculation from the final part to the initial billet. Two assumptions are used in this study: the assumption of proportional loading for cold forging gives an integrated constitutive law without considering the strain path and the viscoplasticity, the assumption of contact between the part and tools allows to replace the tool actions by nodal forces without contact treatment. The comparison with Abaqus shows that the I.A. can obtain a good strain distribution and it will be a good tool for the preliminary preform design.
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