A reduced single-pattern model for the numerical simulation of multi-pattern metal forming

The aim of this study is to develop a reduced single-pattern model for a multi-pattern metal forming process called repetitive corrugation and straightening (RCS) which belongs to the category of Severe Plastic Deformation (SPD) processes. The corrugation die in RCS is composed of multiple similarly repeated patterns. First, a full multi-pattern model with a large number of patterns is developed. An analysis of this model reveals that the mechanical fields stabilize in the patterns away from the free boundary. Then, a reduced model defining a single pattern is developed to represent the stabilized behavior of the multi-pattern model, based on an approximate description of the boundary conditions in the stabilized sections of the multi-pattern model. Three different boundary conditions are proposed to capture the stress redistribution after each stage of the process in the reduced single-pattern model. It is shown that the single-pattern model with a symmetric-periodic boundary condition during unloading is the best choice to reproduce the stress and strain behavior of the stabilized sections of the multi-pattern model.