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.

本研究的目的是为称为重复波纹和矫直 (RCS) 的多图案金属成形工艺开发一种简化的单图案模型，该工艺属于严重塑性变形 (SPD) 工艺类别。RCS 中的波纹模具由多个类似重复的图案组成。首先，开发了具有大量模式的完整多模式模型。对该模型的分析表明，机械场在远离自由边界的模式中稳定。然后，基于多模式模型稳定部分中边界条件的近似描述，开发了定义单一模式的简化模型来表示多模式模型的稳定行为。提出了三种不同的边界条件来捕获简化的单模式模型中每个过程阶段之后的应力重新分布。结果表明，卸载期间具有对称周期边界条件的单模式模型是重现多模式模型稳定部分应力应变行为的最佳选择。