Stress and Strain Paths in Deep Drawing of Cylindrical Cup

Stress-strain relationship at large plastic deformation during sheet metal forming process are accompanying with numerous problems. These problems include the predicting important parameters which effect accuracy and durability of the products made by different methods. Most of presented methods for analysis of sheet metal forming do not taking into account deformation hardening and thickness changes during the forming process and are limited in application, especially in the accuracy of final solutions [1, 2, 3]. Therefore it important to find a mathematical model which can correctly analysis forming problems of sheet metal by taking in to account the thickness changes and deformation hardening. At axi-symmetric forming of sheet metal the accuracy of products depends on the stability of dimension which for an isotropic material in the absence of residual stress is determined by thickness distribution on forming products. Durability of products under the same conditions is defined by total distribution of yield stress of the material. In forming processes of sheet metal the yield stress is a function of effective stress which defined by main deformations parameters. Hence, the problem of predicting of durability and accuracy parameters is reduced to the determination of value and distribution of equivalent deformation in the main direction. This research present a new method to analysis the axisymmetric forming condition of sheet metal in the conditions of thickness change and deformation hardening and this method is applied for analysis deformation of thin ring plates.