Optimum preform and die shape design for improved hardness distribution in cold forged parts

Abstract

To predict and then to control hardness distribution in a cold formed part is important, since it is a critical property due to its effects on the forgability of the part and its performance in use. In cold forming processes, hardness of the workpiece is increased as a result of work hardening. The amount of increase is related to the extent of induced plastic strains. This strain-hardness relation may be expressed analytically. Thus, one may obtain the hardness distribution in a cold formed part, once the material properties and induced plastic strains are known. In this research, a methodology is proposed to improve the hardness distribution in a backward extruded cup by optimizing die and preform shapes. Firstly, a finite element model of the backward extrusion process was developed to obtain the effective strain distribution. Then, an analytical relation between strain and hardness was used to determine the hardness distribution. Two variables defining the punch tip geometry and one variable defining the die were selected as optimization variables. The ranges of values that optimization variables could take were constrained. Nelder-Mead was used as the search algorithm to find the optimum process design. An optimization code was developed incorporating the finite element model and the optimization procedure. The results show that significant improvements in hardness distribution can be achieved using the proposed optimization procedure. It was found that the smaller the die clearance, the more uniform the hardness distribution would be. Moreover, it was observed that a smaller friction constant for die-workpiece interface results in a more homogenized hardness distribution.