Minimization of dies volume using uniform distribution of hollows in the conditions of multi-cycle fatigue dependence on temperature

The research is devoted to development of a model of dies of optimized shape used in the field of metal forming. Use of solid-cast metal dies at the present stage of production requires large material resources, which makes it actual to develop dies models with minimal volume of material due to effective distribution of hollows in correspondence with the required strength resource. The dies mainly experience compressive non-uniform loading in the conditions of drawing and forming, which can lead to the accumulation of damages and lowering of its strength resource in the conditions of long-term operation of a die at high temperatures; therefore, the optimized area is represented in this work by alternating rod elements and hollows. The paper considers the problem of optimizing the volume of a metal die, presents a model for minimizing the die volume with restrictions on multi-cycle fatigue at various temperature conditions. The dependence between the volume of the optimized area and the number of loading cycles is obtained, taking into account the non-uniform loading of the die for axisymmetric forming. The main approach to reducing the die volume due to distribution of hollows was concluded in increase the stress state of the rod elements experiencing compressive stress to the limit values in accordance with the restriction on multi-cycle fatigue. The number of elements providing the required die stress state is calculated for different temperature conditions and preset geometrical parameters of the rod elements. When calculating the configuration of the optimized die area for axisymmetric forming, experimental curves of dependence between stress state and number of cycles for 12Kh1MF1 steel were considered at the constant temperature. The variants of the material distribution in the internal die area at preset temperatures are presented. Reduction of the optimized die volume was compared with a solid cast die. The con-structed mathematical model and the results of calculation of the optimized die volume will significantly reduce the material costs for production of metal forming dies and can be used for further development of the methods for topological optimization of stamping tools, taking into account the features and duration of power and thermal loading.