The Limits of Applicability of the Method of Discontinuous Solutions in the Study of Pipe Drawing Processes

Introduction. Non-contact deformation of the workpiece material, which occurs along the boundaries of the deformation zone, is one of the main factors determining the energy-power parameters of pipe reduction processes. The most widespread practice in the design of metal forming processes is the method of discontinuous solutions, which makes it quite simple to take into account non-contact deformation in numerical simulation of processes. However, for most processes in the technical literature there are no systematic practical recommendations on the application of this method, which inevitably leads to a mismatch of theoretical principles and practice. The aim of the work is to determine the limits of applicability of the method of discontinuous solutions for processes of faultless drawing of pipes through a conical die, depending on the geometric parameters of the workpiece, tool, as well as the degree of deformation and hardening of the processed material. Research Methods. The model of the deformation zone for the process of flawless drawing is considered in two versions: by the method of discontinuous solutions and taking into account non-contact bends of the pipe wall. From the condition of the balance of the shear forces acting on the conditional shear surface and the bending moments caused by the bending of the pipe wall, under various deformation conditions, the boundary values of the thickness parameter are determined, at which it is advisable to carry out numerical simulation of the drawing processes using the discontinuous solution method. In this case, the calculations are performed separately for two sections of the deformation zone corresponding to the bending of the pipe wall at the entrance to and exit from the die. Results and discussions. The numerical implementation of the obtained dependences showed that at the entrance to the deformation zone, the boundary value of the thickness parameter increases with an increase in the taper angle of the die and the hood for the transition, but decreases with an increase in the anti-tension stress and the thickness parameter of the initial workpiece. At the exit from the deformation zone, the boundary value of the thick-walled parameter increases with an increase in the taper angle of the die and decreases with an increase in the stretch coefficient for the transition and the thick-walled parameter of the initial billet. If the parameter of the thickness of the initial billet exceeds the boundary value, then in numerical modeling it is advisable to use the method of discontinuous solutions. If it does not exceed, then other methods and models should be used. The results of a theoretical study can be used in the design of pipe drawing processes.