New Mathematical Stress Analysis in the Compressive Stage of the High-Pressure Torsion Process

In this study, a mathematical analysis based on the slab method is used to drive a formula to calculate the average hydrostatic pressure in the compressive stage of the HPT process. The analytical method used here leads to a relationship for describing the average hydrostatic pressure as a function of the material shear strength, sample volume, cavity volume and force. Based on the results obtained and by employing the Sturm’s theorem for polynomials, a general expression for the minimum force required to start the deformation of the material under compressive force and creation of flash is developed. The analytical results were confirmed by carrying out some experiments by using commercial pure aluminum and copper as test materials. The experimental results showed good congruence with the analytical calculations. The most important outcome of this analysis is that with an appropriate selection of the sample volume, considering the capacity of the HPT press facility and the proper choice of the die cavity volume, favorable average hydrostatic pressure, necessary for the purpose of application can be achieved. Graphic Abstract