Analysis of several methods for the data conversion and fitting of the Garofalo equation applied to an ultrahigh carbon steel

Purpose: To determine the most suitable reduction data method and the optimal fitting method for the Garofalo equation. Two fitting methods were applied. The input data for this fitting are the sets of forming variables {T,σ,ε’} which have been obtained by using four different reduction methods. This procedure is applied to an ultrahigh carbon steel (UHCS). Design/methodology/approach: High temperature torsion tests have been carried out on the UHCS. A wide range of forming variables have been used. A numerical method has been implemented for the experimental data reduction. The fitting of the Garofalo equation has been carried out by means of two numerical methods. An integral method in stages, called RCR method, and a method based on Matlab algorithms called NLD. A comparative analysis of the parameters of the Garofalo equation has been conducted. Findings: The results show that the n and Q parameters are not dependent of the conversion method that has been used, Von Mises, Tresca or Eichinger. However, the α and A parameters seem to depend on the reduction method. Regarding the fitting, the RCR method is quick and efficient and its results, at the first stage, are close to the ones obtained by the NLD method. The evolution of the fitting parameters with strain for each conversion and fitting method has been determined. Research limitations/implications: The evolution of the parameters of the Garofalo equation are influenced by the adiabatic heating that occurs during the torsion testing. It is necessary a correct experimental design to obtain a suitable grid of data which allows an accurate determination of the strain rate sensitivity and the strain hardening coefficient. Practical implications: The fitting of the Garofalo equation for different strain values can provide information on the microscopic processes that take place during deformation. Originality/value: This work is a comparative study of the usual reduction methods and shows the utility of a method for the fitting of the Garofalo equation. This method is convergent, quick and accurate.