The flow curve determination method proposed by Osakada uses two calibration curves to convert the load-reduction in height relationship in an upsettability test into a flow curve. To improve the accuracy of the flow curve, we investigated the effect of work hardening on the calibration curves. We assumed that virtual materials follow the Swift hardening equation, and we performed finite element method analysis on these materials by assuming various material constants of the Swift hardening equation. We found that the work hardening behavior affects the calibration curve for the average equivalent strain, but not that for the restraint factor. We formulated these new calibration curves by polynomials. We proposed a new flow curve determination method based on new formulated calibration curves and an optimization method. This method determines an accurate flow curve after automatically selecting a calibration curve for an appropriate average equivalent strain for various materials according to their work hardening behaviors. We showed that highly accurate flow curves can be obtained by applying the proposed method regardless of the work hardening behavior.

We performed an upsettability test on two steels and converted the obtained results into flow curves by two methods. One is a conventional method using Osakada’s calibration curves, and the other is a Swift-type proposed method based on new formulated calibration curves and an optimization method. The obtained flow curves were applied to the finite element method (FEM) analysis of compression test. The load prediction error of the Swift-type proposed method was reduced by approximately 4 % compared with that of the conventional method. However, the Swift-type proposed method is not very accurate in a very small or large strain region. Then, the converted curves obtained by the Swift-type proposed method were regressed with other four work hardening equations. As a result, we found that the modified Voce equation has the highest regression accuracy. The calibration curves were generated by assuming various material constants of the modified Voce equation, and the modified Voce-type flow curve determination method was proposed. When the flow curves obtained by the proposed modified Voce-type method were applied to the FEM analysis, the load prediction error was further improved by 2 % compared with that in the case of using the flow curves obtained by the Swift-type proposed method.