Method for Determining the Flow Curve of Steel Considering Work Hardening Behavior

An accurate flow curve over a large strain range is necessary and important for highly accurate numerical analysis of the load and deformation behavior during cold forging. A method using the upsettability test is widely used to obtain such a flow curve. This method converts the load–reduction in height relationship into a flow curve by using two calibration curves for the reduction in height–average equivalent strain relationship and reduction in height–restraint factor relationship. We explored the effect of work hardening on the calibration curves to improve the accuracy of load prediction. The work hardening of materials was described by the modified Voce hardening law. Finite element method (FEM) analyses were performed by assuming various material constants of the modified Voce hardening law, and the effect of the work hardening behavior on the calibration curves was investigated and formulated. We found that the work hardening behavior affects the calibration curve for the average equivalent strain and not the calibration curve for the restraint factor. Moreover, both relationships were formulated by polynomials. We proposed a new flow curve determination method that combines an optimization method with the formulated relationships. This method converted the load–reduction in height relationship into an accurate flow curve after automatically selecting a calibration curve for an appropriate average equivalent strain for various steels according to their work hardening behaviors. By applying the flow curve acquired by the proposed method to the FEM analysis of the compression test, the load prediction accuracy improved.