Calibrating the combined hardening rule parameters for burr-free forging simulation of the torque rod joint

Abstract

Joints used in the automotive industry are widely manufactured by forging. A cold upsetting process can provide burr-free forging which reduces economic loss by preventing material waste. In this study, finite element simulations for the upsetting of a torque rod joint made of 41Cr4 steel are performed. The novelty of the present study lies in the fact that the upsetting performance is investigated through simulation having hardening model in order to replace the existing forging process. The performance of hardening models is studied for an accurate simulation and optimum parameters are determined. A combination of the bilinear isotropic hardening rule and Chaboche’s nonlinear kinematic hardening rule is employed with the associated flow rule and Hill48 yield criterion to set up a plasticity model of the upsetting process for the first time. The parameters of the bilinear isotropic hardening rule are determined from monotonic tensile tests. The Chaboche’s parameters are determined by using hysteresis loops obtained from strain-controlled low-cycle fatigue tests. The parameters of both rules are combined. Furthermore, they are calibrated using inverse analysis based on the optimization method. Genetic algorithm is used for optimization. The experimental diameter and height measurements of the joint are compared with those obtained from the optimized model. The results show that the application of the combined hardening rule provides better prediction performance of the upset dimensions with minimum dimensional tolerance. The calibrated parameters are presented for the upsetting process. The calibrated parameters of the combined hardening model for the upsetting are YS = 446.64 MPa, TM = 3363.05 MPa, C₁ = 452.31 MPa, γ₁ = 55.165, C₂ = 212.13 MPa, γ₂ = 12.24, C₃ = 194.191 MPa, γ₃ = 10.00 where $\mathrm{YS},\mathrm{TM},C_1,{\gamma }_1,C_2,{\gamma }_2,C_3,{\gamma }_3$ are hardening models’ parameters. Absolute percent true error (APE) is 0.19%. The parameters are YS = 1.93 MPa, TM = 6.98 MPa, C₁ = 580.79 MPa, γ₁ = 1.08, C₂ = 597.23 MPa, γ₂ = 0.98, C₃ = 565.05 MPa, γ₃ = 2.87 in the case of cyclic load. APE is 1.66%. Also upsetting force requirement and material flow path are presented. The forging process can be replaced by the burr-free upsetting process with necessary changes in the die and press bench design. This replacement will save the 128-gr material per each one of the torque rod joint part.