A Numerical Model for Inelastic Buckling in Cold Upset Forging: Stress Analysis and Optimal Billet Geometry

The forging industry has increasingly emphasised quality and reproducibility, making computer simulations essential for predicting and improving the process. A major challenge in cold upset forging is billet buckling, which leads to defective products. Existing numerical models, such as the Euler and Rankine-Gordon formulas, mainly focus on elastic buckling. This study aimed to develop a numerical model that defined inelastic buckling during forging, particularly in cold upset forging, which could be used to determine the buckled billets and their stresses, identify the deflection point for different billet geometries, and specify the optimum billet geometry for aluminium. A numerical approach was used to model the forging operation and obtain simulation data for stress variation against die strokes. Seven billet geometries (10–40 mm in diameter, each with a length of 120 mm) and three frictional conditions (µ = 0.12, 0.16, and 0.35) were applied. The simulation results showed that the billet geometry and the strain hardening exponent had a crucial impact on the buckling behaviour, while friction seemed to alter the overall billet stresses. Rigorous non-linear regression and iterations showed that the numerical model successfully estimated the buckling stresses but failed to identify the buckling points through stress differences.