Predictive Numerical Modeling of Inelastic Buckling for Process Optimization in Cold Forging of Aluminum, Stainless Steel, and Copper

The growing demand for precision and consistency in the forging industry has heightened the need for predictive simulation tools. While extensive research has focused on parameters such as flow stress, die wear, billet fracture, and residual stresses, the phenomenon of billet buckling, especially during cold upset forging, remains underexplored. Most existing models address only elastic buckling for slender billets using classical approaches like Euler and Rankine-Gordon formulae, which are not suitable for inelastic deformation in shorter billets. This study presents a numerical model developed to analyze inelastic buckling during cold forging and to determine associated stresses and deflection characteristics. The model was validated through finite element simulations across a range of billet geometries (10–40 mm diameter, 120 mm length), materials (aluminum, stainless steel, and copper), and friction coefficients (µ = 0.12, 0.16, and 0.35). Stress distributions were evaluated against die stroke, with particular emphasis on the influence of strain hardening and geometry. The results showed that billet geometry and strain-hardening exponent significantly affect buckling behavior, whereas friction had a secondary effect, mainly altering overall stress levels. A nonlinear regression approach incorporating material properties, geometric parameters, and friction was used to formulate the numerical model. The developed model effectively estimated buckling stresses across various conditions but could not precisely predict buckling points based on stress differentials. This work contributes a novel framework for integrating material, geometric, and process variables into stress prediction during forging, advancing defect control strategies in industrial metal forming.