Numerical investigation on pulling force and residual stresses in split-sleeve cold expansion of 2024-T3 aluminium alloy holes using a variable friction model

Abstract

Three-dimensional elastic-plastic finite element (FE) simulations were conducted to examine the effect of friction models on the performance of the split-sleeve cold expansion process for 2024-T3 aluminium (Al) alloy. To accurately capture the tribological interaction of the MoS₂-based solid lubricant between the mandrel and sleeve, we integrated an empirically derived, contact-pressure-dependent variable friction model into the FE framework. A constant friction coefficient of 0.05 was applied for comparison. For each friction model, response surface analysis was performed using FE simulation results to systematically assess the effects of the cold expansion percentage and workpiece thickness on mandrel pulling force and residual stress fields around the cold-expanded holes. Split-sleeve cold expansion experiments, resulting in aluminium holes with a final diameter of 5.896 mm, were conducted for validation. Our comparative analysis shows that the variable friction model predicts mandrel pulling peak forces with errors within 10 % of the experimental values, whereas the constant friction model yields errors ranging from 11 % to 42 %. The variable friction model effectively captures the tribological behavior of the solid lubricant by accounting for the reduction in friction coefficient at the mandrel-sleeve interface as the mandrel passes through the aluminium hole under increasing contact pressure. The hole diameter estimates obtained using the variable friction model closely match experimental measurements, whereas the constant friction model overestimates hole diameters.