Approximate model of the necking behaviour and application to the void growth prediction

The static elastoplastic characterization of metals consists of the determination, by way of experimental tensile tests,of the curve expressing the equivalent von Mises stress as a function of the equivalent plastic strain for each givenmaterial. For ductile metals capable of undergoing large post-necking deformations, the knowledge of the stress andstrain distributions on the necked cross-section of the tensile specimens is essential for the above characterization. Themost known and used solution of the necking problem, due to Bridgman, leads to material curves affected by an errorranging from few percentages up to more than 10% and requires a significant amount of experimental work in order tomeasure the evolving curvature radius of the necking profile at different stages of each tensile test.According to many experimental and numerical observations, carried out in previous works and reported also in thepresent one, the perturbing effect of the necking phenomenon on the stress and strain distributions has been found to bealmost material-independent, the only material-dependence consisting of the plastic strain value which triggers thewhole necking initiation. The material-independence of the necking effect has been evidenced on a wide set of materialsranging from low and mild steel to inoxidable steel, spheroidized steel, aluminium, copper.Based on these considerations, a new material-independent solution of the necking problem is finally derived,achieving an error level less than half that obtainable with the Bridgman method. The developed method is very simpleto be used because does not require the experimental efforts intrinsic in the use of the Bridgman method. 2004 Elsevier Ltd. All rights reserved.