Correction of the stress–strain curve for 2024 aluminum alloy after necking using the new surface strain method

Abstract

Nowadays, many studies concerning plasticity and numerical simulations indicate that the true stress–strain curve plays a prominent role in the analysis of metal deformation. Hence, a new method is considered to correct the stress–strain curve based on image processing. Since the axial stress mainly becomes triaxial in the neck zone, the relationship obtained from the engineering stress–strain curve is not reliable in terms of authenticity and accuracy. Accordingly, correcting this relationship is highly advantageous and necessary. Due to the triaxial state of stress in the plastic area, longitudinal and surface strains are calculated through image processing and the correction coefficient of the stress–strain curve is obtained based on them. The equation of the stress–strain curve is based on the Hollowman relation until the onset of necking and then becomes almost linear. The finite element method (FEM) is employed for validating the obtained results. Since the corrected stress and strain equation is linear, the objective function of optimization is considered. This optimization is based on minimizing the difference between the three diameters values of the specimen, which are observed through experiment and FEM. Besides, a statistical method with the help of the genetic algorithm is employed to minimize this difference. As a result, an optimal equation is predicted for the 2024 aluminum based on the stress–strain curve of the error rate. Finally, a comparison is made between the results obtained from the surface strain method and the results obtained from the classical methods of Bridgman and Davidenkov, and a good agreement is observed between them.