Analytical Solution of Aluminum Alloy Plates With Holes Subjected to Cold Expansion With Reverse Yielding

Abstract

The expansion induced by cold working is a common process that generates residual stresses. It is used when fatigue damage accumulation and life reduction of aluminum alloy perforated plates is an issue in the aeronautics industry. This process is an attractive solution to extend the fatigue lifetime of these structures. It aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plates with holes commonly used in the manufacture of airplane fuselage. Unfortunately, the life predictions require a good prediction of the residual stresses and in particular when reverse yielding takes place. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed analytical model is based on an elasto-plastic behavior, with a power law material behavior and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite element numerical simulation is used to validate the developed analytical model by comparison of the radial, hoop, longitudinal, and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depend mainly on the interference and strain hardening while reverse yielding reduces the stresses near the hole.