Analytical and Numerical Modelling of Sheet Plate Cold Expanded Hole Subjected to Reverse Yielding

Predicting and mitigating the effect of expansion induced by cold working on damage fatigue accumulation and life assessment of aluminum alloy is a common process in the aeronautics industry, especially to extend the fatigue lifetime of their structures. This process aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plate holes that are employed in manufacturing the airplane fuselage. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed model is based on an elasto-plastic behavior, with a power law material behaviour 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 depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.