A Mathematical Model for Predicting Residual Stresses in Pre-stretched Aluminum Alloy Plate

A mathematical model has been developed to predict the residual stresses level in pre-stretched aluminum alloy plate. This is based on force balances of the residual stress, theory of plastoelasticity and a new conception of free length. The model is relatively simple because only rolling direction residual stress is taken into account, but provides a clear illustration of stress relief mechanism in stretching process. With this model, residual stress distributions of stretched beam can be determined directly by knowing the specimen dimensions, material properties and the original stress. The model offers an useful tool to show the effect of varying tension ratio on the final residual stress level, thus makes it possible to predict stress relief and control residual stresses. An example of using the model is presented by applying published data while showing mechanism of stress relief during stretching. Analysis indicates that it is stretch-caused convergence of the free lengths of strips in beam that lead to reduction in the residual stresses.