A probabilistic approach for optimising hydroformed structures using local surrogate models to control failures

A probabilistic approach is proposed to optimise hydroformed structures by taking into account the potential variabilities. An efficient implementation requires an appropriate strategy for uncertainty representation and propagation. Moreover, the probability of failure associated to each failure mode must be accurately estimated. To this end, the failure modes are controlled locally only at the highly strained regions which reduces the problem complexity and increases the precision of the generated surrogate models. In this study, finite element simulations with material formability diagrams are used to predict the critical zones in which failure modes may initiate. The predicted zones agree well with the experimental and numerical simulations. By this simplification, the optimisation problem is formulated differently while retaining the relevant physical features of the process. To illustrate this strategy, tee-shaped tube hydroforming process is proposed due to its complexity to demonstrate the benefits of the probabilistic approach. The optimisation problem is formulated within deterministic and probabilistic frameworks to determine the optimal loading paths. It will be shown that probabilistic optimum allows better process mechanics and improved thickness distribution in the hydroformed tube. This approach can be extended to other metal forming processes and easily implemented for industrial products within reasonable computational time.