Probabilistic modeling of stress-based FLD in tube hydroforming process

Abstract

Recently a stress-based FLD due to its path-independency has become a new mainstream technology for prediction of forming limit in tube hydroforming processes, which usually have non-linear strain path. However, the random characteristics owing to experimental errors, inherent measuring equipment errors, dimensional tolerance of as-received blank, inconsistent lubrication condition and so on lead to uncertainty with regard to the position of the forming limit curve on the stress-based FLD. In this work, to take into account the uncertainty on the stress-based FLD, a probabilistic modeling on the stress-based FLD with confidence level is firstly attempted. With the assumption of all experimentally measured data as normally distributed random variables, stochastic evaluation of the reliability of the stress-based FLD is carried out. Moreover the statistical correlation between measured data during a bulge test and the material parameters is investigated by using the first-order approximated mean value and variance. The reliability is analytically calculated based on first-order reliability method (FORM) and verified with Monte-Carlo simulation (MCS). Finally, at a given deviation of measured data, the band width of forming limit curve on the stress-based FLD to be able to satisfy the required confidence level is determined.