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Probabilistic Analysis of Process Chain Forming to Crash Regarding Failure Prediction

Numerical analysis of forming and crash processes is usually carried out deterministically. However, the variations of the parameters describing materials and processes cause significant deviations in the prediction quality. This observation becomes more important if the failure prediction in process chains like forming to crash is considered. Usually, the material and process parameters are identified by means of an inverse or a direct identification procedure using experimental data. Nevertheless, the identification process itself contains uncertainty, as mean values are usually utilized for this purpose. It is therefore not known whether the process simulated with the identified parameters is robust and how the variation of parameters influences the quality of failure prediction. Stochastic analysis, replacing the parameters with stochastic distributions, can be performed to find out the variation of outputs due to the variation of input parameters. Since the computational cost of such an analysis would be too high to carry out using only FE simulations, it is performed on metamodels generated with relatively few FE simulations. Assuming the generated metamodel is accurate enough, reliable sensitivity information can also be obtained through methods such as Anova and Sobol Indices. The optimization and probabilistic analysis software LS-Opt serves as an efficient tool to conduct such study. In this paper, parameters of a steel grade used mainly in the automotive industry are replaced with distribution functions reflecting the real deviations of material and process parameters. A suitable sampling algorithm for the selected metamodeling technique is then used to generate parameter sets for the FE simulations. The statistics of the desired outputs and the influence of the material and process parameters are computed on the metamodel. The results show that the variation of modeling parameters such as fracture curve, hardening, and plasticity, causes higher amount of variation on the failure prediction indicators like displacement up to fracture. Furthermore, it has also been found that the standard deviation of results increases with the increasing element size pointing out the importance of reducing uncertainty in the methods used for defining model parameters if coarser meshes are to be used.