A probabilistic characterization, propagation, and sensitivity analysis of uncertainties in a metal forming application

In metal forming processes, after leaving the tooling, formed pieces of metal have a tendency to partially return to their original shape because of their elastic recovery. This phenomenon, referred to as the springback, is quite complex and depends not only on material properties such as Young's modulus and yield stress but also on many process parameters such as sheet thickness and bending angles. The springback is difficult to predict and is a major quality concern in forming processes because when the springback is smaller or larger than expected, it can cause serious problems to subsequent assembly processes due to geometry mismatches.

In this communication, we present a probabilistic analysis of a metal forming application. We consider the bending of a metal sheet with uncertain elastoplastic material properties. First, we use methods from mathematical statistics to obtain a probabilistic characterization of the elastoplastic material properties from data. Next, we map this probabilistic representation of the elastoplastic material properties into a probabilistic representation of the deformed shape of the metal sheet through a mechanical model implemented using the Metafor software. Finally, we conduct a stochastic sensitivity analysis to determine which elastoplastic material properties are most influential in driving uncertainty in the deformed shape after the springback.

Our probabilistic analysis involves so called nonintrusive methods, that is, methods that can be implemented as wrappers around the Metafor software without requiring modification of its source code. Further, it includes recent methods for the propagation and sensitivity analysis of uncertainties characterized by arbitrary probability distributions that may exhibit statistical dependence.