FE-σ - Introducing Microscale Effects into FEM Simulation of Cold Forming

Classical Finite Element method (FEM) simulation of either production or operation of micro-scale parts often fails to predict microscale effects that are caused by the low number of grains in the part for fundamental reasons. While the high number of grains in macro-scale parts effects an average material behavior that can be described well by standard material parameters, micro-scale parts possess only a small number of grains across their smaller dimensions. As a consequence, local disadvantageous properties of a single grain or a few grains can already locally dominate the behavior of a part, or even cause failure. Common methods like multi-scale or Monte-Carlo approaches are either impractical or extremely time consumable. In order to cope with this situation, a modification of the classical FEM called FE‑σ is presented. Here, the uncertainties of the local material properties are described by distributions, which are taken into account in a statistical computation step during each iteration. The resulting stress-strain state, which comes again in the form of distributions, is reduced to its average values for the next iteration. It can also be used to estimate the local failure probability in the part, the failure probability of the whole part, and thus the reliability of the production process. Application of the method to a deep drawing process simulation is presented.