The hood, doors and other panels of a car can be made by aluminium sheets, through complex forming operations. Design of forming processes requires trustable models and simulations.
Forming properties are different in different directions. There are two principle ways to describe this plastic anisotropy of metals. The first one is the continuum theories for materials. The flow properties in various directions are described by the yield function. It is a parametric function calibrated by experimental tests. Unfortunately only a few mechanical tests can be directly used.
The second approach takes into account that metals consist of many small crystals. The properties of each crystal are determined by crystal planes, but crystals are rotated in many directions. The crystal models either resolve all the details of thousands of crystals in a small volume element, requiring huge computer capacity, or simplified statistical models can be applied. In both cases the models are much more demanding than continuum models. In practice these models can be used to perform virtual experiments for calibration of continuum models.
In his PhD work Kai Zhang (firstname.lastname@example.org) implemented and tested both type of models. More efficient numerical algorithms for computer simulations were developed and programmed for the detailed crystal plasticity approach. Three different cases were investigated experimentally. In one of the cases it was found that even for the detailed computer implementation the predictions could not replace experiments for design purposes. A combination of real and virtual experiments was recommended for calibration. For the other two cases the virtual experiments could be trusted.
It was found that the best statistical models, that are more than thousand times faster, can replace detailed simulations of the crystal structure with high accuracy.