A-Area: Semi-analytical methods for predicting the constitutive behavior of microheterogeneous materials

Person in Charge: Dr.-Ing. Katja Jöchen

Motivation and objectives:
The linear and nonlinear behavior of microheterogeneous materials, as, e.g., composites or polycrystalline aggregates, is determined by the constitutive behavior of the individual phases as well as their volume fraction distribution, arrangement and morphology. The aim of this work is to use simplifying assumptions in order to derive effective methods which give a precise but computationally efficient prediction of the macroscopic material behavior accounting for microstructural information.

Investigations	Results
A homogenization method is applied, which accounts for the one- and two-point statistics of the microstructure. This new procedure, which is based on constant stress polarizations with respect to a homogeneous comparison material and being an extension of the Hashin-Shtrikman principle, permits the prediction of stress and strain fluctuations in the microstructured nonlinear material. Especially the texture evolution during cold rolling is investigated in order to validate the new method.	By varying the stiffness of the comparison material in between the extreme limits of 'infinitely stiff' or 'infinitely compliant', very different texture characteristics of the rolling texture are obtained. In the extreme cases, the prediction corresponds to the Taylor and Sachs behavior. By adjusting the comparison material and accounting for heterogeneous crystal spins, the experimentally determined texture is very well reproduced by this much more computationally efficient procedure than the very detailed FE² method.