|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. |