Topological aspects of mean-field crystallographically resolved models

Abstract

It is well-known that the crystallographic texture of a polycrystalline aggregate can be represented by the Orientation Distribution Function (ODF). A similar statistical approach can be extended to other microstructural state variables that are of relevance in the context of obtaining microstructurally based and quantitatively accurate structure-properties relations. In principle such statistical representations are of a non-topological nature, in contrast to an RVE (Representative Volume Element) description of the microstructure. However, by including additional variables to the statistical descriptor specific features of the topology may be taken into account. In this paper the example will be shown on how the plastic anisotropy simulation of a conventional deep drawing grade of Interstitial Free (IF) steel can be improved by considering the crystallographic misorientation of pairs of neighboring crystals, which represent the basic structural units of the 2-point mean field ALAMEL crystal plasticity model. In another example it will be shown how the recrystallization texture of the same deep drawing IF steel can be modelled with improved accuracy if the Strain Induced Boundary Mechanism (SIBM) is taken into account whereby a crystal orientation of low stored energy grows into a neighboring orientation of high stored energy.