Texture prediction from a novel grain cluster-based homogenization scheme

We propose a method, termed relaxed grain cluster (RGC), which homogenizes the response of polycrys- tals, subjected to mechanical loads, from the monocrystal constitutive law in order to predict the evolution of deformation resistance and microstructure properties, e.g. texture. Generalizing existing grain interaction models, we consider a clus-ter of $$ 2 \times 2 \times 2 $$ homogenous grains at each continuum material point. Allowing for additional displacements of the grain interfaces introduces relaxations with respect to the classical full-constraints (FC) Taylor model. This decouples the local grain deformation gradients, but may induce interfacial mismatch between grains. The relaxations are determined as minimizers of the cluster′s total mechanical work density being biased by a (penalty) energy density associated with the interfacial mismatch. In this work the bias is neglected, thus the minimum energy criterium is equivalent to stress equi- librium at each interface. As an example, the evolution of texture for plane-strain compression (simplification for cold rolling) of a commercial aluminum alloy is compared for different configurations of interfacial relaxations. We discuss the resulting variation in texture intensity in light of the different relaxation modes allowed and point out the fully-relaxed RGC scheme to be closest to and in decent agreement with experimental reference.