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In many materials with low crystal symmetry or low stacking fault energies, plastic deformation is accomplished not only by crystallographic slip, but also by twinning. During deformation, twinning plays two important roles. On one hand, it changes the texture evolution associated with reorientation of the twinned portion of the grains. On the other hand, the twin boundaries act as barriers to the propagation of slip and other twin systems. Therefore, to constitutively describe deformation texture evolution of the materials mentioned above, these two effects of twinning must be taken into account. The grain-interaction (GIA) model is one of the most advanced cluster type Taylor models, and has been successfully applied to predict deformation texture evolution of cubic materials, especially of Al and its alloys. The GIA model considers the next-neighbor grain interaction, but it only takes crystallographic slip as deformation mechanism, without twinning. In recent years, various attempts have been made to introduce twinning into deformation texture models. For example the Monte-Carlo approach proposed by Von Houtte and advanced by Tomé as a predominant twin reorientation scheme (PTR), which reorients the selected grains fully by twinning. In the volume fraction transfer (VFT) scheme, the Euler space is partitioned into equal cells, and the volume fractions are assigned to the respective cells and their evolution is recorded with progressing deformation. Recently, the PTR scheme has been further developed as the “meso-scale composite grain (CG)” approach, in which the twins are treated as inclusions, and secondary twins and slip are allowed to be activated inside the primary twins. In this study, we apply the PTR approach to handle twinning in the GIA model and compare the simulation results with that of the experimental data. To simply the problem we firstly ignored the hardening effect caused by twinning, which will be considered in the further work.