An additional length scale is introduced which is not considered by the existing Taylor or viscoplastic self-consistent (VPSC) models.
In these models, a macroscopic deformation is imposed on a representative volume element (RVE) of the macroscopic length scale
(1000 grains). Each grain constitutes a RVE at what will be called the “mesoscopic-1” length scale. Here an additional intermediate
length scale is introduced, called “mesoscopic-2”. Its RVE is a “cluster” of several grains. Within each cluster, the algorithm of the Neffect-
VPSC model is employed to treat grain interactions. The average deformation of each cluster is the macroscopic deformation. This
model gives texture predictions as good as, or better than, the Neffect-VPSC or the ALAMEL models for several tested materials and
kinds of tests. The Taylor, VPSC and the ALAMEL models can be seen as special versions of such cluster-type model. The Taylor
and the VPSC models were then tested to give two bounds of the predicted total slip rate in the aggregate for rolling. The total slip rate
is proportional to the predicted von Mises equivalent stress of the aggregate. The difference among these model predictions was studied
statistically by plotting the x-value distribution as defined and discussed in this paper. It seems that according to a cluster model simulation
for rolling, statistically the strain rates of the hard grains defined in this paper tend to reduce less than the increase in the strain
rate of soft grains in the direction of the imposed strain rate; gradually this diminution/increase reduces for both hard and soft grains as
deformation increases. We call these diminution/increase “relaxations”. Relaxations projected on the five bases in the 5-D plastic strain
rate space for rolling indicate that different numbers of grains in each cluster correspond to different levels of relaxations.