Nearest Neighbor Probabilistic Model for Aluminum Polycrystals

A real-valued random field {Z(i,j)} with piecewise constant samples and defined on a lattice L in R(2) is developed to characterize two-dimensional metallic polycrystals. The subsets defined by constant values of {Z(i,j)} are virtual grains and the values of {Z(i,j)} give Euler angles at the nodes of L. The field {Z(i,j)} is completely defined by its marginal distribution and conditional probabilities associated with the nearest neighbor model. The defining probabilities of {Z(i,j)} need to be estimated from measurements of atomic lattice orientation. Random fields {Z(i,j)} calibrated to the measurements of crystallographic texture in two AA7075 aluminum plates have been used to generate virtual polycrystals. Virtual and actual polycrystals are similar.