Nearest Neighbor Probabilistic Model for Aluminum Polycrystals

A real-valued random field $\left\{Z_{i,j}\right\}$ with piecewise constant samples and defined on a lattice $L$ in ${\mathbb{R}}^2$ is developed to characterize two-dimensional metallic polycrystals. The subsets defined by constant values of $\left\{Z_{i,j}\right\}$ are virtual grains and the values of $\left\{Z_{i,j}\right\}$ give Euler angles at the nodes of $L$ . The field $\left\{Z_{i,j}\right\}$ is completely defined by its marginal distribution and conditional probabilities associated with the nearest neighbor model. The defining probabilities of $\left\{Z_{i,j}\right\}$ need to be estimated from measurements of atomic lattice orientation. Random fields $\left\{Z_{i,j}\right\}$ 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.