Analytical estimation of distance–disorientation function of the material microstructure

This work presents a new functional approach to estimate the distance–disorientation correlation function of a given microstructure. The proposed approach separates the crystallographic domain into texture defined by its Euler angles ( ) and geometrical domain defined by distance distribution function . The crystallographic domain is treated as independent (known) variable and an analytical estimate for the Euclidian distance distribution function is obtained. The proposed analytical solution for the estimation of is based on existing statistical growth models and the logistic probability distribution function. The solution is optimized for the measured experimental data and takes into account morphological features of the microstructure such as grain volume, grain radius and grain size as well as their distribution inside the material. An analytical model is proposed for constructing the distance–disorientation function (DDF) using the estimated Euclidian distance between pixel pairs. The new functional solution is a highly effective way to calculate DDF values, making it suitable for application to the real microstructure optimization problems. The DDF obtained by using the results of probabilistic solution is validated by comparing them with the DDF obtained from experimental electron back-scatter diffraction data.