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High temperature deformation processing of magnesium and its alloys is often accompanied by dynamic recrystallization (DRX). Deformation twinning is one of the main deformation mechanisms in HCP metals, but very few works are available in literature (experimental or modeling) which investigate the

This paper presents the first application of three-dimensional (3D) crosscorrelation microstructure reconstruction implemented for a representative volume element (RVE) to facilitate the microstructure engineering of materials. This has been accomplished by developing a new methodology for reconstructing 3D microstructure using experimental two-dimensional electron backscatter diffraction data. The proposed methodology is based on the analytical representation of the generalized form of the two-point correlation function-the distance-disorientation function (DDF). Microstructure reconstruction is accomplished by extending the simulated annealing techniques to perform three term reconstruction with a minimization of the DDF. The new 3D microstructure reconstruction algorithm is employed to determine the 3D RVE containing all of the relevant microstructure information for accurately computing the mechanical response of solids, especially when local microstructural variations influence the global response of the material as in the case of fracture initiation.

This work presents a new functional approach to estimate the distancedisorientation correlation function of a given microstructure. The proposed approach separates the crystallographic domain into texture defined by its Euler angles (φ 1 , , φ 2 ) and geometrical domain defined by distance distribution function D i j . The crystallographic domain is treated as independent (known) variable and an analytical estimate for the Euclidian distance distribution function (D i j ) is obtained. The proposed analytical solution for the estimation of D i j 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.