A new model using a double-continuity relation for predicting the evolution of pair-correlation functions (PCFs) is presented. The proposed model was developed using statistical continuum theory and is employed to predict the viscoplastic behavior of polycrystalline materials. This model was built based upon the continuity relations and a double divergence law that guarantees the conservation of both orientation and mass; and also satisfies the field equations (equilibrium, constitutive, and compatibility) at every point of the polycrystalline material throughout the deformation process. In the presented model, motion of particles in the real space and rotation of crystallographic orientations in the Euler angle space is monitored using an iterative process assuming that all the amount of deformation is applied uniformly without taking into account the localization effects. To study the accuracy of the proposed model, a commercially pure nickel material was rolled to different amounts of cold work. Texture and statistical analyses of the experimental and simulated microstructures were carried out. For the texture analysis, pole figures, ODF sections, and volume fractions of some ideal orientations of cold-rolling were studied. For the statistical analysis, pair correlation functions (PCFs) were employed and the correlations (auto- and anti-correlations) between ideal orientations and also the coherence length were studied. Simulated results captured from the implementation of the new model are in good agreement with the experimental ones at low and medium rolling deformations (0 to 50% rolling reductions); however, at large levels of deformations (above 70% reductions), because of the formation of cell blocks and relevant inhomogeneity, the occurrence of ideal orientations and their correlation properties in the experimental microstructure is affected by grain subdivision phenomena. This causes distortions in the shape of crystallographic grains at large rolling reductions, and accordingly we observe larger errors in comparison of simulated and experimental microstructures.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





Sadegh Ahmadi, microstructure, crystal plasticity, continuum mechanics, viscoplastic material, simulation