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Based on Voronoi tessellation and the probability theory, a VGRAIN system is created for the generation of grains and grain boundaries for micromaterials. This system requires physical parameters obtained from microstructures of materials, such as the average, minimum and maximum grain sizes. Numerical procedures have been established to link the physical parameters of a material to the control variable in a gamma distribution equation and a method has been developed to solve the probability equation. These are the basis for the development of the VGRAIN system, which can be used to generate different grain structures and shapes that follow a certain pattern according to the probability theory. Statistical analyses have been carried out to investigate the distribution of generated virtual grains. The generated virtual microstructure is then implemented in the commercial FE code, ABAQUS, for mesh generation and micromechanics analysis using crystal plasticity (CP) equations for face-centered cubic (FCC) materials, which are implemented in the commercial FE solver, ABAQUS, through the user-defined subroutines, VUMAT/UMAT. FE analyses have been carried out to demonstrate the effectiveness of the integrated system for the investigation of localized straining and necking, encountered in microforming processes, such as extrusion of micropins, deformation of microfilms and hydroforming of microtubes.

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An integrated crystal viscoplastic modeling process has been developed to account for the effect of microstructure in the mechanical response of polycrystalline materials. Grain distributions, including size, shape and orientation, are generated automatically based on probability theories using VGRAIN software. For each set of control parameters (average, maximum and minimum grain size) used in the micro-film simulations, six grain orientation patterns were generated randomly for a micro-film based on a gamma distribution; a large number of analyses have been carried out to account for statistical variations in the spatial pattern of grain orientations. The simulations are used to investigate the effects of grain size and orientation on necking and flow stress in stainless steel under uniaxial tension, and to quantify the extent that variability in the spatial distribution of orientations affects the predictions. Based on the numerical studies, a map was generated indicating under what circumstances macro-mechanics theory can be used and when Crystal Plasticity (CP) theory must be used to ensure the accuracy of the analysis; if the theories are not used appropriately, huge errors can be expected.

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