Various tools are useful in the design of materials from texture and related higher order structure statistics. This paper presents recent results in two key areas - homogenization methods linking the material structure to its properties, and reconstruction techniques that produce material realizations from the statistics. Homogenization techniques that are based upon material statistics captured by correlation functions have been available for several decades. With recent increases in computational power, and with the added efficiencies of spectral methods, attention has returned to these methods as viable inputs to multiscale models. One such method that involves a more complex integration scheme than the typical Kroner-type approach, is the strong contrast formulation pioneered by Brown, and more recently developed by Torquato. In this paper we utilize spectral techniques to apply the strong contrast formulation to the computationally demanding case of polycrystalline materials, and discuss the potential benefits to material design. Another important capability in the statistical modeling, analysis and design of materials involves the reconstruction of statistical data in order to recover detailed realizations that can be used in deterministic models. Popular reconstruction techniques such as simulated annealing take large amounts of computational power and time to create relatively small realizations. Recent work, based upon image analysis methods, has resulted in dramatic increases in speed. These advances in reconstruction capabilities are presented and some of the issues inherent in the approach are discussed as they relate to material design.

Grain growth in two and three dimensions with anisotropic interfacial properties was simulated using the Monte Carlo method. The relative effects of grain boundary energy and mobility anisotropy on number- and area-weighted misorientation distribution functions (MDFs) were compared. Results indicate that energy anisotropy has a measurable effect on misorientation texture development, while mobility anisotropy does not. Qualitatively similar results are obtained in all simulations regardless of dimensionality or crystal symmetry. Microstructures with random orientation texture appear to evolve steady-state MDFs, while those with a preferred orientation do not. Experimentally measured number- and area-weighted MDFs in polycrystalline magnesia are shown to be comparable to those measured in our simulations.

We have measured and reconstructed via forward modeling a small volume of microstructure of high purity, well annealed nickel using high energy x-ray diffraction microscopy (HEDM). Statistical distributions characterizing grain orientations, intra-granular misorientations, and nearest neighbor grain misorientations are extracted. Results are consistent with recent electron backscatter diffraction measurements. Peaks in the grain neighbor misorientation angle distribution at 60 degrees (Sigma 3) and 39 degrees (Sigma 9) have resolution limited widths of approximate to 0.14 degree FWHM. The analysis demonstrates that HEDM can recover grain and grain boundary statistics comparable to OIM volume measurements; more extensive data sets will lead to full, five parameter grain boundary character distributions. Due to its non-destructive nature, HEDM can then watch, both statistically and through tracking of individual grains and boundaries, the evolution of such distributions with processing of the sample.

Four crystal plasticity codes, the viscoplastic Material Point Simulator (MPS) developed at Cornell and the ViscoPlastic Self-Consistent code (VPSC7b) developed at LANL, and two elastic-viscoplastic codes developed at Drexel University, were employed to calculate deformation textures and mechanical properties of model polycrystalline specimens by simulating isochoric. free upsetting. Uniaxial compression of a model sample with a starting random texture of 5000 grains was carried out at a constant true strain rate of 0.001/s to a true strain of 1.0 with 0.02 strain increments. Material properties simulated a face-centered cubic (FCC) alloy, Type 304 Stainless Steel, and a hexagonal close-packed (HCP) material, unalloyed Ti. Both non-hardening and linear hardening conditions were investigated. Different strain-rate sensitivities simulated deformation conditions appropriate to ambient and elevated temperature conditions. All codes permitted use of the Taylor homogenization hypothesis, resulting in an upper bound for the mechanical properties. All codes produce essentially identical results for the same input material, homogenization hypothesis and deformation conditions. For comparison, one alternative homogenization hypothesis to model grain interactions was examined for each of the MPS and VPSC7b codes.

Examples of texture evolution occurring during annealing of low alloyed Zr sheets submitted to different cold rolling schedules with a moderate thickness reduction (40 and 50\%) are presented here. It is shown that the stability or the texture during primary recrystallisation previously reported for cold rolled Zirconium and Titanium(1-3) is not a general rule. The differences in texture evolution behavior exposed here are linked to the various deformation microstructures which exhibit distinctive heterogeneity distributions. In the case of 40\% cross rolling there is little fragmentation, which induces an oriented nucleation, whereas transverse rolling creates heterogeneous microstructures which favor the abnormal growth of subgrains with specific orientation.

Samples of AA 6022 were deformed at different temperatures, strain and strain rates through channel die compression. Deformed samples, though quenched immediately after deformation, had both deformed grains/bands and recrystallized grains. Using a simple criterion of grain size and in-grain misorientation developments, respective deformed and recrystallized regions could be distinguished. Deformation temperature/strain rate, or the so-called Zener-Holloman (Z) parameter, had clear effects on the deformed microstructure in terms of orientation stability or textural changes and in terms of in-grain misorientation developments. These, in turn, strongly affected the associated recrystallization behavior including relative contributions from particle stimulated nucleation and contributions from deformed grains/bands of different ideal orientations.

Recrystallization textures were investigated in thin layers of both pure Cu and alloyed Cu combined with Nb in roll-bonded composites. Texture analysis using X-ray revealed that Cube orientation was the dominant texture component after recrystallization in rolled monolithic pure Cu whereas 2 1 5 < 2 1 1 > and B/S were the dominant components for the recrystallized alloyed Cu. In the composites, however, the rolling texture is retained during annealing in both the pure Cu and the alloyed Cu layers when the layer thickness enters the sub-micron regime. This is attributed to the nucleation and growth of recrystallizing grains being impeded via a reduction in recrystallization driving pressure and the grain boundary movement and growth being limited due to the layer thickness effect. A new term- confined recrystallization was also introduced to describe more accurately the morphological evolution observed within the sub-micron thick layers after annealing and highlights the contrast to either simple recovery or continuous recrystallization.

The von Neumann-Mullins relation has been extended to higher dimensions by MacPherson and Srolovitz. Their exact solution relates the rate of volume change of ail individual grain in a 3-dimensional isotropic polycrystal to its mean width and total length of triple lines (assuming isotropic boundaries). The objective of this study is to verify that grains in a moving finite element grain growth model obey this law. Algorithms have been developed in order to calculate mean width of individual grains ill digital microstructures for which the grain structure is discretized with both volumetric and surface meshes. Theoretical rate predictions were obtained from the measured mean widths and triple line lengths. Good agreement was found between growth rates measured in the simulations and the predictions of MacPherson-Srolovitz theory for the cases of an isolated shrinking sphere, individual grains in a digitally generated coarse polycrystal, and individual grains in a microstructure reconstructed from serial sectioning of stabilized cubic zirconia. Departures front this relationship appeared to be related to the grain shape.