Almost all metallic structures, in particular aerospace systems, consist of polycrystalline materials. There is an inherent heterogeneity in the structure of polycrystals that results from variation in the morphology and texture of underlying microstructures, characterized by geometrical shape, size and crystallographic orientations. The prediction of scatter in mechanical behavior of metallic systems due to these microstructural heterogeneities is of significant importance to many engineering applications. The inherent heterogeneity can be adequately described by a probabilistic approach. Stochastic representation of material properties can also accommodate uncertainty stemming from incomplete data and missing information. This dissertation is motivated by two challenges involved in developing a probabilistic framework for characterization, realization and upscaling of polycrystalline materials. The first one is concerned with the construction of a sufficiently representative description of random media in terms of morphology and material properties, for an intended purpose. The second important challenge arises in modeling the relationship between the random micro-heterogeneities and the parameters or functions used to describe the physical processes of interest at the coarse scale. One of the essential questions in this regard is whether the coarse scale description is capable of capturing the signature of fine scale characteristics. The inherent heterogeneities in the nature of these fine scale features are reflected on coarse scale observables in the form of random fluctuations around the average response. Hence, any mechanistic model must account for these fluctuations in order to capture the effect of subscale heterogeneities. To address these challenges, we first introduce a statistical characterization of an experimental database on morphology and crystallography. The resulting statistical model is used as a surrogate to further experimental data, required for calibration and validation. We then discuss the construction of a stochastic mechanistic model for mesoscale description of materials with microstructure. The linear elastic constitutive matrix of this model is described mathematically as a random matrix which is bounded from above and below. The identification of model parameters using statistical ensembles of digitally generated random microstructures is presented. We validate the predictive accuracy of the probabilistic model using simulated data resulting from subscale simulations. Also discussed in this work is a simple application problem in order to investigate the capability of the model to detect the signature of mesoscale damages. Finally, we study the effect of heterogeneities on the stochastic wave response of random polycrystalline microstructures making use of the microstructure simulation tool developed in the first part of this work.
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