SUMMARY

The modeling and simulation of advanced engineering materials such as dual phase α+β Titanium alloys at different length-scales is challenging due to the prevalence of numerous, often disparate descriptions of their deformation behavior. The mesoscale mechanical response of lamellar α-β grains is typically described using crystal plasticity models. However, due to the inherent complexity of the underlying crystal structure, several crystal plasticity models have been suggested. At the macroscale level, the model uncertainty precludes the precise identification of kinematic hardening laws. Consequently, the mechanical response predicted using these models is bound to exhibit uncertainties. Since these alloys are widely used in critical applications, there exists a strong incentive to rigorously identify and quantify the uncertainties in physics based models that are used to assess their mechanical behavior. This dissertation is aimed at addressing the aforementioned concerns by developing a comprehensive Bayesian Framework for the estimation of material properties, with quantified uncertainty, as well as the relative model probabilities of different physics-based models at multiple length scales.

The physics-based models considered in this work are calibrated against datasets of experimentally procured spherical indentation measurements. The Bayesian model selection technique is used to estimate the relative model probabilities. The framework delineated and developed in this study will be utilized in multiple case studies to (i) compare crystal plasticity models for the lamellar morphology of Ti-6Al-4V, (ii) assess the relative efficacy of different slip transfer criteria for the lamellar morphology, and (iii) identify the optimal form of macroscale cyclic plasticity models. The work proposed herein is broadly applicable to assess numerous physics-based models with different underlying assumptions and forms for high value complex alloy systems.