Morphological evaluation of 1-site polycrystalline models

Abstract

Mesoscale models consider grain level interactions. Unlike continuum models, they account for the discontinuities stemming from the elastic anisotropy of the crystallites in addition to the directional nature of the dislocation slip. Load fractions on individual grains are decided by considering the individual neighborhood of grains (n-site models), or by making unifying assumptions ignoring the specific neighborhood (1-site models). 1-site models are typically incapable of incorporating the morphology of the grain neighborhood except for the self-consistent models (SCM). This thesis investigates the tools and model adaptations to make self-consistent models capable of modeling single-phase and multi-phase polycrystals with pronounced morphological features. Modeling the effects of these features with 1-site models allow avoiding the more expensive and complicated finite element analyses. To this end, a flexible, object-oriented, Python® based software framework is engendered, called APMF (Adaptable Point Model Framework). APMF can (i) accommodate conventional single-phase applications, (ii) extended with multi-phase materials and (iii) allows extension to any desired constitutive rule or polycrystalline interaction. Models created with APMF are verified with several test cases of single-phase and multi-phase structures. Among 1-site models, SCM implements morphology by adjusting the radii and orientations of the Eshelby ellipsoid (inclusion). The current APMF implementation adds the capacity to assign these parameters independently for each grain. By using limiting shapes of Eshelby ellipsoid (namely, sphere, needle, and disc) and comparing with the simplistic isostrain/isostress rules, the effect of the structured (non-random) morphologies on the behavior of the polycrystals are simulated. As a multi-phase application, residual strains inside a two-phase Cu/Nb bilayer is studied by applying thermally induced eigenstrain on the Nb aggregate. In single-phase polycrystals, to model the interaction correctly, a one-to-one relation between the grain shape and the inclusion shape is observed. On the other hand, to capture the interaction correctly in two-phase materials having different grain shapes, APMF should be extended with hierarchic models.