On the role of defect incompatibilities on mechanical properties of polycrystalline aggregates: a multi-scale study
Upadhyay, Manas Vijay
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The main objective of this thesis is to obtain critical insight on the role of crystalline incompatibilities in strain and curvature, induced in presence of line defects i.e. dislocations and disclinations, on the energy and geometry of specific features of the local microstructure, and on the bulk mechanical response of nanocrystalline/ultra-fine grained materials. To that end, studies are performed at the (1) inter-atomic and fine scale, and (2) at the mesoscale. The modelling approach is based on the field dislocation and disclination mechanics theory of continuously representated dislocations and disclinations. New, thermodynamically rigorous, multi-scale elastic constitutive laws based on the couple stress theory are developed to capture the effect of strain and curvature incompatibilities on the Cauchy and couple stresses. A new meso-scale elasto-viscoplastic constitutive model of defect incompatibilities based on a fast Fourier transform technique is developed. The desired scale transitioning is achieved via novel phenomenological defect density transport equations and the newly developed elastic constitutive laws. At the fine scale, the model is applied to study energetic interactions between strain and curvature incompatibilities associated with grain boundaries and their influence on triple line energies. Results reveal that incompatible lattice strains have the most significant contribution to the energy. Incompatible lattice curvatures have negligible energetic contributions but are necessary to characterize the geometry of grain boundaries. Finally, both incompatible lattice strains and curvatures are necessary to capture the structure sensitive mechanical behavior of grain boundaries. At the mesoscale, deformation of nanocrystalline aggregates characterized by residual curvatures is studied to identify the impact of the latter's presence on the local and bulk mechanical response of the aggregate. Relaxation of local stresses generated from residual curvatures reproduces the effect of GB dislocation emission. Uniaxial tensile loading of nanocrystalline microstructures containing residual curvatures reveals a softening in the yield stress which could explain the breakdown in Hall-Petch law in the nanocrystalline regime. Next, the possibility of characterizing incompatibilities using X-ray or neutron diffraction techniques is tested. Results reveal that only strains and their gradients contribute to the broadening of diffraction peaks; curvatures and their gradients have no contribution. This study leads to the development of a new multi-scale averaged strain based Fourier technique for generating virtual diffraction peaks.