Chairperson: Prof. Ashish Juneja, Department of Civil Engineering, IIT Bombay

External Examiner: Dr. Apu Sarkar, BARC

Internal Examiner: Prof. Shivasubramanian Gopalakrishnan, Department of Mechanical Engineering, IIT Bombay

Thesis Supervisor:  Prof. Alankar

 

Short Abstract: A novel continuum model for grain boundaries in crystals is proposed that uses experimentally obtained data for grain boundary energy variation with misorientation. The model is esentially a PDE - 4th order in space and 1st order in time for isotropic formulation, and a set of coupled PDEs for anisotropic formulation. The model is employed to simulate the idealized evolution of grain boundaries within a grain array, following the methodology outlined in a published study by us that questions decades old phase-field formulations on this topic. The approach of the model involves representing misorientation in a continuum scale through spatial gradients of orientation, considered a fundamental field. Based on experimental findings, the dependence of grain boundary energy density on the orientation gradient is found to be generically non-convex. The model employs gradient descent dynamics for the energy to simulate idealized microstructure evolution, necessitating the energy density to be regularized with a higher-order term to ensure the model's well-posedness. From a mathematical perspective, the formulated energy functional fits the Aviles-Giga (AG)/Cross-Newell (CN) category, albeit with non-uniform well depths, leading to unique structural characteristics in solutions linked to grain boundaries in equilibria. The presented results showcase microstructure evolution, and grain boundary equilibria, illustrating reorientation of grains in 1-D and 2-D. Idealized features such as equilibrium high–angle grain boundaries (HAGBs), curvature-driven grain boundary motion, grain rotation, grain growth, and triple junctions that satisfy the Herring condition in our 2-D simulations are also demonstrated. Inclusion of anisotropy is achieved considering 5 degrees of freedom via a set of coupled PDEs.