research

Microstructural evolution in elastically inhomogeneous systems

I am very happy to be part of iMechanica, and what best way to start than post some stuff that I have been doing recently. I received my PhD for a thesis I submitted to the Department of Materials Engineering (formerly Department of Metallurgy), Indian Institute of Science, Bangalore 560012 INDIA titled Elastic Inhomgeneity Effects on microstructures: a phase field study.

A mismatch in elastic moduli is the primary driving force for certain microstructural changes; for example, such a mismatch can result in rafting, phase inversion, and thin film instability.

My thesis is based on a phase field model, which is developed for the study of microstructural evolution in elastically inhomogeneous systems which evolve under prescribed traction boundary conditions; however, we show that it is also capable of simulating systems which are evolving under prescribed displacements.

The (iterative) Fourier based methodology that we adopt for the solution of the equation of mechanical equilibrium is characterised by comparing our numerical elastic solutions with corresponding analytical sharp interface results; in addition to being accurate, this solution methodology is also very efficient. We integrate this solution methodology into our phase field model, to study microstructural evolution in systems with dilatational misfit.

On the solution to time-dependent Ginzburg-Laudau (TDGL) equation

Time-dependent Ginzburg-Laudau (TDGL) equation is the simplest kinetic equation for the temporal evolution of a continuum field, which assumes that the rate of evolution of the field is linearly proportional to the thermodynamical driving force. The computation model based on this equation is also called phase field model. Phase field simulation can predict quite beautiful patterns of microstructures of material. It has been widely applied to simulating the evolution of microstructure by choosing different field variables. For example, using the single conserved field (concentration field), continuum phase field models has been employed to describe the pattern formation in phase-separating alloys (Nishimori and Onuki, 1990 Phys. Rev. B, 42,980) and the nanoscale pattern formation of an epitaxial monolayer (Lu and Suo, 2001 J. Mech. Phys. Solids, 49,1937). On the other hand, using the nonconserved field (polarization field), the phase field model has been utilized to simulating the formation of domain structure in ferroelectrics (Li et al. 2002  Acta Mater, 50,395). The thermodynamical driving force is usually nonlinear with respect to the field variable. In the case of nonlinearity, the solution to TDGL equation may not be unique. Different grid density, length of iteration step, initial state and random term (introduced to describe the nucleation process) may induce different results in the simulation. Does anyone investigate the effect of these factors on the final pattern? I wonder whether we can prove the solution is unique or not.

Cross-section TEM micrograph of a NiTi crystal in a partially crystallized film

This micrograph indicates the nulceation and growth mechanism in the crystallization of amorphous near-equiatomic NiTi films. The crystal nucleates homogenously inside the bulk of the film, and quickly consume most of the film thickness, and then grows laterally in a two-dimensional growth mode. Heterogeneous nucleation at an interface was not observed due to the composition shift at those locations caused by interfacial reaction.

New Hot Paper Comment by George M. Pharr

I came across this page and think it may be of interest to mechanicians.