Understanding the volume-diffusion governed shape-instabilities in metallic systems

Abstract

The reliability of any day-to-day material is critically dictated by its properties. One factor which governs the behaviour of a material, under a given condition, is the microstructure. Despite the absence of any phase transformation, a change in the microstructure would significantly alter the properties. Therefore, a substantial understanding on the stability of the microstructure is vital to avert any unexpected catastrophic change in the material properties. In the present work, one such numerical approach called phase-field modelling in employed to analyse the stability of two- and three-dimensional finite structures, which dictate the curvature-driven evolution of the microstructure. A characteristic feature of this numerical approach is the introduction of a scalar variable, called the phase field, in addition to the other thermodynamic variables. While the inclusion of the phase field obviates the need for the interface tracking, which is a strenuous aspect of the other conventional techniques, it replaces the sharp interface with a finite diffuse region. Therefore, before adopting and extending the phase-field technique, it is shown that the model recovers the governing law, i.e, Gibbs-Thomson relation, despite the introduction of the diffuse interface. Subsequently, the numerical treatment is employed to investigate the volume-diffusion governed curvature-induced transformation.