SC740 SEMINAR WEEK 13

TOPIC : Simulation of Microstructural Evolution in Sintering by the method of Lines.

By Dr. Wen Zhang

Department of Mathematics and Statistics

Louisiana Tech University

Summary and Comments: By Lee Emmanwori

Dr. Zhang introduced the concept of sintering by using powder with experimental layout of the processes involved. She explained that sintering is a widely used material manufacturing process.

According to Dr. Zhang, from a Microstructural point of view, sintering process can be essentially modeled by a surface and grain boundary diffusion.

She discussed grain boundary, triple point, stress and strain, flux direction, particle length and outer surface area as some of the parameters surrounding the model and simulation of Microstructural Evolution in Sintering. She briefly explained surface diffusion in which materials will flow from high curvature to low curvature and flux will oscillate with damping.

Dr. Zhang described the process with a mathematical model which involves a high order nonlinear time dependent PDE with a moving boundary. The surface is governed by the surface diffusion equation ¶ y/ ¶ t = -¶ J/ ¶ x where J is the surface flux and the triple point, a dihedral angle condition is imposed. She explained that the stress s (x) satisfies capillarity conditions, balance of total force and moment equilibrium equations.

She explained that several simulation models with different geometric figures such as a square were performed until equilibrium was attained at a circle.

The numerical method used was the method of lines with two ODE solvers. Dr. Zhang presented numerous numerical and simulation results along with lots of graphical results.