Numerical Simulation of the Temperature and Stress Field Evolution Applied to the Field Assisted Sintering Technique

The field assisted sintering technique (FAST) is a high-amperage, low-voltage, powder consolidation technique that employs pulsed direct current and uniaxial pressure. Over the past several years, FAST has been successfully used to produce a variety of different materials including metals, composites, and ceramics. In this paper we present a transient finite element model of aluminum oxide sintering that incorporates a coupled electrical, thermal, and mechanical analysis that closely resembles the procedures used in physical experiments. Within this context, we outline the governing equations that pertain to a balanced energy equation and include the effects of thermal and electrical contact forces, radiation, and Joule heating. We couple this with the relevant equations pertaining to mechanical displacements and prescribe the necessary initial and boundary conditions for a complete solution. As part of our transient analysis, we also present our implementation of a proportional integral derivative controller, which (similar to actual experimental conditions) affords the use of a predetermined heating rate conditioned upon a variable voltage. Finally, we discuss implications relating to the temperature and stress fields and suggest possible avenues for improvement.