1. Introduction
The term powder processing refers to compacting powders in dies and sintering the particles together heating to near melting. Generally, this process has been applied to wide variety of materials such as powdered metals, ceramics, glasses, graphites and diamond. Sintering refers to processing a compacted powdered (green) material, which is brittle, by directly heating it to 70-90% of melting temperature, for example, by placing it in a furnace, typically with three chambers:
(i) a burn-off chamber to the vaporize lubricants (used for easy pouring and compaction),
(ii) a high-temperature chamber to sinter, and
(iii) a cooling chamber to ramp down the temperature.
The binding occurs by small-scale mechanisms involving diffusion, plastic flow, recrystallization, grain growth and pore shrinkage. An oxygen-free environment is preferred to minimize oxides. Most importantly, sintering is a method that can be utilized to produce products with complex shapes that cannot be easily made with other processes. However, because powder processing is typically more expensive than other material processing involving full-blown melting, research is ongoing to improve the steps in the process. In this regard, electrically aided sintering techniques for heat delivery have become quite promising. In particular, electrically aided sintering, which uses the material’s inherent resistance to flowing current—resulting in Joule heating to bond the powder components has great promise because it produces desired materials without much post-processing. Furthermore, it has advantages over other methods, such as high purity of processed materials, in particular, because there are few steps during the fabrication approach.
(i) a burn-off chamber to the vaporize lubricants (used for easy pouring and compaction),
(ii) a high-temperature chamber to sinter, and
(iii) a cooling chamber to ramp down the temperature.
The binding occurs by small-scale mechanisms involving diffusion, plastic flow, recrystallization, grain growth and pore shrinkage. An oxygen-free environment is preferred to minimize oxides. Most importantly, sintering is a method that can be utilized to produce products with complex shapes that cannot be easily made with other processes. However, because powder processing is typically more expensive than other material processing involving full-blown melting, research is ongoing to improve the steps in the process. In this regard, electrically aided sintering techniques for heat delivery have become quite promising. In particular, electrically aided sintering, which uses the material’s inherent resistance to flowing current—resulting in Joule heating to bond the powder components has great promise because it produces desired materials without much post-processing. Furthermore, it has advantages over other methods, such as high purity of processed materials, in particular, because there are few steps during the fabrication approach.
2. Objectives:
In this project, we are simulate multi-physical analysis of electrically-aided sintering of compacted powdered materials. The objective of this project is to provide a framework to assemble a series of submodels for electrically-aided compaction, which can be collected into a single expression for the temperature evolution during the process. Each sub-model can be replaced with a different model if desired. We would analyze then analyze the deformation of the cube and the various material parameters like the stresses, densification parameter, temperature, thermal strain, plastic strain with respect to different time frames using the step time function.
In this project, we are simulate multi-physical analysis of electrically-aided sintering of compacted powdered materials. The objective of this project is to provide a framework to assemble a series of submodels for electrically-aided compaction, which can be collected into a single expression for the temperature evolution during the process. Each sub-model can be replaced with a different model if desired. We would analyze then analyze the deformation of the cube and the various material parameters like the stresses, densification parameter, temperature, thermal strain, plastic strain with respect to different time frames using the step time function.
3. Brief Procedure:
We also develop simple framework to investigate the densification and thermal strain changes in an electrically aided compaction process. We also utilize a simple elasto-thermal-plastic strain change deformation model to evaluate the temperature evolution building on Kirchoff St.Venant constitutive relation.
The key quantity of interest is the heat generated from an electrical field. The interconversions of various forms of energy (electromagnetic, thermal, etc) in a system are governed by the first law of thermodynamics,
Building on a classical Kirchhoff-St. Venant constitutive relation, we consider the following simple elasto-thermo-plastic decomposition:
The temperature evolution rate is given by the equation,
In order to estimate the temperature parameters at different time intervals when the time step is given, we follow the explicit forward Euler time marching scheme which is given by
𝜃(𝑡+Δ𝑡)=𝜃(𝑡)+Δ𝑡( 𝜃̇ )
Similar approach is followed for 𝑑̇ 𝑎𝑛𝑑 𝐸𝑝̇
𝑑(𝑡+Δ𝑡)=𝑑(𝑡)+Δ𝑡( 𝑑̇ ),
𝐸𝑝(𝑡+Δ𝑡)=𝐸𝑝(𝑡)+Δ𝑡(𝐸𝑝̇ )
4. MATLAB Analysis:
a. Graphics of the deforming cube at different time intervals:
b. Stress values with respect to time:
c. Norm of Deviatoric stress with respect to time
d. Norm of Plastic Strain wrto time
e. Densification factor wrto time
f. Temperature wrto time
g. Norm of thermal strain wrto time