Andrey L. Maximenko

Localized Overheating Phenomena and Optimization of Spark-Plasma Sintering Tooling Design

The present paper shows the application of a three-dimensional coupled electrical, thermal, mechanical finite element macro-scale modeling framework of Spark Plasma Sintering (SPS) to an actual problem of SPS tooling overheating, encountered during SPS experimentation. The overheating phenomenon is analyzed by varying the geometry of the tooling that exhibits the problem, namely by modeling various tooling configurations involving sequences of disk-shape spacers with step-wise increasing radii. The analysis is conducted by means of finite element simulations, intended to obtain temperature spatial distributions in the graphite press-forms, including punches, dies, and spacers; to identify the temperature peaks and their respective timing, and to propose a more suitable SPS tooling configuration with the avoidance of the overheating as a final aim. Electric currents-based Joule heating, heat transfer, mechanical conditions, and densification are imbedded in the model, utilizing the finite-element software COMSOL™, which possesses a distinguishing ability of coupling multiple physics. Thereby the implementation of a finite element method applicable to a broad range of SPS procedures is carried out, together with the more specific optimization of the SPS tooling design when dealing with excessive heating phenomena.

Modelling of anisotropic sintering in crystalline ceramics

We present a model that describes anisotropic shrinkage during sintering in a powder compact of aligned, elongated particles by deriving the anisotropic sintering stress and the anisotropic generalized viscosity as a function of material and geometric parameters. The powder compact consists of elongated particles, which are perfectly aligned and simply packed with elliptical pores at all the quadra-junctions between the particles. The model considers mass transport by grain boundary diffusion and surface diffusion. Shrinkage rates are calculated for a variety of geometries and are compared to kinetic Monte Carlo simulations.

Densification mechanisms of spark plasma sintering: multi-step pressure dilatometry

The effects of electrical current and mechanical pressure on the densification of spherical copper powder during spark plasma sintering (SPS) are examined. A novel multi-step pressure dilatometry method is introduced to compare the constitutive behavior of the copper powder under nearly equivalent current-insulated and current-assisted SPS process conditions. The strain rate sensitivity agrees with that predicted for a dislocation climb-controlled creep densification mechanism for both processing setups. Accelerated densification rate leading to a higher final relative density is observed for the current-assisted SPS.

Flash (Ultra-Rapid) Spark-Plasma Sintering of Silicon Carbide

A new ultra-rapid process of flash spark plasma sintering is developed. The idea of flash spark plasma sintering (or flash hot pressing - FHP) stems from the conducted theoretical analysis of the role of thermal runaway phenomena for material processing by flash sintering. The major purpose of the present study is to theoretically analyze the thermal runaway nature of flash sintering and to experimentally address the challenge of uncontrollable thermal conditions by the stabilization of the flash sintering process through the application of the external pressure. The effectiveness of the developed FHP technique is demonstrated by the few seconds–long consolidation of SiC powder in an industrial spark plasma sintering device. Specially designed sacrificial dies heat the pre-compacted SiC powder specimens to a critical temperature before applying any voltage to the powder volume and allowing the electrode-punches of the SPS device setup to contact the specimens and pass electric current through them under elevated temperatures. The experimental results demonstrate that flash sintering phenomena can be realized using conventional SPS devices. The usage of hybrid heating SPS devices is pointed out as the mainstream direction for the future studies and utilization of the new flash hot pressing (ultra-rapid spark plasma sintering) technique.

Ponderomotive effects during contact formation in microwave sintering

An assessment of the ponderomotive effect contributions to the kinetics of single contact growth during sintering is carried out. A considerable free surface electromigration during microwave sintering in a polarized electromagnetic field is determined at inter-particle interfaces. It is shown that the electromigration flux reaches its maximum near the inter-particle contact edge and it is equivalent to the compressive stress acting on the contact between particles. The compressive stress is proportional to the intensity of the electric field at the inter-particle neck and inversely proportional to the ratio of the grain boundary and surface diffusivities. The electromigration matter transport can substantially accelerate the shrinkage rate during microwave sintering in comparison with conventional sintering.

Multi-scale modeling of viscous sintering

A new multi-scale numerical approach for the modeling of viscous sintering based on the parallel monitoring of micro- and macro-scale evolutions is proposed. The internal structure of the porous material is described by the set of unit cells defined in the special control points of the material. In the course of sintering both the macroscopic shape change and the evolution of the unit cell geometry are calculated. The approach has no restrictions on the number of internal material parameters and could be used for the analysis of the optimum set of internal characteristics during viscous sintering. Numerical examples demonstrate a high level of macroscopically non-uniform anisotropy development during the constrained sintering of a porous bar with a rectangular cross-section.

Effects of loading modes on densification efficiency of spark plasma sintering: sample study of zirconium carbide consolidation

Abstract Theoretical studies on the densification kinetics of the new spark plasma sinter-forging (SPS-forging) consolidation technique and of the regular SPS have been carried out based on the continuum theory of sintering. Both modelling and verifying experimental results indicate that the loading modes play important roles in the densification efficiency of SPS of porous ZrC specimens. Compared to regular SPS, SPS-forging is shown to be able to enhance the densification more significantly during later sintering stages. The derived analytical constitutive equations are utilised to evaluate the high-temperature creep parameters of ZrC under SPS conditions. SPS-forging and regular SPS setups are combined to form a new SPS hybrid loading mode with the purpose of reducing shape irregularity in the SPS-forged specimens. Loading control is imposed to secure the geometry as well as the densification of ZrC specimens during hybrid SPS process.

Coupled Densification—Shape Distortion Analysis of Liquid Phase Sintering Affected By Gravity

The paper presents a model of nonlinear viscous behavior in the examination of gravity-induced distortion during liquid phase sintering. The model uses a finite element formulation to describe densification, viscous flow, and the associated dimensional changes and component slumping during sintering. The approach assumes sintering is conducted under isothermal conditions with averaged material properties. The numerical results are compared with experimental data and with a mathematical model on the distortion during liquid phase sintering of tungsten heavy alloys. The preliminary conclusions aim to provide better understanding of dimensional control during liquid phase sintering.

Kinetics of shrinkage and shape evolution during liquid phase sintering of tungsten heavy alloy

A numerical model describing gravity-induced shape distortion and densification during solid and liquid phase sintering is proposed. The constitutive formulation is based on the continuum theory of sintering and implemented in commercial finite element software. Simulations under gravity-induced stress are attempted on the basis of the model parameters where viscosity is assumed to be temperature and porosity dependent. Viscosity is assessed through shrinkage and shrinkage rate data obtained experimentally from dilatometry over a controlled temperature regime. Effects of temperature, heating rate, and liquid phase formation on porosity evolution are analyzed. Additionally, sample studies on the influence of heating rate, gravity, friction coefficient, aspect ratio, and volume on the predicted distortion profiles after sintering of a tungsten heavy alloy are also presented. These numerical results are compared with experimental data from the literature.