Thermo-electro-mechanical modeling of spark plasma sintering processes accounting for grain boundary diffusion and surface diffusion

Abstract

In the present research, a numerical modeling approach of the initial stage of consolidation during spark plasma sintering on the microscopic scale is presented. The solution of a fully coupled thermo-electro-mechanical problem also accounting for grain boundary and surface diffusion is found by using a staggered way. The finite-element method is applied for solving the thermo-electro-mechanical problem while the finite-difference method is applied for the diffusion problem. A Lagrange-based non-linear formulation is used to deal with the detailed description of plastic and creep strain accumulation. The numerical model is developed for simulating the structural evolution of the involved particles during sintering of powder compacts taking into account both the free surface diffusion of the particles and the grain boundary diffusion at interparticle contact areas. The numerical results obtained by using the two-particle model—as a representative volume element of the powder—are compared with experimental results for the densification of a copper powder compact. The numerical and experimental results are in excellent agreement.

Multiphysics Simulation and Experimental Investigation of the Densification of Metals by Spark Plasma Sintering

“…The analysis of the SPS problem at the microscopic level shows that large local plastic strains and small elastic strains occur. [ 46 ] In the considered cases, the maximal elastic strain intensity is approx. 200 times smaller than the maximal plastic strain intensity.…”

“…It should be noted that, according to ref., [46] a decrease in the particle size and of the pressure would lead to an increasing influence of the diffusion mechanisms. Also, the effect of electromigration, as explained by ref., [64] will be only noticeable for a significant increase of the electric current.…”

“…Second, the finite difference solution of the surface and grain boundary diffusion problem ( 16), (18) was realized in an in-house Cþþ code tool by means of staggered scheme. [46] Finally, the solutions for volumetric diffusion (17), electromigration (20), and thermomigration (19) coupled with mechanical stress are obtained using ANSYS.…”

“…[39][40][41][42][43][44] The more complex problem, taking into account both coupled diffusion and mechanics, in which the analysis of the sintering process is carried out at the microscopic level considering the inhomogeneity of the stress state, was investigated in refs. [45,46]. As sintering process is a complicated issue, it is important to apply multiphysics modeling and simulations of powder systems for various technological processes.…”

A critical review on spark plasma sintering of copper and its alloys

“…This process is repeated intermittently until the compact achieves full densification. As a result, it causes homogeneous grain size distribution, as well as restricts grain Semenov et al [104,[134][135][136] modeled the SPS process by thermo-electro-mechanical approach. Two limiting conditions have been investigated (i) low mechanical pressure and (ii) high mechanical pressure.…”