The mechanisms of densification in spark plasma sintering (SPS) were investigated both analytically and numerically for a model system of two spherical metallic powder particles. From the microscopic temperature distribution, the possibility of a micro-local overheating of the particleparticle contacts was analysed for different particle sizes, contact geometries, materials, and electrical loads. It is shown that, for particles below the size of one millimetre, local overheating is below one Kelvin. Subsequently, the material transport by thermomigration, electromigration, and diffusion driven by surface curvature and external pressure was derived from microscopic field distributions obtained from analytical calculations and finite-element simulations. The results show that, while the mechanical pressure accelerates material transport by orders of magnitude, the electrical current and the temperature gradients do not. It is also shown that pulsing the current has no significant influence on the densification rate.

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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.