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.
Highlights
Spark plasma sintering (SPS) [1,2,3,4,5], known as field assisted sintering technique (FAST) [5] or pulsed electric current sintering (PECS) [4], is a promising technology for innovative processing in the field of new and advanced materials’ production
The present work describes the sintering processes at the particle level taking into account (i) improved models of plasticity and creep, (ii) frictional contact, (iii) grain boundary and (iv) surface diffusion, (v) thermal gradient and (vi) electric field
Where s is the specific free surface energy of a crystalline solid, κ = 1∕RI + 1∕RII is the mean curvature with RI and RII being the two principal radii of surface curvature, p = −1∕3tr is the hydrostatic pressure and a0 is the chemical potential of the atoms in a stress-free state
Summary
Spark plasma sintering (SPS) [1,2,3,4,5], known as field assisted sintering technique (FAST) [5] or pulsed electric current sintering (PECS) [4], is a promising technology for innovative processing in the field of new and advanced materials’ production. Time t, BR−mt which are , where R generally of the is the particle radius, B, m, n are material/process constants These expressions can be used for the verification of the numerical solution and for the identification of the dominant neck growth mechanism based on the experimentally obtained constants m and n. The present work describes the sintering processes at the particle (microscopic) level taking into account (i) improved models of plasticity and creep, (ii) frictional contact, (iii) grain boundary and (iv) surface diffusion, (v) thermal gradient and (vi) electric field. The numerically obtained results for the evolution of the interparticle neck radius during the SPS process are compared with experimental results for copper powder
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