Constitutive modeling of pressure-assisted powder consolidation by spark plasma sintering: The case of transition metal diborides

A viscoplastic constitutive model is developed to describe the pressure-assisted consolidation of HfB₂, NbB₂, and TiB₂ powders by spark plasma sintering (SPS). Densification is modeled as the superposition of two mechanisms: particle rearrangement at low temperature, represented by a rate-independent plastic slider, and high-temperature viscous flow, described by a dashpot following a Bird–Carreau law. These elements act in series, enabling a smooth transition from plastic to viscous behavior as temperature, porosity, and strain rate evolve. Model thermodynamic consistency is demonstrated by deriving the stress–strain rate law from a dissipation potential and linking it to the plastic yield function. Porosity evolution is described by coupling mass and momentum balance equations, and model parameters (viscosities, activation energy, strain-rate sensitivity) are identified by fitting experimental porosity–time data. The model is validated against literature data and used to identify the most effective operating conditions for achieving full densification of refractory diborides.