Effective Thermal and Electrical Conductivities of AgSnO2 During Sintering. Part II: Constitutive Modeling and Numerical Simulation

During resistance sintering (RS) of a conductive porous material, effective electrical and thermal conductivities have a great influence on the thermal gradients inside the matter, which could induce heterogeneous microstructures. Part I of this investigation focused on the characterization of the effective conductivities of AgSnO2 during sintering conditions, with the understanding of the relations between their evolutions and the microstructure. In Part II, the emphasis is on the development of appropriate constitutive equations able to describe the evolutions of the effective conductivities of AgSnO2 during RS. This work proposes constitutive equations taking into account the two main mechanisms, identified in Part I, which modify the contact conditions between the particles. The first mechanism corresponds to viscoplastic deformations of particles. A creep behavior law is used to calculate the macroscopic deformation and the densification kinetics. The second one deals with bonding diffusion under the effect of temperature, which decreases the contact resistance between the particles. As no specific effect of current has been highlighted in the case of AgSnO2, the effective conductivities' behavior laws are available for RS and for hot pressing (HP). Relationships for effective conductivities are included in the numerical HP model and combined with governing laws. Finite element analyses are compared to experimental results obtained from HP tests to validate and discuss the model.