3D Nonlinear Viscoelastic-Viscoplastic Model for Ramming Paste Used in a Hall-Héroult Cell

Abstract

Ramming paste is a carbonaceous porous material used in Hall-Héroult cells. It is baked in place under varying loads. To model the cell mechanical behavior during its lifespan, it was necessary to develop a constitutive law that included ramming paste creep behavior. A three-dimensional (3D) nonlinear viscoelastic-viscoplastic constitutive law was devised and developed to model the primary and secondary creep stages of baked paste. The model consisted of two parts (i.e., viscoelastic and viscoplastic). Each creep mechanism was based on the existence of a dissipative potential for the hydrostatic and deviatoric parts. Analytical solutions were presented for linear creep behavior. For the nonlinear case, the deviatoric part of the viscoelastic behavior could be obtained numerically, and all other parts analytically. Finally, model parameters were identified for paste baked and tested at different temperatures. A pattern search algorithm was used to optimize the model parameters. A comparison of the results gained from the model with experimental results showed that the devised model well represented the nonlinear viscoelastic-viscoplastic behavior of the paste baked at 250°C and tested at room temperature. In addition, the model was able to predict the qualitative creep behavior of the paste baked at 350, 560, and 1,000°C and tested at 300, 300, and 25°C, respectively.