The aim of this work is to simulate the forming process of green anodes. For this purpose, a nonlinear compressible viscoplastic constitutive law is presented. The concept of natural reference configuration is considered. Within an isothermal thermodynamic framework, a Helmholtz free energy is proposed to take into account the nonlinear compressible deformation process occurring between natural reference configuration and current configuration. A dissipation potential is introduced in order to characterize the irreversible aspect of compaction process. The constitutive law is thus formulated through two equations: (1) an expression of Cauchy stress tensor and (2) a differential equation characterizing the evolution of the natural reference configuration. Material parameters are assumed to be a function of the apparent green density. An experimental study is carried out in order to characterize the compaction behavior of the anode paste. A user's material VUMAT subroutine for finite-element dynamic explicit analysis has been developed and implemented in the abaqus commercial software. To evaluate the model predictive capability, numerical simulations of the compaction forming process of anode paste were performed. Simulation results show that the constitutive law predicts the experimental trends and gives insight of physical responses. This constitutes a first step toward characterizing the anode paste behavior and making a benchmark with experimental results on the forming process of anode paste.
The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust and precise.
The Hall-Héroult process uses prebaked carbon anodes as electrodes. The anode’s quality plays a crucial role in the efficiency of the aluminium production process. During the baking process, the anode undergoes complex physicochemical transformations. Thus, the production of high-quality anodes depends, among others, on the efficient control of their baking process. This paper aims to investigate the evolution of some physical properties of the anode paste mixture during the baking process. These properties include the mass loss fraction, real and apparent densities, the ratio of apparent volume, the permeability, and porosities. For this purpose, experiments consisting of thermogravimetric analysis, dilatometry, air permeability, and helium-pycnometric measurements were carried out. The anode permeability at high temperatures was linked to the air permeability through a permeability correlator due to experimental limitations. Moreover, the real density at high temperatures was estimated by combining real densities of the coal tar pitch and coke aggregates. Different porosities, such as the open porosity and the closed porosity related to the pitch binder, were estimated by taking the permeability at high temperatures into account. In this context, the effect of the permeability correlator, which was introduced to link the permeability at high temperatures to the air permeability, was investigated through a sensitivity analysis. These results allow an estimation of the shrinking index, a new variable introduced to reflect the baking level of the anode mixture, which is linked to the volatile that is released in both open and closed pores. Afterwards, the pore pressure inside closed pores in the coal tar pitch was estimated. The obtained results highlight some new insights related to the baking process of the anode mixture. Moreover, they pave the way for better modeling of the thermo-chemo-mechanical behavior of anodes at high temperatures.
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