Simulation of the electrical resistance sintering process by means of finite difference in a spreadsheet

Abstract In this work, a theoretical model for the metal powder consolidation technique known as Electrical Resistance Sintering (ERS) is proposed and validated. This technique consists of the consolidation of a mass of metal powder by the simultaneous action of pressure and the passage of a high intensity electric current. This electric current heats the powder mass by the Joule effect, while softening it so that the imposed pressure causes its densification. The proposed model meets the set objective of seeking the greatest possible simplicity, without ignoring the key aspects of the technique. In line with this simplicity, the proposed model has a one-dimensional character and is solved numerically by means of Finite Difference through a simulator implemented in the Microsoft Excel™ spreadsheet environment, programming in VBA, with computation times not exceeding 5 min. The adopted strategy takes into account the strong electrical–mechanical-thermal coupling present in the process. The sensors incorporated in the ERS equipment allow the recording of the data necessary to construct the evolution curves of the global porosity and the thermal energy released. The theoretical predictions provided by the simulator have been compared with experimental curves obtained from the electrical consolidation experiments with commercially pure iron powder. Discrepancies between experimental and theoretical values for final global porosity are around 5% (although approaching 20% in the vicinity of critical conditions) and those for final specific thermal energy do not exceed 7%. The reasonable agreement between the experimental and theoretical curves gives confidence that the model, despite its simplifications, reproduces the main characteristics of the process.