Stress analysis of the field-assisted sintering: Electrothermal mechanical interaction

Abstract

Abstract. The field-assisted sintering techniques have the potential to produce bulk nanostructured materials from micro- andsubmicron particles. Using the perturbation theory, the electrothermal, elastic deformation of a consolidated material has beenanalyzed. The material carries a uniform, axial electric current. Explicit expression of the temperature and stress fields hasbeen obtained to the first order of approximation. The maximum temperature difference is proportional to the electric energyinput to the material, and the average pressure applied to the pressing die is a nonlinear function of the electric current. 1. Introduction Using field-assisted processing, various sintering methods have been proposed for preparing bulkmaterials from micron and submicron particles [1–6], especially the preparation of bulk nanostructuredceramics from micrometer-sized powders [6]. These methods have demonstrated numerous advantagesover conventional consolidation processes, such as low processing temperatures and short processingtime. It has beenbelievedthat the basic principle controlling the field-assistedprocessingis the interplaybetween electric Joule heating and local electromechanical stresses which removes the layer of surfaceoxideandenhancesatomicmigration, suchassurfacediffusion, grain boundarydiffusionanddislocationmotion [7].To understand the field-assisted processing, several analyses have been performed with most of themfocusing on the temperature evolution due to the Joule heating [3,8–11]. Recently, the evolution ofthermal stresses has been considered by Wang et al. [12] and Cincotti et al. [13]. Due to the complexityof the problem, most of analyses relied on numerical simulation, which provided some insight to thefield-induced thermal field and stress field in the sintering processes. There are only a few simplemodels, which gave the closed-form solution of the temperature distribution inside the consolidatedgreen compaction. There is no analysis on the electromechanical interaction present in the field-assistedprocessing.Thepassofanelectriccurrentthroughaconductingmaterialwillcausetheincreaseinlocaltemperaturedue to the Joule heating and mechanical deformation due to Maxwell’s stresses. Both the Joule heatingand the Maxwell’s stresses are a function of the electrical current, which need to be carefully analyzed