Cluster model of the porosity of spongy titanium briquettes at the stage of pressing

Abstract

The main factors of the formation of porosity of pressed products based on spongy titanium were studied. Three types of pores were studied and separated – cluster (in the place of particles), inter-cluster, and natural pores of the material. The cluster models of particles packing at the stages of pressing were developed (from bulk density, or the formation of temporary structures to the formation of stable structures). The number of cluster faces in the models depends on coordination number λ, which means tetrahedral (λ=4) clusters at the initial stage and cuboctahedral (λ=12) at the later ones. Based on the Gaussian rule, for spheres packing, it was found that the most correct form of clusters for later pressing stages is cuboctahedral, as the pores between the spheres at the maximum tight packing with the coordination number of 12 have the shape close to cuboctahedrons and octahedrons, but with concave faces. Based on the difference between the volume of spheres, for which particles and clusters in the model were accepted, based on calculated volumes of intercluster octahedrons and cuboctahedrons, the volume of pores in the shape of the Steiner octahedron or cuboctahedron was calculated. In calculating the strength of adhesion between the particles, the proper porosity of spongy titanium is determined through the assumption that a part of the powder is a conglomerate that is formed from hollow spheres of the regular shape at the stage of titanium reduction by the magnesium thermal method. Accordingly, in the formula for calculating the strength of adhesion, the force that influences a particle will consist of the difference between forces of elastic deformation and the destruction of hollow spheres contained in the deformed volume. The developed models were proved by the results of practical research. Actual measurements show the average exponential ratio of the porosity to pressing pressure, which makes it possible to calculate s maximum inter-cluster porosity at the maximum compaction of 66 % and the compression factor of the studied material of 0.15.