Final Stage Densification of Hot Pressing

Abstract

A new predictive densification equation of pressure sintering during final stage is proposed. Geometrical models by which the expressioni isderived are polyhedral space filling bodies, e.g. tetrakaidecahedron and rhombic-dodecahedron, and pores which are surrounded by corners of the bodies.It is also assumed that the densification occurs by the transport of lattice vacancies from the neighborhood of a pore to adjacent grain boundaries and concentration gradient of the vacancies are simply proportional to compressive stress at flattend contact face of the body.If the size of contact area can be expressed as a function of porosity, effective stress (σe), that is, the compressive stress may be formularized as σe=σa⋅f(P) where σa and f(P) are applied stress and a function of porosity, respectively. From geometrical considerations of the models, a general expression is obtained as, A=S(1-KP2/3)where, A is a size of contact areas per polyhedron, S is a constant equals total surface area of polyhedron at zero porosity, K is also a constant differs in different polyhedron and P is porosity.Furthermore, this equation can be simplified as, A′=(1-P)3/2 when P<0.3, where A′=(A/SK)-[(1/K)-1.05]A linear relationship between A and (1-P)3/2, therefore, would be expected.Then, effective stress may be given as, σe=σa/(1-P)3/2It was found the results obtained by Coble and Kingery relating the torsional creep of poly-crystalline alumina to the amount of porosity present, plotted as strain rate versus 1/(1-P)3/2, a close approximation to a straight line was obtained.An isothermal densification equation, derived from a combination of Nabarro-Herring diffusional creep equation and the effective stress, is given as, dρ/dt=10σaDΩ/R2kTρ1/2 or ρ3/2=30σaDΩt/2R2kT+const.One may predict linear relationship between dρ/dt and ρ-1/2 as well as ρ3/2 and t (time).