An empirical model for hot isostatic pressing of metal powders

Abstract

A new mathematical model is proposed to describe time dependent pressurization and densification of metal powders at constant temperature. It is a first order ordinary differential equation in the pressure and a densification measure, which incorporates instantaneous response, equilibrium response, and creep response. The model is based, to some extent, on micromechanical (hollow sphere) analysis. However, the development is mostly empirical, based on previously published experimental data on hot isostatic pressing of lead and tin powders. These data show that an initial rapid change in pressure (30 seconds rise time) is accompanied by equally rapid change in relative density. This suggests that a creep law may not be adequate to describe the response to rapid change of pressure. Accordingly, the pressure rate is included in the proposed model. The data support the assumed linear instantaneous and equilibrium response laws and the exponential creep response law. Agreement between theoretical creep curves and experimental data is very good.