Microscopic Models and Mechanisms

Mechanistic models of the microscopic mechanisms in the HIP process was pioneered by Ashby et al. (Ref 5, 10, 11, 12, 13) in the early 1980s and is based on the interaction among powder particles during the consolidation process. Ashby and his collaborators did most of the early work on this subject and opened up many avenues for further study by later investigators. They divided the entire consolidation process into three stages, based on powder packing and how the porosity is located relative to the powder particles. Stage 0 describes the density reached by the packing of the loose powder. Stage 1 describes the early stages of densification (relative density less than 0.9) when the porosity is still connected. Stage 2 describes the final densification (relative density greater than 0.9) when the residual porosity is in the form of small holes. A schematic of these two stages is shown in Fig. 12.

Fig. 12 Ashby stage 1 and stage 2 densification. From Ref 13

Although this work assumes that the powder consists of spherical particles of a single size, other authors have attempted to determine densification rates with spherical particles (Ref 14, 15, 16, 17) of nonuniform size distribution. Ashby recognized that the mechanism of densification depends on the temperature and pressure at any given time in the HIP cycle and derived equations in each stage for plastic yielding, power-law creep, Nabarro-Herring creep, and diffusion. For the complete derivation of all the equations used for each of these mechanisms, see Ref 16. This section presents the final results of this derivation.

Plastic Yielding Densification. Yielding occurs during the initial stage provided the effective pressure, Peff, on the particle is equal to or greater than three times the yield stress of the material. The external pressure that just causes yielding is:

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