Densification mechanism maps for hot isostatic pressing (HIP) of unequal sized particles
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I.
INTRODUCTION
HOT Isostatic Pressing
(HIP) is an elevated temperature densification technique employed in powder metallurgy processing operations. The material in powder form, typically having powder particle sizes ranging from 10 to 100/zm, is first cold consolidated to provide what is termed the green compact. This green compact is then subjected during the HIP cycle to isostatic pressures at an elevated temperature where diffusion and thermally assisted deformation can occur. Such thermally activated processes during the HIP hasten complete densification of the initial green consolidate. As reviewed by Hanes et al.,~ HIP has been employed for the densification of powder consolidates of steels, non-ferrous alloys, superalloys, and ceramics. The only comprehensive analytical study of the mechanisms of deformation and densification during HIP is that of Arzt, Ashby, and Easterling. 2 This analytical work elegantly defined the regimes during HIP of the various mechanisms of deformation on densification in terms of densification mechanism maps and provided the first basis for a scientific understanding of HIP. However, for the sake of simplicity, the model considered only the monosized particle case and, in effect, constrained all particles to deform or densify in a uniform manner. In practice, the powders have a distribution of sizes, and the effect of this size variation on the densification during HIP has not been previously examined. In what follows, a new model is developed for the mechanism of densification of unequal sized particles during HIP from which the HIP densification mechanism maps are derived. Since a full size distribution of particles is difficult to treat rigorously, the approximation is made that the powders are of a bimodal nature, that is, consisting of populations of two distinct sizes, and the generalization to a full size distribution is discussed on the basis of the results of this treatment. S. V. NAIR is Assistant Professor, Department of Mechanical Engineering, University of Massachusetts at Amherst, Amherst, MA 01003. J.K. TIEN is Professor and Director, Center for Strategic Materials, Henry Krumb School of Mines, Columbia University, New York, NY 10027. Manuscript submitted June 24, 1985.
METALLURGICALTRANSACTIONS A
II.
THE MODEL
Let R~ and R2 (R2 > R~) be the two powder particle diameters and f~ and f2 be the particle weight fractions in the initial (prior to HIP) packing. The major assumptions are as in the model of Arzt et al. ,2 namely, that all particles are spherical and densification is not a particle rearrangement process, but due to deformation at interparticle necks. In the very final stages of densification, these assumptions may not be valid since the densifying compact cannot be considered as an aggregate of spherical particles, but as a solid with holes having certain size and shape distributions.3 However, in the following, any added refinements necessary to more accurately describe final stage densification will not be introduced. When pressure is applied to a
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