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Deformation theory of hot-pressing

University of British Columbia

The possible deformation behaviour of spheres in a compact has been theoretically analyzed and experimentally verified. The change in contact area radius 'a' relative to the particle radius R has been related to the bulk density and bulk strain for four possible modes of packing: simple cubic (Z = 6), orthorhombic (Z = 8), rhombohedral (Z = 12), and body-centered cubic (Z = 8). An equation relating the above parameters can be represented by D — D。= [formula omitted] D。(a/R)² for different types of packings, D and D。 being the densities at any a/R and at a/R = 0, respectively. It has been shown experimentally by deforming monosized lead spheres at room temperature, 50 and 100°C in a cylindrical die, that the overall deformation is similar to that of the orthorhombically packed spheres. A change in the coordination number Z during the deformation process was also observed and may partially account for the deviation from the theoretically predicted values. Similar experiments using sapphire and K-Monel spheres were also carried out in the temperature range 1570 - 1700°C and 800 - 1000°C respectively. The results showed that the deformation behaviour was very similar to that of the lead spheres. A study of the geometry of deformation revealed that most of the spheres deformed in a random manner, although individual colonies of orthorhombic, tetragonal and rhombohedral packings were observed. It was also observed that the deformed faces that were approximately perpendicular to the direction of pressing were about 2.2 times larger than those parallel to the direction of pressing. This observation has been subsequently used to modify the theoretical models. The particle rearrangement and plastic flow have been found to be the predominant mechanisms for the densification of lead, K-Monel, and sapphire spheres under the experimental conditions used in this investigation. The criterion for yielding of two hemispheres of the same material in contact was used to incorporate the yield strength in the basic density equation. This equation has been found to fit the data obtained during the hot-pressing of the spheres. It has been observed that the deformation of sapphire single crystal spheres takes place by a complex deformation process. The presence of the basal and prismatic slip has been identified in the spheres deformed at 1570 and 1700°C. Presence of cross slip is also confirmed by the optical and electron micrographs at these temperatures.

Text

2011-10-14

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http://hdl.handle.net/2429/37985

Metals and Materials Engineering

University of British Columbia

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