| Stochastic Model on Granule Collapse during Cold Isostatic Pressing |
| Kouichi YASUDA |
| Tokyo Institute of Technology |
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Powder processing with granule is widely used in pharmaceutical, food, and ceramics industries due to its high productivity, and homogeneity of powder compacts has a great influence on its mechanical properties and reliability. As one of effective compaction, cold isostatic pressing (CIP) has been applied to improve the homogeneity of the compacts; however, still there is a change in the local density in the compacts by CIP. The authors proposed a deterministic model in which a concentric multiple shell structure was analyzed by elastic theory to express a stress distribution in the compact during CIP, considering the changes in density and Young¡¯s modulus of each shell. In this presentation, the authors step forward to develop a stochastic model on granule collapse during CIP because granule is known to have a stress distribution for collapse. So, we assume that a spherical preform has a continuous distribution of Young¡¯s modulus E(r) as a function of radius r, and is compressed by isostatic pressing. The radial displacement u(r) is given by solving the following a derivative equation,
, where is Poisson¡¯s ratio. The radial stress is obtained from the displacement as below,
This stress can be normalized by using the applied stress P (viz.CIP pressure) as below,
By taking some assumption, the joint probability density function h(P, r) can be expressed by the following equation,
, where m and P0 are shape and scale parameters of Weibull distribution for granule collapse, and Ve and V0 are the effective volume and unit volume. The collapse probability can be obtained as a function of applied pressure P and location r by integrating h(P, r) to have a marginal distribution of it.
References:
[1] K.Yasuda et al., Materials Science and Technology 2006: Processing (2006) p. 495-506.
[2] K.Yasuda, S.Tanaka, and M.Naito, J.Soc.Powder Technol. Japan, 51 (2014) 153-162.
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Acknowledgements : This research was in-part supported by Grant-in-Aid for Scientific Researches (A) (24246108) and (C) (25420706) from Japan Society for the Promotion of Science, and also Joint Research Project of Joining and Welding Research Institute, Osaka University, and also Collaborative Research Project (No.78) of Materials and Structures Laboratory, Tokyo Institute of Technology.
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