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Shape Effects of the Yield Locus on the Rankine Coefficient

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The Rankine coefficient is the ratio of the vertical pressure (maximum principal stress) and horizontal pressure (minimum principal stress) acting on a powder bed. The value of the Rankine coefficient is usually determined from the yield locus, which comes from the shear test results either by linear approximation using the Coulomb equation or by curve fitting using the Warren–Spring equation. Since the shape of the yield locus is obtained by approximation, the Rankine coefficient might change with the estimation method. The Rankine coefficient is an important coefficient for estimating the pressure distribution in a powder bed. However, no studies about the effect of the yield locus estimation method on the Rankine coefficient can be found in the past literature. In this paper, first we study the effect of three approximations, i.e. the Coulomb equation, the Warren–Spring equation and an equation proposed by the authors, on the Rankine coefficient. Based on these results, we investigate how the selection of the yield locus estimation method affects the Rankine coefficient. Then we compare the Rankine coefficients obtained from consolidation tests and from each of these yield loci, thereby demonstrating the validity of our proposed approximation equation.

Affiliations: 1: Ono Pharmaceutical Co., Ltd, 3-1-1 Sakurai, Shimamoto, Mishimagun, Osaka 618-8585, Japan; 2: Graduate School of Engineering, Department of Mechanical and System Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2201, Japan; 3: Graduate School of Engineering, Department of Mechanical and System Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2201, Japan;, Email:


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