Yield design homogenization method for compaction of monosized spherical powders

The compaction of a package of monosized spherical solid grains by rate-independent plasticity deformation is examined in this paper through the use of both yield design homogenization method and finite element simulation. Both modes of compaction, isostatic and closed die, are considered. In this study, the arrangement of powder consists of hexagonal array of identical spherical grains touching each other in its initial state. During the compaction process the response of the powder compacts is monitored in terms of behaviors of appropriate representative unit cells subject to axisymmetrical loading conditions. The kinematic approach of the yield design homogenization method has been used to determine external estimates of macroscopic strength criteria of powders at various stages of compaction. The obtained upper bound estimates are based on consideration of discontinuous incompressible velocity fields satisfying conditions of homogeneous strain rate. The shapes and sizes of the macroscopic yield surfaces are determined at various stages of compaction and it has been found that they depend upon the loading history as well as the relative density of the compact. Finite element simulations similar to those of Ogbonna N. and Fleck N. A. [1995] "Compaction of an array of spherical particles," Acta Metall. Mater. 43(2), 603-620. have also been performed in order to (i) obtain the deformation modes as well as the evolution of the deformation mechanism of the powder compact during the whole process of compaction; (ii) derive the evolution of contact sizes between adjacent grains; (iii) examine the dependence of the macroscopic yield surface upon the degree of compaction, using the "yield probing technique" Gurson, A. L. and Yuan, D. W. [1995] A Material Model for a Ceramic Powder Based on Ultrasound, TRS Bend Bar, and Axisymmetric Triaxial Compression Test Results (ASME, New York), pp. 5768, and (iv) validate, to some extent, the results provided by the kinematic approach.