A mathematical theory of plasticity for the upsetting of compressible P/M materials

A mathematical equation for the calculation of the flow stress in the case of the simple compression test is proposed for the P/M sintered preforms. A new yield function developed by Doraivelu et al, taking into account the hydrostatic stress, is considered for the development of the above equation. Similarly, another equation for the determination of the hydrostatic stress in the case of the simple compression test is proposed for P/M sintered preforms. Both of the above two equations depend upon two factors, namely: (i) the value of Poisson's ratio; and (ii) the relative density of the P/M preform; during the compression test. Because then exists a relationship between Poisson's ratio and the relative density for P/M preforms, it is proposed that the flow stress or the hydrostatic stress equations can be written in terms of either Poisson's ratio or the relative density. It is observed that at relative densities of below 0.71 the aggregate is geometrically unstable and crumbles during deformation. In the range 0.71 less than or equal to R less than or equal to 1.0, the strain transferred to the matrix increases continuously until it asymptotically approaches the strain applied to the aggregate. (C) 2000 Elsevier Science S.A. All rights reserved.