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Axisymmetric deformation of an anisotropic porous material is analyzed. A model of the material is proposed ; the material consists of ellipsoidal cells each of which has an ellipsoidal pore in the center of the matrix. The velocity field in the matrix is assumed and the upper bound approach is attempted. The yield criterion of the porous materials with various volume fractions of pore Vf is represented as ellipses on the σm-σ3 (the hydrostatic and principal stresses) plane. Their axes become smaller with increasing Vf and rotate clockwisely or counter clockwisely at an angle δ from the σm axis. The angle δ increases with increasing anisotropy. The direction of the rotation is dependent upon the aspect ratio of pore.

Indentation of sintered metals with square-based pyramids is performed and the relationship between the hardness and the compressive flow stress of the sintered metals in obtained. When the semi-angle α of the pyramid is 68°, which corresponds to the semi-angle of a Vickers hardness indenter, the ratio of the hardness to the flow stress is dependent upon the relative density. However, when α is 45°, the ratio is a constant value of 2.7 without influence of the relative density. Therefore, the flow stress of the sintered metals can be estimated from the hardness measured by using the indenter with the semi-angle of 45°.

The relationship between the Brinell hardness HB and the flow stress σe of sintered porous metals is examined considering the ratio d/D ; the diameter of indentation to that of the indenter. When d/D=0.4, at which the Brinell hardness test is usually done, the ratio c=HB/σe varies from 2 to 3 with a relative density ρ of 0.70 to 0.97. However, when d/D=0.7 to 0.9, the ratio c is almost constant at 2.5 to 2.8 without influence of the relative density. Therefore, the flow stress of porous metals can be estimated from the Brinell hardness test at a ratio d/D of 0.7 to 0.9.

An analysis of indentation of a porous material with square-based pyramids is made. The analysis is based on an approximate energy method using a velocity field which is constructed with the slip line field for the wedge indentation of the porous material. The hardness, that is, the indentation pressure is expressed as a function of the yield stress and the relative density of the porous material. Experiments on the indentation with square-based pyramids are also carried out using workhardened and annealed specimens of sintered copper powder. The experimental results are compared with the theoretical results.