The Effects of Fill-Nonuniformities on the Densified States of Cylindrical Green P/M Compacts Public
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We focus attention on single-punch compaction of metal powders in cylindrical dies. In one case, we consider solid cylindrical compacts, and take the die walls to be frictionless in order to isolate the effects of initial nonuniformities in powder fill on the final green density distribution of the compact. First, a model is introduced in which the die is filled with <I>n</I> distinct powders that occupy concentric annular regions within the die. The model requires that the balance of mass, the balance of momentum, and a realistic equation of state be satisfied in each region, and includes a plausible constitutive relation that relates the induced radial pressure in each powder region to the corresponding axial pressure and the relative movements of the interfaces that confine the region. For specified powder properties, the model predicts the movements of the interface between the powders, the final density in each region, the pressure maintained in each region, and the total compaction load required. In the special case of two powders (<I>n</I>=2), we predict how the radial movement of the single interface depends on the mismatch between the properties of the two powders. For large values of <I>n</I>, and for powder properties that change gradually from one powder to the next, the model approximates a single powder filled nonuniformly in the die. Finally, a model is developed for a single powder with continuously varying powder properties. Formally, the model may be obtained by taking the limit of the <I>n</I>-powder model as <I>n</I> becomes unbounded. Employing the continuous model, we determine how nonuniformities in initial fill density can be offset by nonuniformities in other powder properties to yield perfectly uniform green densities. In a second case, we consider axisymmetric, hollow, cylindrical compacts, and include the effects of friction at the die wall and the core rod. The ratio of the induced radial pressure to the applied axial pressure is assumed to be constant throughout the compaction, and Coulomb friction acts between the powder and the die wall as well as between the powder and the core rod. We derive a closed form solution for the axial and radial variation of the axial pressure, radial pressure, and shear stress throughout the compact. This solution is combined with a plausible equation of state to predict the final green density distribution and the variation of applied load throughout the compact.
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