On the development of constitutive relations for metallic powders
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I.
INTRODUCTION
P R O C E S S E S for cold consolidation of metal powders, such as cold isostatic pressing (CIP) and cold uniaxial strain compression (constrained compression), rely on external stress to drive deformation of the powder aggregate by time-independent plastic flow. In contrast, consolidation by sintering is a time-dependent process, in which mass transport by diffusion is driven by the reduction of surface energy accompanying consolidation. Hot isostatic pressing (HIP) and related processes generally proceed by a combination of time-independent plasticity, time-dependent plasticity (creep), and mass transport mechanisms. The present article is concerned with consolidation of metal powders by timeindependent plastic flow. Previous experimental investigations of consolidation of metal powders by time-independent plastic flow have focused primarily on determining the relationship between applied stress and relative density for consolidation by hydrostatic compression and by constrained compression, ll-61 These results have provided valuable insights into the effects of powder particle and material characteristics on consolidation. However, few results have been reported for plastic deformation of metal powders subjected to a wider range of stress states. For example, experimental observations of yielding for uniaxial stress tension and compression of partially consolidated particulate aggregates would be invaluable for testing models of metal powder plasticity, but few such results have been reported. Cold consolidation of metal powders has also been considered from a theoretical perspective. Consolidation J.A. WERT, Professor, is with the Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903. T.J. WATSON, formerly with the Department of Materials Science and Engineering, University of Virginia, is with the Manufacturing Science and Technology Group, Pratt and Whitney Inc., West Palm Beach, FL 334t0. Manuscript submitted September 24, 1992. METALLURGICAL TRANSACTIONS A
by time-independent plastic flow is conveniently represented using yield surfaces that depend on relative density (D) as well as on the stress invariants. Doraivelu et al. 171 have recently summarized models that generate yield criteria of the form A J2 + BI~ - 6112o = 0
[11
where 1~ is the first invariant of the stress tensor, J2 is the second invariant of the deviatoric stress tensor, A, B, and 6 are material parameters that depend on relative density, and Y0 is the yield strength of the fully dense material. Yield criteria of this form generate elliptical yield surfaces in stress space, termed quadratic yield surfaces. Irrespective of the manner in which A, B, and depend on relative density, all quadratic yield surfaces share several salient characteristics: they are symmetric with respect to hydrostatic tension and compression and they exhibit rotational symmetry about the hydrostatic stress axis. Symmetry, with respect to hydrostatic tension and compression, results from the I~ term in
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