Macroscopic Models of HIP

Developments Prior to about 1990. The earliest attempts to develop a macroscopic model were the work of Kuhn and Downey (Ref 22) and Green (Ref 23), who proposed a plasticity theory for porous metals. They independently developed yield criteria and stress-strain relationships for these materials. Both of these theories suggest that the yield criterion is a function of the first invariant of stress, J\, and the second invariant of the deviatoric stress, J2. The relationship is expressed:

where CVand ,;iare functions of the relative density. They also defined the stress-strain relationship:

where a function of relative density, d X is a nonnegative constant, and nm is the hydrostatic stress. Shima and Oyane (Ref 24) built on this work and rewrote Eq 9 as follows:

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