J S2 bp2 cs2 0Eq

where S is the magnitude of the deviatoric stress in the powder aggregate, s is a measure of the deviatoric stress in the powder particle, p is the pressure, and the parameters b and c are functions of relative density to be determined from experiments.

Based on this constitutive model, the following material properties are required:

• Flow behavior of the particles

• Constitutive functions. b(P) and c(P) for the powder aggregate

• Specific heat of the powder as a function of temperature

• Thermal conductivity of the powder as a function of density

In addition, the accuracy of the model must be verified by some basic finite element simulations and empirical testing. The experimental tests are required to fully specify the constitutive model of the powder and can material. The experimental characterization of powder determines the flow behavior of particles and the constitutive functions of the aggregate.

Partial HIP Testing. The macroscopic solution of the boundary value problem involving powder aggregate under hydrostatic pressure can be obtained from the analytical expression given below and the power-law creep model for the particle flow behavior. The corresponding density evolution takes the form:

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