## A F1a P

strain increment x , and radial strain increment a corresponding to a range of values of cell pressure ¿,r.

The results of applying Eq 86 to the experimental data of Pavier and Doremus (Ref 14) for the Distalloy AE blend are shown in Fig. 15. Because noise is inherently present in such information, a cursory smoothing using a moving average scheme was performed prior to computing the increments of strain. In addition, the elastic components of strain were assumed to be negligible. For low relative densities, this assumption is reasonable. However, as plastic incompressibility is approached, the validity of the assumption must be checked. A curve fit for b(D) results in the following expression:

Fig. 15 Function b(D) for an iron powder blend comprising 99.5% by weight Distalloy AE, 0.5% by weight graphite, and 1% wax Hoechst micropulver

Isostatic Compaction Test for c(D). The state of stress in the isostatic compaction test is one of pure pressure, with no shear or deviatoric stress present. The isotropic test provides a convenient means of evaluating the evolution of relative density as a function of increasing cell pressure. Data are obtained by increasing cell pressure to a point before unloading the cell to determine the resulting powder relative density. Following Pavier and Doremus (Ref 14), the relation between the relative density for the powder under hydrostatic loading and the applied pressure or hydrostatic stress was determined to be:

46.2976

where Py is expressed in MPa and represents the pressure at yield given a value of relative density, D in the isostatic test.

It is reasonable to assume that the material is continuously yielding with load. Further, since shear stress is completely absent, Eq 60 reduces to:

If particle hardening is considered, the calculation of c(D) involves the simultaneous integration of partial differential equations for the evolution of particle yield stress and the functions b(D) and c(D). However, for simplicity, assume the powder particles are perfectly plastic and obtain c(D) from (Eq 89):

Using the forms for pressure and b(D) from Eq 88 and 87, and assuming a mean value of 375 MPa for particle yield stress, the function c(D) is calculated and plotted in Fig. 16.

Fig. 16 Functions b(D) and c(D) for a iron powder blend comprising 99.5% by weight Distalloy AE, 0.5% by weight graphite, and 1% wax Hoechst micropulver

Verification of Calibrated Model. This section evaluates the accuracy of the calibration performed for functions b(D) and c(D) for the Distalloy AE blend considered using triaxial test data. Analysis data were generated through a finite element simulation of the triaxial tests conducted. Because hardening of the powder particles is a likely event, it is considered here. Specifically, the material of the powder particle was modeled as having a yield stress of 250 MPa with a hardening of 333 MPa. These values were obtained from data reported by Trasorras et al. (Ref 36). Figure 17 shows a comparison of the predicted powder density as it evolves during the triaxial tests against data measured by Pavier et al. (Ref 14). There is very good agreement between simulation and experiment. Figure 18 shows a plot of axial strain versus radial strain for a triaxial cell pressure of 250 MPa. The strains are measured relative to the onset of shear in the specimen, marked by an increase in axial stress over the cell pressure. Figure 19 shows a plot of axial stress versus axial strain for the same triaxial cell pressure of 250 MPa. Again, the simulations compare well with the experiments.

Pressure, MPa

Fig. 17 Density evolution in a triaxial test: comparison of FEA results with experiment

Pressure, MPa

Fig. 17 Density evolution in a triaxial test: comparison of FEA results with experiment

-0.01 O 0.01 0.02 0.03 0.04 0.05 0.06 Radial si rain

Fig. 18 Axial versus radial strain in a triaxial test with 250 MPa cell pressure: comparison of FEA results with experiment

Fig. 19 Axial stress versus strain in a triaxial test with 250 MPa cell pressure: comparison of FEA results with experiment

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