Fig 2 Yield surfaces determined by Kim et al Ref 5 from tensiontorsion tests on sintered iron powders

Akisanya et al. (Ref 10) used the probing method to determine yield surfaces for samples of spherical powders, which were either hydrostatically compacted or compacted by simulating closed-die compaction. These tests were performed using a triaxial cell in which hydrostatic pressure and uniaxial compression could be applied independently. Yield surfaces obtained for a relative density of 0.8 are shown in Fig. 3 using the axes of = - Sr and Sm. Note that in these experiments > and thus Ss is negative with Ss = -Se. It is important to note that the shape of the yield surfaces obtained by compacting the samples using these two different methods are significantly different from each other. Thus, the states of the materials are different even though the densities are the same.


• Closed-o Hydro &t



nitial ading point


■ A


X /

Fig. 3 Yield surface for spherical copper powders determined by Akisanya et al. (Ref 10) for isostatically pressed and close-die compacted samples

Another convenient way of presenting experimental data is in the form of isodensity plots. These plots are constructed by loading samples proportionally (either by maintaining the stresses or the strains proportional to each other) and then determining the stress states that correspond to a given density. If the material response can be described using the relative density as the only state variable, then these surfaces would be equivalent to the yield surfaces of the material. It is evident from the results of Fig. 3 that more than one state variable is required to describe the response. However, in many practical situations, an element of material experiences near proportional loading and isodensity or similar plots provide valuable information about the constitutive behavior. Brown and Abou-Chedid (Ref 11) constructed a series of isodensity plots in Se - ¿Lm space for spherical copper and sponge iron (Hoeganaes MH-100) powders (Fig. 4, 5). The solid symbols in these figures represent the yield strength in uniaxial compression following biaxial compression to the desired density. The major observations here are the different forms of the surface for the different powders, and the fact that the spherical powder has limited strength in uniaxial compression. These conclusions are consistent with the experiments of Akisanya et al. (Ref 10) presented in Fig. 3. The irregular powders, however, exhibit significant strength in uniaxial compression. Also, the irregular powders tested by Watson and Wert (Ref 9) had a significant yield strength when loaded in tension, while samples of spherical powder compacts can readily be broken in tension, often by hand, due to the lack of interlocking of the particles. These plots will be discussed and evaluated in the following sections. There are however, three important points to note at this stage:

• It is possible to identify a yield surface for a powder compact.

• The state of the material is a function of the prior history of loading. This influences the size and shape of the yield surface.

• The yield behavior depends on the morphology of the powder particles. Irregular particles interlock, giving tensile strength, while compacts of smooth spherical particles can be readily pulled apart.

Relative density, % ^ 67.5 o 70.0

□ 84

3.0 3.0 ).0

* ^^

k< x


50 100 150 Pressure (P), MPa

Fig. 4 Isodensity surfaces for spherical copper powders tested by Brown and Abou-Chedid (Ref 11)

Fig. 4 Isodensity surfaces for spherical copper powders tested by Brown and Abou-Chedid (Ref 11)

Fig. 5 Isodensity surfaces for irregular iron powders tested by Brown and Abou-Chedid (Ref 11)

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