Deformation of Powder Compacts Experimental Observations

Before examining the structure of constitutive laws for powder compaction, it is instructive to identify the major physical processes that occur within the compact as it is deformed and to determine how these are likely to influence the macroscopic behavior. When the powder is initially poured into a die or mold, the particles are arranged randomly with particles only in point contact with each other.

Consider the situation where the compact is densified hydrostatically. As the pressure is increased, plastic flow occurs in the vicinity of the contacts. As a result, the contact zones spread, the centers of the particles move closer together, and the material densifies. During the initial stages of this process, the porosity remains connected, consisting of a network of interconnected channels threading through the material. In the micromechanical models, this is referred to as stage 1 compaction. As the material is densified further, the channels pinch off, leaving a distribution of isolated pores (stage 2). Throughout this process, because of the initial random structure, the porosity is randomly distributed throughout the material, particularly during stage 1 compaction. If, however, the sample is much larger than the mean particle size, no preferential orientations or distributions of pores develop, and the structure remains macroscopically isotropic. A single state variable can then be used to describe the structure and macroscopic response. A convenient state variable is the relative density D, which is defined as the ratio of the density of the compact to the density of the material, so that at full density D = 1.

In practical compaction processes, the densifying material can see complex stress states and histories. As a result, the structure that develops is no longer isotropic, and it may not be appropriate to describe this structure and the macroscopic response using a single state variable. For example, consider the case of frictionless closed-die compaction. As a cylinder is compacted along its axis, there is no straining in the transverse direction. The contact patches that develop between the deforming particles are therefore larger normal to the direction of loading than along the axis. Also, the size of these patches is different from those in a compact that has been densified hydrostatically to the same relative density. Thus, the relative density does not uniquely describe either the microstructure or the macroscopic response.

Any constitutive law that is developed needs to be validated experimentally. An examination of the types of experiments that have been performed and how the results from these tests are commonly presented follows. The analysis is based on the identification of a yield surface for the material (which is a surface in stress space within which the material responds elastically; plastic deformation can only occur for stress states on the yield surface). The size and shape of the yield surface is a function of the history of loading. The yield surface can be determined using a number of different methods. A number of samples can be prepared in the same way (for example, hydrostatically compacted to the same relative density). Each sample is then loaded along a different path in stress space until it yields. The yield surface is then formed by connecting the different yield points. Alternatively, a single specimen can be used. After compacting to the desired state, a series of probing experiments can be performed by unloading and reloading along a range of different stress paths until yield occurs. The yield surface can be mapped out in exactly the same way as before. When using this method, it is important to ensure that only a small amount of plastic straining occurs during each probe so that there is no significant change of microstructure (i.e., state) over the series of probing tests.

When examining a range of different stress states, it proves convenient to present the results in terms of global measures of stress. Two convenient quantities are the von Mises effective stress, £e, and the mean (or hydrostatic) stress, Sm. If Si, £2, and £3 are the principal stresses,

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