Constitutive Models for Metal Powder Compaction

This section examines the response of powder compacts under mechanical loading histories that are typical of those experienced during the manufacture of powder metal parts. Deformation of a powder compact occurs as the result of rearrangement and plastic deformation of the particles. Frictional resistance, as particles slide over each other, can also contribute to the macroscopic response. If the packing is initially loose, then the initial stages of compaction are dominated by particle rearrangement, with little or no plastic deformation occurring between the contacting particles. If, however, the initial apparent density of the powder is relatively high, further macroscopic plastic deformation under constrained compressive stress states is dominated by plastic deformation of the particles themselves.

Knowledge of the major physical processes that occur when a powder compact is deformed can be used to guide the development of constitutive models of the compaction process. At the microlevel, the constitutive response of fully dense materials governs plastic deformation between the contacting particles. The macroscopic response can then be determined by combining the contributions from individual contacts. There are general theoretical techniques that can be employed to achieve this and determine what general statements can be made about the structure of the macroscopic constitutive laws. Micromechanical models have been developed using these techniques. It may not be appropriate to precisely follow this route, but, instead, to develop empirical constitutive laws based on observations made at the macroscopic level. The results then provide a suitable structure and general guidelines for the construction of these models. As the material approaches full density, these models should reduce to classical incompressible models. Therefore, these models serve a second purpose; they provide a starting point from which more general constitutive relationships can be developed.

Throughout the article, the response of an element of material in a particle of the compact (referred to as a "microscopic element") is identified in terms of the local stress (7,; and local strain When evaluating the response of a powder compact, a representative "macroscopic element" of material, which contains a large number of particles but is small compared to the size of a pressed component, is identified. The response of such an element is expressed in terms of a macroscopic average stress and strain

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