CONSOLIDATION OF METAL POWDER into useful products generally follows a three-step process: (1) powder transfer into a container or die, (2) powder compaction through applied force, and (3) sintering. Particular processes combine two of these steps into one. For example, hot isostatic pressing combines steps two and three through the simultaneous application of pressure and temperature in an autoclave. This article describes step two, the mechanical response of the powder to the applied compaction forces. Density of the powder transferred into the container depends on the properties of the powder and on the method of transfer, which may include tapping and vibrating. Consideration of packing density is beyond the scope of this article; however, a comprehensive review of this topic can be found in Ref 1. Proper design of compaction processes requires a description of the mechanical or thermomechanical behavior of the powder. Issues related to applications of practical interest include:

• Compaction in rigid dies: Density distribution in the compact, effect of tooling motion histories on density, tooling stresses and tooling deflections, stresses in the compact during ejection and fracture likelihood

• Cold isostatic pressing: Geometric distortion of the pressed component, effect of container dimensions and material on distortion

• Hot isostatic pressing: Geometric distortion of the pressed component, effect of pressure and temperature cycles on distortion, effect of container design on distortion

• Powder forging: Density distribution in the formed part, forging loads, and tooling stresses

Unfortunately, the complex nature of powder mechanical behavior, coupled with complex geometry and boundary conditions, precludes analytical solutions to these problems. During the late 1980s, the maturing of numerical solutions to finite strain plasticity allowed initial attempts at modeling powder compaction processes. Powder compaction modeling has not achieved widespread industrial use yet. However, many useful and encouraging results have been published, and it seems likely that during the next decade, modeling will become central to the design of compaction processes.

Formally, powder compaction modeling requires the solution of a boundary value problem-- a set of partial differential equations representing:

• Balance laws: conservation of mass, momentum balance, and conservation of energy

• Constitutive laws: stress-strain relation and friction laws

The finite element method (FEM) is the numerical technique most widely used to solve these equations. Modern FEM codes incorporate constitutive models for a wide variety of materials. Some of them are suited to modeling metal powders. Furthermore, these codes also provide facilities for the user to implement a particular constitutive law.

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