## Die Compaction Process Simulation Model

The finite element method is commonly applied to metalworking deformation processes to predict the stress state present in the component during manufacture. This method involves dividing the component into very small, but finite, regions following a set procedure based on the rules of application of the particular finite element methodology being used. This technique allows replacing a set of differential equations describing the overall constitutive behavior of the material with an equivalent but approximate set of algebraic equations which describe the material behavior locally at a fixed nodal point. By writing algebraic equations for each nodal point and then using the computer to simultaneously solve those equations for all nodal points, a solution describing the local values of the characteristic of interest can be generated. This solution may provide a strain map, show temperature gradients, or areas of isostress.

These methods have been widely applied to evaluate the state of stress or the temperature distribution in a component, such as a turbine blade, during its use. However, the application of this technique to processing is complicated by the requirement that some nodes may be required to slide past others, for example to describe the flow of metal along the surface of a forging die. Furthermore, this sliding may require incorporation of dynamic friction conditions. Both of these situations present serious programming problems to the finite element analyst.

The use of finite element techniques to describe metal powder die compaction is complicated by the large strains which occur during compactionâ€”strains which exceed those that can be accounted for using traditional stress analysis finite element techniques. This distorts the geometric grid and deleteriously affects the predictive capabilities of the finite element system. Thus it becomes necessary to define a new nodal pattern after partial compaction has occurred. This remeshing is quite tedious and time consuming leading the necessity to develop techniques which automatically remesh. The application of finite element techniques to metal powder die compaction is further complicated by the nonuniform movement of the powder particles during compaction creating a variation in density throughout the compact. Both the load transfer characteristics within the metal powder compact and the nature of frictional behavior between the powder compact surface and the die wall are a function of density. These functional relationships with density are unknown and difficult to account for in the existing finite element methods.

Recent work has focused on incorporating the elasto-plastic constitutive equations for metal powder deformation into a finite element methodology. Figure 10 presents density gradient predictions for simple right cylinders of varying aspect ratios. Although the effects of friction have not yet been fully incorporated, the model predicts density variations consistent with the experimental results published in the literature.

Fig. 10 Isodensity lines predicted by the die compaction model

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