## Powder Injection Molding

Powder Injection Molding (PIM) is a net-shape processing technique for making complex metal and ceramic components. In the PIM process, a metal or ceramics powder, mixed with a suitable carrier, is injected into a die cavity in a manner similar to plastic injection molding (Ref 6).

The process uses a feedstock that is composed of fine (typically <20 /'m) powder particles blended with waxes and polymers. After injection, the green preform shape is ejected from the die cavity and then subjected to a debinding process to remove the polymeric material prior to sintering. This extraction of the binder can be accomplished by thermal or chemical means. The resulting porous shell (approximately 65 to 70% of theoretical density) is heated to 1200 to 1370 °C (2200 to 2500 °F) for 30 to 120 min to sinter the metal powder particles into a solid mass. The resulting component is about 30 to 35% smaller in volume than the molded component and typically 96 to 98% of theoretical density.

This process offers two significant advantages over die compaction. The geometric shape is not limited by axial punch movement, and the mechanical properties of the sintered component are generally higher, primarily due to a higher final density. However, powder injection tooling is generally more expensive than die compaction tooling and the size of parts that can be made is limited by the difficulty of removing the polymeric carrier without damaging the integrity of the green preformed component. Powder injection molding presents an economical route to mass produce small complex shaped parts (typically less than 50 g) that are difficult to form or machine by conventional methods.

In PIM, the mold filling phase is the most critical step in the manufacture of a part. Defects, such as sink marks, voids, weld lines, and density variations, can occur from poor tooling design or improper selection of processing parameters, such as injection temperature and pressure. Traditionally, the design of PIM process tooling, as well as the selection of processing parameters, has been made by expensive and time consuming trial and error procedures. An efficient way to reduce these costs and improve the design to manufacture cycle time is through the use of process simulation. Parametric studies of the injection variables can be conducted by computer simulation. The results of these studies provide guidance in process planning and reduce process development time.

The determination of a meaningful constitutive description of the flow behavior of the polymer/powder mixture during injection is a key to successfully broadening the application of powder injection molding to the manufacture of engineering components by using computer simulation as a tool. This description is complicated, requiring knowledge of two phase non-Newtonian flow that incorporates the effect of local shear rate on viscosity and the effect of viscous heating on the temperature distribution in the component.

These constitutive equations describing viscous flow can be used to solve the conservation of heat, mass, and momentum equations that describe fluid flow. For example, finite difference methods have been used to produce solutions describing the flow during the filling of the mold and the subsequent temperature gradients developed during cooling.

Constitutive Behavior. The mathematics of describing the constitutive behavior of the molten polymer-particulate mixture has been presented elsewhere (Ref 7). In essence, by combining the solution of the mathematical description of the flow with certain geometric constraints, the relationship between stress and displacement, the constitutive behavior, can be quantitatively described.

Thus, powder injection molding is viewed as a fluid flow problem where classical equations of state can be used to describe the behavior of the polymer-particulate mixture. The melt is assumed to be incompressible and the governing differential equations for the conservation of mass, momentum, and energy are known from first principles. These governing differential equations are solved by assuming an appropriate viscosity model (for polymer-powder particle mixtures, viscosity is assumed to be a function of shear rate and temperature) and incorporating appropriate values for key materials properties, such as density, specific heat, and thermal conductivity.

Two additional process characteristics are incorporated into this mathematical description--the volume fraction of the mold that is filled by the melt and the volume fraction of the molten material that has solidified. By tracking the volume fraction of the mold that has been filled at a given time, and relating that volume to the velocity vector for the flow system, the location of the melt front can be calculated at any time during fill. Similarly, by assuming that the solidification rate is proportional to the liquid fraction of the polymeric binder and proportional to the square of the undercooling of the melt, the solid fraction of solidified polymer can be calculated at any given time. Coupling this calculation with the thermal equilibrium requirements provides the basis for determining the location of the liquid/solid interface at any time throughout the die cavity.

Powder Injection Molding Process Simulation. During the last decade, many process modeling techniques have been developed in material processing. Tremendous success has been achieved in the development and application of process modeling technology in molten metal operations. Both the finite difference method and the finite element method have been used successfully in casting processes that involve filling a sand or metal mold with molten metal to produce parts with complex three-dimensional (3-D) geometries (Ref 8, 9, 10, 11, 12, and 13). Considerable progress has also been made in modeling polymer and powder injection molding processes (Ref 14, 15, 16, and 17). Most of polymer processing and PIM models have been based on the generalized Hele-Shaw model for thin cavities. This may be adequate for modeling parts comprised of thin-wall sections, but may not be effective for modeling general parts with arbitrary complex 3-D geometries. Development of a general program capable of simulating the PIM process in arbitrary 3-D geometries has become increasingly imperative. This could be accomplished by using either the finite element method (FEM), the finite difference method (FDM), finite volume method, or a combination of them. Generally speaking, the FEM technique gives a more precise description of the geometry, and possibly more accurate results than FDM. However, FEM requires greater memory storage, more complicated programming, and longer computing time. Hence, the finite difference technique has been applied in this article.

The PIM simulation model is based on an existing casting simulation program which models the mold filling and solidification of general 3-D metal castings. This casting model was modified to include special features, such as viscous heating, associated with the PIM process. In essence, the geometric shape to be analyzed, the component, is divided into a large number of brick-type cells. Finite difference formulations are written for each equation included in the descriptive set incorporated into the constitutive behavior equations. These equations are then solved simultaneously leading to a coupled analysis of velocity, temperature, shear rate, and mass transfer (Ref 7).

The finite difference method is similar to the finite element method in that it provides a means for converting a partial differential equation into a set of algebraic equations. It differs from the finite element method in that the region of interest is divided into n discrete intervals or control volumes at which values of the differential equation are approximated using mathematical techniques such as a Taylor series expansion. Although some accuracy may be lost because stepped rectangular cells are used to represent sloped boundaries, the FDM technique allows the use of a large number of cells (elements) because of its simplicity in programming and efficiency in computing. For a given amount of computer memory, the FDM method can compute values for 20 to 50 times more cells than the FEM technique. As such, it is capable of describing small localized phenomena and large thermal or velocity gradients. Thus, it is especially suitable for modeling PIM and polymer processing where the thermal and momentum gradients are large due to low thermal conductivity combined with a rapid filling rate.

In the computing technique incorporated into the model, the complete partial differential equations describing the PIM processes are solved implicitly by the finite difference method. The technique takes into account the time-dependent non-Newtonial fluid flow behavior with free surface and viscous heating phenomena in arbitrary 3-D geometries. The complex 3-D domain is subdivided into small brick-type cells. Sloped surfaces are approximated in a zig-zag fashion. A uniform mesh is used throughout the model. The typical number of cells used for an industrial part is approximately 100,000 to 500,000. The discrete values of the velocity components are located at cell faces, while all other variables are located at the centers of the cell (Ref 8). Useful information, such as flow front locations, distribution of velocities, temperature, shear rates, and weld lines are obtained through the simulation. Figures 11 and 12 compare the flow fronts from an injected part (Fig. 11) and the numerical simulation of the injection process (Fig. 12).

There are several advantages of the computational and modeling techniques used:

• No term of the momentum and energy transport equations is neglected in the formulation. The partial differential equations are solved as they appear in their original forms, so that the model is capable of predicting any flow configuration, including jetting phenomena.

• The model can readily analyze general three-dimensional geometries.

• The finite difference method (FDM) is used.

• As a result of the simplicity in the formulation and the computation of this technique, the input of the geometry and the meshing of the part are much easier than with FEM techniques.

Several assumptions and simplifications are made to streamline this modeling technique. Variations in density and the heat capacity of feedstock and mold materials are assumed negligible in space and time. The solidification rate of the feedstock is assumed proportional to the square of the degree of undercooling and proportional to the liquid fraction of the binder material. Perfect contact is assumed between the feedstock and the mold during filling, so that heat transfer at the melt-mold interface is controlled by conduction. Heat transfer from the melt to the air in the mold cavity is assumed negligible since the filling time is short and the heat capacity of the air per unit volume is small.

## Post a comment