Automotive and consumer electronics are two disparate industries that rely heavily on injection molding. Moreover, they both involve updating of products on a regular basis. Both these industries have been leaders in the development of concurrent engineering, meaning the parallelization of tasks from inception to manufacture. Regardless of the degree to which concurrent engineering is practiced, there is no doubt that simulation is a valuable aid in linking design to manufacture. For injection molding, the benefit of simulation is based on the fact that it is cheaper and faster to avoid problems in the design phase than to fix them in production.
In this chapter, some necessary terms are defined. In particular, the concept of stress in a fluid is introduced. We also define the rate of strain tensor for a fluid and introduce the generalized Newtonian fluid. These concepts are used in subsequent chapters when discussing material properties and the governing equations for simulation of injection molding.
The physical properties of polymers depend to a large extent on their molecular structure. To simulate injection molding, we need to measure properties for their use in the simulation; however, the process itself affects the properties. The relationship between processing and properties is still an area of research. Indeed, this lack of understanding is a major deficiency of current simulation software. Some ideas on how to advance this area are given in Part II of this book.
In this chapter, the equations governing the flow of a compressible, viscous fluid are derived. These equations are applicable to the flow of a polymer melt and are obtained using the conservation principles of mass, momentum, and energy.
The equations provided in Chapter 4 are quite general and comprise a very comprehensive model for injection molding. In this chapter we consider some approximations that may be made to allow simulation of the molding process. Many approximations are available and each will affect accuracy, computational speed and, choice of numericalmethod for solution.
Despite simplification of governing equations, the resulting equations are still such that a numerical approach to their solution is necessary. The key numerical methods are finite differences and finite elements. In this chapter, we discuss the application of these methods to the resulting equations. Some historical comments on numerical methods may be found in Appendix A. It should be noted that the numerical methods employed in commercial products were related to the available computer power at the time. So in looking at various numerical schemes, one should have some feeling for the CPU and memory limitations in the past.
Many simulations for predicting orientation in short-fiber reinforced thermoplastics adopt the Folgar-Tucker model [122], which was described in Chapter 5. The Folgar-Tucker model adds into the Jeffery equation an isotropic rotary diffusion term to account for fiber-fiber interactions. The diffusivity is assumed to be proportional to the generalized shear rate, which is believed to be a valid assumption. However, the model delegates the strength of fiber-fiber interactions to just a single scalar constant, or the coefficient of interaction CI, which is used as a fitting parameter. Since there is no fundamental basis to determine the value of CI, Tucker and his co-workers find the value of CI> by adjusting it to match the experimentallymeasured fiber orientation tensor component a11. There is, however, no guarantee for other components to match the experimental data at the same time. Since the fiber orientation is influenced by several factors, the diffusivity may be, on occasion, used inappropriately to correct errors due to other factors. Furthermore, as mentioned previously, closure approximations have to be used to relate the fourth-order tensor to the second-order one. The CI value has also been found to vary significantly with different closure approximation schemes (Cintra and Tucker [62]).
This chapter will be limited to the prediction of the elastic moduli and the coefficients of thermal expansion for fiber-reinforced composites. These properties are derived from calculated fiber orientation distributions during the molding process and used in warpage or structural analysis, as discussed in Section 5.3.7. These generally use short-term properties. In reality, these properties are time-dependent. Some progress in modeling efforts in properties like long-termfailure of unfilled polymers can be found in Klompen et al. [205,206].
Traditional short fiber-reinforced injection molding compounds, available since the 1960s, have been widely used in industry, because they not only produce improved strength properties, but also have the ability to flow readily in injection molds. Short fiber thermoplastic composite pellets used for injection molding are manufactured by extrusion, where the polymer and chopped strands of fibers are mixed in single or twin screw extruders, extruded, and pelletized. As a result of fiber length attrition during extrusion compounding, this technique produces short fibers, which are typically 0.2–0.4 mm long with aspect ratios of 20–50. The fibers are encapsulated in the polymer matrix to form the pellets, inside which the fibers are randomly oriented; as shown in Figure 9.1(a).
An essential requirement for improving injection molding simulation is the incorporation of crystallization effects. In Section 5.3.5, we remarked that the use of a single no-flow or transition temperature is unjustified for semi-crystallinematerials. It can lead to errors in fill pattern prediction and calculation of shrinkage and warpage. Moreover, if we are to be able to predict properties of semi-crystalline materials after molding, and when subjected to variable environments, we need to incorporate crystallization calculations explicitly.
Injection molding simulation needs to consider both molten flow and solidification of thematerial. To achieve accurate results in a flow analysis, it is important to predict the solidification layer thickness accurately. There are two ways in which the solidification layer thickness can be determined:
In injection molding, various colorants are typically added to the virgin polymer to produce colorful products, ranging from toys and mobile phones to computer cases and car parts. Colorants can be either soluble organic dyes or insoluble particulate pigments. While the former are often used to color textiles, the latter are of more importance in the plastics industry.
Successful manufacture of injection molded products requires not only meeting the designed dimensional tolerances, but also having a long-term dimensional stability under conditions at which the product is subjected to post-molding thermal treatments. It would be useful to clarify the term “shrinkage,” since the same term may have different meanings when used in different situations.
The formation of weldlines is undesirable in injection molding, since it results in poor appearance and poor mechanical strength of injection-molded products.
It has been 17 years since the first edition of Flow Analysis of Injection Molds [196] was published in 1995. Over the years, there has been significant progress and changes of focus in the research areas relevant to injection-molding simulation.
