Injection Molding

Injection molding, defined as a cyclic process for producing identical articles from a mold, is the most widely used polymer processing operation. The main advantage of this process is the capacity of repetitively fabricating parts having complex geometries at high production rates.

The term “rheology” dates back to 1929 (Tanner and Walters 1998) and is used to describe the mechanical response of materials. Polymeric materials generally show a more complex response than classical Newtonian fluids or linear viscoelastic bodies. Nevertheless, the kinematics and the conservation laws are the same for all bodies. The presentation here is condensed; one may consult other books for amplification (Bird et al. 1987a; Huilgol and Phan-Thien 1997; Tanner 2000). We begin with kinematics.

Most injection-molded parts are thin walled, i.e., they have a small thickness compared to other typical dimensions. Therefore, one can reduce the three-dimensional flow to a simpler two-dimensional problem, using the lubrication approximation (Richardson 1972). We consider a polymer flow through a thin cavity with a slowly varying gap-wise dimension and arbitrary in-plane dimensions. Assume that x ₁, x ₂ are the planar coordinates, x ₃ is the gap-wise direction coordinate. The flow occurs between two walls at \( x_{3} = \pm h/2 \). Adjacent to each wall there is a frozen layer of the solidified polymer so that the polymer melt flows between two solid–liquid interfaces at \( x_{3} = s^{ - } (x_{1} ,x_{2} ){\text{ and }}x_{3} = s^{ + } (x_{1} ,x_{2} ) \) (see Fig. 3.1).

The majority of polymers used in industry are semicrystalline. Crystallization occurs during the processing, and consists of two stages:

A sustained industrial interest has been shown in fiber-filled polymers. When fibers are combined with a polymer matrix that provides cohesion, the fibers become the load bearing component of the composite, and enhance the strength and stiffness of the material. Many articles made from the fiber-reinforced composites are produced by injection molding or compression molding. The thermo-mechanical properties of the end-product highly depend on the fiber orientation distribution induced by the flow of fiber suspension during processing. Therefore, the flow of fiber suspensions needs to be understood in order to predict the fiber orientation distribution and its effects on the end properties of the products.

It is known that the dimension of an injection-molded product, as it cools after the molding process, is usually different from the corresponding dimension of the mold cavity. The geometric reduction in the size of the part is referred to as mold shrinkage, or as-molded shrinkage, or simply shrinkage. According to ASTM standards (ASTM D955-08), shrinkage is measured 24–48 h after demolding. Warpage, or warping, is the distortion induced by the inhomogeneous shrinkage. According to Austin (1991) and Shoemaker (2006), variations in shrinkage can be further classified into three types: (i) shrinkage difference in different directions due to the material anisotropy; (ii) shrinkage variations from region to region in the part due to non-uniform pressure and temperature distributions over the part; (iii) non-uniform shrinkage across the thickness due to the differential cooling on opposing mold faces.

In injection molding, the mold has two functions: (i) to form the shape of the part to be manufactured, and (ii) to extract heat from the material to solidify the part as quickly as possible. For performing the second function, the mold has a cooling system within it. The basic cooling system consists of the cooling lines in the form of circular holes drilled in the mold so that the coolant flowing through the cooling lines will extract the heat out from the hot polymer melt. The location of cooling lines depends on the part geometry, cavity configuration, and the location of ejection pins and moving components of the mold. Figure 7.1 illustrates the cooling lines and their relation to the part. In the figure the cooling system consists of two circuits, one (Circuit 1) in the fixed half of the mold, and the other (circuit 2) in the moving half. This example has been used by Zheng et al. (1996) in a study aimed at prediction of warpage.

Analytical solutions to injection molding problems are very rare due to the complexities of the governing equations, the material behavior and the cavity geometry. To get useful results, we have to seek numerical solutions. In any numerical solution procedure, the governing equations are discretized to form a set of algebraic equations, possibly nonlinear, and computational algorithms are developed to solve the algebraic equations. Different discretization processes and different solution algorithms form a variety of numerical methods; each method has some advantage over the others in a certain class of problems. In this Chapter, we shall deal with several numerical methods including the finite element method, the finite difference method, the meshless particle method, and the boundary element method. However, the aim of this Chapter is not to provide in-depth discussions about the fundamental aspects of numerical methods or a comprehensive reference to the computer aided engineering software. Instead, the focus of the Chapter is to provide a guide to some special issues and computational techniques dealing with injection molding problems.