Molten thermoplastics exhibit viscoelastic behavior, a combination of flow properties of viscous fluids and elastic solids. When a viscous fluid flows, part of driving energy is converted into viscous heat and disappears; however, when an elastic solid deforms, energy that drives deformation is stored. In daily life, flow of water is a typical viscous fluid, and deformation of rubber is an elastic body.
In addition to these two material flow behaviors, there are also two flow deformations, shear and extension, as shown in Figure 4-1 (a) and (b). In filling stage of injection molding, flow of thermoplastic melt is dominated by shear flow, as shown in Figure 4-1(c), and there is relative sliding between elements of each layer of material. In addition, when melt flows through a region of sudden size change, as shown in Figure 4-1(d), extensional flow becomes much more important.

 

Figure 4-1 (a) Shear flow; (b) Extensional flow; (c) Shear flow in cavity; (d) Extensional flow in filling cavity
Thermoplastics exhibit viscoelastic behavior by combining properties of ideal viscous fluids and ideal elastic solids when subjected to stress. Under certain conditions, melt is continuously deformed by shear stress like a liquid; however, once stress is relieved, melt returns to its original shape like an elastic solid, as shown in Figure 4-2 (b) and (c). This viscoelastic behavior is due to fact that polymer is in molten state, and molecular weight exhibits a chaotic coil pattern, which will allow molecular chains to move or slide when subjected to external forces. However, entangled polymer chains make system behave like an elastic solid when an external force is applied or released. For example, after stress is relieved, molecular chain will be subjected to a recovery stress, so that molecular chain will return to equilibrium state of chaotic curling. This recovery stress may not act immediately because there is still entanglement of molecular chains within polymer system.

 

Figure 4-2 (a) An ideal viscous liquid exhibits continuous deformation under stress;
(b) Ideal elastic solid will be deformed immediately after external force is removed, and it will completely return to its original shape after external force is removed;
(c) Thermoplastic melts are like liquids and continuously deform under shear stress. However, once stress is relieved, it behaves like an elastic solid, partially deforming and returning to its original shape.

Shear viscosity is resistance of plastics to shear flow. It is ratio of shear stress to shear rate, see Figure 4-3. Polymer melts are highly viscous due to their long molecular chain structure, typically ranging from 2 to 3000 Pa (10-1 Pa for water and 1020 Pa for glass).
 
Figure 4-3 illustrates definition of polymer melt viscosity by simple shear flow
Water is a typical Newtonian fluid, and viscosity of Newtonian fluid is related to temperature but not to shear rate. However, most polymer melts are non-Newtonian fluids whose viscosity is not only related to temperature but also to shear strain rate.
When polymer is deformed, some molecules are no longer entangled, and molecular chains can slide with each other and align in direction of force. As a result, flow resistance of polymer decreases with deformation, which is called shear thinning behavior ( shearing-thinning behavior), which means that viscosity of polymer is reduced when subjected to high shear rates, and also provides convenience of polymer melt processing. For example, pushing water in an open line with twice pressure doubles flow rate of water. However, pushing polymer melt in an open line at twice pressure may increase flow rate by a factor of 2 to 15 depending on material used.
Concept of shear viscosity is introduced, and then looked at distribution of shear rate in cavity during injection molding. In general, the faster relative movement between connecting layers of material, the higher shear rate. Therefore, a typical melt flow velocity curve is shown in Figure 4-4(a), which has the highest shear rate at interface between melt and mold; or, if there is a polymer solidification layer, the highest shear rate is at solid-liquid interface. On the other hand, due to symmetrical flow in the center layer of plastic part, relative movement between materials is close to zero, and shear rate is also close to zero, as shown in Figure 4-4(b). Shear rate is an important flow parameter because it affects magnitude of melt viscosity and shear heat (viscous heat). Typical melt shear ranges for injection molding processes range from 102 to 105 1/s.

 

Figure 4-4 (a) Typical velocity distribution curve of relative flow elements;
(b) Distribution of shear rate in the filling stage of injection molding.
Mobility of polymer molecular chains increases with increase of temperature. As shown in Figure 4-5, with increase of shear rate and temperature, viscosity of melt will decrease, improvement of molecular chain mobility will promote more regular molecular chain arrangement and reduce degree of molecular chain entanglement. In addition, viscosity of melt is also related to pressure. The higher pressure, the stickier melt. Rheological properties of a material express shear viscosity as a function of shear rate, temperature and pressure.
 
Figure 4-5 Relationship between polymer viscosity and shear rate, temperature, and pressure

Injection pressure of injection machine is driving force to overcome flow resistance of melt. Injection pressure pushes melt into cavity for filling and pressure keeping, and melt flows from high pressure area to low pressure area, just like water flows from a high place to a low place. In injection stage, a high pressure is accumulated in nozzle to overcome flow resistance of polymer melt, and pressure gradually decreases along flow length toward polymer melt wavefront. If cavity is well vented, atmospheric pressure will eventually be reached at melt front. Pressure distribution is shown in Figure 4-6.

 

Figure 4-6 Pressure reduction along melt delivery system and cavity
The higher pressure at cavity inlet, the higher pressure gradient (pressure drop per flow length). As melt flow length increases, inlet pressure must be increased to generate same pressure gradient to maintain polymer melt velocity, as shown in Figure 4-7.

 

Figure 4-7 Relationship between melt speed and pressure gradient
According to simplified theory of classical fluid mechanics, injection pressure required to fill melt delivery system (vertical runner, runner and gate) and mold cavity is related to materials used, design, and process parameters. Figures 4-8 show injection pressure as a function of each parameter. Using P for injection pressure and n for material constant, most polymers have a value of n between 0.15 and 0.36, 0.3 is a good approximation, and melt flows in sprues, runners, cylindrical gates, etc. Required injection pressure in a circular pipe is:
 
Injection pressure required for melt to flow in belt-shaped pipe of thin shell mold cavity is:
 
Flow rate of melt is related to Melt Index (MI), which is also called flow conductance, and flow index is an indicator of ease of melt flow. In practice, flow index is a function of part geometry (eg wall thickness, surface features) and viscosity of melt. Flow index decreases with increasing meat thickness, but decreases with increasing melt viscosity, see Figure 4-9.
During injection molding, under specific molding conditions and thickness of plastic part, length of melt that can flow will be determined according to thermal properties and shear properties of material. This property can be expressed as flow length of melt, as shown in Figure 4- 10 shown.

 

Figure 4-8 Function relationship between injection pressure and material viscosity, flow length, volume flow rate and meat thickness

 

Figure 4-9 Flow Index vs. Wall Thickness and Viscosity

 

Figure 4-10 Melt flow length depends on thickness and temperature of plastic part
By plotting injection pressure of injection molding cavity filling against filling time, a U-shaped curve can usually be obtained, as shown in Figure 4-11, where the lowest injection pressure occurs in the middle of curve. To use shorter filling times, high melt speeds and high injection pressures are required to fill cavity. To use a longer filling time, you can provide a longer cooling time for plastic, which leads to an increase in viscosity of melt and also requires a higher injection pressure to fill mold cavity. Shape of injection pressure versus fill time curve is highly dependent on material used, cavity geometry, and mold design.

 

Figure 4-11 U-shaped curve of injection pressure versus filling time
Finally, it must be pointed out that dynamics of cavity filling can sometimes be complicated by interaction between melt velocity (or shear rate), melt viscosity, and melt temperature. Note that melt viscosity decreases with increasing shear rate and temperature. High shear rate and high shear heat caused by high melt speeds may reduce viscosity, resulting in faster flow rates and higher shear rates and melt temperatures. So materials that are sensitive to shear effects are inherently unstable.

Figure 4-12 compares design and forming parameters that affect injection pressure.

Figure 4-12 Relationship between injection pressure and design, forming parameters and materials

Filling Pattern is flow of melt in conveying system and cavity over time, as shown in Figure 4-13. Filling mode has a decisive influence on quality of plastic part. Ideal filling mode is that melt reaches every corner of cavity at the same time at a constant melt front velocity (MFV) during the entire process; otherwise, areas in cavity that are filled first will overflow due to overfilling. Filling mold cavity with changing melt wavefront velocity will result in changes in molecular chain or fiber orientation.

 

Figure 4-13 Image of computer simulation of melt filling mode

Advancing speed of melt wave front is abbreviated as MFV, and cross-sectional area of advancing melt wave front is abbreviated as MFA. MFA can be obtained by multiplying lateral length of melt wave front by thickness of plastic part, or cross-sectional area of runner, or sum of the two as needed. Anytime,
Volume flow rate = melt wave front velocity (MFV) × melt wave front area (MFA)
For plastic parts with complex shapes, using a fixed screw speed does not guarantee a fixed melt wavefront speed. When cross-sectional area of mold cavity changes, even if injection machine maintains a fixed injection speed, changing melt wave front speed may still fill part of mold cavity first. Figure 4-14 shows that increased melt wavefront velocity around insert creates high pressure and high alignment on both sides of insert, resulting in potentially uneven shrinkage and warpage of molded part.

 

Figure 4-14 Melt wave front velocity (MFV) and melt wave front area (MFA). Differences in MFV can cause plastic molecules (represented by dots) to stretch in different ways, resulting in differences in molecular and fiber orientation, resulting in differences in shrinkage or warping.
In filling stage of injection molding, molecular chains or fillers of plastic material will be aligned according to action of shear stress. Since mold temperature is usually relatively low, alignment near surface solidifies almost instantaneously. Orientation of molecular chains and fibers depends on hydrodynamics of melt and directionality of fiber extension. At melt wave front, due to combination of shear flow and extensional flow, melt is continuously forced to flow from thick center layer to mold wall, resulting in a fountain flow effect, which has a great influence on molecular chain/fiber alignment on the surface of plastic part. Please refer to description of Figure 4-15.

 

Figure 4-15 Fiber orientation of surface layer and center layer of plastic parts
The higher MFV of plastic part, the higher surface pressure and the higher degree of molecular chain alignment. MFV difference during filling will make alignment difference in plastic part, resulting in different shrinkage and warping. Therefore, fixed MFV should be maintained as much as possible during filling, so that the entire plastic part has uniform molecular chain alignment.
MFV and MFA are important design parameters for flow balance. Unbalanced flow MFA will have a sudden change, when part of mold cavity corner is full, part of melt is still flowing. For any complex geometry, MFA variation within cavity should be minimized to determine optimal gate location. When flow is balanced, there is minimal change in the area of melt wavefront, as shown in Figure 4-16.

 

Figure 4-16 (a) Balanced and unbalanced flows resulting from changes in MFA; and (b) their corresponding filling patterns.

Rheology is study of deformation and flow processing characteristics of materials under stress, including shear rate, shear viscosity, viscoelasticity, viscous heat, extensional viscosity, etc. Most molten plastics exhibit quasi-plastic behavior, that is, according to power law,
, n < 1
When plastic is moved by shear stress, its viscosity decreases with increase of shear rate, which is called shear thinning of polymer materials. Generally, plastic characteristic index provided by manufacturers is flow index MI (Melt index). Generally, MI value of plastics is between 1 and 25. The larger MI value, the smaller viscosity of plastic and the smaller molecular weight; otherwise , the smaller MI value, the greater viscosity of plastic and the greater molecular weight. MI value is just a point on shear viscosity curve of plastic. (Note: Viscosity unit 1 cp = 0.001 Pa s, cp = centipoise, Pa = N/m2)
Other factors that affect properties of plastics include molecular weight and molecular weight distribution, molecular orientation, glass transition temperature and additives.

One of characteristics of plastics is that molecular weight is very large. Molecular weight distribution curve, method and conditions of its polymerization have a close influence on manufactured molded products. The larger molecular weight, the higher glass transition temperature Tg, improved mechanical properties, heat resistance and impact strength, but viscosity also increases with increase of molecular weight, which makes processing difficult. In terms of molecular weight distribution, short molecular chains affect tensile and impact strength, medium molecular chains affect solution viscosity and low-shear melt flow, and amount of long molecular chains affects melt elasticity.

It means that polymer chain starts to have a large link movement, that is, temperature at which it breaks away from hard-bound glass state and starts to be more ductile. Size of Tg has a great influence on properties of plastics, so it is often an important indicator for judging properties of plastics. In glass state, it exhibits rigid properties similar to glass, but in rubber state, it becomes a softer rubber property.

Original properties of plastic materials will change with external factors and forces. For example, viscosity of polymer melts (representing material flow resistance) increases with molecular weight, but decreases with temperature. Furthermore, molecular orientation caused by high shear stress acting on material also reduces viscosity of plastic melt.

Including stabilizers, lubricants, plasticizers, flame retardants, colorants, foaming agents, antistatic agents, fillers, and reinforcing materials, etc., can be used to modify physical and mechanical properties of improved plastic.