Fundamentals of Polymer Engineering Part 16 ppt

Although the barrel isheated to a temperature above the melting point of the polymer, the region veryclose to the base of the hopper is often water cooled to prevent polymer frommelting

15.1 INTRODUCTION

Thus far, we have talked about how polymers are synthesized, how they arecharacterized, and how they behave as solids, melts, or in the form of solutions.Ultimately, however, it is necessary to convert the polymer into useful products.Typically, these may be rods, pipes, films, fibers, or molded articles Mostfrequently these materials are made from a single polymer Increasingly,though, blends, filled polymers, and composite materials are used It should benoted that even when a single polymer is used, it is rarely a chemically purematerial Almost invariably, it contains additives that act as dyes, plasticizers,antioxidants, and so on A variety of physical structures can result, depending onthe kind of polymer and additives used and also on how these materials areprocessed Because the final structure obtained determines the physical properties

of the product, the process used has to be chosen with care For inexpensive,high-volume disposable items such as beverage containers or toys, the mostinexpensive process is used The manufacture of high-value-added sophisticateditems such as compact disks or optical lenses, on the other hand, requires a greatdeal of engineering and an intimate knowledge of the fundamentals of polymerbehavior

In this chapter, we discuss just three of the most common polymerprocessing operations-extrusion, injection molding, and fiber spinning Because

most polymers are sold in the form of pellets, an extruder is required to melt,homogenize, and pump the thermoplastic material Although articles such astubes, rods, and flat sheets can be made by extrusion, an extruder is often coupledwith other polymer processing machinery A knowledge of extrusion is therefore

a prerequisite for studying other polymer processing operations Note thatextrusion is a continuous operation As opposed to this, injection molding is acyclic operation used to make a very wide variety of low- and high-technologyitems of everyday use It is now also being used to fabricate ceramic heat enginecomponents, which have complex shapes and are useful for high-temperatureapplications Ceramics such as silicon carbide and silicon nitride are hard,refractory materials, and injection molding is one of the very few processesthat can be used for the purpose of mass production Fiber spinning is studied notonly because it is the mainstay of the synthetic textiles industry but also because it

is used to make novel fibers out of liquid-crystalline polymers, graphite, glass,and ceramics for use in composite materials It is also a process where polymerelasticity becomes important due to the extensional nature of the flow field Incontrast, extrusion and injection molding are shear-dominated processes.Although this is the last chapter of the book, it is really an introduction tothe very practical and fascinating topic of manufacturing items made frompolymeric materials The major purpose of this chapter is to describe thesethree operations and also to show how first principles are used to mathematicallysimulate these or any other process Such analyses are a sine qua non forimproving product quality, for designing new products, and for process optimiza-tion The material presented here is necessarily simplified, and we have restrictedourselves wherever possible to steady-state and isothermal operations; extensions

to more realistic situations are conceptually straightforward, and we haveprovided citations of the appropriate technical literature For more details onthe process of constructing mathematical models, the reader is directed to theexcellent book by Denn [1]

the polymer being processed is hygroscopic, it is usually dried beforehand and thehopper is blanketed by a dry inert gas such as nitrogen Although the barrel isheated to a temperature above the melting point of the polymer, the region veryclose to the base of the hopper is often water cooled to prevent polymer frommelting in the hopper and forming a solid plug, which would block additionalpolymer from entering the extruder The rotation of the screw forces the polymer

to move along the channel, and it does so initially as a solid plug, then as asemisolid, and, finally, as a melt The channel depth is usually fairly large in thesolids-conveying zone and it decreases progressively as the polymer melts andultimately becomes constant in the melt zone Although it is convenient to think

in terms of these three separate zones and the screw geometry often reflects thisthinking, it is probably true that the processes of solids conveying, melting, andmelt pressurization occur simultaneously For the purposes of analysis, though,

we shall still treat the three zones separately Of course, if the extruder is feddirectly by a polymerization reactor, as happens during the manufacture ofsynthetic textiles by melt spinning, the solids-conveying and melting zones areabsent Only the melt zone remains; it is also called the metering zone

The purpose of any mathematical model of steady-state extrusion is torelate quantities such as energy dissipation, the volumetric flow rate, the meltingprofile, the temperature profile, and the pressure profile to the extruder geometry,

to the processing variables such as barrel temperature and screw rpm, and to thematerial properties of the polymer In order to accomplish this task, we also need

to know the details of the die that is attached to the extruder Because the process,

in general, is nonisothermal and the rheological models are nonlinear, analyticalsolutions cannot be obtained for realistic cases of interest Invariably, numericaltechniques of solution have to be used Here, though, we will consider thesimplest possible cases with a view toward both elucidating the physics of theproblem and illustrating the approach to be taken for problem solving Analyses

for more realistic situations are available in the literature; here, the mathematics ismore complicated, but the basic approach is the same It should be realized,though, that the process of determining the screw geometry to yield desiredextruder performance is much more difficult than determining extruder perfor-mance for a given geometry.

A section of a simplified screw is shown in Figure 15.2 to define the variables thatcharacterize the screw geometry [3] The notation used is that of Tadmor andKlein [3] The inside diameter of the barrel is Db, whereas the screw diameter isD; both of these quantities can range from 1 to 12 in A typical value of the ratio

of the screw length to its diameter is 24 The channel depth is H , and it is clearfromFigure 15.1that both H and D vary with axial position The radial clearancebetween the tip of the flights and the inner surface of the barrel is df, and L is theaxial distance moved by the screw during one full revolution The width of thescrew flight in the axial direction is b, and the width in a direction perpendicular

to the flight is e Finally, W is the distance between flights measured cular to the flights, and y, the helix angle, is the angle between the flight and theplane perpendicular to the screw axis In general, y, b, and W vary with radialposition; nonetheless, we will take them to be constant We will also assume that

perpendi-df is negligible and that there is no leakage of material over the flights Also, forpurposes of analysis, we will assume that Db is approximately the same as D

To begin the analysis, we recognize that flow occurs because friction at thesurface of the barrel makes the plastic material slide down the channel and gotoward the extruder exit as the screw is rotated This motion of a material element,resulting from the relative velocity between the barrel and the screw, can be

FIGURE15.2 Line a–a indicates a cut perpendicular to the flight at the barrel surface.(From Ref 3.)

studied more easily by allowing the barrel to rotate in a direction opposite to that

of screw rotation and holding the screw stationary Further, if we realize that thecurvature of the screw is hardly felt by the polymer, we can consider that thepolymer is moving down a long, rectangular cross-sectional channel due to themovement of the upper surface This is shown in Figure 15.3 In effect, we canunwind the channel and use Cartesian coordinates for the analysis

This is the region from the point at which material enters the hopper to a point inthe extruder channel where melting begins Although a large number of modelshave been proposed to determine the flow rate of solids in this region, theaccepted analysis is that of Darnell and Mol [4], which is presented here insimplified form

As polymer pellets move down the channel, they become compacted into aplug that moves at a velocity Vp in the down channel or z direction In general,there is slip between the plug and both the barrel and screw surfaces The barrelmoves at a velocity Vb, which in magnitude equals pDN , where N is therevolutions per unit time of the screw; this velocity vector makes an angle y tothe down-channel direction Clearly, the velocity of the barrel relative to the plug

is (Vb
Vp) and it makes an angle (y þ f) to the z direction; this is the angle atwhich the barrel appears to move for an observer moving with the plug.With reference to Figure 15.4, we have

tan f ¼ Vpl Vb
Vpl

tan y

 
1

ð15:2:1Þ

where Vplis the component of the plug velocity along the screw axis Thus,

where fbis the coefficient of friction between the plug and the barrel surface, p isthe isotropic pressure within the plug, and dz is the thickness of the plug Apressure gradient develops across the plug and the force due to this is as follows:

FIGURE15.4 Diagram showing the different velocity vectors

As will be evident later, dp is a positive number, so pressure increases withincreasing z.

Normal forces act on the plug at the flights due to the presence of theisotropic pressure Thus, we have

The normal force that acts on the other flight is

where F* is a reaction force

Finally, there are friction forces on the two flights and on the screw surface,

as shown in Figure 15.5 Their magnitudes are as follows:

F1sin f þ ðF6
F2Þ sin y
ðF7
F8Þ cos y þ ðF3þ F4þ F5Þ sin y ¼ 0

ð15:2:12Þ

FIGURE15.5 Forces acting on the solid plug (From Ref 3.)

Introducing expressions for the various forces into Eq (15.2.12) andrearranging, we find that

We began this analysis seeking the angle f so that we could calculate thesolids-conveying rate from Eq (15.2.4) Now, f is found to be given implicitly in

an extruder?

Solution: The flow rate is maximum when there is no obstruction at the extruderexit (i.e., Dp ¼ 0) and when there is no friction between the polymer and thescrew surface Under these conditions, Eq (15.2.12) becomes

In closing this section we mention that Chung has observed that the model

of Darnell and Mol is strictly valid only up to the point that the polymer begins tomelt [7] Because the barrel temperature is kept above the melting point of thepolymer, a layer of liquid forms fairly quickly and coats the solid plug As aconsequence, Eqs (15.2.5) and (15.2.9)–(15.2.11) have to be modified and theforces F1, F3, F4, and F5 calculated using the shear stress in the molten polymerfilm A result of this modification is that f becomes a function of the screwrevolutions per minute (rpm) [7,8] We also mention that Campbell and Dontulahave proposed a new model that does not require us to assume that the screw isstationary [9] This model appears to give better agreement with experimentaldata

15.2.3 Melting Zone

Melting of the polymer occurs due to energy transfer from the heated barrel andalso due to viscous dissipation within the polymer itself This melting does nothappen instantly but takes place over a significant part of the screw length Thepurpose of any analysis of the melting process is to predict the fraction ofpolymer that is melted at any down-channel location and to relate this quantity tomaterial, geometrical, and operating variables

Maddock [10] and Tadmor and Klein [3] studied the melting process by

‘‘carcass analysis’’: They extruded colored polymer and stopped the extruderperiodically By cooling the polymer and extracting the screw, they could trackthe progress of melting and also determine the sequence of events that ultimatelyresulted in a homogeneous melt They found that a thin liquid film was formedbetween the solid bed of the polymer and the barrel surface This is shown inFigure 15.6 Because of the relative motion between the barrel and the polymerbed, the molten polymer was continually swept from the thin film in the xdirection into a region at the rear of the bed between the flight surface and thebed Liquid lost in this manner was replaced by freshly melted polymer so that thefilm thickness d and the bed thickness both remained constant As meltingproceeded, the solid polymer was transported at a constant velocity Vsyto the thinfilm–solid bed interface and, correspondingly, the bed width X decreased withincreasing down-channel distance

A large number of models, of varying degrees of complexity, exist forcalculating X as a function of distance z [3,8,11,12] In the simplest case, it isassumed that the solid polymer is crystalline with a sharp melting point Tmand alatent heat of fusion l and that the molten polymer is a Newtonian liquid It is alsoassumed that the solid and melt physical properties such as the density, specific

FIGURE15.6 Melting of a polymer inside the extruder (From Ref 2.)

jVjj2¼ jVbj2þ jVszj2
2jVbkVszj cos y ð15:2:25Þ

If we now consider a coordinate system xyz with its origin located at thesolid bed–melt interface (see Fig 15.6) and moving with a velocity Vsz, thedifferential form of the energy balance as applied to the melt film is given by

, provided thatthis is considered to be a flow between two infinite parallel plates

Integrating Eq (15.2.26) twice with respect to y and using the conditions

T ð0Þ ¼ Tmand T ðdÞ ¼ Tb gives the following:

For the purpose of integrating Eq (15.2.29), it is assumed that thetemperature far away from the interface at y ¼
1 is the screw temperature

Ts Because T ð0Þ is Tm, then, we have within the solid bed

qy2¼
ks dT

dyð0Þ ¼
rscsVsyðTm
TsÞ ð15:2:31ÞThe difference in heat fluxes across the interface represents the energy needed tomelt the polymer per unit time per unit interface area Thus, we have

jqy1j
jqy2j ¼ Vsyrsl ð15:2:32ÞIntroducing Eqs (15.2.28) and (15.2.31) into Eq (15.2.32) gives

Vsyrsl ¼km

d ðTb
TmÞ þZv2

2d
rscsVsyðTm
TsÞ ð15:2:33Þwhich involves two unknowns, d and Vsy

An additional relation between d and Vsyis needed, and this is obtained byproposing that the mass that enters the melt film in the y direction from the solidbed all leaves with the melt in the x direction Consequently, we have thefollowing:

d ¼ 2kmðTb
TmÞ þ Zv2

Vbxrm½csðTm
TsÞ þ l

X1=2¼ c1X1=2 ð15:2:35Þ

where the constant c1 is defined by Eq (15.2.35)

The polymer that melts has to come from the bed of the solid polymerwhose width X decreases with down-channel distance This change in width isobtained from a mass balance on the solid polymer as follows:

The foregoing analysis combines experimental observations with mentals of transport phenomena to analytically relate X to z It is obviously quiterestrictive Given the known behavior of polymeric fluids, we can immediatelythink of a number of modifications, such as making the shear viscosity in Eq.(15.2.26) depend on temperature and shear rate We can also relax the assumptionthat T ð
1Þ ¼ Ts and assume that the screw is adiabatic [13] These modifica-tions have all been done, and the results are available in the literature Themodifications bring model predictions closer to experimental observations butalso necessitate numerical or iterative calculations The various melting modelshave been reviewed by Lindt [14]

funda-Finally, we note that there is usually a region preceding the melting zonewherein a melt film exists but in the absence of a melt pool This is called thedelay zone; its length is small, typically one to two screw turns [11] Empiricalcorrelations exist for estimating the extent of the delay zone [3]

The completely molten polymer entering the melt zone is usually pressurizedbefore it leaves the extruder Pressure builds up because relative motion betweenthe barrel and the screw forces the polymer downstream, but the exit is partiallyblocked by a shaping die In modeling this zone, we are interested in relating thevolumetric flow rate to the screw rpm and in calculating the pressure rise for agiven volumetric flow rate This is fairly easy to do if we take the polymer to beNewtonian and the melt conveying process to be isothermal All that we have to

do is to solve the Navier–Stokes equation in the z direction for the flow situationshown earlier in Figure 15.3 Whereas the z component of the barrel velocitycontributes to the volumetric flow rate out of the extruder, the x componentmerely causes recirculation of fluid, because there is no leakage over the flights

Because polymer viscosities are usually very large, the Reynolds numbers aresmall and we can safely neglect fluid inertia in the analysis that follows Inaddition, we can take pressure to be independent of y because the channel depth isvery small in comparison to both the width and length The simplified form of the

z component of the Navier–Stokes equation is as follows:

Introducing Eq (15.2.41) into Eq (15.2.42) gives

Q ¼VbzHW

2
WH312Z

Solution: In the absence of a die,Dp is zero and Eq (15.2.43) predicts that

Q ¼p  5:03  N cosð6:3Þ  0:36  1:1

2

¼ 3:11N cm3=secand the result does not depend on the shear viscosity of the polymer

The experimental results of Campbell et al., along with the theoreticalpredictions, are shown inFigure 15.7[15] Although the measured output varies

linearly with N as expected, the theory overpredicts the results This happensbecause the theory is valid for an infinitely wide channel, whereas there isactually just a finitely wide channel To correct for the finite width, we multiplythe theoretical output by the following correction factor [15]:

Fd ¼16W

p3H

P 1

i3tanh ipH2W

 

ð15:2:44Þ

which, for conditions of Example 15.2, has a value of 0.82 Excellent agreement

is found with data when this correction is applied, and the line marked ‘‘correctedtheory’’ passes through all the data points in Figure 15.7 Interestingly enough,this perfect agreement between theory and practice is not obtained when theextruder is operated with the barrel stationary and the screw moving Campbell et

al ascribe this to the small contribution made to the flow by the helical flights[15] They have proposed a theory that takes this contribution into account andeliminates the mismatch [15]

The flow rate calculated in Example 15.2 is the maximum possible flow ratethrough the extruder In general, the extruder is equipped with a die whose shapedepends on whether the end product will be rods, tubes, fibers, or flat films Inthis case, the Dp in Eq (15.2.43) is nonzero and positive To obtain thevolumetric flow rate now, we need an independent equation for the pressurerise; this is developed by considering the flow of the polymer through the die ForNewtonian liquids, we can easily show that the volumetric flow rate through the

FIGURE15.7 Theoretical and experimental flow rate for barrel rotation (From Ref.15.)

die has to be proportional to the pressure drop across the die For the fullydeveloped flow through a rod die (a tube), for example (see Chap 14), we have

If you read the previous section again, you will realize that the change inpressure across the melting zone remains an unknown quantity Because the meltpool geometry is similar to the screw channel geometry, the pressure rise iscalculated by again solving the Navier–Stokes equation

In order to predict extruder performance, we have to solve the equationsdescribing the three different extruder zones in sequence This is becauseinformation generated in one zone is an input for a different zone Even then,the solution is iterative [16] We begin by assuming the mass flow rate andcalculating the pressure change across each zone for a specified rpm If thecalculated pressure at the die exit, obtained by adding up the individual pressuredrops, differs from atmospheric, we guess the flow rate again and repeat thecomputations until agreement is obtained Typical pressure profiles for theextrusion of polyethylene through a 4.5-cm diameter extruder are shown in

Figure 15.8 It can sometimes happen, due to the nonlinear nature of theequations involved, that there is more than one admissible solution This impliesthe existence of multiple steady states, which can be the cause of surges inthroughput as the extruder cycles between different steady states

In any proper extruder simulation, we also must take into account thenonisothermal nature of the process, because a significant amount of heat isgenerated due to viscous dissipation In addition, we cannot ignore the shear-thinning behavior of the molten polymer All this, along with the iterative nature

of the calculations, mandates the use of a computer However, it is possible toobtain reasonable answers to fairly realistic steady-state problems using just apersonal computer [2] Using computer models of the type described byVincelette et al [2], it is possible to try to optimize extruder performance withrespect to energy consumption or temperature uniformity or any other criterion ofinterest Note again, though, that in this brief treatment of single-screw extrusion,

we have not considered phenomena such as leakage flow over the flights and thevariation of the coefficient of friction between the polymer and the extrudersurface We have also not accounted for complexities arising from features such

as extruder venting, a variable channel depth, and the change in parameters (such

as the helix angle) with axial position For a discussion of all these effects, thereader is referred to advanced texts on the subject [3,6,17].

A single-screw extruder is an excellent device for melting and pumping polymers,but it is not an efficient mixer due to the nature of the flow patterns inside theextruder channels During polymer processing, however, we often need to do thefollowing:

1 Blend in additives such as pigments, stabilizers, and flame retardants

2 Add fillers such as carbon black, mica or calcium carbonate

3 Disperse nanofillers such as montmorillonite and carbon nanotubes

4 Mix elastomers such as ABS or EPDM that act as toughening agents

5 Put in reinforcements like short glass fibers

6 Make polymeric alloys using two miscible plastics

7 Carry out reactive extrusion for the synthesis of copolymers

For all of these purposes, it is generally desirable that the dispersed phaseleaving the extruder be in the form of primary particles (not agglomerates), ifsolid, and that it have molecular dimensions, if liquid Also, it is necessary thatthe concentration of the dispersed phase be uniform throughout the mixture; this

is a particularly challenging proposition when the process has to be run in a

FIGURE15.8 Predicted and experimental pressure profiles N ¼ 1 (1), 0.8 (2), 0.6 (3),0.4 (4), 0.2 (5) min
1 (From Ref 2)

continuous manner and the dispersed phase is only a small volume fraction of thetotal mixture.

A simple method of providing mixing in a single-screw extruder, especiallyfor liquid–liquid systems, is by introducing mixing pins that are a series ofobstacles protruding from the screw surface; these force the polymer stream todivide and recombine around the pins Alternately, one may add mixing devices

to the end of the extruder These devices may be motionless, or they may havemoving parts such as in the case of kneading gears Motionless mixers or staticmixers consist of blades or obstructions that are placed lengthwise in a tube,forming open but intersecting channels [18] When the extruder forces liquid toflow through these channels, the melt has to go around the obstacles andrecombine periodically, and this ultimately leads to a very homogeneous mixture

A recent innovation in static mixer technology has been the development of theextensional flow mixer [19] Here, material is made to flow through a series ofconverging and diverging regions of increasing intensity This again results in afine and well-dispersed morphology, but at the expense of a higher pressure drop.Note that a single-screw extruder in combination with a static mixer is well suitedfor the manufacture of polymer alloys or blends and for making color concen-trates or master batches

An immense amount of plastic, particularly nylon, polycarbonate, andpolyester, is compounded with short glass fibers The addition of up to 40 wt%glass to the polymer significantly increases the heat distortion temperature andallows the compounded product to be used for under-the-hood automotiveapplications The process of compounding polymers with glass fibers is typicallycarried out with the help of twin-screw extruders; multiple strands of the glass-filled resin are extruded into a water bath and then cut, often under water, to givepellets that are ready for injection molding into finished products As the nameimplies, a twin-screw extruder (TSE) has two screws which are generally parallel

to each other, but, unlike single-screw extruders, the screw diameter here does notvary with axial position If the screws turn in opposite directions, we have acounterrotating TSE, whereas if the two rotate in the same direction, we have acorotating TSE Shown in Figure 15.9is the top view of a corotating machine[20]; this is a fully intermeshing extruder because the two (identical) screws aresituated as close to each other as possible Note that the counterrotating geometryfeatures screws having leads of opposite hands A beneficial consequence ofintermeshing screws is that, during extruder operation, each screw wipes theentire surface of the other screw The polymer can, therefore, not remain insidethe extruder for long periods of time, and thermal degradation is prevented Theresidence time distribution is narrow, and the residence time can be made as short

as 5–10 sec [21] Flushing the extruder between different product grades istherefore quick and easy

If the screw cross section is circular and the screws are intermeshing, thebarrel cross section has to be a figure 8, and this is shown inFigure 15.10 Here,each screw has three tips (i.e., it is trilobal), although newer extruders are bilobal.The intermeshing nature of the screws dictates the channel geometry, and, if wesection a screw parallel to its axis, the channel shape that results is the onepresented inFigure 15.11 The channel shape changes as we change the number

of tips (parallel channels), and this affects the average shear rate in the channeland the mixing characteristics of the extruder Each screw of a corotating TSE isassembled by sliding a number of modular elements on to a shaft in a desiredsequence and then locking the elements in place Two of the basic elements thatmake up any screw are screw bushings (also called conveying elements) andkneading disks When conveying elements are employed, the screws look likethose shown in Figure 15.9 If we unwind the channels of trilobal conveyingelements, we get five parallel channels as shown inFigure 15.12 As the screwsturn, the polymer is conveyed from one screw to the other and back, and the flow

is very much a drag flow, quite like that in a single-screw extruder

The reason that a TSE is considered to be superior to a single screwextruder is due to the mixing provided by the presence of kneading disks A

FIGURE15.9 Cut-away view of a self-wiping, corotating twin-screw extruder (FromRef 20.)

collection of kneading disks is known as a kneading block (KB), and a typical KB

is shown inFigure 15.13 [22] A KB consists of a number of disks having thesame cross section (or number of lobes) as the conveying elements but stucktogether at different stagger angles The result may be looked upon as aconveying element having a helix angle of 90 Material is sheared and severelysqueezed as it goes through the KB, and the extent of deformation can becontrolled by varying the number of disks, their width, and the stagger angle.Indeed, by changing the nature and location of the different elements, we can alterthe ‘‘severity’’ of the screw This is what makes a corotating twin-screw extruder

FIGURE15.10 Cross-sectional view of a three-tip screw in a self-wiping, corotatingtwin-screw extruder (From Ref 20.)

FIGURE15.11 Channel configuration corresponding toFigures 15.9and15.10 (FromRef 20.)

so versatile Note that TSEs allow for multiple feeding ports at different locations

on the barrel so that glass, for example, may be introduced after the polymer hasmelted and also for the application of vacuum for purposes of devolatalization.Also, a TSE is typically ‘‘starve-fed,’’ and there is no relation between the screwrpm and the extruder throughput In other words, we do not use a hopper to feedthe extruder Instead, a single-screw device feeds solid polymer to the TSE at anydesired rate, and as a consequence, the conveying channels of the TSE are onlypartially filled with polymer; the degree of fill is typically 25–50%, and it changes

as the screw pitch changes There is, therefore, no pressurization of melt in thescrew bushings A consequence of this is a decoupling of the different parts of theextruder, and what happens in one portion of the extruder does not instantly affectwhat happens in another portion of the extruder Through the KBs, though, theconveying capacity is small, material backs up, and in the region before the KBthe degree of fill reaches 100% Here, the polymer gets pressurized, and it is thisincrease in pressure that forces the polymer to go through the kneading disks Foradditional details, we refer the reader to excellent books on the topic [6,21,23]

FIGURE15.12 Unwound channels of three-tip screw elements Arrows show themotion of the fluid as it is transferred from one screw to the other in the intermeshingregion (From Ref 20.)

15.3 INJECTION MOLDING

One of the conceptually simplest methods of fabricating a plastic component,though complex in geometry, is to make a mold or cavity that is identical in shapeand size to the article of interest and to fill it with a molten polymer, which thensolidifies and yields the desired product This is the essence of the process ofinjection molding, and machines are now available that can mass produce itemsranging in weight from a fraction of an ounce to several pounds and do so withlittle or no human intervention As a consequence, production costs are low, butstart-up costs can be high due to the high costs of both the injection-moldingmachine and the molds themselves The process is versatile, though, and can

be used to mold thermoplastics as well as thermosets In addition, fillers can beadded to make high-strength composite materials and foaming agents can

FIGURE15.13 Isometric view of a bilobal kneading block (From Ref 22.)

tered are polymethyl methacrylate for lenses and light covers, and polycarbonatesand ABS for appliance housings and automobile parts.

As shown in schematic form in Figure 15.14, an injection-molding machine

is essentially a screw extruder attached to a mold The action of the extruderresults in a pool of molten polymer directly in front of the screw tip, and thiscauses a buildup in pressure that forces the screw to retract backward Once apredetermined amount of polymer (the shot size) has been collected, screwrotation stops and the entire screw moves forward like a plunger pushing materialinto the mold This type of machine is therefore known as a reciprocating-screwinjection-molding machine Once the polymer has solidified, the mold is opened,

FIGURE15.14 In the CINPRES I process, a controlled volume of inert gas free N2) is injected through the nozzle into the center of the still-molten polymer (FromRef 24.)

(oxygen-the part is removed, and (oxygen-the cycle of operations is repeated Typical cycle timesrange from a few seconds to a minute Injection-molding machines are normallydescribed in terms of the screw diameter, the maximum shot size in ounces, andthe force in tons with which the mold is clamped to the injection unit of themachine.

A mold is typically composed of two parts, called the cavity and the core.The cavity gives the molding its external form, whereas the core gives it theinternal form This is seen in Figure 15.15, which shows a mold used to make aplastic tumbler It is clear that an empty space having the shape and size of thetumbler is formed when the cavity and core are clamped together Most moldsdesigned for long service life are made from alloy steels and can cost several tens

of thousands of dollars To consistently make moldings having the correctdimensions, it is necessary that the mold material be wear resistant and corrosionresistant and not distort during thermal cycling; chrome and nickel plating arecommon Details of mold design and of the mechanical aspects of opening andclosing molds and ejecting solidified parts are available in the book by Pye [25].Note that most molds are water-cooled Also, a mold frequently has multiplecavities

The melt that collects near the reciprocating screw leaves the injection unitthrough a nozzle that is essentially a tapered tube, which is often independentlyheated [26] and may also contain a screen pack The simplest way to connect thenozzle to the mold shown in Figure 15.15 is through the use of a sprue bush,which is another tapered passage of circular cross section, as shown in Figure

15.16 For multicavity molds, however, we need a runner system to join the sprue

to the gate or entry point of each cavity Because we want all the cavities to fill up

at the same time, the runners have to be balanced; one possible arrangement is

FIGURE15.15 A simple mold

shown inFigure 15.17 The runner system should be such that the cavities fill uprapidly with a minimum amount of pressure drop, and this suggests the use of alarge cross-sectional area At the same time, though, we want the material in therunner to solidify quickly after mold filling, and this is possible if the runner crosssection is small It can, however, not be so small that the runner freezes before themold is full, because this results in a useless molding called a short shot Forthese reasons and the fact that the polymer in the runner has to be removed withthe molding and recycled, the actual runner length and diameter are a compromisemeant to satisfy conflicting requirements Similarly, the gate diameter has to besmall for ease of runner removal but large enough that the high shear rates andviscous heating in the gate region do not result in thermal and mechanicaldegradation of the melt.

If we monitor the pressure at the gate as a function of time duringcommercial injection molding, we typically get the result shown in Figure

15.18, so that the overall process can be divided into three distinct stages Inthe first stage, the mold fills up with polymer and there is a moderate increase inpressure Once the mold is full, the second stage begins and pressure risesdrastically in order that additional material be packed into the mold to compen-sate for the shrinkage caused by the slightly higher density of the solid polymerrelative to the melt Finally, during the cooling stage, the gate freezes and there is

a progressive reduction in pressure As Spencer and Gilmore explain, if flow intothe mold did not take place during the packing stage, the formation of a solidshell at the mold walls would prevent the shrinkage of the molten polymer inside[27] Stresses would then arise, leading to the collapse of the shell and theformation of sink marks If the shell were thick enough to resist collapse, aAddison Wesley Longman Ltd.)

vacuum bubble would form and, in any case, some of the thermal stresses wouldremain in the molded article A consequence of the frozen-in stress would be thatdimensional changes could occur on raising the temperature of the molding.Even though the presence of the packing stage eliminates thermal stresses,this is a mixed blessing This is because polymer chain extension and orientationoccur along with flow during the packing part of the cycle Unlike that during thefilling stage, this orientation is unable to relax due to the increased melt viscosityand attendant large relaxation times resulting from cooling The orientationtherefore remains frozen-in and leads to anisotropic material properties Inaddition, dimensional changes again take place on heating, and the materialtends to craze and crack much more easily The packing time is therefore picked

FIGURE15.17 Feed system: (a) typical shot consisting of moldings with sprue, runner,and gates attached; (b) section through feed portion of mold (From Pye, R G W.:Injection Mould Design, 4th ed., Longman, London, 1989 Reprinted by permission ofAddison Wesley Longman Ltd.)

to minimize stresses resulting from both quenching and polymer chain tion A further level of complexity arises if the polymer is crystallizable Becausethe rate and nature of crystallization depend on the thermal and deformationalhistory, different morphologies can be obtained, depending on how the moldingcycle is run, and this can endow the molding with totally different physicalproperties.

orienta-The major machine variables in injection molding include the melttemperature, mold temperature, injection speed, gate pressure, the packingtime, and the cooling time The interplay of these variables determines thepressure, temperature, and velocity profiles within the mold and the position andshape of the advancing front during mold filling These field variables, in turn,determine the structure that is ultimately witnessed in the molded part Anymathematical model of injection molding is therefore directed at calculating thevalues of the primary microscopic variables as a function of time during themolding cycle This is done by examining the three stages of the injectionmolding cycle separately Given the complexity of the process, this is not an easyjob Nonetheless, we shall try to illustrate the procedure using a simplerectangular mold geometry

White and Dee carried out flow visualization studies for the injection molding ofpolyethylene and polystyrene melts into an end-gated rectangular mold [28].Experiments were conducted under isothermal conditions and also for situationswhere the mold temperature was below the polymer glass transition temperature

or the melting point, as appropriate The apparatus used was a modified capillaryrheometer in which, instead of a capillary die, a combined-nozzle mold assemblywas attached to the barrel, as shown inFigure 15.19 The mold could be heated to

any desired temperature and it had a glass window that permitted observation ofthe flow patterns within Results for the flow-front progression and the streamlineshape are displayed in Figure 15.20 for isothermal experiments conducted at

200C Here, the fluid was injected slowly and there was no influence of thepolymer type In each case, there was radial flow at the gate and, once the cornerswere filled, the front shape became almost flat and this front moved forward andfilled the mold The corresponding results for injection into a cold mold at 80Care shown inFigure 15.21[28] Now, the front is much more curved and there ispronounced outward flow toward the mold wall In addition, because of theincrease in polymer viscosity resulting from cooling, stagnant regions develop incorners and near the mold wall

To a good approximation, most of the polymer that flows into the mold can

be considered to be flowing in almost fully developed flow between two parallelplates For this situation, the melt at the midplane moves at a velocity that isgreater than the average velocity At the front, however, the fluid not only has to

FIGURE15.19 Injection-molding apparatus (From Ref 28.)