Injection Molded Semicrystalline

Polymers: Structure Development and

Modeling

A variety of molding processes is used commercially,including injection, compression, transfer, blow, androtational molding. Which process is employed de-pends largely on the design, final application, andrequirements of the finished product. Among thesemolding processes, the most important commerciallyis injection molding. In this process, molten polymersare injected under high pressure into a cold moldcavity in the case of thermoplastics, or into a heatedmold cavity in the case of thermosets. With thermo-plastics, cooling continues until the material hassolidified sufficiently to permit ejection of the moldedproducts from the mold without damage. Therefore insemicrystalline polymers the final products have com-plex distributions of crystalline morphology, such asskin-core structure. Skin-core structure is the typicalcross-sectional morphology of an injection moldedpolymer. Recently, computer-aided-engineering(CAE) has become a powerful tool for investigatingprocess analysis. CAE is useful for optimizing themolding conditions, and for helping in the design ofthe molds, and has several other functions such as flowanalysis, packing and cooling analysis, warpage analy-sis, etc. These analyses of semicrystalline polymerssometimes give poor reliability, due to complex distri-butions of crystalline morphology. Therefore it isnecessary to develop a simulation of crystallization inthe injection molding process. Furthermore, thiscrystallization simulation may clarify the mechanismof crystallization in the injection process.

1. Injection Molding Sequence and Technique

Injection molding machines consist of two basiccomponents: the injection unit and the clamping unit.The material is heated and melted by the injectionunits, and it is transferred under high pressure into amold, which is held shut by the clamping unit. Atypical operating sequence starts with the feeding ofthe material by gravity from a hopper, the screw beingin the forward position. The rotation of the screwplasticizes the material and conveys it forward in thescrew barrel. Accumulation of the molten material atthe front of the screw tip forces the screw backwards.After the injection unit is activated, the screw movesforward, pushing the materials from the injection unit,through a nozzle, into the mold. Usually, the injectionmolding cycle may be considered to consist of threestages: filling, packing, and cooling. During the fillingstage, the polymer melt is filled within a short injectiontime into an empty cavity of the mold, which is fixedby the clamping unit. After filling is completed, moremolten polymer is then packed into the cavity at high

pressure to compensate for shrinkage as the materialcools. Cooling continues after packing is completed.During the cooling stage, the material solidifies andthe pressure decreases. The cycle continues untilenough rigidity is achieved to permit ejection of thepart without damage. The cycle is repeated to producethe next part.

Normally, commercial injection molding involvesmold cavities of complex geometry, sometimes withinserts, and a variety of obstructions to direct the flow.The gates in the mold may be located at variouspositions, and can have a multitude of shapes anddimensions. In some cases, multiple gates are em-ployed to fill a single mold cavity. All these arrange-ments may have a profound influence on the dynamicsof the molding process and on the ultimate character-istics of the molded articles. In particular, somemolding arrangements lead to the formation of weldlines in regions where melt fronts intersect inside thecavity. Unless carefully manipulated and controlled,weld lines can represent very weak areas in themolding, leading to premature failure.

2. Structure Development

While the polymer melt passes through very narrowpassages of the injection mold such as sprues, runners,gates, and cavities, polymer chains undergo defor-mation under the high shear stress and rapid coolingnear the mold surface. Thus, injection molded partsproduced from semicrystalline polymer melts exhibit acomplex distribution of crystalline morphology. Toclarify the mechanism of formation of these complexstructures in injection molded products, we need toconfirm the basic characteristics of polymer meltsunder shear and elongation, e.g., planar, uniaxial, andbiaxial, and to understand the crystallization mech-anism. According to the characteristics of the crystal-lization kinetics of semicrystalline polymers, thesepolymers can be classified into two categories: fastcrystallizing polymers, e.g., polyethylene, polypropyl-ene (PP), polyamide, polyoxymethylene, etc.; andslowly crystallizing polymers, e.g., poly(ethylene tere-phthalate) (PET), poly(phenylene sulfide), poly(ethyl-ene 2,6-naphthalene dicarboxylate), etc., A typicalcross-sectional morphology by optical microscopy ofan injection-molded PP part is given in Fig. 1(a). Themolded PP parts possess an oriented skin layer and aspherulitic core. Between these two regions, an in-termediate morphology of ellipsoidal spherulites isobserved.

The general observations described above wereconfirmed by the studies of Kantz et al. (1972) andKatti and Schultz (1982) on PP molded bars, usingoptical microscopy and wide-angle x-ray scattering(WAXS). In particular, the c-axes and a*-axes werefound to be bimodally oriented to the mechanicaldirection (MD), and the b-axes rotated around theMD, in the skin layer; and the c-axis and a*-axis

1

Injection Molded Semicrystalline Polymers: Structure Development and Modeling

Figure 1Polarizing light micrographs of the morphology of (a) polypropylene, and (b) poly(ethylene terephthalate) parts: cross-section of rectangular molded parts at 75mm from the gate. Both samples molded at injection speed of 2.5cm$s−", andmold temperature in the case of polypropylene and poly(ethylene terephthalate) is 40 and 64°C, respectively.

orientation to the MD was weak, and the b-axesrotated around the MD, in the core layer. Fujiyama(1995) also reported the crystalline structure of aninjection molded polypropylene with filler and somenucleating agents dealing with the effect of moldingconditions. The molecular orientation as a function ofproduct depth was analyzed, using WAXS and infra-red spectroscopy. It was found that the sub-skin layer,which means the intermediate layer between skin andcore layer, had maximum orientation. This molecularorientation within the sub-skin layer was stronglyinfluenced by molecular weight, and the sub-skin layerindicated low molecular orientation in the case of lowmolecular weight (Trotignon and Verdu 1987).

Polyoxymethylene molded products have also beeninvestigated, and the observations were similar tothose of PP. Decreasing mold wall temperatureincreased the extent of the oriented regions and de-creased the amount of spherulites. Transmissionelectron microscopy (TEM) and small-angle x-rayscattering (SAXS) examinations of these injectionmolded parts confirmed the oriented character of theouter layers. The results have been used to develop amorphological model of the molded parts in terms offolded chain lamellae, randomly oriented in the centerof the pot, and oriented with chains in the flowdirection in the outer layers.

The morphology of slowly crystallizing polymerssuch as poly(phenylene sulfide), poly(ethylene 2,6-

naphthalene dicarboxylate), and syndiotactic poly-styrene (Ulcer et al. 1996) were investigated. Thesepolymers have high glass transition temperature aboveroom temperature, and high flow activation energythat arises from a primary molecular structure con-taining aromatic groups. A typical cross-sectionalmorphology of an injection molded PET part is givenin Fig. 1(b). Amorphous–crystalline–amorphousmulti-layer structures in PET were observed in thegap-wise direction in the case of low injection speedand comparatively low mold temperature. Thesestructural features were found to be very sensitive tocooling rate and shear stress effects.

3. Modeling

3.1 General Equation in the Injection MoldingProcess

Ideally, engineering analysis, mathematical modeling,or computer simulation of the injection moldingprocess should permit the treatment of flow and heattransfer phenomena in complex injection moldingcavities. Modern finite element numerical techniquesmake this possible. Even with the finite elementmethod, the polymers, molds and phenomena in-volved are so complex that simplification is essential.

One common approach involves the mold networkmethod. According to this method, the complex mold

2

Injection Molded Semicrystalline Polymers: Structure Development and Modeling

cavity is divided into a number of units of reasonablysimple geometry (e.g., rectangular, circular, or cyl-indrical segments). The solutions for the melt behaviorin each of the simpler units are treated separately andare sometimes readily available in graphical, numeri-cal, or analytical forms. To obtain the overall solutionfor the complete cavity, the solutions for the individualcomponents of the network are coupled and dovetailedto ensure the systematic integration of the results fromeach segment. Recently, commercial software for theanalysis of injection molding process has been de-veloped with the finite element method or the finitedifference method. It is useful for optimizing themolding conditions and for aiding in the design of themolds.

The filling stage is concerned with the unsteady-state flow of a hot, compressible, viscoelastic melt intoan empty cavity, which is held at a temperature belowthe solidification temperature of the melt. In this sense,the process can be fully described in terms of theequations of conservation of mass, momentum andenergy, coupled with appropriate thermodynamicrelationships and a set of constitutive relations whichdescribe the behavior of the material under theinfluence of stress and thermal fields. In generaltensorial formulation, the conservation equations areas follows.

Continuity:

Dρ

Dt¯®ρ(~[ ν) (1)

Momentum:

ρDν

Dt¯®~P®(~[ τ)­ρg (2)

Energy:

ρCv

DT

Dt¯®(~[ q)®T

E

F

¦p

¦T

G

H ρ

(~[ ν)®(τ:~ν) (3)

where ρ is the density, � the velocity, p the pressure, τthe stress tensor, q the heat flux, T the temperature,and t the time. To obtain a solution of the aboveequations, each stage of the process is associated witha set of initial and boundary conditions coupled withsimplifying assumptions.

In the filling stage, which starts with an emptycavity, a free surface exists at the advancing melt front.In a rectangular cavity, the part filled with the melt isshown in Fig. 2. Near the gate, the flow is radial untilthe flow front reaches the wall. Away from the gate,the flow is characterized by a dominant axial velocitycomponent. In the front region, the melt, channelingthrough the center, tends to move towards the cavitywall in what is referred to as the ‘‘fountain flow.’’Although it is possible to analyze the details of the flowstructure in the cavity by dealing with the appropriate

Figure 2Filling pattern in the melt front of a rectangular injectionmolding cavity.

three-dimensional (3-D) flow equations, it is muchsimpler to treat the flow regions and to solve thecorresponding two-dimensional (2-D) flow equations.In most cases, the flow simulation has employed 2-Dsolutions by using theHele–Shaw flow approximation.This approximation may apply to thin mold cavitieswith large aspect ratios, and in which out-of-planeflows are neglected.

Both finite element and finite difference numericaltechniques may be employed to obtain computersolutions of the relevant equations. The former meth-ods are more complex, but they are well suited fordealingwith complexmold cavities and the free surfaceflows at the melt front (Ito et al. 1996). An interestingapproach for dealing with the fountain flow near thesurface is based on the finite difference method inconjunction with the marker-and-cell. Recently, in-stead of carrying out the full 3-D analysis, a hybrid 2-D}3-D technique was proposed, which solves the 3-Dfluid flow equations only in the fountain flow region,while the 2-D Hele–Shaw formulation is employedbehind the flow front region. Another approximationis based on the so-called 2.5-D analysis, employing a 2-D flow analysis and a solution to the 3-D energyequation regarding temperature distribution andcrystallization effects using Boundary Fitted Curvi-linear Coordinate transformation. Hsiung et al. (1996)developed the model using a Lagrangian approach tosimulate the stress distribution along the gap-wisedirection inside the injection molding.

There are a variety of constitutive rheologicalequations that may be employed to describe the

3

Injection Molded Semicrystalline Polymers: Structure Development and Modeling

viscous or viscoelastic behavior of the polymer meltduring the process. The most commonly employedrheological models in the injection molding processinclude the following: Newtonian liquid, power lawmodel, second-order fluid, Leonov equation, andintegral constitutive K-BKZ equation (Chang andChiou 1994). Whereas some of the models describeonly the viscous behavior of the fluid, other modelsreflect some of the viscoelastic characteristics of thematerial.

The approach for the simulation of the packingstage is similar to that for the filling stage. For thepacking stage, the deceleration of the flow reinforcesthe importance of the unsteady-state terms, and shouldnot be neglected. During packing, the contribution ofthe unsteady-state terms will tend to be larger thanthat of the convective terms in the equation.

The dominant feature in the packing and coolingstage is the compressibility of the polymer melt. Thisemphasizes the need for selecting an appropriateequation of state to describe the pressure–volume–temperature (PVT) relationships for the melt. Anumber of equations of state have been employed inconjunction with the processing of polymer melts, themajority of which are based on the van der Waalsequation of state.

After the filling and packing of the cavity, the gatefreezes and no additional material enters the cavity.Since fluid motion is negligible or absent during thisstage, the problem is reduced to the transient heattransfer by conduction from the polymer melt to themold walls. The convection in the 2-D stream-wisedirection and thermal conduction in the gap-wisedirection are considered in the energy equation. Alsothe generation of heat due to shear flow is taken intoaccount.

ρCp

E

F

¦T

¦t­u

¦T

¦x­�

¦T

¦y

G

H

¯¦

¦z

E

F

λ¦T

¦z

G

H

­τzx

¦u

¦z­τ

zy

¦�

¦z(4)

where x and y are the stream-wise direction, z thethickness direction, and t the time. u is the velocity inthe x-direction and � the velocity in the y-direction,respectively. τ is the shear stress, T the temperature,with ρ, C

p, and λ representing the density, specific

heat, and thermal conductivity. In order to allow forthe effect of latent heat of crystallization, the latentheat is included in the specific heat as follows:

Cp¯C «

p­∆H

dx

dt(5)

where Cp

is the effective specific heat capacity of thematerial, C «

pis the specific heat of the material at the

same temperature in the absence of crystallization,

×

Figure 3Gap-wise distribution of predicted spherulite size ofpolypropylene part at 0.5mm from the gate. Samplemolded at injection speed of 22.2cm$s−" and moldtemperature of 0°C. S: surface layer; D1: 0.2mm from thesurface; D2: 0.4mm from the surface; D3: center layer.

∆H is the latent heat of crystallization, and x is theweight fraction crystallinity in the system.

3.2 Crystallization Kinetics using CrystallizationRate Constant

Simulation of crystallization during injection moldinghas been performed (Kamal and Lafleur 1986, Hsiunget al. 1996, Titomanlio et al. 1995, Isayev et al. 1995),where the form of the crystallization kinetics is thegeneralized Avrami equation by Nakamura et al.(1972). This model is based on the assumption ofisokinetic conditions, and it describes the crystal-lization process by a single parameter, i.e., crystal-lization rate constant.

x(t )

x¢

¯ 1®exp

A

B

®E

F

& t

!

K (T (t ) dt

G

H

nC

D

(6)

where x(t) is crystallinity, x¢ is the final crystallinity, nis the Avrami index determined from isothermalexperiments, and K(T ) (¯ [k(T )] "/n ) is connectedwith the crystallization rate constant of isothermalcrystallization k(T ). A crystallization kinetics modelthat took into account the effect of shear stress oncrystallization rate constant and induction time hasbeen proposed, and the distributions of crystallinityalong the stream-wise and gap-wise predicted; goodagreement with experimental values was observed(Hsiung et al. 1996). Another model of shear-inducedcrystallization kinetics in the injection molding processwas proposed by Isayev et al. (1995), which took intoaccount the shear effect on the rheological parameters,

4

Injection Molded Semicrystalline Polymers: Structure Development and Modeling

Figure 4Gap-wise distribution of predicted (line) and measured (symbol) relative crystallinity of (a) polypropylene, and (b)poly(ethylene terephthalate) parts at 50mm from the gate. Sample molding conditions are indicated in caption for Fig. 1.

i.e., shear rate and relaxation time. This simulationmodel is based on the theory of Eder and Janeschitz-Kriegl et al. (1990), which assumes that the locationsof nucleation are created by the flow. Friedl andMcCaffrey (1991) simulated the crystallinity distri-bution of polyoxymethylene across a rectangular part,and crystallinity profile through a section, where themacrokinetics approach of Malkin et al. (1984) wasused to model the crystallization behavior during theinjection molding process. In addition, Titomanlio etal. (1995) proposed a model of crystallization kineticswhich took into account the effect of pressure on theequilibrium crystallinity, and showed that they wereable to increase the accuracy of the prediction of thecrystallinity distribution by considering the pressureeffect.

3.3 Crystallization Kinetics Considering Nucleationand Crystal Growth Process

The actual crystallization process, however, consistsof two elementary processes: nucleation of crystalsand their growth. These two processes are indepen-dently influenced by temperature, pressure and shearstress. In order to simulate the crystal morphology andmore realistic crystallization behavior during themolding process, crystallization kinetics should bedescribed using separate terms for the nucleation rateand the crystal growth rate.

Ishizuka and Koyama (1977) have shown that thecrystallization behavior of a running filament is wellreproduced by using generalized Avrami kinetics, thattake into account the temperature dependence of thenucleation rate and the crystal growth rate. In the case

of a heterogeneous nucleation process, the crystallinityx(t) is given by:

®ln

E

F

1®x(t)

x¢

G

H

¯1

x¢

ρc

ρl

A

B

& t

!

dNa

dτ�(t, τ) dτ­Na (0)�(t, 0)

C

D

(7)

where

�(t, τ)¯kf

A

B

& t

τ

G(u) du

C

D

m

(8)

Here x¢ is the final crystallinity, G(u) the crystalgrowth rate at time u, and N(t) the number of nuclei attime t. m is the dimension of the growth of the crystal,and k

fis the corresponding shape factor. In the case of

three-dimensional crystal growth, m¯ 3 and kf¯

4π}3 are adapted. ρc

and ρl

are the density of thecrystalline and liquid phases, respectively. The effectsof orientation were also considered through the effectof shear stress on the melting temperature in thenucleation rate and crystal growth rate, which wasbased on work by Kobayashi and Nagasawa (1970).

Crystallization behavior in the injection moldingprocess has been estimated using crystallization kinet-ics with the density of nuclei and crystal growth rate byOkamoto et al. (1995) and Ito et al. (1996). Theyconsidered the effect of shear stress on the crystal-lization kinetics, experimentally or theoretically. It isgenerally considered that the crystallization in largeproducts starts at the filling stage, where the polymeris subjected to rapid cooling, high pressure, and highshear stress. Therefore it is necessary to consider the

5

Injection Molded Semicrystalline Polymers: Structure Development and Modeling

influence of pressure on the crystallization behavior,because the pressure in the injection molding processof large products often reaches more than 150MPaduring the filling stage, and the high pressure acceler-ates the crystallization. Simulation of crystallization athigh pressure under non-isothermal conditions wascarried out, and these simulation values agreed wellwith experimental values, including the effect ofpressure on the melting temperature and glass tran-sition temperature on nucleation and crystal growthrates. Later, Ito et al. (1996) described in more detailthe effects of pressure and shear stress on the crystal-lization behaviors during injection molding. Theydemonstrated that the model developed is a quan-titative phenomenological model that can predict notonly the crystallinity distribution, but also the spheru-lite size distribution in stream-wise and gap-wisedirections. The predicted spherulite distribution in thegap-wise direction of injection molded PP part isshown in Fig. 3. Moreover, in order to accuratelypredict the flow and crystallization phenomena in theinjection molding process, material physical proper-ties—such as density, thermal conductivity, and spe-cific heat—should be taken into account, as well as thecrystallinity dependence of these material properties.They also linked the simulation model betweencrystallization and the flow with the effect of crystal-lization on material physical properties. Figure 4shows the distribution of relative crystallinity in thegap-wise direction of injection molded PP and PETparts. The gap-wise distribution of relative crystal-linity was in good agreement with experimental values.

See also: Polymer Processing: A Modeling Approach;Polymer Injection Molding: Modeling for Prop-erties; Polymer Injection Molding: Flow-inducedCrystallization

Bibliography

Chang R-Y, Chiou S-Y 1994 Integral constitutive model (K-BKZ) to describe viscoelastic flow in injection molding. Int.Polym. Proc. IX, 365–72

Eder G, Janeschitz-Kriegl H, Liedauer S 1990 Crystallizationprocesses in quiescent and moving polymer melts under heattransfer conditions. Prog. Polym. Sci. 15, 629–714

Friedl C F, McCaffrey N J 1991 Crystallisation prediction ininjection molding. Soc. Plast. Eng. ANTEC’91 Tech. Pap., pp.330–2

Copyright ' 2001 Elsevier Science Ltd.All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmittedin any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording orotherwise, without permission in writing from the publishers.

Encyclopedia of Materials : Science and TechnologyISBN: 0-08-0431526

pp. 4082–4088

Fujiyama M 1995 Structures and properties of injection mold-ings of β-crystal nucleator-added polypropylenes. Int. Polym.Proc. X, 172–8

Hsiung C M, Cakmak M, Ulcer Y 1996 A structure-orientedmodel to simulate the shear-induced crystallization in in-jection molded polymers: a Lagrangian approach. Polymer37, 4555–71

Isayev A I, Chan T W, Gmerek M, Shimojo K 1995 Injectionmolding of semicrystalline polymers—II: Modeling andexperiments. J. Appl. Polym. Sci. 55, 821–38

Ishizuka O, Koyama K 1977 Crystallization of running filamentin melt spinning of polypropylene. Polymer 18, 913–8

Ito H, Minagawa K, Takimoto J, Tada K, Koyama K 1996Effect of pressure and shear stress on crystallization behaviorsin injection molding. Int. Polym. Proc. XI, 363–8

Kamal M R, Lafleur P G 1986 Computer simulation of injectionmold filling for viscoelastic melts with fountain flow. Polym.Eng. Sci. 26, 190–6

Katti S S, Schultz J M 1982 The microstructure of injection-molded semicrystalline polymers: a review. Polym. Eng. Sci.22, 1001–17

Kantz M R, Newman Jr. H D, Stigale F H 1972 The skin-coremorphology and structure-property relationships in injection-molded polypropylene. J. Appl. Polym. Sci. 16, 1249–60

Kobayashi K, Nagasawa T 1970 Crystallization of shearedpolymer melts. J. Macromol. Sci.—Phys. B4, 331–45

Malkin A Y, Beghishev V P, Keapin I A, Bolgov S A 1984General treatment of polymer crystallization kinetics—I: Anew macrokinetic equation and its experimental verification.Polym. Eng. Sci. 24, 1396–401

Nakamura K, Watanabe T, Katayama K, Amano T 1972Nonisothermal crystallization of polymers—I: Relationshipbetween crystallization temperature, crystallinity, and coolingconditions. J. Appl. Polym. Sci. 16, 1077–91

Okamoto M, Shinoda Y, Kinami N, Okuyama T 1995 Noniso-thermal crystallization of poly(ethylene terephthalate) and itsblends in the injection-molding process. J. Appl. Polym. Sci.57, 1055–61

Spencer R S, Gilmore G D 1951 Some flow phenomena in theinjection molding of polystyrene. J. Coll. Sci. 6, 118–32

Titomanlio G, Speranza V, Brucato V 1995 On the simulation ofthe thermoplastic injection molding process. Int. Polym. Proc.X, 55–61

Trotignon J-P, Verdu J 1987 Skin-core structure: fatiguebehavior relationships for injection-molded parts of poly-propylene—I: Influence of molecular weight and injectionconditions on the morphology. J. Appl. Polym. Sci. 34, 1–18

Ulcer Y, Cakmak M, Miao J, Hsiung C M 1996 Structuralgradients developed in injection-molded syndiotactic poly-styrene. J. Appl. Polym. Sci. 60, 669–91

H. Ito

6