Analysis of Shrinkage Development of a Semicrystalline Polymer during InjectionMolding

Felice De Santis,* Roberto Pantani, Vito Speranza, and Giuseppe Titomanlio

Department of Chemical and Food Engineering, UniVersity of Salerno, 84084 Fisciano (SA), Italy

The phenomenon of shrinkage in injection molding is particularly relevant for the processing of semicrystallinepolymers. Nevertheless, if compared with the considerable effort spent by researchers to investigate the evolutionof shrinkage and thermal stresses in amorphous polymers, the research work devoted to shrinkage ofsemicrystalline polymers is rather limited in the literature. In this work, the influence of holding pressure andtime, and geometric constraints, on the shrinkage of a semicrystalline polymer was explored. Adopting atechnique based on strain gauges, the time at which shrinkage started inside the mold was measured as afunction of the holding pressure. Experimental results were compared with predictions for shrinkage obtainedby a code developed at the University of Salerno, which takes into account crystallization kinetics and theeffect of crystallinity on material properties. In particular, a solidification criterion based on the degree ofcrystallinity was identified.

Introduction

The modern trend to produce molded objects with very tighttolerances causes an increasing interest toward the shrinkagephenomenon. Indeed, many papers have been published on theshrinkage behavior of various materials under different moldingconditions. Despite this, if compared with the considerable effortspent by researchers to investigate (both experimentally andtheoretically) the evolution of shrinkage and thermal stressesin amorphous polymers, the relevant research work for semi-crystalline polymers is rather scarce.1-3 On one hand, this isquite surprising, because the phenomenon of shrinkage forsemicrystalline polymers is more significant, with respect toamorphous materials.4,5 On the other hand, this is justified bythe fact that the phenomenon is strictly related to the evolutionof crystallinity in processing conditions, which is, per se, quitedifficult to be predicted. The evolution of crystallinity was takeninto account in the modern models for shrinkage from the verybeginning. In 1995, Titomanlio and Jansen considered the effectof crystallinity6,7 through the volume reduction due to crystal-lization. However, in 1997, Han and Wang8 already noted thedifficulty of considering the crystallization kinetics for shrink-age predictions, and they suggested that the problem could beovercome just for slowly crystallizing polymers (PET). Theauthors still noted that, even if, for these materials, theimportance of accurate calculation of crystallinity is less critical,shrinkage predictions were heavily affected by the difficulty ofconsidering the effect of crystallinity on material properties, evenduring material characterization. After that work, only very fewpapers have tried to analyze the phenomenon.9-11 In fact,modern approaches to the phenomenon of dimensional accuracyin injection molding link the evolution of shrinkage from theinstant of first solidification to a force balance between restrain-ing forces (due to the thermal contraction) and constraining ones(which rely on pressure effects and interactions between moldwalls and the polymer surface). If the former ones overcomethe latter ones, shrinkage should start even if the sample is stillinside the mold. Such an approach requires a completeunderstanding of the solidification phenomenon taking placeinside the cavity during the molding cycle. This is confirmed

by the fact that poor predictions for shrinkage are obtained whencrystallization is disregarded and the semicrystalline materialis considered to behave like an amorphous polymer.5

In this work, with reference to a semicrystalline materialmolded in a simple rectangular cavity, the development ofshrinkage is investigated highlighting both experimentally andtheoretically the effects of in-mold shrinkage on product finaldimensions.

Experimental Section

Material. An isotactic polypropylene (iPP) that wasproduced by Montell (now Basell, commercial name HifaxBA238G3) was adopted for the injection tests. This materialis a heterophasic polypropylene with high isotactic index.In particular, Hifax BA238G3 is a typical industrial polymer,polypropylene-ethylene-propylene rubber (iPP-EPR) co-polymer with a small percentage of talc. Impact strength isimproved by the ethylene-propylene rubber phase (EPR,copolymer C2-C3, at ∼50% of each component) dispersedin the polypropylene matrix; rubber weight percentage is∼26%; a small percentage of talc (∼1.5%) is also present inthe resin. The crystallinity equilibrium value of the iPP phase(representing 72.5% of total samples mass) is 60% (or 43.5%of the sample). Some of material properties are given inTable 1.

A complete characterization of material crystallization kineticscan be found in ref 12. The complete rheological description,

* Author to whom correspondence should be addressed. E-mail:fedesantis@unisa.it.

Table 1. Material Specification for PP, Hifax BA238G3

property ASTM method value

Physical Properties

melt flow rate (230 °C, 2.16 kg) D 1238 L 13 g/10 minspecific gravity D 792 900 kg/m3

Mechanical Properties

flexural modulus D 790 1700 MPatensile strength D 638 20 MPaelongation, ultimate D 638 400%

Thermal Properties

Vicat softening point (49 N) D 1525 55 °CHDT (1.82 MPa) D 648 50 °C

Ind. Eng. Chem. Res. 2010, 49, 2469–2476 2469

10.1021/ie901316p 2010 American Chemical SocietyPublished on Web 01/28/2010

including the effect of pressure and crystallinity on viscosity,is reported in ref 13.

Equipment. Molding experiments were performed using a650 kN clamping force “Penta 65/185” (Metalmeccanica Plast)injection molding machine with an injection nozzle 15 mm inlength and 2.2 mm in diameter. The impression was a line-gated rectangular plaque with nominal dimensions of 120 mm× 30 mm × 2 mm. The gate thickness and length were 1.5mm and 6 mm. The sprue diameter tapered from 8 mm to 5mm over 80 mm.

Five pressure transducers were located along the flow path:before the nozzle (P0), just before the gate (P1), and in the cavityat 15, 60, and 105 mm downstream from the gate (identified asP2, P3 and P4, respectively). The pressure evolution in thesefive positions was recorded for all tests during the entire process.

Processing Conditions. The moldings were produced witha mold temperature of 25 °C and an injection temperature of230 °C; the flow rate was set in the machine controller to 27cm3/s, resulting in an injection time of ∼0.5 s. Several valueswere given relative to a specific holding pressure (Ph) andholding time (th). The time after holding (cooling time) wasconstantly kept at 15 s. To allow for stabilization of the process,seven moldings were rejected between each test. Moldingconditions are summarized in Table 2.

Examples of the in-mold pressure recordings are reported inFigures 1 and 2: extremely different molding conditions wereexplored and, as a consequence, extremely different pressureevolutions inside the cavity were recorded.

Pressure evolutions during tests performed with a holdingpressure of 40 MPa and two holding times (2 and 10 s) areshown in Figure 1. As reported in the caption, symbols aredecimated in the plots (i.e., less symbols are reported withrespect to the number of points, although the lines connect eachpoint acquired).

The pressure spike present some seconds after the holdingpressure is released in each experimental pressure profile inposition P0 (namely, inside the injection chamber) and, conse-quently, present also in the pressure profile imposed to thesimulation software, refers to the counterpressure that the screwuses to fill the injection chamber for the following shot.

In the left plot of Figure 1, the holding pressure is releasedbefore complete gate solidification with a dramatic decrease ofpressure evolution inside the cavity occurs: because of theinversion of pressure gradients, some material flows back fromthe cavity and pressure quickly fades down. This phenomenon,usually called “backflow”, determines lower sample weight (theweights of the samples are reported in Figure 5, shown later inthis work).

In Figure 2, the pressure evolutions during tests performedwith two holding pressures (18 and 70 MPa) and a holding timeof 10 s are also reported.

As expected, a higher holding pressure induces higherpressure levels inside the cavity. Furthermore, inside the cavity,just downstream from the gate, a residual pressure was stillpresent at mold opening when a holding pressure of 70 MPawas adopted (see the right plot in Figure 2).

Adopting a very wide range of conditions, it was possible toexplore an extremely wide range of situations that occur insidethe cavity, from backflow to residual pressure at mold opening.

It has been shown14 that an inflection point in the pressureevolution just upstream from the gate (P1) occurs when the gatesolidifies. Correspondingly, the pressure curve just downstreamfrom the gate (P2) changes its concavity from downward toupward. From the plots of pressure evolution reported in Figures1 and 2, it can be evidenced that the gate solidification occursbetween 6 s and 8 s.

For all tests, the “as molded shrinkage” was measured 10min after ejection at a room temperature of 25 °C, and the resultsof these measurements were averaged over three consecutivemolded parts (dispersion bars are very small and fall insidesymbols in all figures) for each combination of holdingconditions.

Shrinkage (percentage) was calculated as

where L0 is the dimension in the impression and L is thecorresponding part dimension. According to this definition,shrinkage is opposite to the strain, and it will be negative if thepart dimension becomes larger than the impression. The moldtemperature is well-balanced, so that the mold is symmetric withrespect to the midplane, and, as a consequence, no warpagewas observed.

During some of the tests, the shrinkage evolution wasmonitored from the start of injection to mold opening by means

Figure 1. Pressure evolutions at different positions along the flow path for test performed with a holding pressure of Ph ) 40 MPa and holding times of th

) 2 s (left plot) and th ) 10 s (right plot). Symbols are defined in the plots.

Table 2. Holding Processing Conditions

holding time, th (s) holding pressure, Ph (MPa)

0, 2, 4, 6, 8, 10, 18 4010 18, 30, 40, 50, 60, 70

shrinkage )L0 - L

L0× 100 (1)

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of a strain gauge placed in the cavity near the pressure transducerlocations (P3 in Figure 3). During injection, the polymersolidifies on the strain gauge, which, afterward, follows theshrinkage process inside the mold at that position.15 The adoptedstrain gauge (Kyowa Electronic Instruments Co., Model KFRP-5-350-C1-1) was calibrated for the effects of temperature andpressure in a previous work.15 Indeed, it was verified in thatwork that, as expected, based on its characteristics, the effectsof temperature and pressure in the range of interest for injectionmolding could be neglected.

When the holding pressure or time are small, part shrinkagestarts before mold opening. To stress the effect of the in-moldshrinkage onset on the final sample shrinkage, the experimentalprotocol was repeated, preventing the rectangular sample fromin-mold free shrinkage by means of a physical constraint. Thisconstraint was achieved by a steel bar with dimensions of 30mm × 5 mm × 0.5 mm, bonded using a cyanoacrylate glue onthe cavity surface at position P4, 105 mm downstream fromthe gate (see Figure 3).

The temperature evolution was also monitored from the startof injection to mold opening by means of a thin thermocoupleplaced in the cavity near the pressure transducer locations (P2,P3, and P4), as shown in Figure 3. As for the strain gauge, thepolymer solidifies on the thermocouple (Omega EngineeringLtd., U.K., Part No. CO2-K, Cement-On Surface Thermo-couples, response time of 2-5 ms), which, afterward, followsthe temperature evolution of the surface of the molded partinside the mold at that position. The total thickness of thethermocouple was 0.06 mm; therefore, the measured temperaturemust be related to a distance of ∼0.03 mm from the mold wall.

The signals (pressure, temperature, strain gauge) are sampledand recorded by a data acquisition system (National InstrumentsCorporation, USA, Model PCI 1200, DAQ Board). A specificsoftware code (based on National Instruments LabView, “G”programming language) was developed to synchronize all therecorded experimental data.

Experimental Results. Results of the in-plane shrinkage(both in the flow direction and in the cross-flow direction), asa function of the holding pressure and the holding time, areshown in Figures 4 and 5, respectively. These results refer totests performed with both the constrained sample, as shown inFigure 3, and the unconstrained sample. The two holdingvariables have similar effects on shrinkage: the shrinkagedecreases as either the holding pressure or holding timeincreases.

Figure 5 clearly shows that holding times of >8 s do not causesignificant shrinkage reduction. Indeed, as parallel experiments

Figure 2. Pressure evolutions at different positions along the flow path for test performed with a holding time of th ) 10 s and a holding pressure of eitherPh ) 18 MPa (left plot) or Ph ) 70 MPa (right plot). Symbols are defined in the plots.

Figure 3. Dimensions (in millimeters) of te mold, runner system, and spruefor a rectangular-shaped mold. P0, P1, P2, P3, and P4 denote the positionsof the pressure transducers.

Figure 4. Experimental final shrinkage along the flow and cross-flowdirections, relative to holding pressure at a constant holding time of 10 s,for free and constrained shrinkage cases.

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confirmed on part weight shown also in Figure 5, for a holdingpressure of 40 MPa, the gate freezes 6-8 s from the end ofinjection, which is consistent with the pressure evolutions inposition P1.

Both Figures 4 and 5 show that the effect of constraints onthe final shrinkage is significant when the holding pressure issmall or the holding time is short, and it vanishes at high holdingpressures (>50 MPa for th ) 10 s) and long holding times. Thisis a clear indication that, under these conditions, shrinkage startsin the mold before complete solidification. Indeed, the onlyeffect of the constraint in the mold may be preventing the samplefrom undergoing shrinkage inside the mold: if the shrinkagewould start after complete solidification, its effect would be zeroon the final dimensions of elastic solids. Moreover, the resultsshow that the shrinkages in the flow and across flow directionshave similar values when the constraint is not present and thatthe width shrinkage seems to be affected very little by theconstraint in the length direction.

One of the experimental strain recordings is shown in Figure6: the shrinkage onset at ∼8 s is clearly identified, the sampleshrinkage keeps increasing inside the mold and it undergoesanother sharp and much larger increase at the mold opening.Recordings of the strain gauges, subsequent to mold opening,showed that shrinkage did not vary significantly, at least up toa few minutes after the mold opening.

One of the experimental temperature recordings is alsoreported in Figure 6; a slight change in the temperature evolutiontrend at ∼10 s could be identified. This change probably occurswhen the part moves away from the mold, so that, because oflosing the contact with the mold, the external layer of the partis heated by more internal layers10 and affects the strainmeasurement.

The experimental shrinkage onset inside the mold, asdetermined by the in-mold strain gauge technique, is shown inFigure 7 (solid circles). The onset time, at which shrinkage starts,is delayed by increasing the holding pressure. A correctprediction of shrinkage onset prediction is really important whenthe shrinkage starts before the part solidification, i.e., for lowerholding pressures.

Modeling

The experimental results were compared with the predictionsof a software code developed at the University of Salerno(UNISA),16whichcantakeintoaccount thematerialcrystallization.

In particular, a generation term due to crystallization wasconsidered in the energy balance. Furthermore, the effect ofcrystallization on density and viscosity was explicitly taken intoaccount.

The nozzle was assumed to be at the injection temperature.The runner and the cavity surface were assumed to be at themold temperature. A time-dependent heat-transfer coefficientwas imposed at the polymer/steel surface. The experimentallydetermined filling time was imposed to the simulation. Afterfilling, the experimental pressure evolution measured inside theinjection chamber was imposed (namely, in P0). The crystal-lization kinetics were described by means of a nonisothermalformulation of the Avrami model, whose parameters wheredetermined by accounting for both the calorimetric and experi-mental density data of thin samples subjected to knownquenching histories.12 The material rheological behavior wasdescribed by a modified form of the Cross-WLF equation,which continues to take into account the effect of crystallinityand pressure and viscosity.7 The no-flow condition was relatedto the crystallinity degree as described in ref 7. In particular,simulations of the molding tests were performed assuming anonflow crystallization degree of ∼10% (that is, 25% of

Figure 5. Left axis: experimental as molded shrinkage along flow and cross-flow directions versus holding time at a constant holding pressure of 40MPa, for free and constrained shrinkage cases. Right axis: part weight versusholding time.

Figure 6. Pressure evolution at different positions (left axis) and typicalshrinkage evolution along flow direction (right axis) obtained with a straingauge, in position P3, and temperature evolution obtained with a thermo-couple placed close to the strain gauge (holding pressure of Ph ) 40 MPa,holding time of th ) 10 s). Symbols are defined in the plot.

Figure 7. Shrinkage onset inside the mold as a function of the holdingpressure at the position P3. Solid circles refer to strain gauge experimentaldata. Lines correspond to the predictions using eq 3. Lines and open symbolsrefer to predictions using experimental (triangles) and simulated (squares)pressure curves from UNISA code, respectively. Stars refer to partsolidification time evaluated by UNISA code.

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crystallinity equilibrium degree, with this latter value beingevaluated in ref 6 to be 44% of the polymer volume). The PVTdescription was obtained as a simple weighted average ofcrystalline and amorphous phases based on the degree ofcrystallinity.6 The mold deformation was kept into account byassuming a linear relationship between cavity thickness andpressure: the value used for the mold compliance (1.27 × 10-3

MPa-1) describes a local cavity enlargement of ∼25 µm for alocal pressure of 10 MPa.17

The results of the calculated pressure evolution, reported inFigure 8 for testing with a holding time of 10 s and a holdingpressure of 40 MPa (experimental evolution reported in Figure1), compare satisfactorily with the experimental data for allmolding conditions used in this work.

The simulated temperature for tests performed with a holdingpressure of 40 MPa and a holding time of 10 s are shown inFigure 9. Experimental data substantially show the same trendin all positions on the external layer of the part. Localtemperature calculations of the UNISA code compare satisfac-torily with the experimental data.

Shrinkage calculations of the UNISA code are based on athermomechanical model6,18 that relies on the assumption thatthe stresses in each layer start to develop as soon as the layer

solidifies, and the relaxation in the solid polymer is negligiblebecause of the high cooling rate.

The in-plane strain evolution, sx, of a semicrystalline materialsolidifying as an elastic solid in a rectangular slab is describedby

where ν is the Poisson coefficient, tso the time at which the firstlayer solidifies, F the polymer density, evaluated averaging thedensities of the different phases with their fractions, E the elasticmodulus for an isotropic material, given as

and � the material volume compressibility, given as

The superimposed bar above the numerator in eq 2 denotes aver-aging over the solidified layers. The material propertiessnamely,the elastic modulus (E) and the material volume compressibility(�)sare considered functions of pressure, temperature, andcrystallinity, according to eqs 2a and 2b, respectively.

The first term inside the integral is the isotropic shrinkage,dependent on temperature (T), pressure (P), and crystallinityevolution (�); the second term continues to take into into accountthe effect of stresses, σx, which must satisfy the following forcebalance:

where zs(t) is the solid layer thickness (0 at wall, b ) 1 mm atthe midplane); Ffr is the friction force, defined as

Ffr ) µ∫x

LP(x, t) dx

(where µ is the friction factor and L is the total cavity length orwidth); Fs is the stretching (positive in the balance) force exertedby the melt on the solid polymer; and Fw is the force exertedby the mold wall at the bottom of the cavity, which preventssample expansion, or at any constraining element.

The friction factor (µ) value used for calculations was 0.12,as measured at room temperature on the cavity surface for iPP.15

The integral of the first term in eq 2 increases with time andeven before shrinkage starts, namely, until sx ) 0, the averagestress σjx increases while both Fw and Ffr change to satisfy eq 3.

Before the shrinkage begins, the average stress evolution withtime can be calculated by eq 2 with sx ) 0. As soon as theshrinkage starts inside the mold, the force exerted by the moldwall (Fw) becomes zero. Therefore, the shrinkage onset is givenby the force balance equation (eq 3), where Fw is set to zero.

Solidification Criterion. The solidification criterion identifiesa condition at which the material can be considered to be anelastic solid. This condition is different from the so-called “no-flow condition”, which is based on an increase of viscosity andhas been used above for injection molding process modeling.The relevant issue for shrinkage is to quantify the significance

Figure 8. Pressure evolutions at different positions along the flow path assimulated with UNISA code for test with a holding time of 10 s and aholding pressure of 40 MPa. Symbols are decimated in the plot.

Figure 9. Temperature evolutions inside the polymer, at 0.03 mm from thesurface, in different positions along the flow path. The simulated curve wascalculated with UNISA code in position P3 for tests with a holding time of10 s and a holding pressure of 40 MPa. Symbols are decimated in the plot.

sx(t) ) ∫tso

t [E(T, P, �)(- 13F(T, P, �)

dF(T, P, �)dt )

Ej(T, P, �)+

1 - νEj(T, P, �)

dσ̄x(t)

dt ] dt (2)

E ) 31 - 2ν

�(T, P, �)(2a)

� ) 1F(T, P, �)

∂F(T, P, �)∂P

(2b)

σ̄x(t) )Ffr + Fw + Fs

zs(t)(3)

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of relaxation below the solidification point. Indeed, if the coolingtime is sufficiently small, when compared to the relaxation time,stress relaxation below solidification cannot occur, and thusstrains and stresses are frozen-in. This happens when theDeborah number (De), which is defined as the ratio betweenthe relaxation time and the cooling time, becomes significantlylarger than 1 (namely, on the order of 10):

where q is the cooling rate; Tsol and �sol are the temperatureand the degree of crystallinity at solidification, respectively; andTc(t) and �c(t) represent the temperature and crystallinity reachedby the material during the cooling process, subsequent to thesolidification condition. τj is a characteristic relaxation time ofthe polymer averaged between Tsol (and �sol) and Tc (and �c).

The polymer can be considered already solid (stress andorientation relaxation would be negligible during subsequentcooling) at Tsol and �sol if eq 4 is satisfied for all conditionsreached during subsequent cooling, and denoted by c in eq 4.Certainly eq 4 is satisfied if Tc is sufficiently close to Tsol; as Tc

decreases (and �c increases), for a given set of starting conditions(Tsol, �sol), τj increases (also of orders of magnitude) and, undersolidification conditions, eq 4 must be satisfied for any (Tc, �c)couple reached during the cooling.

The cooling rate inside an injection-molded object is depend-ent on the distance from the skin: it reaches a rate of severalhundred Kelvin per second close to the mold, but soon becomesof the order of 10 K/s in more internal layers and, for thickobjects, even smaller. Thus, the solidification conditions (Tsol,�sol) are functions of the cooling rate and, consistently, shouldbe taken as a function of the distance from the mold wall. Inthe following in this paper, however, a single condition isadopted (whatever the distance from the mold wall). Thatcondition was identified assuming that the difference (Tsol -Tc) is of the order of magnitude of 10 K and the cooling rate ison the order of 10 K/s.

According to eq 4, with the value chosen for De, therelaxation time at solidification τj (and also its initial value τsol)should be of the order of 10 s.

The relaxation time for semicrystalline materials is a strongfunction of crystallinity degree (�). This means that, rather thana solidification temperature, we are looking for a solidificationdegree of crystallinity (�sol).

In a recent paper,19 Acierno et al. analyzed the rheologicalbehavior of the same polymer that we adopted in this work, byconducting parallel calorimetric and rheological measurementsduring isothermal crystallization. The rheological tests wereconducted at a frequency of 1 rad/s. A characteristic relaxationtime can be defined assuming a Maxwell element:

where G′ and G′′ are the storage and loss moduli, respectively,and ω is the frequency (in this case, ω ) 1 rad/s).

Analyzing the data reported in ref 19, we evaluated thecharacteristic relaxation time determined from rheological testsat constant temperature versus the degree of crystallinitymeasured by parallel calorimetric tests. The result is reportedin Figure 10.

It is clear that a relaxation time of ∼10 s can be reachedonly when the degree of crystallinity is close to the maximum,at least for the temperatures considered in Figure 10. Further-

more, a dynamic-mechanical (DMA) test was conducted on amolded sample, heating it from room temperature to completemelting at a rate of 4 K/min. The value of storage modulus (E′)and loss modulus (E′′) are reported in Figure 11 versustemperature, together with a curve of crystallinity obtained bydifferential scanning calorimetry at the same scanning rate (4K/min).

Again, it is clear that the material begins to lose its mechanicalproperties when the degree of crystallinity is still very high.

According to the results obtained above, the degree ofcrystallinity previously described, at which the material can beassumed to behave as elastic solid, is close to the maximumvalue. As expected, the value of crystallinity to be adopted assolidification criterion is higher than that which causes a sharpincrease in viscosity values (namely, the no-flow crystallinity).

Model Predictions. Searching for a value of the crystallinitydegree above which the material can be assumed to be an elasticsolid, the shrinkage for the injection-molded test obtained at Ph

) 40 MPa and th ) 10 s was modeled assuming different valuesfor the relative degree of crystallinity (�s) from 0.1 to 0.95. Theresults are reported in Figure 12. It can be observed that,obviously, the shrinkage reduces upon increasing �s, and thatthe values of predicted shrinkage reach the experimental valueswhen �s ) 0.95. This result is consistent with the observation

τ̄((Tsol, �sol), (Tc, �c))

(Tsol - Tc)/q) De g 10 (4)

τ ) G′ωG′′ (5)

Figure 10. Characteristic relaxation time of Hifax BA238G3, evaluatedbased on the data reported in ref 19. Symbols are defined in the plot.

Figure 11. Storage modulus (E′) and loss modulus (E′′) measured duringa dynamic-mechanical (DMA) test heating from room temperature tocomplete melting at a rate of 4 K/min.

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that the crystallinity degree below which the material can beconsidered an elastic solid (negligible stress/relaxation duringcooling) is quite high and close to the maximum value.

Therefore, in the following, the degree of crystallinity belowwhich the material was assumed to be an elastic solid is 95%of the crystallinity equilibrium value, which is an absolutecrystallinity of 41%. When this condition is adopted in thesimulation, the time of complete solidification of the samplecross section inside the cavity becomes ∼10 s, almost inde-pendently upon the molding condition (Figure 7). It can beobserved from the results reported in Figure 7 that, for all thetests conducted with holding pressures of 18, 30, and 40 MPa,the shrinkage starts before complete solidification, which isconsistent with the shrinkage results in the presence ofconstraints. The results of the model predictions for theshrinkage onset inside the mold, as a function of the holdingpressure, are also shown as lines in Figure 7. The pressureevolution simulations compare well with experimental data, buta slight difference in solidification pressure has a major effecton the estimation of the shrinkage onset time (Figure 7), inparticular, for high holding pressures. A correct estimation ofthe time at which shrinkage starts using experimental pressureevolution confirms that the force balance inside the mold (eq3) is correctly described and allows correct shrinkage predictionsin the case of shrinkage starting before complete solidification.

In Figures 13 and 14, the results of the shrinkage along theflow direction, as a function of the holding pressure and time,are compared with the predictions of the model. It is evidentfrom these figures that (i) the predictions satisfactorily agreewith experimental as-molded shrinkage results, and (ii) the effectof constraints on the as-molded shrinkage is correctly described.In particular, with reference to Figure 13, the model correctlypredicts an effect of the constraint only for holding pressuresof <50 MPa, which is only for the conditions in which theshrinkage starts before sample complete solidification (seeFigure 7).

Slight differences in regard to the order of experimentaluncertainty for shrinkage are observed and can be ascribed toa nonperfect description of pressure curves (see Figure 8). Justone point lies far from the predicted values: the sample moldedwith a holding time of 2 s, in presence of a constraint, shrinksmuch more than calculated. This can be due to a not perfectly

rigid constraint or to the attainment of the yield stress in thesolid polymer during shrinkage.

Conclusions

This paper reports a study of shrinkage in injection moldingof a semicrystalline polymer: particular attention is given tothe effect of the holding time and pressure on the shrinkageevolution from the instant of first solidification inside the moldto just after molding.

Shrinkage onset was observed before mold opening by amethod based on strain gauges.

The as-molded shrinkage experimental results confirmed thatthe shrinkage decreases when the holding pressure and theholding time are increased; the holding time has an effect onshrinkage only if the holding pressure is released below gatesolidification. The effect of the presence of constraints insidethe mold affects (reduces) the as-molded shrinkage at lowholding pressures and times, i.e., when shrinkage can start insidethe mold before complete solidification.

The use of strain gauges to directly measure the shrinkageinside the mold shows that the shrinkage onset is delayed byincreasing the holding pressure.

The injection molding tests were modeled by a software codedeveloped at the University of Salerno (UNISA code), whichtakes into account the crystallization kinetics.

Figure 12. Predicted free and constrained shrinkage, as a function ofsolidification crystallinity. Experimental, free and constrained, shrinkageare reported as horizontal, continuous, and dashed lines.

Figure 13. As-molded shrinkage in the flow direction, as a function of theholding pressure at a constant holding time of 10 s. Lines correspond topredictions determined by UNISA code.

Figure 14. As-molded shrinkage in the flow direction, as a function of theholding time at a constant holding pressure of 40 MPa. Lines correspondto predictions determined by UNISA code.

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In particular, both the no-flow condition and the solidificationcondition (from a mechanical point of view) were based on thedegree of crystallinity. The shrinkage results are well-describedif a solidification absolute crystallinity of ∼40% is chosen; sucha result is consistent with literature rheology evolution of thesame material during crystallization and with cooling time, incomparison to relaxation time.

By adopting such a solidification crystallinity, the softwarewas able to correctly predict the as-molded shrinkage in bothconstrained and unconstrained cases, and to accurately estimatethe time of shrinkage onset.

Acknowledgment

The authors thank Stefano Acierno and Antonio J. Pontesfor the helpful comments on rheological and mechanicalbehavior of the adopted material.

Supporting Information Available: Figures of all theexperiments showing the results of pressure evolutions foreach holding time and holding pressure. Figures of all relatedprediction of pressure evolution for each holding pressureusing UNISA code. Figures of shrinkage evolution in themold, for different holding pressures. (PDF) This materialis available free of charge via the Internet at http://pubs.acs.org.

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ReceiVed for reView August 26, 2009ReVised manuscript receiVed January 8, 2010

Accepted January 11, 2010

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2476 Ind. Eng. Chem. Res., Vol. 49, No. 5, 2010