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Adopting the Experimental Pressure Evolution to Monitor Online the Shrinkage in Injection Molding V. Speranza,* U. Vietri, and R. Pantani Department of Industrial Engineering, University of Salerno, via Ponte don Melillo, I-84084 Fisciano (SA), Italy ABSTRACT: In this work, a procedure is reported which is suitable to analyze online the quality of molded parts in terms of shrinkage. The procedure is based on the evaluation of the average solidification pressure, namely the average along the thickness of the pressure at which each layer solidifies, a parameter which is known to correlate well with shrinkage. The calculation of this parameter normally requires the estimation of the solidification history, information which is currently not reachable experimentally. The procedure reported in this work allows adoption of the pressure evolution measured by a piezoelectric pressure transducer to make an estimation of the solidification profile and thus of the average solidification pressure. The procedure is applied to the data of shrinkage measured on an amorphous PS and a semicrystalline iPP in a wide range of processing conditions.

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along the thickness direction of a molding,11 the local solidification history is not experimentally obtainable, and thus it is necessary to perform the simulation of the whole injection molding test in order to obtain it. In this work a different approach based on the use of the experimental pressure profile alone, to obtain local thermal solidification history, and thus the experimental average solidification pressure, was implemented.

INTRODUCTION The quality of molded parts depends on the processing conditions and this creates a continuous demand of developing advanced techniques for monitoring and controlling the process.1 In-mold sensors can be obviously a valuable help for online measurements and hence for monitoring and control purposes.2 Ultrasonic3 and capacitive4 sensors have been applied to measure the part weight, optical fibers5 have proven to be able to measure thickness shrinkage, and strain gauges6,7 were adopted to follow the shrinkage evolution from the instant of first solidification. However, these methods are normally limited to scientific purposes: industries are traditionally disinclined toward the introduction of molds instrumented with a suitable number of sensors which could effectively monitor the injection molding process. In spite of this, traditional hardware-based temperature and pressure transducers have been widely employed in the industry; however, the correlation between measured evolution of temperature and pressure and product quality is not immediate.8 Indeed, it can be easily demonstrated9 that even the complete pressure curve cannot be adopted as a suitable parameter to fully describe shrinkage, and a criterion based on the reproducibility of the pressure profiles can cause the rejection of parts which are consistent with quality parameters. In a previous work9 an attempt was made to identify a single parameter satisfactorily correlated with chosen quality parameters (i.e., in-plane shrinkage), in order to give a useful approach regarding online quality control in the injection molding process. It was demonstrated that the local average solidification pressure Ps (the average over the thickness of the pressures at which each layer solidifies locally) was a suitable parameter for quality part description in the injection molding process, being consistent with the literature indications.10 The knowledge of the local average solidification pressure Ps requires the determination of both the local pressure history and the local solidification history. Despite recent attempts made to experimentally determine the temperature profile © 2012 American Chemical Society

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EXPERIMENTAL SECTION

Materials. Two different thermoplastic polymers were used; an amorphous polystyrene (aPS) and a semicrystalline polypropylene (iPP). The aPS was a general purpose polystyrene (Styron PS 678E) supplied by Dow Chemicals. A complete characterization of the resin can be found in the literature.12−19 The iPP was produced by Montell (now Basell, commercial name Hifax BA238G3). This material is a heterophasic polypropylene−ethylene−propylene rubber (iPP−EPR) copolymer with a small percentage of talc. Also for this material, a complete characterization can be found in the literature.20−27 Molding Conditions. The molding experiments were conducted in previous works for both aPS9 and iPP.25,20,23 For each of the molding conditions, data of pressure evolution were measured at three positions inside the cavity at 15, 60, and 105 mm from the gate; the cavity being 120 mm long, those positions (referred to as P2, P3, and P4, respectively) are located at 15 mm from the cavity entrance, central in the cavity, and at 15 mm from the cavity tip. Other two transducers were located inside the injection chamber (pos. P0) and soon upstream from the gate (pos. P1). A schematic view of the cavity adopted for all the molding tests is shown in Figure 1. Received: Revised: Accepted: Published: 16034

September 10, 2012 November 13, 2012 November 13, 2012 November 13, 2012 dx.doi.org/10.1021/ie302432v | Ind. Eng. Chem. Res. 2012, 51, 16034−16041

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic view of the geometry adopted for all the molding tests. The dimensions considered for shrinkage measurements are indicated as thick double arrows.

Table 1. Summary of Molding Conditions for aPS.9 For Each Series of Experiments, The Parameter Characterizing the Series Is Reported in Bold series

Ph [bar]

th [s]

tinj [s]

Tinj [°C]

Tmold [°C]

gate thickness [mm]

cavity thickness [mm]

nozzle [mm]

A1 B1 C1 D1 E1 F1 G1

80 to 1100 80 to 1300 330 to 1300 80 to 1300 80 to 900 90 to 1050 80 to 1050

12 12 12 12 12 12 12

0.45 0.45 2.2 0.6 0.45 0.56 0.45

220 200 220 220 220 220 220

25 25 25 25 55 25 25

1.5 1.5 1.5 0.5 1.5 1.5 1.5

2 2 2 2 2 4 2

11 11 11 11 11 11 90

Table 2. Summary of Molding Conditions for iPP.20 series

Ph [bar]

th [s]

tinj [s]

Tinj [°C]

Tmold [°C]

gate thickness [mm]

cavity thickness [mm]

nozzle [mm]

A2 B2

180 to 700 400

10 6 to 18

0.5 0.5

230 230

25 25

1.5 1.5

2 2

11 11

For aPS, a very wide range of processing and geometric parameters were changed. Seven series of experiments were carried out, each one characterized by the variation of a single parameter (namely injection temperature, injection time, mold temperature, cavity thickness, gate thickness, and nozzle length) with respect the reference series (series A1). For each series, several holding pressures were adopted from 80 bar up to more than 1000 bar. This resulted in a huge number (of the order of 100) of molding experiments. A summary of the molding conditions is reported in Table 1. As far as iPP is concerned, a single nozzle (the 11 mm long nozzle adopted for aPS), a single cavity thickness (the 2 mm thick cavity adopted for aPS), and a single gate (the 1.5 mm thick gate adopted for aPS) were used. Two series of experiments were carried out: the first one (series A2) in which the holding pressure varied for a constant holding time (longer than gate sealing time27), the second one (series B2) in which the holding time varied from values shorter to longer than gate sealing time for a constant holding pressure (see Table 2). This resulted in about 10 molding conditions. Shrinkage Measurements. In this work, we adopted width shrinkage as the quality parameter. This choice was made

because width shrinkage is strongly dependent on the local solidification conditions and is less sensitive to the presence of constraints with respect to length shrinkage and to mold deformation with respect to thickness shrinkage. The shrinkage was defined as the relative difference between mold and product width (both evaluated at 25 °C), that is, the following relationship was adopted: s i = (d i − dsi)/d i

(1)

where s was the shrinkage, ds is the sample local width, and d is the local cavity width (Figure 1). The subscripts indicate the position inside the cavity where width shrinkage was measured, namely at the positions of pressure transducers inside the cavity (si indicates the transducer position Pi). This means that for each molding condition, three results of shrinkage were obtained, each one related to a particular local history of temperature and pressure. This further increases the number of data on which the procedure presented in this work is validated.

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RESULTS AND DISCUSSION Definition of the Average Solidification Pressure. The definition of the average solidification pressure arises on 16035

dx.doi.org/10.1021/ie302432v | Ind. Eng. Chem. Res. 2012, 51, 16034−16041


Article

Figure 2. Algorithm for determining the values of tsol and τ.

considering a viscouselastic model for shrinkage,28 namely on assuming that the polymer melt turns into an elastic solid as soon as it solidifies. Since solidification proceeds from the mold surfaces to the core, solidification pressure is different for each layer, thus each layer has a different stress-free configuration (larger dimensions for layers solidified under high pressure29). On ejection, each layer will experience a different stress so as to bring all of them to the same final length. On the basis of these considerations, the average value over the thickness of the pressures at which each layer solidifies, Ps, was introduced to keep into account the effect of pressure on shrinkage.

solidification reaches the midplane of the local section. The superimposed cross bar indicates the average over the thickness. For amorphous materials, according to eq 3, the pressure decay after gate sealing closely follows the temperature decrease. For semicrystalline materials, this direct dependence between pressure and temperature evolutions holds only if “solidification” takes place at levels of crystallinity close to the final value, where “final” means the value reached at long times, when sample shrinkage is assessed. In this case, the last term of eq 3 can be neglected. According to literature indications,20 this condition is verified if the term “solidification” is related to stress relaxation: the material is considered “solid” if stress relaxation is negligible during the subsequent cooling. Let Tin, T∞, and t denote the initial temperature of molten polymer (namely the injection temperature), the equilibrium temperature (namely the mold temperature), and the local contact time respectively. For simplicity, convection and dissipation effects will be neglected and thermal properties will be assumed constant. The Biot number (Bi = hL/k, where h is the heat transfer coefficient at the polymer-mold interface, L is the local half-thickness, k is the thermal conductivity), will be assumed to be infinite, that is the temperature will be fixed at the mold wall. A different hypothesis can obviously be done. Furthermore, the initial temperature profile at each position along the flow-path will be assumed to be flat and equal to Tin. Under these conditions, the evolution of average temperature over cavity thickness is reported below31

1

Ps =

∫y*=0 P(t ) dys*(t )

(2)

in which y* is the normalized distance from the skin (y* = 0 at the mold surface and y* = 1 at the midplane) and y*s identifies the layer which is solidifying at time t (ys* = 1 at complete solidification and afterward). It was demonstrated10,9 that, for a given polymer, the average solidification pressure is directly related to the local shrinkage. However, the definition of the average solidification pressure requires the knowledge of the temperature histories inside the polymer, in order to define y*s (t). The main purpose of the present work is to define a suitable method to reach this piece of information by using experimental local pressure alone. Estimating Solidification Time from Experimental Pressure Evolution. At each position inside the cavity, after the local solidification time, tsol, the pressure evolution follows the temperature and crystallinity profiles on the basis of the relationship reported as follows:30 α κV P = Psol + V (T̅ − Tsol (χ ̅ − χsol ̅ )− ̅ ) βV βV (3)

T̅ − T∞ ⎛ 2 ⎞2 =⎜ ⎟ Tin − T∞ ⎝ π ⎠

∞

∑ n=0

⎡ 2 t⎤ exp⎢ −(2n + 1)2 ⎥ ⎣ τ⎦ (2n + 1)2 (4)

where τ is a characteristic time for cooling, namely

where αv and βv are material thermal expansion and compressibility coefficients, χ is the crystallinity degree, and κv is a coefficient taking into account the density increase due to crystallization (κV = 1/ρ(∂ρ/∂χ)T,P where ρ is the density). The subscript “sol” indicates that the variables are calculated at the time of local complete solidification, namely when the

τ=

⎛ 2 ⎞2 L2 ⎜ ⎟ ⎝π ⎠ α

(5)

In eq 5, L is the local half-thickness and α is the thermal diffusivity of the material. 16036



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Figure 3. Illustration of the exponential fitting on some of the pressure curves analyzed in this work recorded during injection molding of PS.

Figure 4. Illustration of the exponential fitting on some of the pressure curves analyzed in this work recorded during injection molding of iPP.

Equation 4 can be approximated by simpler expressions, valid for long times, namely for Fourier numbers (Fo = αt/L2) larger than about 0.1 (which is normally true for times larger than solidification time): T̅ − T∞ ⎛ t⎞ 8 ≃ 2 exp⎜ − ⎟ ⎝ τ⎠ Tin − T∞ π

Matching eqs 3 and 6, and rearranging, one obtains the relationship for local pressure profile (valid for t > tsol and Fo > 0.1). ⎛ t⎞ P = P∞ + A exp⎜ − ⎟ ⎝ τ⎠

(6)

(7)

The parameter P∞ in eq 7 is a constant, which can be calculated by eq 8 that follows from eq 3 in which the contribution given by the crystallinity degree is neglected under the hypothesis

This equation is often applied to calculate the evolution of the average temperature of the polymer in injection molded parts.2 16037



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Figure 5. Values of the parameter τ found for all the pressure curves analyzed in this work: (A) PS; (B) iPP.

that “solidification” takes place at levels of crystallinity close to the final value: α P∞ = Psol + V (T∞ − Tsol ̅ ) βV (8)

this fact is a confirmation of the reliability of the method since on doubling the thickness of the cavity the value of τ should indeed increase of a factor 4. Furthermore, the values found by the regression procedure are close to what can be calculated substituting the value of thermal diffusivity (α = 10−7m2/s32) in eq 5, reported in Figure 5a as horizontal lines. Similar observations also hold true for the results of τ found for iPP. Here the number of molding tests is lower; however, again the values found are close to what can be calculated substituting the value of thermal diffusivity of iPP (α = 7 × 10−8 m2/s21) in eq 5. An advantage of the procedure reported above is that it is possible to estimate the local solidification time without any knowledge of the local thickness: the procedure can thus be applied also on a cavity of unknown or variable thickness. Estimating Solidification Profile from Experimental Pressure Evolution. The temperature as a function of time and position can be approximated as31

P∞ represents the pressure which would be reached at very long times, when the polymer reaches the thermal equilibrium with the mold. If P∞ is positive, it coincides with the residual pressure. However, it can also be negative, obviously losing any physical meaning, if the solid polymer detaches from cavity walls. According to eq 7, the pressure evolution should be described by an exponential function after the local solidification time. Starting from this consideration, a nonlinear regression can be carried out on experimental pressure curve according to the algorithm reported in Figure 2, which determines the values of tsol (namely the time after which the pressure curve is well described by an exponential curve as in eq 7), and of τ (namely the characteristic time of that exponential). The results of the procedure are shown in Figure 3 for some of the molding tests carried out with PS. It can be observed that, after a few seconds, the experimental pressure evolutions are well described by the exponential curves at all positions and for all conditions. The solidification time (namely the time after which the plots follow an exponential trend) obviously depends on the chosen value of ε (see Figure 3). However, on choosing different values up to about 10 bar, the variation of tsol was within 1 s, thus confirming that the experimental pressure evolution strongly departs from an exponential function during the early instants of the packing phase. Also the differences in solidification times at the different positions are detected, and it was found that, in most of the cases, the solidification took place in pos. P4 (at cavity tip) at earlier times with respect to pos. P2 and P3, as expected on the basis of the fact that the temperature is higher closer to the injection point. A similar description was also found for iPP, as reported in Figure 4: again, the pressure evolution is well described by an exponential curve from a given time afterward. The values found for τ for both PS and iPP are reported in Figure 5. As far as PS is concerned (Figure 5a) it can be noticed that all the values found for τ (again it is worth noticing that we are dealing with some hundreds of values) collapse around two numbers, one for the series obtained with the thicker cavity and one for the series obtained with the thinner cavity, which differ of a factor of about 4. Considering the definition of τ (eq 5)

T − T∞ 4 = Tin − T∞ π

∞

∑ n=0

⎡ ( −1)n t⎤ exp⎢ −(2n + 1)2 ⎥ ⎣ 2n + 1 τ⎦

⎤ ⎡ π cos⎢(2n + 1) (1 − y*)⎥ ⎦ ⎣ 2

(9)

Obviously, on making this assumption, we are neglecting the variation of physical properties of the polymer with cooling and the effect of convection.33 Especially the latter aspect could induce significant deviations in the prediction of the solidification profile, particularly close to the gate (pos. P2). For Fo > 0.1, namely for long times, eq 9 becomes T − T∞ ⎤ ⎛ t ⎞ ⎡π 4 ≃ exp⎜ − ⎟ cos⎢ (1 − y*)⎥ ⎦ ⎣ ⎝ ⎠ π τ Tin − T∞ 2

(10)

This relationship allows the detection of a relationship between the local solidification time and the solidification temperature: Tsol − T∞ ⎛ t ⎞ 4 ≃ exp⎜ − sol ⎟ ⎝ τ ⎠ π Tin − T∞

(11)

In the following, it will be assumed that each layer solidifies at the same temperature. This assumption is certainly reasonable for amorphous polymers and for semicrystalline fast crystallizing polymers. In the case of slowly crystallizing polymers, the solidification temperature can be significantly different for different layers. 16038



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By combining eqs 10 and 11, the local solidification profile can be obtained: ⎡ t − tsol ⎞⎤ * (t ) ≃ 1 − 2 acos⎢exp⎜⎛ ⎟ ys,long ⎣ ⎝ τ ⎠⎥⎦ π

(12)

The subscript “long” indicates that this solution is valid for Fo > 0.1, namely for long times. A solution of heat conduction for short times can be obtained by the penetration theory: ⎡ ⎢ y* T − T∞ ≃ erf⎢ Tin − T∞ ⎢ 2 ⎢⎣ 4 π

2

( ) τt

⎤ ⎥ ⎥ ⎥ ⎥⎦

(13)

This allows the calculation of the solidification evolution inside the layers which solidify at short times (Fo < 0.1) ⎡ t ⎤ ⎛ ⎞2 * (t ) ≃ erf −1⎢ 4 exp⎜⎛ − sol ⎟⎞⎥ 4⎜ 2 ⎟ t ys,short ⎣ π ⎝ τ ⎠⎦ ⎝ π ⎠ τ

Figure 6. Measured width shrinkage vs average solidification pressure for each cavity position and for all tests carried out in this work on polystyrene.

(14)

A relationship which allows a description of the solidification layer profile in the whole time range can be given as a combination of eqs 12 and 1433

(18)

reported versus the local value of average solidification pressure. As mentioned above, the measured shrinkage data concern about some hundreds of data of different conditions, namely: 3 locations for each sample, about 15 conditions for each series (changing the holding pressure), and 8 different series. Most of shrinkage data collect on a single plot to confirm on one side the suitability of Ps in correlating the quality of molded part and on the other side the reliability of the procedure reported in this work to obtain a single parameter which is able to correlate with shrinkage, whose value can be determined by the experimental pressure evolution, only. For the same average solidification pressure, the differences were less than 0.2% (it is worth recalling that the accuracy of measurement for shrinkage is ±0.03%). In Figure 7, a similar plot is reported for iPP: again, most of shrinkage data collect on a single plot. The procedure described in this work is suitable for a mastercurve approach: a series of molding tests can be carried out for the chosen material, recording the pressure curves and measuring the shrinkage close to the pressure transducer; for

Equation 16 describes a transition from 0 to 1 in the neighborhoods of Fo = 0.1. Equations from 12 to 17 show that the knowledge of tsol, namely the local solidification time, and of τ, allows the estimation of the whole solidification profile. It is worth mentioning that the method does not require knowledge of initial, mold, and solidification temperatures, whose determination presents a certain degree of uncertainty and does not require any characterization of the physical parameters of the material. Even the cavity thickness could be unknown. Estimating Solidification Profile from Experimental Pressure Evolution. Once the local solidification profile is known, the local average solidification pressure can be easily calculated by eq 2. As reported in the literature10,9 local shrinkage should be directly correlated to Ps. The procedure outlined above was then applied to all the pressure curves of each molding test: first, the values of tsol and τ were obtained at each position and then the solidification profile was calculated. Eventually, the values of Ps were found. In Figure 6 experimental values of shrinkage measured at each cavity position and for all tests carried out on PS are

Figure 7. Measured width shrinkage vs average solidification pressure for each cavity position and for all tests carried out in this work on polypropylene.

* (t ) + ξ(t )[y* (t ) − y* (t )] ys*(t ) = ys,short s,long s,short

(15)

in which the function ξ(t) should be zero at low Fourier numbers and 1 at high Fourier numbers. A possible expression is 1 ξ(t ) = 1 − 1 + exp[10(t − tc)] (16) with

⎛ π ⎞2 tc = 0.1⎜ ⎟ τ ⎝2⎠

(17)

and with Fo being related to τ according to the following equation Fo =

⎛ 2 ⎞2 t ⎜ ⎟ ⎝π ⎠ τ

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(4) Fung, K. T.; Gao, F.; Chen, X. Application of a capacitive transducer for online part weight prediction and fault detection in injection molding. Polym. Eng. Sci. 2007, 47, 347. (5) Bur, T. Optical monitoring of polypropylene injection molding. J. Reinf. Plast. Compos. 1998, 17, 1382. (6) Pantani, R.; Jansen, K. M. B.; Titomanlio, G. In-mould shrinkage measurements of PS samples with strain gages. Int. Polym. Process. 1997, 12, 396. (7) Panchal, R. R.; Kazmer, D. O. In-situ shrinkage sensor for injection molding. J. Manuf. Sci. Eng. 2010, 132, 064503. (8) Kurt, M.; Kamber, O. S.; Kaynak, Y.; Atakok, G.; Girit, O. Experimental investigation of plastic injection molding: Assessment of the effects of cavity pressure and mold temperature on the quality of the final products. Mater. Design. 2009, 30, 3217. (9) Speranza, V.; Vietri, U.; Pantani, R. Monitoring of injection molding of thermoplastics: Average solidification pressure as a key parameter for quality control. Macromol. Res. 2011, 19, 542. (10) Jansen, K. M. B.; Pantani, R.; Titomanlio, G. As-molded shrinkage measurements on polystyrene injection molded products. Polym. Eng. Sci. 1998, 38, 254. (11) Liu, S.; Su, P.; Lin, K. In-situ temperature measurements in the depths of injection molded parts. Measurement 2009, 42, 771. (12) Vietri, U.; Sorrentino, A.; Speranza, V.; Pantani, R. Improving the predictions of injection molding simulation software. Polym. Eng. Sci. 2011, 51, 2542. (13) Sorrentino, A.; Pantani, R. Pressure-dependent viscosity and free volume of atactic and syndiotactic polystyrene. Rheol. Acta 2009, 48, 467. (14) Pantani, R.; Sorrentino, A. Pressure effect on viscosity for atactic and syndiotactic polystyrene. Polym. Bull. 2005, 54, 365. (15) Pantani, R. Validation of a model to predict birefringence in injection molding. Eur. Polym. J. 2005, 41, 1484. (16) Pantani, R.; Sorrentino, A.; Speranza, V.; Titomanlio, G. Molecular orientation in injection molding: Experiments and analysis. Rheol. Acta 2004, 43, 109. (17) Pantani, R.; Speranza, V.; Sorrentino, A.; Titomanlio, G. Molecular orientation and strain in injection moulding of thermoplastics. Macromol. Symp. 2002, 185, 293. (18) Pantani, R.; Titomanlio, G. Effect of pressure and temperature history on volume relaxation of amorphous polystyrene. J. Polym. Sci., Polym. Phys. 2003, 41, 1526. (19) Pantani, R. Pressure and cooling rate-induced densification of atactic polystyrene. J. Appl. Polym. Sci. 2003, 89, 184. (20) De Santis, F.; Pantani, R.; Speranza, V.; Titomanlio, G. Analysis of Shrinkage Development of a Semicrystalline Polymer during Injection Molding. Ind. Eng. Chem. Res. 2010, 49, 2469. (21) Pantani, R.; Speranza, V.; Titomanlio, G. Relevance of crystallisation kinetics in the simulation of the injection molding process. Int. Polym. Process. 2001, 16, 61. (22) Pantani, R.; Balzano, L.; Peters, G. Flow-induced morphology of iPP solidified in a shear device. Macromol. Mater. Eng. 2011, n/a−n/a. (23) Pontes, A.; Pantani, R.; Titomanlio, G.; Pouzada, A. S. Solidification criterion on shrinkage predictions for semi-crystalline injection moulded samples. Int. Polym. Process. 2000, 15, 284. (24) Pontes, A.; Pouzada, A. S.; Pantani, R.; Titomanlio, G. Ejection force of tubular injection moldings. Part II: A prediction model. Polym. Eng. Sci. 2005, 45, 325. (25) De Santis, F.; Pantani, R.; Speranza, V.; Titomanlio, G. Asmolded shrinkage on industrial polypropylene injection molded parts: Experiments and analysis. Int. J. Mater. Form. 2008, 1, 719. (26) Pantani, R.; Titomanlio, G. Description of PVT behavior of an industrial polypropylene−EPR copolymer in process conditions. J. Appl. Polym. Sci. 2001, 81, 267. (27) Pantani, R.; De Santis, F.; Brucato, V.; Titomanlio, G. Analysis of gate freeze-off time in injection molding. Polym. Eng. Sci. 2004, 44, 1. (28) Jansen, K. M. B.; Titomanlio, G. Effect of pressure history on shrinkage and residual stressesInjection molding with constrained shrinkage. Polym. Eng. Sci. 1996, 36, 2029.

each pressure curve the value of Ps is calculated and a master curve of shrinkage versus Ps is built; afterward, the procedure is able to automatically associate a value of shrinkage to each test by calculating online the value of Ps from each experimental pressure curve. On observing Figure 6, it is possible to notice that for very low values of average solidification pressure, shrinkage decreases very rapidly on increasing Ps. This happens because in those conditions (very low pressures or very short holding times) shrinkage takes place inside the cavity before complete solidification.6 On increasing Ps, the plot becomes linear. This is consistent with the fact that, according to the model by Jansen and Titomanlio,28,34 when shrinkage starts after complete solidification, the plot reporting the shrinkage versus the average solidification pressure is linear, with a slope equal to the material linear compressibility. If one calculates the slope of the data reported in Figure 6 for average solidification pressures larger than 100 bar the value found is 0.8 × 10−5 bar, not far from the value of linear compressibility of the PS adopted for this work (10−5 bar10). Similarly, for the slope of the data reported in Figure 7 for average solidification pressures larger than 100 bar the value found is 2.5 × 10−5 bar, not far from the value of linear compressibility of the iPP adopted for this work (2 × 10−5 bar20).

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CONCLUSIONS In this work a procedure was defined and illustrated which allows the calculation, by analyzing the local pressure evolution measured by a conventional pressure transducer, of a parameter, namely the average solidification pressure, which is known to be critical for the description of local shrinkage. The procedure was applied to a general purpose PS and to an industrial iPP, injection molded in a very wide range of processing conditions, also changing key geometrical parameters. The described procedure is particularly suitable for online monitoring of the chosen quality parameter and requires neither the knowledge of local thickness nor of the molding conditions. Furthermore, it can be applied without any characterization of the physical parameters of the material. The procedure is suitable for a master-curve approach in which some data of shrinkage versus the average solidification pressure can be used as a reference in order to estimate the shrinkage of the part by analyzing the local pressure evolution.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Chen, Z. B.; Turng, L. S. A review of current developments in process and quality control for injection molding. Adv. Polym. Technol. 2005, 24, 165. (2) Michaeli, W.; Schreiber, A. Online control of the injection molding process based on process variables. Adv. Polym. Technol. 2009, 28, 65. (3) Visvanathan, K.; Balasubramaniam, K. Ultrasonic torsional guided wave sensor for flow front monitoring inside molds. Rev. Sci. Instrum. 2007, 78, 015110. 16040



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(29) Pantani, R.; Titomanlio, G. Analysis of shrinkage development of injection moulded PS samples. Int. Polym. Process. 1999, 14, 183. (30) Pantani, R.; Titomanlio, G. Chapter 3 Dimensional Accuracy in Injection Molding: State of the Art and Open Challenges. Precision Injection Molding; Carl Hanser Verlag: Munich, Germany, 2006. (31) Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids; Clarendon Press: Oxford, 1986. (32) Pantani, R.; Speranza, V.; Titomanlio, G. Relevance of moldinduced thermal boundary conditions and cavity deformation in the simulation of injection molding. Polym. Eng. Sci. 2001, 41, 2022. (33) Jansen, K. M. B. Residual-stresses in quenched and injectionmolded products. Int. Polym. Process. 1994, 9, 82. (34) Titomanlio, G.; Jansen, K. M. B. In-mold shrinkage and stress prediction in injection molding. Polym. Eng. Sci. 1996, 36, 2041.

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