Numerical Modeling of Bubble Growth in Microcellular ...

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J. A. Reglero Ruiz*, M. Vincent , J.-F. Agassant

International Polymer Processing downloaded from www.hanser-elibrary.com by Hanser Verlag (Office) on March 16, 2016 For personal use only.

Centre de Mise en Forme des Matériaux, MINES ParisTech, UMR CNRS 7635, Sophia Antipolis, France

Numerical Modeling of Bubble Growth in Microcellular Polypropylene Produced in a Core-Back Injection Process Using Chemical Blowing Agents A core-back polypropylene foaming injection process using chemical blowing agents (CBA) has been studied. First, injection tests were carried out with two different CBAs and the different morphologies of the obtained samples have been analyzed. Structural parameters such as cell density and average radius size were calculated. Then, a bubble growth model was developed to predict the foaming development during the process, controlled by the depressurization of the mold cavity during the short core-back opening coupled with the evolution of the temperature during core-back and subsequent cooling. A good agreement is found between theoretical predictions and experimental results.

1 Introduction The foaming process to produce microcellular thermoplastics has been widely analyzed in the last decades. Microcellular plastics are formed by cell nucleation and growth of bubbles in the polymer matrix. Chemical blowing agents (CBA) or physical blowing agents (PBA) are used to introduce the gas that creates the cellular structure. A typical polymer foaming process involves several steps: the dissolution under an elevated pressure of a gas blowing agent (PBA or CBA) in the molten polymer, the nucleation of a population of gas clusters in the supersaturated solution upon the release of pressure to the ambient pressure and finally the growth of nucleated bubbles in the polymer to their ultimate equilibrium size. The final foam density depends on the original gas loading, the gas fraction which remains dissolved in the polymer matrix when it solidifies, the gas losses to the environment, and the depressurization rate. The cell size and cell size distribution depend on the kinetics of nucleation, the bub* Mail address: José Antonio Reglero Ruiz, MINES ParisTech-Centre de Mise en Forme des Matériaux (CEMEF), UMR CNRS 7635, 1, rue Claude Daunesse, CS 10207, 06904-Sophia Antipolis Cedex, France E-mail: [email protected]

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ble growth process following nucleation and the coalescence during expansion. The PBA process consists in introducing a physical blowing agent, usually N2 or CO2, directly into the barrel in a supercritical fluid state (SCF), in proportions around 2 % in weight (Tomasko et al., 2009; Park and Suh, 1996). The injection machine must be modified, resulting in an initial increase of the production costs. The Mucell process (Trexel Inc., Wilmington, MA, USA) is now largely used to produce injected foamed parts. The second process uses chemical blowing agents (CBA) (Behravesh et al., 1996; Bociaga and Palutkiewicz, 2013). The foaming agent is added in the form of pellets to the feeder of the injection machine, in a proportion between 1 and 2 % in weight. The foaming agent usually employed for polypropylene is a low density polyethylene charged with a percentage of inorganic compounds, such as citric acid or sodium bicarbonate, which decompose at temperatures close to the melting point of the polymer, generating the gas, mainly CO2 and water vapor. The polymer with the solubilized gas is then injected into the mold, and foaming occurs by depressurization during the injection process. For both techniques (PBA or CBA) the viscosity of the polymer/dissolved gas system is lower than the viscosity of the polymer melt itself, so the parts can be injection molded with a slightly lower pressure. The presence of a solid outer skin leads to a correct surface quality of molded parts. Moreover, the cell growth mechanism favors the part packing and reduces residual stresses. The main advantage of CBA process compared to PBA is that no modification of the injection machine is needed, because the foaming agent is directly added into the barrel through the hopper. On the other hand, a more accurate control of the plastication parameters is required to obtain optimal injected foamed parts. The core-back expansion process which is investigated in this paper derives from the classical injection molding process. A command module is added to control the movement of the mobile part of the mold. After mold filling and a short packing step where solidified layers without bubbles developing, the mold is accurately opened to quickly increase the cavity volume and rapidly reduce pressure. The sudden pressure drop en-

Carl Hanser Verlag, Munich Intern. Polymer Processing XXXI (2016) 1


J. A. Reglero Ruiz et al.: Numerical Modeling of Bubble Growth in Microcellular PP hances bubble nucleation and achieves a fine cell structure within the polymer foam. Thus, core-back foam injection molding is effective in achieving a high expansion ratio with uniform cell structure. In the case of CBA foaming process, it can be considered in a first approximation that the decomposition reaction is complete in the screw-barrel system and that all the gas is generated, diffused and solubilized into the polymer matrix. The solubilization of the gas into the polymer depends of the pressure and time during the plastication process. One of the main problems associated with foam injection molding is related to foam evolution during filling stage. It is known that foaming starts generally during mold filling thus leading to inhomogeneous foam structures, as observed by Villamizar and Han, 1978. The resulting products usually have severe surface defects such as swirl marks and lack of smoothness (Cha and Yoon, 2005; Guo et al., 2007). The introduction of a gas counter pressure (GCP) has been recently proved to improve the surface quality of molded parts as well as the homogeneity of the microcellular structure. In this process, after mold closing, the mold cavity is pressurized around 2 MPa, and the melt is injected in the mold cavity in this highpressure environment. This reduces melt foaming during mold filling and the fracture of the cells, and the swirl marks on the surface of plastic parts are decreased or eliminated. Many studies have been devoted to the development of numerical models for the bubble growth in polymeric foaming process. In the early work (Amon and Denson, 1984), a mathematical analysis of a bubble growth in a Newtonian matrix is presented. Bikard et al. (2005) and Bruchon and Coupez (2008) solved the same problem with a 3D finite element method which allows accounting for the simultaneous growing of multiple bubbles. Koopmans et al. (2000) introduced a viscoelastic multimode Maxwell behavior for the polymer matrix in a \bubble influence volume" surrounding the growing bubble. They also accounted for non-isothermal phenomena occurring at die exit in an extrusion process. Otsuki and Kanai (2005) used the Phan-Thien Tanner viscoelastic constitutive equation which limits the dramatic increase of the elongation viscosity in the Maxwell model. Shafi et al. (1996, 1997) and Joshi et al. (1998) developed a homogeneous nucleation model that they coupled to the Newtonian Amon and Denson bubble growing model. Taki (2008) compared these calculation results to experiments performed under several pressure release rates. There are a few studies concerning the modeling of bubble growth in injection processes. Ishikawa et al. (1996) analyzed the foaming behavior in core-back expansion molding of polypropylene and compared the results to numerical modeling. However, this interesting study is only focused on bubble growth process during core-back expansion, and it is limited to isothermal conditions. The physical evolution of the polymer-gas system depends strongly on the temperature, pressure and kinetics of the chemical reactions. In our previous work (Reglero Ruiz et al., 2015), a simple experiment has been designed to analyze the foaming expansion as a function of time of a polypropylene containing three types of CBA, in static conditions (no flow). The expansion ratio has been measured by direct observation from optical measurements and image analysis. A single bubble simulation based on DSC and TGA experiments, assuming Intern. Polymer Processing XXXI (2016) 1

each CBA particle is a nucleation site and accounting for gas diffusion in the surrounding polymer matrix has been built. The sensitivity of the model to physical and processing parameters has been tested and the results compared to the experiments with a good agreement. Following this previous work, the present investigation applies the same modeling scheme to injection foaming processes. Thus, the study is focused on the morphological observation and modeling of polypropylene injection foaming using two different Chemical Blowing Agents and a core-back expansion molding process coupled with GCP. First, a detailed analysis of the raw materials, both polypropylene and CBAs, will be presented. Then, the resulting morphology of the injected samples will be analyzed. In the last part of the paper, a bubble growth model, which couples the depressurization process, the core-back process and the temperature evolution during cooling is presented. Finally, a comparison between experimental and theoretical results will be discussed. 2 Raw Materials A pure polypropylene with a melt flow index of 65 g/10 min (ISO R1133), and a density of 0.91 g cm–3 was employed. Two different endothermic chemical blowing agents referred as CBA-1 and CBA-2 have been used. These foaming agents are polyethylene-based compounds. CBA-1 contains 35 wt.% of citric acid and 35 wt.% of sodium bicarbonate, and CBA-2 contains 70 wt.% of citric acid (wt.% respect to the polyethylene matrix). In the following, CBA refers to the compound and not to the reactive elements only. Thermal characterization was carried out using equipment of Perkin Elmer, Waltham, MA, USA, model DSC 400, under nitrogen atmosphere at a heating rate of 70 8C min–1. This value was chosen to assure a similar heating rate as observed in the plastication system of the injection units. This allows determining the polypropylene fusion temperature and the decomposition temperatures of each reaction of the reactive elements included in the CBA pellets. The melting temperature of the polypropylene matrix is between 160 8C and 170 8C and the melting temperature of the polyethylene in the CBAs is around 100 8C. The decomposition reaction temperature of the citric acid in CBA-2 is around 215 8C. For the CBA-1, at heating rates above 20 8C min–1, only the coupled reaction of the sodium bicarbonate and the citric acid is dominant. It appears between 200 8C and 220 8C (Reglero Ruiz et al., 2015). The crystallization behavior of the polypropylene was also analyzed using DSC tests. After a first heating ramp from room temperature to 275 8C, polymers were cooled down at two different rates (70 8C min–1 and 5 8C min–1), to evaluate the effect of the cooling rate on the crystallization temperature. The crystallization temperature is around 125 8C when cooling rate is 70 8C min–1, and 155 8C when cooling rate is 5 8C min–1. TGA measurements were carried out at the IMP laboratory (Université Jean Monnet, Saint Etienne, France) using equipment of Mettler Toledo, Columbus, OH, USA, under nitrogen atmosphere and a heating rate of 70 8C min–1 to determine the quantity of gas released by the reactive elements in the CBA pellets (Fig. 1). The relative weight loss refers to the original weight of the granule containing 30 wt. % of polyethylene and 27


J. A. Reglero Ruiz et al.: Numerical Modeling of Bubble Growth in Microcellular PP

Fig. 1. TGA curves of the CBA particles (heating rate 70 8C min–1)

70 wt. % of reactive elements. Before polyethylene decomposition which begins around 450 8C, the weight loss is associated to the gas escaping the sample, which is composed of CO2 and H2O. The temperature at the beginning of the decomposition reaction of CBA-1 and CBA-2 are respectively 190 8C and 215 8C. The citric acid decomposition reaction in CBA-1 is coupled with the sodium bicarbonate reaction as it can be observed in the small change in the slope about 220 8C. At 400 8C the weight loss is nearly stabilized. We will assume that the decomposition reactions of both CBAs are completed. The weight percentage of gas created for CBA-1 and CBA-2 are respectively 30 % and 35 %. The TGA results are in qualitative agreement with the DSC measurements, with a reaction occurring at temperature lower for CBA-1 than for CBA-2. Rheological characterization of raw materials was carried out using a TA Instruments Ares, New Castle, DE, USA, rotational rheometer. Tests were performed in dynamic mode between parallel plates (diameter 25 mm, gap 2 mm) with frequencies between 1 s–1 and 100 s–1, and temperatures between 180 8C and 220 8C. The viscosity curves relating the viscosity g to the shear rate c_ were fitted with a Carreau Yasuda law, coupled with an Arrhenius law for the thermal dependence, according to the following equations: _ TÞ ¼ aT ðTÞgðT0 Þð1 þ ðkca _ T ðTÞÞa Þ gðc; aT ðTÞ ¼ exp

Ea 1 < T

1 T0

:

ðm 1Þ=a

;

ð1Þ ð2Þ

The Carreau Yasuda law parameters were: k = 0.21 s, a = 0.485, m = 0.478, g(T0) = 498 Pa s. The reference temperature T0 was 210 8C, and the activation energy EA was 26 913 J/mol. < is the gas constant. 3 Experiments Injection tests were carried out using a machine of 80 tons clamping force (Engel, Schwertberg, Austria) with a maximal injection capacity of 150 cm3. It is equipped with a shut-off 28

nozzle. The barrel temperature profile reaches 230 8C at the plastication unit nozzle, and the residence time of the melt in the screw/barrel system is long enough to assure that all the decomposition reactions are completed. Moreover, all the decomposition reactions of the CBAs start after the polypropylene fusion which assures that the gas can be diluted in the melted matrix. Moreover, according to the screw back pressure (7 MPa) and shut-off nozzle, it can be assumed that all the generated gas is diluted in the molten polymer before injecting the material. The total quantity of gas generated can be estimated from the TGA curves presented in Fig. 1. For a value of 2 wt.% of CBA added into the hopper, 0.02 g of CBA are introduced per g of polypropylene, which gives a relative value of gas of 0.006 ggas/gPP for CBA-1 and 0.007 ggas/gPP for CBA-2. Part of the gas generated corresponds to H2O vapor that after foaming and cooling remains in the samples as condensed water vapor. Specifically, about 30 % of all the gas generated corresponds to H2O vapor and the rest is CO2. The maximum quantity of CO2 that can be diluted at the temperature and pressure conditions in the nozzle is about 0.05 gCO2/gPP, as it is demonstrated in the work of Lei et al. (2007). Thus, the quantity of gas generated in our injection process is well below the solubility limit. Rectangular plates (length: 165 mm; width: 95 mm) were molded. The gate is located close to the middle of the plate width. The initial plate thickness during mold filling and packing is increased during core-back reaching a final thickness of 2.5 mm to allow the space for bubble growth. The total volume of the sample including sprue and gate was about 36 cm3. The injection temperature was 230 8C, and injection flow rate was fixed at 180 cm3 s–1. Mold temperature was set at 50 8C. During the filling stage, a Gas Counter Pressure (GCP) of 1.5 MPa is imposed in the cavity to block the foaming expansion in the polymer melt before the end of filling. The packing pressure is much higher. This assures that foaming mostly takes place during core-back process. The packing stage takes about 1 s. A pressure transducer is located in the mold 5 mm downstream the gate. Figure 2A presents the experimental pressure evolution on the whole cycle and Fig. 2B is focused on the core-back opening step, together with the saturation pressures of the gas released for both CBAs. The same pressure curves were obtained for CBA 1 or 2. At the end of the packing step, the pressure reaches 0. Then, in the early stage of the mold opening, pressure increases to reach 0.32 MPa (t = 2 s). This is associated to the bubble growth. Then, as the mold opens, the pressure decreases and reaches atmospheric pressure at time 2.4 s. Two sets of injection tests were carried out, for CBA-1 and CBA-2. All the injection parameters were the same in both tests. A minimum of three plates for each condition were analyzed to evaluate the reproducibility of the morphology results. Morphological observations were carried out in samples fractured at ambient temperature to assure a good contrast between solid and foamed regions. The fracture surfaces were observed with optical microscopy. Figures 3A and B correspond to CBA-1 in directions parallel and perpendicular to the flow direction (which is horizontal on the figures; the vertical side of the picture corresponds to the part thickness) and Figs. 3C and 3D correspond to CBA-2 also in parallel and perpendicular Intern. Polymer Processing XXXI (2016) 1


J. A. Reglero Ruiz et al.: Numerical Modeling of Bubble Growth in Microcellular PP directions. All images were taken from the center of each plate, with a good reproducibility in each test. In Fig. 3A, zones A, B, C and D represent the four different regions that will be lately analyzed in the bubble growth modeling. A deep analysis of the morphology of the samples obtained can be found in Reglero Ruiz et al., 2015. All the foamed samples present a typical solid outer skin, with a thickness of 350 lm each side. The final density of the plates was about 0.60 g cm–3 for both CBAs, which indicates a foaming expansion ratio of 1.5. The core foamed density was calculated from the mixture’s law, using the relative thickness of the solid and core regions and the value of the density of

the solid polypropylene (0.91 g cm–3). The value obtained was about 0.45 g cm–3 in all the cases. The experimental determination of average bubble radius was carried out by image analysis using the ImageJ software (National Institutes of Health, Bethesda, MD, USA). The minimal observable size is 10 mm using optical microscopy. The experimental average 3D radius R can be deduced from the 2D image assuming a spherical geometry of the cells, from the following equation: PN n i Ri : ð3Þ R ¼ Pi¼1 N i¼1 ni

A)

B)

Fig. 2. Pressure evolution during injection process, A) comparison between experimental results and Rem3D prediction, B) depressurization curve during mold opening

A)

C)

B)

D)

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Fig. 3. Optical micrographs obtained from injected samples (bar scale 1 mm), A) CBA-1, parallel to flow, B) CBA-1, perpendicular to flow, C) CBA-2, parallel to flow, D) CBA-2, perpendicular to flow

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J. A. Reglero Ruiz et al.: Numerical Modeling of Bubble Growth in Microcellular PP The calculation was performed for five different SEM micrographs of each sample. The dispersion value was about ±10 %. Samples obtained with CBA-1 (Fig. 3A and B), present bigger bubbles than samples obtained with CBA-2 (Fig. 3 C and D). Average values of bubble radius are about 70 lm for samples obtained with CBA-1 and 40 lm for samples obtained with CBA-2, with small variations between the core and the external regions as shown in Table 2, placed later in the paper. 4 Foaming Process Modeling


4.1 Modeling Strategy Modeling of the core-back injection foaming process has been carried out at two scales. The temperature evolution is calculated at the scale of the part, in the thickness referred as the y axis. The bubble growth is calculated at the scale of the bubble. The following strategy has been followed: 4.1.1 At the Scale of the Part 1. Mold filling and packing is computed using REM3D software (Silva et al., 2009) with the following parameters: injection temperature 230 8C, flow rate of 180 cm3 s–1 and mold temperature 50 8C. The influence of dissolved gas on viscosity will be neglected (Lee et al., 1999) and the viscosity of polypropylene will be considered. As indicated on Fig. 2, the computed pressure is consistent with the experimental one during filling and packing which allows being confident in the temperature profile through the plate thickness, especially at the end of the packing stage as shown in Fig. 4 for a point located in the middle of the plate. This temperature profile is quite uniform in the plate. The region below the crystallization temperature TC is shown. TC has been taken equal to 125 8C from the DSC measurements at a cooling rate of 70 8C min–1. Points A, B, C and D represent the regions of the plate in which bubble growth is modeled. Point O is located at the interface between molten and crystallized polymer. 2. During the core back step, the heat transfer equation is solved in the thickness (y direction) with a total thickness (2a) changing between two time steps. Thermal conductivity and heat capacity are function of the foam development. Enthalpy of crystallization is not accounted for. The tem-

perature profile of the molten core is homotetically transported for the next time step with a larger thickness. After the end of the mold opening phase, the temperature calculation proceeds with a constant thickness. The thermophysical parameters continue to evolve as foaming proceeds.

4.1.2 Bubble Growth Calculation 1. The nucleation process is not modeled and bubbles with an initial radius such that dR/dt = 0 (see Eq. 4), are distributed through the plate thickness and their developments are followed during the whole process. The initial radius corresponds to the minimum of free energy and it varies through the plate thickness (see Table 1). More detailed information can be found in Colton et al. (1987). 2. Bubble growth develops as a function of pressure and temperature. Physical parameters, such as viscosity, diffusion coefficient and surface tension are function of the temperature. The initial concentration of diluted gas is determined according to the TGA measurements. It is supposed to remain constant at an infinite distance from the bubble. 3. The pressure decrease during the core-back mold opening step cannot be easily computed and the experimental pressure trace (Fig. 2B) has been used.

Fig. 4. Temperature profile through the plate thickness after filling and packing (computed in the central part of the plate)

Region

T 8C

g Pa s

D 10 m2 s–1

c J m–2

K mol m–3 Pa–1

R0CBA1 m

R0CBA2 m

O A B C D

125 180 200 225 235

2 084 776 574 407 358

3.90 5.39 5.94 6.62 6.89

1.51 · 10–2 1.28 · 10–2 1.19 · 10–2 1.09 · 10–2 1.04 · 10–2

5.51 · 10–4 8.38 · 10–4 9.42 · 10–3 1.07 · 10–3 1.12 · 10–3

8.07 · 10–8 1.86 · 10–7 2.74 · 10–7 5.76 · 10–7 9.84 · 10–7

5.72 · 10–8 1.07 · 10–7 1.35 · 10–7 1.86 · 10–7 2.16 · 10–7

–9

Table 1. Values of temperature, viscosity, diffusion coefficient, surface tension, solubility factor and bubble radius for each region at the intial time

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Intern. Polymer Processing XXXI (2016) 1

J. A. Reglero Ruiz et al.: Numerical Modeling of Bubble Growth in Microcellular PP 4. After core-back, (0.4 s), foaming continues to develop at atmospheric pressure and at decreasing temperature.

Pext ðtÞ ¼


4.2 Equations and Numerical Simulation A schematic of the bubble growth is shown in Fig. 5. The gas created by the CBA decomposition during the plastication step dissolves into the molten polymer under a given pressure. Thus, the initial gas concentration is uniform in the matrix, namely C0. When depressurization occurs during the core-back opening, the gas-polymer system reaches a supersaturation state and bubble nucleation and growth begins with a diffusion of the gas from the polymer to the bubble. Therefore the gas concentration C is a function of the bubble radius R and time t. As mentioned before, the concentration far from the bubble is supposed to remain constant and equal to C0. The following assumptions are made: 1. The bubble is spherically symmetric when it nucleates and remains so for the entire period of growth. 2. The polymer matrix is Newtonian. As it is assumed that blowing takes place after the injection molding step, very low rates of strain are encountered during foaming, with values about 10–6 s–1 (Reglero Ruiz et al., 2015), so it is possible to neglect the shear thinning behavior of the polymer matrix. 3. The growth process is considered isothermal inside each single bubble. Latent heat of reaction is neglected. 4. Inertia effects are neglected and the polymer matrix is assumed to be incompressible, which is reasonable in the pressure range studied. 5. The gas inside the bubble follows the ideal gas law. 6. The matrix is considered as an infinite medium and one single bubble is considered at each position through the part thickness. The ordinary differential equation for the bubble radius growth as a function of time (momentum balance), writes according to Taki (2008): dR R ¼ Pgas dt 4g

Pext

2c ; R

R is the bubble radius, g is the polymer viscosity, Pgas is the pressure in the bubble, c is the surface tension. The external pressure evolution Pext can be described by:

ð4Þ

Pcore back ðtÞ; 2 t 2:4 s Pamb ¼ 0:1 MPa; t > 2:4 s:

ð5Þ

Pamb is the ambient pressure after core-back process. The diffusion equation writes: dC qC qC DðTÞ q 2 qC ¼ þ uðr; tÞ ¼ 2 r : dt qt qr r qr qr

ð6Þ

C(r,t) is the concentration of dissolved gas in the polymer matrix at a given time t and radius r. D is the diffusion coefficient. As demonstrated in Reglero Ruiz et al. (2015), it is possible to qC neglect the term uðr; tÞ . The gas balance of a bubble is given qr by: dn d 4pR3 Pgas ¼ 3