la Loire (CCIPL), where each simulation took approximately 2 minutes in one single core, and the total optimization process took roughly 12 hours in 40 cores.

<figure><img src="image_2541.png" /><figcaption>Figure 5: TO solutions obtained by the gradient-based approach [8], and the gradient-free proposed in this work. In (a) and (b) blue regions represent copper material, while red zones represent PMMA material. In (c) the heat flux in $\Omega_{task}$ in time is compared.</figcaption></figure>

<figure><img src="image_2542.png" /><figcaption>Figure 6: Results obtained by the topologic optimization scheme: (a) convergence of the objective function, (b) constraint computation, (c) temperature at A-B in $\Gamma_p$ (see Fig. 1b).</figcaption></figure>

Results Obtained by the PSO-TO in the Injection Mold. The convergence tendency of $f_{obj}$ is evident from Fig. 6a, and the final best value was $\sigma_p = 1.62$ K after reaching 15000 $f_{obj}$ evaluations. The accomplishment of the maximum temperature constraint at $\Gamma_e$ can be observed in Fig. 6b, and the resulting $\bar{T}_e$ was 334.68 °C. The results are summarized in Table 4 where it can be deduced that, for the same cycle time ($t_f = 140$ s), a marked improvement is obtained in the temperature homogeneity by combining the two thermoplastics, reducing $\sigma_p$ by 52 %, and obtaining a similar value to that of steel.

<table><caption>Table 4: Results obtained by the mono-material and the optimized multi-material molds.</caption><thead><tr><th></th><th>Steel</th><th>Plastic (mono-material)</th><th>Plastic (multi-material)</th></tr></thead><tbody><tr><td>t<sub>f</sub> [s]</td><td>23.5</td><td>140</td><td>140</td></tr><tr><td>T&#773;<sub>e</sub> [K]</td><td>336.31</td><td>334.12</td><td>334.68</td></tr><tr><td>T&#773;<sub>p</sub> [K]</td><td>310.82</td><td>331.76</td><td>332.67</td></tr><tr><td>σ<sub>p</sub> [K]</td><td>1.42</td><td>3.37</td><td>1.62</td></tr><tr><td>ΔT<sub>Γ<sub>2</sub></sub> [K]</td><td>7,14</td><td>23.56</td><td>13.32</td></tr></tbody></table>
It can be seen from the profile temperature presented in Fig. 6c that the main peak of delta
temperature is given near the central zone of the T-shaped part (arc length = 0.13 m). This region
is of course, the most challenging one to evenly cool down. The optimized topology of the multi-
material injection mold is presented in Fig. 7. It is interesting to notice that the scheme proposes
the insulating polymer mainly at the corners of the T-shaped part. This is explained by the fact that
such regions with high surface-to-volume ratios cool down quicker than other regions. On the other
hand, the opposite occurs at the near-ribbed region of the piece with a slower cooling, and thus,
the scheme proposes the high-conductive polymer at its surroundings. In Fig. 8 are represented the
temperature field within the injected part at t<sub>e</sub> = 140 s for the mono-material and the multi-
material optimized molds. The improvement in temperature homogeneity at the end of cooling is
very marked for the optimized mold, where, if disregard the central part of the piece, the
temperatures remain fairly constant.

<figure><img src="image_2550.png" /><figcaption>Figure 7: TO result of material distribution within the mold.</figcaption></figure>

<figure><img src="image_2551.png" /><figcaption>Figure 8: Temperature at the T-shaped injected part at t<sub>e</sub> = 140 s, obtained by the non-
optimized mono-material mold (top), and the optimized multi-material thermoplastic mold
(bottom).</figcaption></figure>

Conclusions

A numerical scheme for topology optimization of a thermoplastic injection mold was presented in detail. The scheme proved to successfully handle transient heat flux manipulation addressing complex geometries and complex heat transfer scenarios such as those encountered in the injection molding process featuring thermal contact resistances, cooling channels, and multiple injection cycles. The performance of the scheme was tested on a heat flux shielding scenario in the transient regime and the results were compared with those of the literature. The gradient-free TO scheme proposed here proved to slightly outperform the gradient-based TO approach. The methodology was successfully applied to the thermal design of thermoplastic injection mold combining two polymers of different thermal conductivity. It was shown that by employing the low-conductivity polymer at easy-to-cool regions such as corners, the standard temperature deviation at the part surface can be improved by 52 % while employing the same cycle time of the highly conductive mono-material case. Furthermore, the delta temperature at the part surface can be reduced by up
It can be seen from the profile temperature presented in Fig. 6c that the main peak of delta temperature is given near the central zone of the T-shaped part (arc length = 0.13 m). This region is of course, the most challenging one to evenly cool down. The optimized topology of the multi-material injection mold is presented in Fig. 7. It is interesting to notice that the scheme proposes the insulating polymer mainly at the corners of the T-shaped part. This is explained by the fact that such regions with high surface-to-volume ratios cool down quicker than other regions. On the other hand, the opposite occurs at the near-ribbed region of the piece with a slower cooling, and thus, the scheme proposes the high-conductive polymer at its surroundings. In Fig. 8 are represented the temperature field within the injected part at $t_e = 140$ s for the mono-material and the multi-material optimized molds. The improvement in temperature homogeneity at the end of cooling is very marked for the optimized mold, where, if disregard the central part of the piece, the temperatures remain fairly constant.

<figure><img src="image_2543.png" /><figcaption>Figure 7: TO result of material distribution within the mold.</figcaption></figure>

<figure><img src="image_2544.png" /><figcaption>Figure 8: Temperature at the T-shaped injected part at $t_e = 140$ s, obtained by the non-optimized mono-material mold (top), and the optimized multi-material thermoplastic mold (bottom).</figcaption></figure>

## Conclusions

A numerical scheme for topology optimization of a thermoplastic injection mold was presented in detail. The scheme proved to successfully handle transient heat flux manipulation addressing complex geometries and complex heat transfer scenarios such as those encountered in the injection molding process featuring thermal contact resistances, cooling channels, and multiple injection cycles. The performance of the scheme was tested on a heat flux shielding scenario in the transient regime and the results were compared with those of the literature. The gradient-free TO scheme proposed here proved to slightly outperform the gradient-based TO approach. The methodology was successfully applied to the thermal design of thermoplastic injection mold combining two polymers of different thermal conductivity. It was shown that by employing the low-conductivity polymer at easy-to-cool regions such as corners, the standard temperature deviation at the part surface can be improved by 52 % while employing the same cycle time of the highly conductive mono-material case. Furthermore, the delta temperature at the part surface can be reduced by up
to 10 °C when employing the multi-material thermoplastic mold. Future works comprise addressing three-dimensional cases featuring complex geometries with the consequent larger number of design variables.

## References

[1] A. Agazzi, Contribution à l'optimisation de la thermique des outillages dans le procédé d'injection des polymères thermoplastiques, Ph.D. thesis, Université de Nantes (2011).

[2] C.-C. Kuo, S.-X. Qiu, G.-Y. Lee, J. Zhou, H.-Q. He, Characterizations of polymer injection molding tools with conformal cooling channels fabricated by direct and indirect rapid tooling technologies, Int. J. Adv. Manuf. Technol. 117 (2021) 343-360. https://doi.org/10.1007/s00170-021-07778-w

[3] B. A. Storti, V. Sobotka, Thermal design of cooling channels in an injection plastic mold by overset-based numerical optimization technique, in: International Heat Transfer Conference Digital Library, Begel House Inc., 2023. https://doi.org/10.1615/IHTC17.210-10

[4] B. A. Storti, V. Sobotka, A numerical framework for three-dimensional optimization of cooling channels in thermoplastic printed molds, Appl. Therm. Eng. 238 (2024) 121988. https://doi.org/10.1016/j.applthermaleng.2023.121988

[5] A. Agazzi, V. Sobotka, R. LeGoff, Y. Jarny, Optimal cooling design in injection moulding process – a new approach based on morphological surfaces Appl. Therm. Eng. 52 (1) (2013) 170-178. https://doi.org/10.1016/j.applthermaleng.2012.11.019

[6] A. R. J. Hussain, A. A. Alahyari, S. A. Eastman, C. Thibaud-Erkey, S. Johnston, M. J. Sobkowicz, Review of polymers for heat exchanger applications: Factors concerning thermal conductivity, Appl. Therm. Eng. 113 (2017) 1118-1127. https://doi.org/10.1016/j.applthermaleng.2016.11.041

[7] I. Peralta, V. D. Fachinotti, J. C. Alvarez Hostos, A brief review on thermal metamaterials for cloaking and heat flux manipulation, Adv. Eng. Mater. 22 (2) (2020) 1901034. https://doi.org/10.1002/adem.201901034

[8] J. C. A. Hostos, B. Storti, N. Lefevre, V. Sobotka, S. L. Corre, V. D. Fachinotti, Design via topology optimisation and experimental assessment of thermal metadevices for conductive heat flux shielding in transient regime, Int. J. Heat Mass Transf. 212 (2023) 124238. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124238

[9] G. V. Alekseev, D. A. Tereshko, Particle swarm optimization-based algorithms for solving inverse problems of designing thermal cloaking and shielding devices, Int. J. Heat Mass Transf. 135 (2019) 1269-1277. https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.072

[10] I. Peralta, V. D. Fachinotti, A. A. Ciarbonetti, Optimization-based design of a heat flux concentrator, Sci. Rep. 7 (1) (2017) 40591. https://doi.org/10.1038/srep40591

[11] I. Peralta, V. D. Fachinotti, Optimization-based design of heat flux manipulation devices with emphasis on fabricability, Sci. Rep. 7 (1) (2017) 6261. https://doi.org/10.1038/s41598-017-06565-6

[12] L. Q. Tang, K. Pochiraju, C. Chassapis, S. Manoochehri, A Computer-Aided Optimization Approach for the Design of Injection Mold Cooling Systems, J. Mech. Des. 120 (2) (1998) 165-174. https://doi.org/10.1115/1.2826955

[13] V. Sobotka, A. Agazzi, N. Boyard, D. Delaunay, Parametric model for the analytical determination of the solidification and cooling times of semi-crystalline polymers, Appl. Therm. Eng. 50 (1) (2013) 416-421. https://doi.org/10.1016/j.applthermaleng.2012.07.019

[14] A. E. Albanesi, I. Peralta, F. Bre, B. A. Storti, V. D. Fachinotti, An optimization method based on the evolutionary and topology approaches to reduce the mass of composite wind turbine blades, Struct. Multidiscipl. Optim. 62 (2020) 619-643. https://doi.org/10.1007/s00158-020-02518-2
to 10 °C when employing the multi-material thermoplastic mold. Future works comprise addressing three-dimensional cases featuring complex geometries with the consequent larger number of design variables.

## References

[1] A. Agazzi, Contribution à l'optimisation de la thermique des outillages dans le procédé d'injection des polymères thermoplastiques, Ph.D. thesis, Université de Nantes (2011).

[2] C.-C. Kuo, S.-X. Qiu, G.-Y. Lee, J. Zhou, H.-Q. He, Characterizations of polymer injection molding tools with conformal cooling channels fabricated by direct and indirect rapid tooling technologies, Int. J. Adv. Manuf. Technol. 117 (2021) 343-360. https://doi.org/10.1007/s00170-021-07778-w

[3] B. A. Storti, V. Sobotka, Thermal design of cooling channels in an injection plastic mold by overset-based numerical optimization technique, in: International Heat Transfer Conference Digital Library, Begel House Inc., 2023. https://doi.org/10.1615/IHTC17.210-10

[4] B. A. Storti, V. Sobotka, A numerical framework for three-dimensional optimization of cooling channels in thermoplastic printed molds, Appl. Therm. Eng. 238 (2024) 121988. https://doi.org/10.1016/j.applthermaleng.2023.121988

[5] A. Agazzi, V. Sobotka, R. LeGoff, Y. Jarny, Optimal cooling design in injection moulding process – a new approach based on morphological surfaces Appl. Therm. Eng. 52 (1) (2013) 170-178. https://doi.org/10.1016/j.applthermaleng.2012.11.019

[6] A. R. J. Hussain, A. A. Alahyari, S. A. Eastman, C. Thibaud-Erkey, S. Johnston, M. J. Sobkowicz, Review of polymers for heat exchanger applications: Factors concerning thermal conductivity, Appl. Therm. Eng. 113 (2017) 1118-1127. https://doi.org/10.1016/j.applthermaleng.2016.11.041

[7] I. Peralta, V. D. Fachinotti, J. C. Alvarez Hostos, A brief review on thermal metamaterials for cloaking and heat flux manipulation, Adv. Eng. Mater. 22 (2) (2020) 1901034. https://doi.org/10.1002/adem.201901034

[8] J. C. A. Hostos, B. Storti, N. Lefevre, V. Sobotka, S. L. Corre, V. D. Fachinotti, Design via topology optimisation and experimental assessment of thermal metadevices for conductive heat flux shielding in transient regime, Int. J. Heat Mass Transf. 212 (2023) 124238. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124238

[9] G. V. Alekseev, D. A. Tereshko, Particle swarm optimization-based algorithms for solving inverse problems of designing thermal cloaking and shielding devices, Int. J. Heat Mass Transf. 135 (2019) 1269-1277. https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.072

[10] I. Peralta, V. D. Fachinotti, A. A. Ciarbonetti, Optimization-based design of a heat flux concentrator, Sci. Rep. 7 (1) (2017) 40591. https://doi.org/10.1038/srep40591

[11] I. Peralta, V. D. Fachinotti, Optimization-based design of heat flux manipulation devices with emphasis on fabricability, Sci. Rep. 7 (1) (2017) 6261. https://doi.org/10.1038/s41598-017-06565-6

[12] L. Q. Tang, K. Pochiraju, C. Chassapis, S. Manoochehri, A Computer-Aided Optimization Approach for the Design of Injection Mold Cooling Systems, J. Mech. Des. 120 (2) (1998) 165-174. https://doi.org/10.1115/1.2826955

[13] V. Sobotka, A. Agazzi, N. Boyard, D. Delaunay, Parametric model for the analytical determination of the solidification and cooling times of semi-crystalline polymers, Appl. Therm. Eng. 50 (1) (2013) 416-421. https://doi.org/10.1016/j.applthermaleng.2012.07.019

[14] A. E. Albanesi, I. Peralta, F. Bre, B. A. Storti, V. D. Fachinotti, An optimization method based on the evolutionary and topology approaches to reduce the mass of composite wind turbine blades, Struct. Multidiscipl. Optim. 62 (2020) 619-643. https://doi.org/10.1007/s00158-020-02518-2
# A melt flow index-based approach for the viscosity curves determination

oubellaouch Keltoum<sup>1,a*</sup>, Pelaccia Riccardo<sup>1,b</sup>, Pozzi Paolo<sup>2,c</sup>,
zaniboni Giulia<sup>1,d</sup>, orazi Leonardo<sup>1,e</sup>, Donati Lorenzo<sup>3,f</sup>,
reggiani Barbara<sup>1,g</sup>

<sup>1</sup>Department of Sciences and methods for engineering, University of Modena and Reggio Emilia, Via Amendola 2, 42122, Reggio Emilia, Italy

<sup>2</sup>Department of engineering Enzo Ferrari, University of Modena and Reggio Emilia, Via P. Vivarelli 10, 41125, Modena, Italy

<sup>3</sup>Department of Industrial Engineering, University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

a keltoum.oubellaouch@unimore.it, b riccardo.pelaccia@unimore.it, c paolo.pozzi@unimore.it,
d giulia.zaniboni@unimore.it, e Leonardo.orazi@unimore.it, f l.donati@unibo.it,
g barbara.reggiani@unimore.it

**Keywords:** Melt Flow Index, Capillary Rheometer, Viscosity Curves, Optimization

**Abstract.** To optimize the polymers processing technologies, a rheological characterization of the polymer is essential to predict its behavior at specific temperatures and under varying shear rates. Simulating this process requires providing the simulation software with viscosity curves for the polymer to be processed, ensuring a reliable simulation. However, traditional rheological characterization utilizing a capillary rheometer is known for its high cost, time-intensive nature, and the need for skilled operators. In this study, a more cost-effective approach is proposed, using the Melt Flow Indexer (MFI) to obtain the experimental viscosity curves. These undergo an innovative numerical procedure based on simulating the MFI tests, reducing the numerical-experimental error in terms of pressure applied to the molten polymer. This methodology is applied to characterize three different thermoplastic polymers: polypropylene, 30% glass-reinforced polypropylene and 30% glass-reinforced polyamide. The viscosity curves obtained through this methodology are then compared to those obtained using the capillary rheometer, serving as a reference to assess the accuracy of the proposed approach.

**Introduction**

Polymeric melts are complex fluids marked by a particular rheological behavior, divided into three zones depending on the temperature and the applied rate of deformation. For a given temperature, the first regime, called the first Newtonian plateau, is obtained with low shear rates and characterized by viscosity that asymptotically approaches a constant value known as zero-shear viscosity. Instead, in the second regime with intermediate shear rates, called pseudoplastic, the viscosity decreases as the shear rate increases, following the shear thinning behavior, described by the power law. Whereas in the third regime, at high shear rates, viscosity asymptotically approaches a constant value known as the limiting viscosity and called the second Newtonian plateau [1].

Since different polymers' processing technologies happen on different shear rates, understanding and characterizing the polymers' rheological behavior is crucial in optimizing processing conditions and evaluating the applicability of a material to a given technology [2]. The flow within the extrusion head during the polymer extrusion process or inside the feed system tubes in an injection molding process can be analyzed using the Hagen-Poiseuille flow model [3].

<figure><img src="image_2552.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
# A melt flow index-based approach for the viscosity curves determination

oubellaouch Keltoum<sup>1,a*</sup>, Pelaccia Riccardo<sup>1,b</sup>, Pozzi Paolo<sup>2,c</sup>,
zaniboni Giulia<sup>1,d</sup>, orazi Leonardo<sup>1,e</sup>, Donati Lorenzo<sup>3,f</sup>,
reggiani Barbara<sup>1,g</sup>

<sup>1</sup>Department of Sciences and methods for engineering, University of Modena and Reggio Emilia, Via Amendola 2, 42122, Reggio Emilia, Italy

<sup>2</sup>Department of engineering Enzo Ferrari, University of Modena and Reggio Emilia, Via P. Vivarelli 10, 41125, Modena, Italy

<sup>3</sup>Department of Industrial Engineering, University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

<sup>a</sup>keltoum.oubellaouch@unimore.it, <sup>b</sup>riccardo.pelaccia@unimore.it, <sup>c</sup>paolo.pozzi@unimore.it, <sup>d</sup>giulia.zaniboni@unimore.it, <sup>e</sup>Leonardo.orazi@unimore.it, <sup>f</sup>l.donati@unibo.it, <sup>g</sup>barbara.reggiani@unimore.it

**Keywords:** Melt Flow Index, Capillary Rheometer, Viscosity Curves, Optimization

**Abstract.** To optimize the polymers processing technologies, a rheological characterization of the polymer is essential to predict its behavior at specific temperatures and under varying shear rates. Simulating this process requires providing the simulation software with viscosity curves for the polymer to be processed, ensuring a reliable simulation. However, traditional rheological characterization utilizing a capillary rheometer is known for its high cost, time-intensive nature, and the need for skilled operators. In this study, a more cost-effective approach is proposed, using the Melt Flow Indexer (MFI) to obtain the experimental viscosity curves. These undergo an innovative numerical procedure based on simulating the MFI tests, reducing the numerical-experimental error in terms of pressure applied to the molten polymer. This methodology is applied to characterize three different thermoplastic polymers: polypropylene, 30% glass-reinforced polypropylene and 30% glass-reinforced polyamide. The viscosity curves obtained through this methodology are then compared to those obtained using the capillary rheometer, serving as a reference to assess the accuracy of the proposed approach.

**Introduction**

Polymeric melts are complex fluids marked by a particular rheological behavior, divided into three zones depending on the temperature and the applied rate of deformation. For a given temperature, the first regime, called the first Newtonian plateau, is obtained with low shear rates and characterized by viscosity that asymptotically approaches a constant value known as zero-shear viscosity. Instead, in the second regime with intermediate shear rates, called pseudoplastic, the viscosity decreases as the shear rate increases, following the shear thinning behavior, described by the power law. Whereas in the third regime, at high shear rates, viscosity asymptotically approaches a constant value known as the limiting viscosity and called the second Newtonian plateau [1].

Since different polymers' processing technologies happen on different shear rates, understanding and characterizing the polymers' rheological behavior is crucial in optimizing processing conditions and evaluating the applicability of a material to a given technology [2]. The flow within the extrusion head during the polymer extrusion process or inside the feed system tubes in an injection molding process can be analyzed using the Hagen-Poiseuille flow model [3].

<figure><img src="image_2545.png" /></figure>
This model describes laminar flow inside a cylindrical pipe or tube, making certain simplifying assumptions. These assumptions encompass the incompressibility of the fluid, an isothermal, stationary and laminar flow, and the restriction that the flow velocity is only in the direction of the flow, with the other velocity components being negligible. This flow model is also applicable within the die of a capillary rheometer, providing a means to assess the flow behavior of polymer melts under controlled conditions of temperature and velocity. A capillary rheometer consists of a heated barrel with a capillary connected at its bottom, featuring specific length and radius (Fig. 1 (a)). The polymer is loaded into the barrel, and after a period of preheating, a piston controlled at a constant velocity pushes the polymer melt, causing it to be extruded through the capillary die. Hypothesizing the polymer melt to be a Newtonian fluid, the shear rate and the shear stress are therefore approximated using the following equations [4]:

$$ \dot{\gamma}_a = \frac{4Q}{\pi R_n^3}. \qquad (1) $$

$$ \tau_a = \frac{R_n \cdot P}{2L}. \qquad (2) $$

where Q represents the polymer flow rate in $cm^3.s^{-1}$, which is an input data to be configured during the test using the capillary rheometer. Specifically, it is determined by controlling the velocity applied to the piston during the test. $R_n$ and L refer to the radius and length of the capillary die in cm, respectively. P denotes the pressure at the entrance of the capillary die measured using a sensor positioned at the capillary entrance.

The pressure profile inside the capillary die exhibits a curvature due to the so called end effects. Therefore, the calculated shear stress $\tau_a$ using eq. 2, has to be corrected to obtain the shear stress at the wall $\tau_w$ using the Bagley correction [5]. To carry out this correction, at least two capillaries with the same radius and different length are needed.

<figure><img src="image_2553.png" /><figcaption>Fig. 1 Typical configuration of (a) the capillary rheometer (b) the Melt Flow Indexer</figcaption></figure>

On the other hand, the apparent shear rate calculated with eq. 1 also requires correction. This equation is only valid for Newtonian fluids. For pseudoplastic fluids, a correction method proposed by Rabinowitch [3] is employed to calculate the shear rate at the wall, $\gamma_w$.

Another method employed to assess the characteristics of a polymer melt involves using the Melt Flow Indexer, sometimes referred to as the extrusion plastometer. As seen in Fig. 1 (b), also this instrument consists of a heated barrel with a capillary connected at its bottom, featuring
This model describes laminar flow inside a cylindrical pipe or tube, making certain simplifying assumptions. These assumptions encompass the incompressibility of the fluid, an isothermal, stationary and laminar flow, and the restriction that the flow velocity is only in the direction of the flow, with the other velocity components being negligible. This flow model is also applicable within the die of a capillary rheometer, providing a means to assess the flow behavior of polymer melts under controlled conditions of temperature and velocity. A capillary rheometer consists of a heated barrel with a capillary connected at its bottom, featuring specific length and radius (Fig. 1 (a)). The polymer is loaded into the barrel, and after a period of preheating, a piston controlled at a constant velocity pushes the polymer melt, causing it to be extruded through the capillary die. Hypothesizing the polymer melt to be a Newtonian fluid, the shear rate and the shear stress are therefore approximated using the following equations [4]:

$$ \dot{\gamma}_a = \frac{4Q}{\pi R_n^3}. \qquad (1) $$

$$ \tau_a = \frac{R_n \cdot P}{2L}. \qquad (2) $$

where Q represents the polymer flow rate in $cm^3.s^{-1}$, which is an input data to be configured during the test using the capillary rheometer. Specifically, it is determined by controlling the velocity applied to the piston during the test. $R_n$ and L refer to the radius and length of the capillary die in cm, respectively. P denotes the pressure at the entrance of the capillary die measured using a sensor positioned at the capillary entrance.

The pressure profile inside the capillary die exhibits a curvature due to the so called end effects. Therefore, the calculated shear stress $\tau_a$ using eq. 2, has to be corrected to obtain the shear stress at the wall $\tau_w$ using the Bagley correction [5]. To carry out this correction, at least two capillaries with the same radius and different length are needed.

<figure><img src="image_2546.png" /><figcaption>Fig. 1 Typical configuration of (a) the capillary rheometer (b) the Melt Flow Indexer</figcaption></figure>

On the other hand, the apparent shear rate calculated with eq. 1 also requires correction. This equation is only valid for Newtonian fluids. For pseudoplastic fluids, a correction method proposed by Rabinowitch [3] is employed to calculate the shear rate at the wall, $\gamma_w$.

Another method employed to assess the characteristics of a polymer melt involves using the Melt Flow Indexer, sometimes referred to as the extrusion plastometer. As seen in Fig. 1 (b), also this instrument consists of a heated barrel with a capillary connected at its bottom, featuring
specific dimensions (2.095 mm diameter and 8 mm length). The polymer, preheated to the targeted temperature, is introduced into the barrel bore and subsequently extruded through the capillary die thanks to the piston actuated by the dead loads positioned at its top. This device is typically employed to determine both the Melt Flow Index (MFI) and the Melt Volume Flow-rate (MVR) of a specific polymer, operating under predefined conditions of temperature and a constant applied load. The MFI along with the MVR serves as an indicator of the polymer's fluidity, precisely quantifying the weight (or the volume, in the case of the MVR) of the extruded polymer in a span of 10 minutes [6].

While in the capillary rheometer the polymer flow rate is controlled (constant velocity applied to the piston during the test) and the pressure applied to the polymer is assessed, in the Melt Flow Indexer, thanks to the dead load applied upon the piston, the pressure applied to the molten polymer is controlled while the polymer flow rate is measured. Another difference lies in the fact that the capillary rheometer comes with at least two capillaries of the same diameter and two different lengths, so that the Bagley correction can be performed, whereas the Melt Flow Indexer comes with only one capillary of standardized dimensions. Notably, the Melt Flow Indexer stands out as an economical machine. Hence, there is a compelling opportunity to utilize it instead of the capillary rheometer for acquiring polymer viscosity curves. This work aims to introduce an innovative and cost-effective experimental-numerical approach for plastic processors to obtain viscosity curves using the Melt Flow Indexer, thereby presenting a viable alternative to the capillary rheometer.

## Materials and Methods

In the present work, three diverse polymers were investigated: polypropylene (PP), 30% glass-reinforced polypropylene (PPGF30) and 30% glass-reinforced polyamide (PA6GF30). The standard operating temperature ranges for the examined materials are as follows: 190 °C, 260 °C for PP, 190 °C, 260 °C for PPGF30, and 240 °C, 280 °C for PA6GF30. All the three materials were analyzed at three different temperatures, carefully selected from their respective operating ranges. In particular, the PP and the PPGF30 were analyzed at 200 °C, 230 °C and 250 °C. Whereas the PA6GF30 was analyzed at 245 °C, 260 °C and 275 °C. Since the 30% glass reinforced polyamide is an hygroscopic polymer, it was dried for 6 hours at a temperature of 80 °C before its rheological characterization. Regarding the MFI tests, they were performed using a Melt Flow Indexer called the XNR-400C model. For each temperature setting, four different load conditions were selected: 2.16 Kg, 5 Kg, 10 Kg, and 16.965 Kg for PP; 1.2 Kg, 5 Kg, 16.6 Kg, and 27.432 Kg for PPGF30; and 2.16 Kg, 5 Kg, 10 Kg, and 20.125 Kg for PA6GF30. Consequently, twelve MFI tests were conducted, and each configuration was replicated at least three times to mitigate potential operator-induced errors. As explained in the introduction section, the Melt Flow Indexer could be seen as a simplified capillary rheometer where, instead of controlling the piston velocity, this is actuated through a dead load positioned at its top. At this point, it is possible to use eq. 1 and eq. 2 to calculate the shear rate and shear stress of the polymer in a given MFI test, and in this case L, Rn, P and Q are the MFI capillary length (L = 8 mm) and diameter (Rn = 1.04775 mm) the pressure applied to the molten polymer during the MFI test and the flow rate measured during the MFI test, respectively. The Melt Flow Indexer is commonly equipped with an encoder that allows for the measurement of the piston displacement during a specified test, enabling the determination of the extruded polymer volume. In each test, the time t necessary for the piston to undergo a 30 mm displacement is recorded. The associated volume for that 30mm length, denoted as V=2.149 cm³, along with the measured time, is subsequently utilized to calculate the flow rate by the following equation:

$$Q = \frac{V}{t} \qquad (3)$$
specific dimensions (2.095 mm diameter and 8 mm length). The polymer, preheated to the targeted temperature, is introduced into the barrel bore and subsequently extruded through the capillary die thanks to the piston actuated by the dead loads positioned at its top. This device is typically employed to determine both the Melt Flow Index (MFI) and the Melt Volume Flow-rate (MVR) of a specific polymer, operating under predefined conditions of temperature and a constant applied load. The MFI along with the MVR serves as an indicator of the polymer's fluidity, precisely quantifying the weight (or the volume, in the case of the MVR) of the extruded polymer in a span of 10 minutes [6].

While in the capillary rheometer the polymer flow rate is controlled (constant velocity applied to the piston during the test) and the pressure applied to the polymer is assessed, in the Melt Flow Indexer, thanks to the dead load applied upon the piston, the pressure applied to the molten polymer is controlled while the polymer flow rate is measured. Another difference lies in the fact that the capillary rheometer comes with at least two capillaries of the same diameter and two different lengths, so that the Bagley correction can be performed, whereas the Melt Flow Indexer comes with only one capillary of standardized dimensions. Notably, the Melt Flow Indexer stands out as an economical machine. Hence, there is a compelling opportunity to utilize it instead of the capillary rheometer for acquiring polymer viscosity curves. This work aims to introduce an innovative and cost-effective experimental-numerical approach for plastic processors to obtain viscosity curves using the Melt Flow Indexer, thereby presenting a viable alternative to the capillary rheometer.

## Materials and Methods

In the present work, three diverse polymers were investigated: polypropylene (PP), 30% glass-reinforced polypropylene (PPGF30) and 30% glass-reinforced polyamide (PA6GF30). The standard operating temperature ranges for the examined materials are as follows: 190 °C, 260 °C for PP, 190 °C, 260 °C for PPGF30, and 240 °C, 280 °C for PA6GF30. All the three materials were analyzed at three different temperatures, carefully selected from their respective operating ranges. In particular, the PP and the PPGF30 were analyzed at 200 °C, 230 °C and 250 °C. Whereas the PA6GF30 was analyzed at 245 °C, 260 °C and 275 °C. Since the 30% glass reinforced polyamide is an hygroscopic polymer, it was dried for 6 hours at a temperature of 80 °C before its rheological characterization. Regarding the MFI tests, they were performed using a Melt Flow Indexer called the XNR-400C model. For each temperature setting, four different load conditions were selected: 2.16 Kg, 5 Kg, 10 Kg, and 16.965 Kg for PP; 1.2 Kg, 5 Kg, 16.6 Kg, and 27.432 Kg for PPGF30; and 2.16 Kg, 5 Kg, 10 Kg, and 20.125 Kg for PA6GF30. Consequently, twelve MFI tests were conducted, and each configuration was replicated at least three times to mitigate potential operator-induced errors. As explained in the introduction section, the Melt Flow Indexer could be seen as a simplified capillary rheometer where, instead of controlling the piston velocity, this is actuated through a dead load positioned at its top. At this point, it is possible to use eq. 1 and eq. 2 to calculate the shear rate and shear stress of the polymer in a given MFI test, and in this case L, Rn, P and Q are the MFI capillary length (L = 8 mm) and diameter (Rn = 1.04775 mm) the pressure applied to the molten polymer during the MFI test and the flow rate measured during the MFI test, respectively. The Melt Flow Indexer is commonly equipped with an encoder that allows for the measurement of the piston displacement during a specified test, enabling the determination of the extruded polymer volume. In each test, the time t necessary for the piston to undergo a 30 mm displacement is recorded. The associated volume for that 30mm length, denoted as V=2.149 cm³, along with the measured time, is subsequently utilized to calculate the flow rate by the following equation:

$$Q = \frac{V}{t} \qquad (3)$$
Whereas for the pressure *P* calculation, knowing the total load positioned upon the piston, together with the mass of the piston, the pressure could be measured using the following equation:

$$P = \frac{Mg}{\pi R_p^2} \qquad (4)$$

where *M* is the weight applied during the test, *g* is the gravity acceleration (g = 9.80655 N.kg⁻¹) and *R*<sub>p</sub> is the piston radius (*R*<sub>p</sub> = 4.7371 mm). Therefore, for each of the investigated polymers, for each temperature *T* and for each MFI test, the pressure applied to the molten polymer is fixed (due to the application of a constant load *M* upon the piston) and the melt volume flow rate is calculated in cm³/s. The results of all the performed MFI tests are summarized in Table 1.

<table><caption>Table 1 Results of the Melt Flow Index tests for all the three investigated polymers</caption><thead><tr><th rowspan="2">Polymer</th><th colspan="5">Measured Flow Rate Q [cm³/s]</th></tr><tr><th>T [°C] \ M [kg]</th><th>2.16</th><th>5</th><th>10</th><th>16.965</th></tr></thead><tbody><tr><td rowspan="3">PP</td><td>200</td><td>0.008</td><td>0.034</td><td>0.154</td><td>0.557</td></tr><tr><td>230</td><td>0.015</td><td>0.064</td><td>0.269</td><td>1.074</td></tr><tr><td>250</td><td>0.023</td><td>0.101</td><td>0.38</td><td>1.978</td></tr><tr><td rowspan="3">PPGF30</td><td>200</td><td>0.001</td><td>0.012</td><td>0.126</td><td>0.402</td></tr><tr><td>230</td><td>0.002</td><td>0.022</td><td>0.274</td><td>0.926</td></tr><tr><td>250</td><td>0.004</td><td>0.031</td><td>0.398</td><td>1.287</td></tr><tr><td rowspan="3">PA6GF30</td><td>245</td><td>0.031</td><td>0.082</td><td>0.188</td><td>0.526</td></tr><tr><td>260</td><td>0.047</td><td>0.125</td><td>0.264</td><td>0.929</td></tr><tr><td>275</td><td>0.075</td><td>0.183</td><td>0.382</td><td>1.243</td></tr></tbody></table>

For each MFI test, subsequent to the calculation of the shear rate $\dot{\gamma}_a$ and shear stress $\tau_a$ by eq. 1 and eq. 2, respectively, the viscosity $\eta_a$ can be determined using the following equation:

$$\eta_a = \frac{\tau_a}{\dot{\gamma}_a} \qquad (5)$$

Consequently, each MFI test yields a single viscosity versus shear rate point. The viscosity versus shear rate data for each investigated polymer at all three temperatures were fitted using the Cross-WLF rheological model. This model, widely employed in plastic processing simulation software, is characterized by the following equation:

$$\eta = \frac{\eta_0}{1 + \left( \frac{\eta_0 \dot{\gamma}}{\tau^*} \right)^{1-n}} \qquad (6)$$

In this context, *n* represents the power law index and $\tau^*$ denotes the critical shear stress. The zero shear viscosity, denoted as $\eta_0$, is defined as follows:

$$\eta_0 = D_1 \cdot e^{\frac{-A_1(T-T^*)}{A_2+(T-T^*)}} \qquad (7)$$

where $T^* = D_2 + D_3 \cdot p$, $A_2 = A_3 + D_3 \cdot p$, *T* is the melt temperature, and *p* is the pressure. Generally, pressure's impact on viscosity is commonly disregarded in many cases. Consequently, in our current investigation, $D_3$ is assumed to be zero for simplicity. Consequently, the data fitted
Whereas for the pressure *P* calculation, knowing the total load positioned upon the piston, together with the mass of the piston, the pressure could be measured using the following equation:

$$P = \frac{Mg}{\pi R_p^2} \qquad (4)$$

where *M* is the weight applied during the test, *g* is the gravity acceleration (g = 9.80655 N.kg⁻¹) and *R*<sub>*p*</sub> is the piston radius (*R*<sub>*p*</sub> = 4.7371 mm). Therefore, for each of the investigated polymers, for each temperature *T* and for each MFI test, the pressure applied to the molten polymer is fixed (due to the application of a constant load *M* upon the piston) and the melt volume flow rate is calculated in cm³/s. The results of all the performed MFI tests are summarized in Table 1.

<table><caption>Table 1 Results of the Melt Flow Index tests for all the three investigated polymers</caption><thead><tr><th rowspan="2">Polymer</th><th colspan="5">Measured Flow Rate Q [cm³/s]</th></tr><tr><th>T [°C] \ M [kg]</th><th>2.16</th><th>5</th><th>10</th><th>16.965</th></tr></thead><tbody><tr><td rowspan="3">PP</td><td>200</td><td>0.008</td><td>0.034</td><td>0.154</td><td>0.557</td></tr><tr><td>230</td><td>0.015</td><td>0.064</td><td>0.269</td><td>1.074</td></tr><tr><td>250</td><td>0.023</td><td>0.101</td><td>0.38</td><td>1.978</td></tr><tr><td rowspan="3">PPGF30</td><td>200</td><td>0.001</td><td>0.012</td><td>0.126</td><td>0.402</td></tr><tr><td>230</td><td>0.002</td><td>0.022</td><td>0.274</td><td>0.926</td></tr><tr><td>250</td><td>0.004</td><td>0.031</td><td>0.398</td><td>1.287</td></tr><tr><td rowspan="3">PA6GF30</td><td>245</td><td>0.031</td><td>0.082</td><td>0.188</td><td>0.526</td></tr><tr><td>260</td><td>0.047</td><td>0.125</td><td>0.264</td><td>0.929</td></tr><tr><td>275</td><td>0.075</td><td>0.183</td><td>0.382</td><td>1.243</td></tr></tbody></table>

For each MFI test, subsequent to the calculation of the shear rate $\dot{\gamma}_a$ and shear stress $\tau_a$ by eq. 1 and eq. 2, respectively, the viscosity $\eta_a$ can be determined using the following equation:

$$\eta_a = \frac{\tau_a}{\dot{\gamma}_a} \qquad (5)$$

Consequently, each MFI test yields a single viscosity versus shear rate point. The viscosity versus shear rate data for each investigated polymer at all three temperatures were fitted using the Cross-WLF rheological model. This model, widely employed in plastic processing simulation software, is characterized by the following equation:

$$\eta = \frac{\eta_0}{1 + \left( \frac{\eta_0 \dot{\gamma}}{\tau^*} \right)^{1-n}} \qquad (6)$$

In this context, *n* represents the power law index and $\tau^*$ denotes the critical shear stress. The zero shear viscosity, denoted as $\eta_0$, is defined as follows:

$$\eta_0 = D_1 \cdot e^{\frac{-A_1(T-T^*)}{A_2+(T-T^*)}} \qquad (7)$$

where $T^* = D_2 + D_3 \cdot p$, $A_2 = A_3 + D_3 \cdot p$, *T* is the melt temperature, and *p* is the pressure. Generally, pressure's impact on viscosity is commonly disregarded in many cases. Consequently, in our current investigation, $D_3$ is assumed to be zero for simplicity. Consequently, the data fitted
coefficients considered in the present work to describe the Cross-WLF rheological model are: $A_1, A_2, D_1, D_2, n$ and $\tau^*$.

Given the simplifying assumptions seen in the introduction section and approximative formulas (equation 1 and equation 2) employed to generate viscosity points through the MFI instrument, it becomes necessary to apply corrections to the resulting experimental viscosity curves. One approach to rectify these curves is through the numerical simulation of the MFI test. On the left of Fig. 2, we have the setup of a typical MFI instrument: during an MFI test, the input is the applied load, i.e., the actual pressure applied during the test, and the output is the measured flow rate, which is used to obtain viscosity curves through the approximative formulations.

<figure><img src="image_2554.png" /><figcaption>Fig. 2 Experimental-Numerical approach for the viscosity curves determination</figcaption></figure>

On the right of Fig. 2 instead, the proposed model for simulating the MFI test in Autodesk Moldflow Insight (AMI) is presented. In this case, the input includes the flow rate $Q$ measured experimentally during the test and the derived viscosity curves, while the output provides the simulated value of the pressure applied to the polymer during the MFI test. The objective is to compare the simulated pressure to the actual pressure. If these pressures match, then the viscosity curves used in the simulation are deemed accurate; otherwise, corrections to the input viscosity curves need to be applied.

As evident from Fig. 2, in order to simulate the MFI test, which involves extrusion into space, a large rectangle was utilized as the cavity to be filled in the model. Since both the cylinder and the capillary are heated to the temperature of the MFI test, they were modeled as a hot runner and a hot gate, respectively, with the same dimensions. Process parameters included setting the MFI test temperature as both the melt and mold temperatures. Meanwhile, the flow rate $Q$ measured during the actual MFI test serves as a process control parameter in the simulation.

The concept behind calibration is as follows: starting from the experimental viscosity curves obtained with the MFI, the goal is to find the actual viscosity curves that, for each MFI test, minimize the error between the actual pressure applied by the load to the molten polymer and the numerical pressure predicted by AMI. Therefore, we are dealing with an optimization problem where the design variables are the viscosity curves, i.e., the set of parameters of the Cross-WLF model that describe them. The objective functions are the numerical-experimental errors of the pressure applied to the polymer during the MFI tests. Therefore, for three different temperatures
coefficients considered in the present work to describe the Cross-WLF rheological model are: $A_1, A_2, D_1, D_2, n$ and $\tau^*$.

Given the simplifying assumptions seen in the introduction section and approximative formulas (equation 1 and equation 2) employed to generate viscosity points through the MFI instrument, it becomes necessary to apply corrections to the resulting experimental viscosity curves. One approach to rectify these curves is through the numerical simulation of the MFI test. On the left of Fig. 2, we have the setup of a typical MFI instrument: during an MFI test, the input is the applied load, i.e., the actual pressure applied during the test, and the output is the measured flow rate, which is used to obtain viscosity curves through the approximative formulations.

<figure><img src="image_2547.png" /><figcaption>Fig. 2 Experimental-Numerical approach for the viscosity curves determination</figcaption></figure>

On the right of Fig. 2 instead, the proposed model for simulating the MFI test in Autodesk Moldflow Insight (AMI) is presented. In this case, the input includes the flow rate $Q$ measured experimentally during the test and the derived viscosity curves, while the output provides the simulated value of the pressure applied to the polymer during the MFI test. The objective is to compare the simulated pressure to the actual pressure. If these pressures match, then the viscosity curves used in the simulation are deemed accurate; otherwise, corrections to the input viscosity curves need to be applied.

As evident from Fig. 2, in order to simulate the MFI test, which involves extrusion into space, a large rectangle was utilized as the cavity to be filled in the model. Since both the cylinder and the capillary are heated to the temperature of the MFI test, they were modeled as a hot runner and a hot gate, respectively, with the same dimensions. Process parameters included setting the MFI test temperature as both the melt and mold temperatures. Meanwhile, the flow rate $Q$ measured during the actual MFI test serves as a process control parameter in the simulation.

The concept behind calibration is as follows: starting from the experimental viscosity curves obtained with the MFI, the goal is to find the actual viscosity curves that, for each MFI test, minimize the error between the actual pressure applied by the load to the molten polymer and the numerical pressure predicted by AMI. Therefore, we are dealing with an optimization problem where the design variables are the viscosity curves, i.e., the set of parameters of the Cross-WLF model that describe them. The objective functions are the numerical-experimental errors of the pressure applied to the polymer during the MFI tests. Therefore, for three different temperatures
and four different loads, we would have twelve objective functions to minimize. However, to simplify the optimization problem and avoid twelve objective functions, the average of these errors was considered as a single objective function:

$$ \frac{1}{12} * \sum_{k=1}^{12} 100 * \frac{|P_{actual}^k - P_{predicted}^k|}{P_{actual}^k} \quad (8) $$

The iterative procedure for resolving the optimization problem was executed using the modeFRONTIER software. The original Non-dominated Sorting Genetic Algorithm II (NSGA II) was chosen as the optimization algorithm, encompassing 15 generations and an initial Design of Experiments (DOE) with 10 configurations (equivalent to 150 iterations). For each iteration, modeFRONTIER employs that algorithm to propose a new set of Cross-WLF parameters (design variables) and assign them to the input variables. In modeFRONTIER software, a script was written in Visual Basic Scripting language where all the necessary commands were implemented:

* Opening of Moldflow project, containing simulations for the 12 MFI tests.

* Configuring the new set of design variables for all 12 simulations.

* Running all the 12 simulations

* Retrieving the values of injection pressure for all the 12 simulations and assigning them to output variables in modeFRONTIER.

Subsequently, the objective function is computed using eq. 8. At the end of the optimization procedure (150 iterations), the set of parameters yielding the minimum value of the objective function is identified. This specific set of parameters corresponds to the viscosity curves found using the proposed method proposed in the present paper. To validate the accuracy of the proposed method, a comparison was imperative between the acquired viscosity curves and those obtained using the conventional approach: a capillary rheometer. Subsequently, the viscosity curves of the examined polymers were determined utilizing the Ceast Rheologic 2500 capillary rheometer. Each test involved varying the shear rate within the range of 50 s⁻¹ to 2000 s⁻¹, employing specific values of 50 s⁻¹, 100 s⁻¹, 200 s⁻¹, 500 s⁻¹, 1000 s⁻¹, 2000 s⁻¹. Throughout these tests, the shear rate was imposed on the polymer through the controlled piston velocity. Additionally, a pressure sensor positioned at the capillary entrance providing real-time pressure values of the polymer. Subsequently, eq. 1 and eq. 2 were used to calculate the shear rate and the shear stress, respectively. In order to perform the Bagley correction, the tests were performed using two capillaries with identical diameter (1 mm) but different lengths (10 mm and 20 mm). To enhance precision and minimize potential operator-induced errors, each test was replicated at least three times. After performing the Bagley correction also the Rabinowitch one was applied to obtain accurate results.

## Results and discussion

Fig. 3, Fig. 4 and Fig. 5 show the viscosity curves at three different temperatures of the PP, PPGF30 and PA6GF30, respectively. For all the three investigated polymers, the dashed lines represent the curves obtained by fitting the experimental viscosity points directly obtained with the MFI (before applying the optimization procedure). On the other hand, the solid lines represent the viscosity curves obtained at the end of the optimization procedure. Using the proposed procedure, the objective function were reduced from 95% to 6.4% for the PP, from 120% to 10% for the PPGF30 and from 49% to 8% for the PA6GF30. Upon analysis of the figures for all investigated polymers, it is evident that the experimentally obtained viscosity curves using the MFI apparatus initially exhibit high viscosity values. Subsequently, through the application of the numerical optimization procedure, the curves are not only shifted downward but also show an increased inclination of the pseudoplastic segment.
and four different loads, we would have twelve objective functions to minimize. However, to simplify the optimization problem and avoid twelve objective functions, the average of these errors was considered as a single objective function:

$$ \frac{1}{12} * \sum_{k=1}^{12} 100 * \frac{|P_{actual}^{k} - P_{predicted}^{k}|}{P_{actual}^{k}} \quad (8) $$

The iterative procedure for resolving the optimization problem was executed using the modeFRONTIER software. The original Non-dominated Sorting Genetic Algorithm II (NSGA II) was chosen as the optimization algorithm, encompassing 15 generations and an initial Design of Experiments (DOE) with 10 configurations (equivalent to 150 iterations). For each iteration, modeFRONTIER employs that algorithm to propose a new set of Cross-WLF parameters (design variables) and assign them to the input variables. In modeFRONTIER software, a script was written in Visual Basic Scripting language where all the necessary commands were implemented:

* Opening of Moldflow project, containing simulations for the 12 MFI tests.

* Configuring the new set of design variables for all 12 simulations.

* Running all the 12 simulations

* Retrieving the values of injection pressure for all the 12 simulations and assigning them to output variables in modeFRONTIER.

Subsequently, the objective function is computed using eq. 8. At the end of the optimization procedure (150 iterations), the set of parameters yielding the minimum value of the objective function is identified. This specific set of parameters corresponds to the viscosity curves found using the proposed method proposed in the present paper. To validate the accuracy of the proposed method, a comparison was imperative between the acquired viscosity curves and those obtained using the conventional approach: a capillary rheometer. Subsequently, the viscosity curves of the examined polymers were determined utilizing the Ceast Rheologic 2500 capillary rheometer. Each test involved varying the shear rate within the range of 50 s⁻¹ to 2000 s⁻¹, employing specific values of 50 s⁻¹, 100 s⁻¹, 200 s⁻¹, 500 s⁻¹, 1000 s⁻¹, 2000 s⁻¹. Throughout these tests, the shear rate was imposed on the polymer through the controlled piston velocity. Additionally, a pressure sensor positioned at the capillary entrance providing real-time pressure values of the polymer. Subsequently, eq. 1 and eq. 2 were used to calculate the shear rate and the shear stress, respectively. In order to perform the Bagley correction, the tests were performed using two capillaries with identical diameter (1 mm) but different lengths (10 mm and 20 mm). To enhance precision and minimize potential operator-induced errors, each test was replicated at least three times. After performing the Bagley correction also the Rabinowitch one was applied to obtain accurate results.

## Results and discussion

Fig. 3, Fig. 4 and Fig. 5 show the viscosity curves at three different temperatures of the PP, PPGF30 and PA6GF30, respectively. For all the three investigated polymers, the dashed lines represent the curves obtained by fitting the experimental viscosity points directly obtained with the MFI (before applying the optimization procedure). On the other hand, the solid lines represent the viscosity curves obtained at the end of the optimization procedure. Using the proposed procedure, the objective function were reduced from 95% to 6.4% for the PP, from 120% to 10% for the PPGF30 and from 49% to 8% for the PA6GF30. Upon analysis of the figures for all investigated polymers, it is evident that the experimentally obtained viscosity curves using the MFI apparatus initially exhibit high viscosity values. Subsequently, through the application of the numerical optimization procedure, the curves are not only shifted downward but also show an increased inclination of the pseudoplastic segment.
<figure><img src="image_2555.png" /><figcaption>Fig. 3 Viscosity curves obtained at the end of the optimization procedure superimposed to those of the first iteration of the procedure for the Polypropylene (PP)</figcaption></figure>

<figure><img src="image_2556.png" /><figcaption>Fig. 4 Viscosity curves obtained at the end of the optimization procedure superimposed to those of the first iteration of the procedure for the 30% glass reinforced polypropylene</figcaption></figure>
<figure><img src="image_2548.png" /><figcaption>Fig. 3 Viscosity curves obtained at the end of the optimization procedure superimposed to those of the first iteration of the procedure for the Polypropylene (PP)</figcaption></figure>

<figure><img src="image_2549.png" /><figcaption>Fig. 4 Viscosity curves obtained at the end of the optimization procedure superimposed to those of the first iteration of the procedure for the 30% glass reinforced polypropylene</figcaption></figure>
<figure><img src="image_2557.png" /><figcaption>Fig. 5 Viscosity curves obtained at the end of the optimization procedure superimposed to those of the first iteration of the procedure for the 30% glass reinforced polyamide</figcaption></figure>

Fig. 6, Fig. 7 and Fig. 8 depict viscosity curves at three different temperatures for PP, PPGF30, and PA6GF30, respectively. In all three investigated polymers, dashed lines represent curves obtained using the proposed methodology based on MFI, while solid lines represent actual viscosity curves obtained through the conventional capillary rheometer methodology. The figures clearly illustrate a good match between curves obtained by the two methodologies, particularly in the shear rate interval between 50 s⁻¹ and 5000 s⁻¹, characteristic of the capillary rheometer. Notably, excellent matching is observed for PP and PPGF30, while a deviation between curves obtained with the two methodologies is noticeable for PA6GF30 in that interval. This disparity may be attributed to the hygroscopic nature of PA6GF30. It is plausible that this polymer absorbs more humidity, especially before the tests conducted at the capillary rheometer, due to the unavailability of a dryer in proximity to the capillary rheometer. To quantify the deviation and underscore the significance of the proposed numerical optimization procedure, we compared the error between the curves obtained by the capillary rheometer and the non-optimized curves derived experimentally through the MFI with the error between the curves obtained by the capillary rheometer and the optimized curves through the experimental-numerical procedure, for each material. The error was calculated by considering all viscosity points within the shear rate range of 50 s⁻¹ to 5000 s⁻¹, with an increment of 5 s⁻¹. These errors were computed for each temperature, and then their averages were considered to streamline the comparisons. The results of the comparisons revealed that the error after the application of the optimization procedure was reduced by 89%, 97% and 74% for the PP, PPGF30 and PA6GF30, respectively, demonstrating the effectiveness of the proposed methodology in providing accurate viscosity curves.
<figure><img src="image_2550.png" /><figcaption>Fig. 5 Viscosity curves obtained at the end of the optimization procedure superimposed to those of the first iteration of the procedure for the 30% glass reinforced polyamide</figcaption></figure>

Fig. 6, Fig. 7 and Fig. 8 depict viscosity curves at three different temperatures for PP, PPGF30, and PA6GF30, respectively. In all three investigated polymers, dashed lines represent curves obtained using the proposed methodology based on MFI, while solid lines represent actual viscosity curves obtained through the conventional capillary rheometer methodology. The figures clearly illustrate a good match between curves obtained by the two methodologies, particularly in the shear rate interval between 50 s⁻¹ and 5000 s⁻¹, characteristic of the capillary rheometer. Notably, excellent matching is observed for PP and PPGF30, while a deviation between curves obtained with the two methodologies is noticeable for PA6GF30 in that interval. This disparity may be attributed to the hygroscopic nature of PA6GF30. It is plausible that this polymer absorbs more humidity, especially before the tests conducted at the capillary rheometer, due to the unavailability of a dryer in proximity to the capillary rheometer. To quantify the deviation and underscore the significance of the proposed numerical optimization procedure, we compared the error between the curves obtained by the capillary rheometer and the non-optimized curves derived experimentally through the MFI with the error between the curves obtained by the capillary rheometer and the optimized curves through the experimental-numerical procedure, for each material. The error was calculated by considering all viscosity points within the shear rate range of 50 s⁻¹ to 5000 s⁻¹, with an increment of 5 s⁻¹. These errors were computed for each temperature, and then their averages were considered to streamline the comparisons. The results of the comparisons revealed that the error after the application of the optimization procedure was reduced by 89%, 97% and 74% for the PP, PPGF30 and PA6GF30, respectively, demonstrating the effectiveness of the proposed methodology in providing accurate viscosity curves.
<figure><img src="image_2558.png" /><figcaption>Fig. 6 Viscosity curves obtained at the end of the optimization procedure superimposed to those obtained by the capillary rheometer for the polypropylene</figcaption></figure>

<figure><img src="image_2559.png" /><figcaption>Fig. 7 Viscosity curves obtained at the end of the optimization procedure superimposed to those obtained by the capillary rheometer for the 30% glass reinforced polypropylene</figcaption></figure>
<figure><img src="image_2551.png" /><figcaption>Fig. 6 Viscosity curves obtained at the end of the optimization procedure superimposed to those obtained by the capillary rheometer for the polypropylene</figcaption></figure>

<figure><img src="image_2552.png" /><figcaption>Fig. 7 Viscosity curves obtained at the end of the optimization procedure superimposed to those obtained by the capillary rheometer for the 30% glass reinforced polypropylene</figcaption></figure>
<figure><img src="image_2560.png" /><figcaption>Fig. 8 Viscosity curves obtained at the end of the optimization procedure superimposed to those obtained by the capillary rheometer for the 30% glass reinforced polyamide</figcaption></figure>

## Summary

In the present work, an innovative procedure was proposed for performing the rheological characterization of polymers using the MFI apparatus. To correct the experimental rheological curves obtained directly from the MFI, this test was simulated in the injection molding software Moldflow Insight, integrating it with an optimization strategy to identify new rheological curves that minimize numerical-experimental errors in terms of pressure applied to the molten polymer during the MFI test. This identification method was implemented in the optimization platform modeFRONTIER. The proposed procedure permits to identify the Cross-WLF viscosity model parameters implemented in the majority of the plastic processing simulation software. Particularly, this method could be an efficient aid to plastic injection molding processors that can't afford neither a capillary rheometer nor a skilled operators in the rheological characterization field. The only needed instrument is an MFI apparatus which is known to cost ten times lower than a capillary rheometer. The proposed methodology was applied to polypropylene, 30% glass reinforced polypropylene and 30% glass reinforced polyamide. The obtained curves were compared to those acquired conventionally using the capillary rheometer, and favorable matches in viscosity curves were observed, showing errors of less than 18%, 5% and 40% for the PP, PPGF30 and PA6GF30, respectively.

## References

[1] J. Drabek, M. Zatloukal, and M. Martyn, "Effect of molecular weight on secondary Newtonian plateau at high shear rates for linear isotactic melt blown polypropylenes," *Journal of Non-Newtonian Fluid Mechanics*, vol. 251, pp. 107-118, Jan. 2018. https://doi.org/10.1016/j.jnnfm.2017.11.009.

[2] K. Oubellaouch et al., "Assessment of fiber orientation models predictability by comparison with X-ray µCT data in injection-molded short glass fiber-reinforced polyamide," *The International Journal of Advanced Manufacturing Technology*.

[3] T. A. Osswald and G. Menges, *Materials Science of Polymers for Engineers*, 3rd ed. München: Carl Hanser Verlag GmbH & Co. KG, 2012. doi: 10.3139/9781569905241.

[4] A. Shenoy, *Thermoplastic Melt Rheology and Processing*, 0 ed. CRC Press, 1996.

[5] E. B. Bagley, "End Corrections in the Capillary Flow of Polyethylene," *Journal of Applied Physics*, vol. 28, no. 5, pp. 624-627, May 1957. https://doi.org/10.1063/1.1722814.

[6] A. V. Shenoy, D. R. Saini, and V. M. Nadkarni, "Rheograms for engineering thermoplastics from melt flow index," *Rheol Acta*, vol. 22, no. 2, pp. 209-222, Mar. 1983. https://doi.org/10.1007/BF01332373.
<figure><img src="image_2553.png" /><figcaption>Fig. 8 Viscosity curves obtained at the end of the optimization procedure superimposed to those obtained by the capillary rheometer for the 30% glass reinforced polyamide</figcaption></figure>

## Summary

In the present work, an innovative procedure was proposed for performing the rheological characterization of polymers using the MFI apparatus. To correct the experimental rheological curves obtained directly from the MFI, this test was simulated in the injection molding software Moldflow Insight, integrating it with an optimization strategy to identify new rheological curves that minimize numerical-experimental errors in terms of pressure applied to the molten polymer during the MFI test. This identification method was implemented in the optimization platform modeFRONTIER. The proposed procedure permits to identify the Cross-WLF viscosity model parameters implemented in the majority of the plastic processing simulation software. Particularly, this method could be an efficient aid to plastic injection molding processors that can't afford neither a capillary rheometer nor a skilled operators in the rheological characterization field. The only needed instrument is an MFI apparatus which is known to cost ten times lower than a capillary rheometer. The proposed methodology was applied to polypropylene, 30% glass reinforced polypropylene and 30% glass reinforced polyamide. The obtained curves were compared to those acquired conventionally using the capillary rheometer, and favorable matches in viscosity curves were observed, showing errors of less than 18%, 5% and 40% for the PP, PPGF30 and PA6GF30, respectively.

## References

[1] J. Drabek, M. Zatloukal, and M. Martyn, "Effect of molecular weight on secondary Newtonian plateau at high shear rates for linear isotactic melt blown polypropylenes," *Journal of Non-Newtonian Fluid Mechanics*, vol. 251, pp. 107-118, Jan. 2018. https://doi.org/10.1016/j.jnnfm.2017.11.009.

[2] K. Oubellaouch et al., "Assessment of fiber orientation models predictability by comparison with X-ray µCT data in injection-molded short glass fiber-reinforced polyamide," *The International Journal of Advanced Manufacturing Technology*.

[3] T. A. Osswald and G. Menges, *Materials Science of Polymers for Engineers*, 3rd ed. München: Carl Hanser Verlag GmbH & Co. KG, 2012. doi: 10.3139/9781569905241.

[4] A. Shenoy, *Thermoplastic Melt Rheology and Processing*, 0 ed. CRC Press, 1996.

[5] E. B. Bagley, "End Corrections in the Capillary Flow of Polyethylene," *Journal of Applied Physics*, vol. 28, no. 5, pp. 624-627, May 1957. https://doi.org/10.1063/1.1722814.

[6] A. V. Shenoy, D. R. Saini, and V. M. Nadkarni, "Rheograms for engineering thermoplastics from melt flow index," *Rheol Acta*, vol. 22, no. 2, pp. 209-222, Mar. 1983. https://doi.org/10.1007/BF01332373.
# Investigation of the effects of gas-counter-pressure injection molding on the properties and manufacturability of post-consumer recycled polypropylene

BORTOLETTO Anna¹,ᵃ*, BOVO Enrico¹,ᵇ, SORGATO Marco¹,ᶜ and LUCCHETTA Giovanni¹,ᵈ

¹Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131, Padova, Italy

**Keywords:** Gas Counter Pressure, Injection Molding, Recycling, Post-Consumer Polypropylene

**Abstract.** In contemporary times, the most effective strategy for mitigating the environmental effects of plastics and their manufacturing is recycling. However, producing high-quality items from recycled materials remains a challenge. This study addresses these challenges, specifically focusing on the injection molding process for recycled polypropylene. Key issues identified include poor surface finish of the molded items, mold contamination with oily residues, and strong odors during processing. The proposed solution involves the innovative use of gas counter pressure in conjunction with injection molding. The study explores various nitrogen pressure levels to assess their impact. Findings indicate that an optimal pressure level significantly improves the surface quality of the products and reduces the accumulation of dirt in the mold cavities. While gas counter pressure does not mitigate odor emissions, it represents a promising step forward in developing a high-quality recycled polypropylene compound. This approach could pave the way for more advanced recycling techniques, enhancing the quality of products made from recycled plastics.

## Introduction

Plastic demand has increased exponentially over the last few decades, pushing the production from 1.5 million tons in 1950 to more than 390 million tons in 2021 [1 - 2]. Recycling is considered the best solution to reduce plastic's environmental impact because it decreases the need for virgin material in the production of new components and the quantity of underground waste [3 - 4].

There are two different categories of plastic that can be recycled, distinguished by their source. The first is post-industrial (PIR) waste, which comes directly from the industry (scrap material, non-conforming pieces, feeding systems, etc). The second category is post-consumer (PCR) waste, which derives from the urban collection of waste: different types of materials and plastics are mixed, and they are contaminated, for example, by organic residues of food or dirt [5 - 6]. Recycling PCR waste is still an open challenge that requires improvement in each processing step to produce a high-quality material and product.

Within post-consumer waste, one of the most interesting plastics to study is recycled polypropylene (PP), the primary material used in Europe's plastic-intensive packaging industry [7]. Polypropylene also exhibits characteristics that make it potentially suitable for upcycling, with the right combination of mechanical recycling, compounding, and injection molding parameters. Upcycling consists of using recycled materials to manufacture a product with greater value than the previous one [8]. Currently, upcycling faces limitations caused due to issues arising during the re-processing of rPP through injection molding [9]. The origin of these issues can be traced to

<figure><img src="image_2561.png" /></figure>

<footnote>ªanna.bortoletto.4@phd.unipd.it, ᵇenrico.bovo.1@phd.unipd.it, ᶜmarco.sorgato@unipd.it,</footnote>

<footnote>ᵈgiovanni.lucchetta@unipd.it</footnote>
# Investigation of the effects of gas-counter-pressure injection molding on the properties and manufacturability of post-consumer recycled polypropylene

BORTOLETTO Anna¹,ᵃ*, BOVO Enrico¹,ᵇ, SORGATO Marco¹,ᶜ and LUCCHETTA Giovanni¹,ᵈ

¹Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131, Padova, Italy

ᵃanna.bortoletto.4@phd.unipd.it, ᵇenrico.bovo.1@phd.unipd.it, ᶜmarco.sorgato@unipd.it,

ᵈgiovanni.lucchetta@unipd.it

**Keywords:** Gas Counter Pressure, Injection Molding, Recycling, Post-Consumer Polypropylene

**Abstract.** In contemporary times, the most effective strategy for mitigating the environmental effects of plastics and their manufacturing is recycling. However, producing high-quality items from recycled materials remains a challenge. This study addresses these challenges, specifically focusing on the injection molding process for recycled polypropylene. Key issues identified include poor surface finish of the molded items, mold contamination with oily residues, and strong odors during processing. The proposed solution involves the innovative use of gas counter pressure in conjunction with injection molding. The study explores various nitrogen pressure levels to assess their impact. Findings indicate that an optimal pressure level significantly improves the surface quality of the products and reduces the accumulation of dirt in the mold cavities. While gas counter pressure does not mitigate odor emissions, it represents a promising step forward in developing a high-quality recycled polypropylene compound. This approach could pave the way for more advanced recycling techniques, enhancing the quality of products made from recycled plastics.

**Introduction**

Plastic demand has increased exponentially over the last few decades, pushing the production from 1.5 million tons in 1950 to more than 390 million tons in 2021 [1 - 2]. Recycling is considered the best solution to reduce plastic's environmental impact because it decreases the need for virgin material in the production of new components and the quantity of underground waste [3 - 4].

There are two different categories of plastic that can be recycled, distinguished by their source. The first is post-industrial (PIR) waste, which comes directly from the industry (scrap material, non-conforming pieces, feeding systems, etc). The second category is post-consumer (PCR) waste, which derives from the urban collection of waste: different types of materials and plastics are mixed, and they are contaminated, for example, by organic residues of food or dirt [5 - 6]. Recycling PCR waste is still an open challenge that requires improvement in each processing step to produce a high-quality material and product.

Within post-consumer waste, one of the most interesting plastics to study is recycled polypropylene (PP), the primary material used in Europe's plastic-intensive packaging industry [7]. Polypropylene also exhibits characteristics that make it potentially suitable for upcycling, with the right combination of mechanical recycling, compounding, and injection molding parameters. Upcycling consists of using recycled materials to manufacture a product with greater value than the previous one [8]. Currently, upcycling faces limitations caused due to issues arising during the re-processing of rPP through injection molding [9]. The origin of these issues can be traced to

<figure><img src="image_2554.png" /></figure>
contaminating absorbed during the first usage of PP, because of the material's high permeability. These contaminants, which may include organic residues from food, inks, adhesives, or others [10 - 11], remain in the rPP even after the cleaning steps of the recycling process. When exposed to the high temperatures and shear stresses of the injection molding, they undergo degradation, affecting the manufacturability of the material. Specifically, issues such as a compromised surface appearance, odorous emissions, and contamination of the mold cavity surface with oily substances can be observed [12]. These problems will be analyzed one by one in the following paragraphs.

The surface of parts molded using PCR PP is often altered by white/light-grey stripes elongated along the flow direction [13], commonly referred as silver streaks. Degraded contaminants within the plastic melt form gas bubbles that expand when they reach the flow front, as they are subjected to a pressure close to the atmospheric conditions. The bubbles are then pushed by the fountain flow to the walls of the cavity [14], where they break and freeze within the skin layer forming silver streaks. In MicroCellular Injection Molding, the use of high mold temperature increases the surface quality [15]. A hot mold allows the skin layer to keep a certain fluidity, and the flowing heart's material pushes the base of the bubbles little by little until closure. In recent studies, the technology of gas counter pressure was applied to MuCell to solve the silver streaks problem [16 - 17]. Gas counter pressure consists of injecting pressurized gas, usually nitrogen or carbon dioxide, from the opposite direction of the polymer melt to counteract the expansion of the degraded gases [18].

The presence of silver streaks on the part's surface not only represents an aesthetic problem but also causes the accumulation of dirt on the mold cavity surface. Gases condense on colder cavity walls, releasing oily and greasy components that clog the vents and accumulate in the mold cavity, forming a film of dirt. Sorgato et al. proposed a self-cleaning solution to mold vent clogging by exploiting laser-induced surface structures [19].

Some of the degraded gases emit a strong odor that is partially released in the environment immediately after production and partially throughout the components' life. Van Laere et al. found 203 VOCs (volatile organic compounds) in plastic waste from the food packaging industry and 142 VOCs in other packaging products [20]. Addressing the strong odor of recycled plastic is crucial for its indoor applications, where it is necessary to grant safety and comfort for the users. Different tests were conducted by Prado et al. to verify if recycled PCR PP filled with talc could conform to the emissions norms of automotive. The results showed that the components were above the acceptance limits for all three different tests: GMW 3205, VDA 270, and ISO 13299 [21]. Fraunhofer ICT adopted the extrusion process with a stripping agent to reduce the plastic's aroma. The stripping was performed using a supercritical fluid (carbon dioxide) to remove odorous substances from the melt in a twin-screw co-rotating extruder [22 - 23]. Water or nitrogen were also used as stripping agents [24].

Given the various challenges identified in the literature, there is a clear need for innovative solutions, particularly regarding the issue of mold contamination and odorous emissions in PCR PP. This gap in the current research landscape sets the stage for our investigation. Thus, through the contributions of previous studies, this research aims to test a new application of the GCP technique to address these specific challenges in molding PCR PP. Different gas counter-pressure levels were used, and their effect was compared to the outcome of the traditional injection molding process. The influence of the pressure on the defects and the mold contamination was analyzed through image analysis, while a fogging test was used to determine its effect on odor emissions.

## Materials and methods

Injection Molding. The injection molding experiments were conducted using a 100% recycled Polypropylene (rPP) from Sirmax S.p.a. called Sertene X200C RC. It is a non-filled polypropylene, recycled from post-consumer waste, mainly food packaging.
contaminating absorbed during the first usage of PP, because of the material's high permeability. These contaminants, which may include organic residues from food, inks, adhesives, or others [10 - 11], remain in the rPP even after the cleaning steps of the recycling process. When exposed to the high temperatures and shear stresses of the injection molding, they undergo degradation, affecting the manufacturability of the material. Specifically, issues such as a compromised surface appearance, odorous emissions, and contamination of the mold cavity surface with oily substances can be observed [12]. These problems will be analyzed one by one in the following paragraphs.

The surface of parts molded using PCR PP is often altered by white/light-grey stripes elongated along the flow direction [13], commonly referred as silver streaks. Degraded contaminants within the plastic melt form gas bubbles that expand when they reach the flow front, as they are subjected to a pressure close to the atmospheric conditions. The bubbles are then pushed by the fountain flow to the walls of the cavity [14], where they break and freeze within the skin layer forming silver streaks. In MicroCellular Injection Molding, the use of high mold temperature increases the surface quality [15]. A hot mold allows the skin layer to keep a certain fluidity, and the flowing heart's material pushes the base of the bubbles little by little until closure. In recent studies, the technology of gas counter pressure was applied to MuCell to solve the silver streaks problem [16 - 17]. Gas counter pressure consists of injecting pressurized gas, usually nitrogen or carbon dioxide, from the opposite direction of the polymer melt to counteract the expansion of the degraded gases [18].

The presence of silver streaks on the part's surface not only represents an aesthetic problem but also causes the accumulation of dirt on the mold cavity surface. Gases condense on colder cavity walls, releasing oily and greasy components that clog the vents and accumulate in the mold cavity, forming a film of dirt. Sorgato et al. proposed a self-cleaning solution to mold vent clogging by exploiting laser-induced surface structures [19].

Some of the degraded gases emit a strong odor that is partially released in the environment immediately after production and partially throughout the components' life. Van Laere et al. found 203 VOCs (volatile organic compounds) in plastic waste from the food packaging industry and 142 VOCs in other packaging products [20]. Addressing the strong odor of recycled plastic is crucial for its indoor applications, where it is necessary to grant safety and comfort for the users. Different tests were conducted by Prado et al. to verify if recycled PCR PP filled with talc could conform to the emissions norms of automotive. The results showed that the components were above the acceptance limits for all three different tests: GMW 3205, VDA 270, and ISO 13299 [21]. Fraunhofer ICT adopted the extrusion process with a stripping agent to reduce the plastic's aroma. The stripping was performed using a supercritical fluid (carbon dioxide) to remove odorous substances from the melt in a twin-screw co-rotating extruder [22 - 23]. Water or nitrogen were also used as stripping agents [24].

Given the various challenges identified in the literature, there is a clear need for innovative solutions, particularly regarding the issue of mold contamination and odorous emissions in PCR PP. This gap in the current research landscape sets the stage for our investigation. Thus, through the contributions of previous studies, this research aims to test a new application of the GCP technique to address these specific challenges in molding PCR PP. Different gas counter-pressure levels were used, and their effect was compared to the outcome of the traditional injection molding process. The influence of the pressure on the defects and the mold contamination was analyzed through image analysis, while a fogging test was used to determine its effect on odor emissions.

## Materials and methods

Injection Molding. The injection molding experiments were conducted using a 100% recycled Polypropylene (rPP) from Sirmax S.p.a. called Sertene X200C RC. It is a non-filled polypropylene, recycled from post-consumer waste, mainly food packaging.
<figure><img src="image_2562.png" /><figcaption>Fig. 1 - Prototypal mold suitable for GCP usage (a); specimen to perform the analysis (b).</figcaption></figure>

The specimen is a plate with dimensions of 183 mm x 50 mm x 2 mm (Fig. 1b), molded with a full-hydraulic Battenfeld HM 110/525H/210s. The injection molding machine is linked to the gas counter pressure system, which consists of compressor control module by Maximator (RM/500/2/VP/80/500/N2). It works through a pneumatic compressor that takes the nitrogen from a tank at 180 bar and compresses it to the desired pressure. The gas path to reach the cavity is displayed in Fig. 1a. Nitrogen enters the cavity through a gas valve placed at the opposite side from the gate and an O-ring was placed around the cavity to avoid any leakage. (Fig. 1a). The signal to start the injection of the gas is given by a sensor that is activated at the closure of the two plates of the mold with a limit switch.

The injection molding parameters used for defects and mold contamination analysis are displayed in Table 2. The only variable is the gas level of GCP, as it is the primary focus of this work.

<table><caption>Table 1. Injection molding parameters to mold the specimens for the analysis.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Melt temperature (T<sub>melt</sub>)</td><td>250 °C</td></tr><tr><td>Mold temperature (T<sub>mold</sub>)</td><td>40 °C</td></tr><tr><td>Residence time (t<sub>res</sub>)</td><td>120 s</td></tr><tr><td>GCP holding time</td><td>2 s</td></tr><tr><td>Gas pressure (GCP)</td><td>0; 15; 40; 60 bar</td></tr></tbody></table>

For the analysis of the emissions, only the extreme values of gas counter pressure were tested (0 bar and 60 bar). A more thorough testing campaign was not carried out on this matter because the initial results showed a complete lack of improvements, as it will be seen in the specific section.

Superficial Defects Evaluation. A method based on image analysis was used to evaluate the defects on the molded plate surface. This was possible thanks to the color difference between the defect and the clean base material. Photos were taken using a repeatable setting with the professional camera Nikon D3500. Twenty plates were analyzed for each nitrogen level to have a statistical sample variation and the analysis was conducted using the programming language of Python. From the raw photo, some processing was made to gradually reduce the area to study to
<figure><img src="image_2555.png" /><figcaption>Fig. 1 - Prototypal mold suitable for GCP usage (a); specimen to perform the analysis (b).</figcaption></figure>

The specimen is a plate with dimensions of 183 mm x 50 mm x 2 mm (Fig. 1b), molded with a full-hydraulic Battenfeld HM 110/525H/210s. The injection molding machine is linked to the gas counter pressure system, which consists of compressor control module by Maximator (RM/500/2/VP/80/500/N2). It works through a pneumatic compressor that takes the nitrogen from a tank at 180 bar and compresses it to the desired pressure. The gas path to reach the cavity is displayed in Fig. 1a. Nitrogen enters the cavity through a gas valve placed at the opposite side from the gate and an O-ring was placed around the cavity to avoid any leakage. (Fig. 1a). The signal to start the injection of the gas is given by a sensor that is activated at the closure of the two plates of the mold with a limit switch.

The injection molding parameters used for defects and mold contamination analysis are displayed in Table 2. The only variable is the gas level of GCP, as it is the primary focus of this work.

<table><caption>Table 1. Injection molding parameters to mold the specimens for the analysis.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Melt temperature (T<sub>melt</sub>)</td><td>250 °C</td></tr><tr><td>Mold temperature (T<sub>mold</sub>)</td><td>40 °C</td></tr><tr><td>Residence time (t<sub>res</sub>)</td><td>120 s</td></tr><tr><td>GCP holding time</td><td>2 s</td></tr><tr><td>Gas pressure (GCP)</td><td>0; 15; 40; 60 bar</td></tr></tbody></table>

For the analysis of the emissions, only the extreme values of gas counter pressure were tested (0 bar and 60 bar). A more thorough testing campaign was not carried out on this matter because the initial results showed a complete lack of improvements, as it will be seen in the specific section.

Superficial Defects Evaluation. A method based on image analysis was used to evaluate the defects on the molded plate surface. This was possible thanks to the color difference between the defect and the clean base material. Photos were taken using a repeatable setting with the professional camera Nikon D3500. Twenty plates were analyzed for each nitrogen level to have a statistical sample variation and the analysis was conducted using the programming language of Python. From the raw photo, some processing was made to gradually reduce the area to study to
the region between the two ejectors, eliminating the background (Fig. 2a). This region was called ROI and transformed into grayscale before the defects evaluation.

<figure><img src="image_2563.png" /><figcaption>Fig. 2 – Definition of the region of interest (a); explanation of the strategy used by the code to evaluate the standard deviation (b).</figcaption></figure>

The ROI was divided into a grid of 6000 rectangles (20 columns, 300 rows). These rectangles were called sliders, and for each of them, the value of the standard deviation of the plate color was calculated and then averaged with the values of the same row (Fig. 2b).

<figure><img src="image_2564.png" /><figcaption>Fig. 3 - Output of the Python code: graph with the 300 values of standard deviation for each row.</figcaption></figure>

The code output was one value of standard deviation per row, from 1 to 300, displayed in a graph similar to the one in Fig. 3. The higher the standard deviation is, the more different the color of the molded piece is from the clean material.

Mold Contamination Evaluation. Photos of the mold were taken and then processed with a Python code to evaluate the dirt accumulated on the cavity surface. This strategy worked once again thanks to a difference of color, between the clean and dirt areas of the mold cavity surface. The cavity surface was photographed after molding 50 plates for each set of parameters with a repetitive setup. The image analysis was conducted using Python. Before the quantification of the accumulated dirt, photos were processed in the following way:

- the region of interest was reduced to an area between the holes for the ejectors, leaving the borders out of the selection;
the region between the two ejectors, eliminating the background (Fig. 2a). This region was called ROI and transformed into grayscale before the defects evaluation.

<figure><img src="image_2556.png" /><figcaption>Fig. 2 – Definition of the region of interest (a); explanation of the strategy used by the code to evaluate the standard deviation (b).</figcaption></figure>

The ROI was divided into a grid of 6000 rectangles (20 columns, 300 rows). These rectangles were called sliders, and for each of them, the value of the standard deviation of the plate color was calculated and then averaged with the values of the same row (Fig. 2b).

<figure><img src="image_2557.png" /><figcaption>Fig. 3 - Output of the Python code: graph with the 300 values of standard deviation for each row.</figcaption></figure>

The code output was one value of standard deviation per row, from 1 to 300, displayed in a graph similar to the one in Fig. 3. The higher the standard deviation is, the more different the color of the molded piece is from the clean material.

Mold Contamination Evaluation. Photos of the mold were taken and then processed with a Python code to evaluate the dirt accumulated on the cavity surface. This strategy worked once again thanks to a difference of color, between the clean and dirt areas of the mold cavity surface. The cavity surface was photographed after molding 50 plates for each set of parameters with a repetitive setup. The image analysis was conducted using Python. Before the quantification of the accumulated dirt, photos were processed in the following way:

- the region of interest was reduced to an area between the holes for the ejectors, leaving the borders out of the selection;
- the resulting image was transformed into a grayscale.

The analysis was based on an Otsu thresholding [25], which means that the image was transformed into a binary mode with only two levels of color (black and white). The white is identified with level 255, while the black has level 0. Each pixel is assigned to black or white based on its grey value compared to the threshold one: if it is higher than the threshold, it becomes white; if it is lower, it becomes black.

Emissions Evaluation. Following DIN 75201, the fogging test was used to evaluate emissions. This test quantifies volatile compounds (VOCs) emitted from a specimen under specified conditions, but it cannot identify them. Thus, the results do not indicate how much of the calculated emissions are odorous, but they highlight a possible improvement in the general emission of VOCs thanks to the use of GCP. The required equipment includes a fogging machine, cooling device, beakers, glass plates, metal and fluorocarbon rubber rings, aluminum foils (103 mm diameter, 0.03 mm thickness), and an analytical balance with a 0.01 mg accuracy. Thermofisher's Horizon FTS (Fog Testing System) with a recirculating chiller Accel 250LC was used.

The specimens were cut to have a circular shape with a diameter of (80 ± 1) mm, and two disks were stuck inside the beaker to reach the weight of (10 ± 2) g. The beaker was closed with one sealing ring, one aluminum foil, one glass plate, and one cooling plate. The aluminum foil was weighed before the test with an accuracy of ± 0.01 mg. The beaker was left inside the machine for 16 hours ± 10 minutes at a temperature of 100 ± 0.5 °C, after which the aluminum foil was dried in a desiccator with silica gel for 4 hours. The output was the difference in weight of the foil from before to after the test, which identifies the amount of condensable components in the specimen. The test was repeated six times for each set of GCP parameters.

## Results and discussion

Superficial Defects. For each value of gas counter pressure, 20 plates were photographed and analyzed, and the code's output was a graph with 300 values of standard deviation along the region of interest. From these outputs, a mean graph was created, as depicted in Fig. 4, where the values of global means are also reported in the areas they correspond to.
- the resulting image was transformed into a grayscale.

The analysis was based on an Otsu thresholding [25], which means that the image was transformed into a binary mode with only two levels of color (black and white). The white is identified with level 255, while the black has level 0. Each pixel is assigned to black or white based on its grey value compared to the threshold one: if it is higher than the threshold, it becomes white; if it is lower, it becomes black.

Emissions Evaluation. Following DIN 75201, the fogging test was used to evaluate emissions. This test quantifies volatile compounds (VOCs) emitted from a specimen under specified conditions, but it cannot identify them. Thus, the results do not indicate how much of the calculated emissions are odorous, but they highlight a possible improvement in the general emission of VOCs thanks to the use of GCP. The required equipment includes a fogging machine, cooling device, beakers, glass plates, metal and fluorocarbon rubber rings, aluminum foils (103 mm diameter, 0.03 mm thickness), and an analytical balance with a 0.01 mg accuracy. Thermofisher's Horizon FTS (Fog Testing System) with a recirculating chiller Accel 250LC was used.

The specimens were cut to have a circular shape with a diameter of (80 ± 1) mm, and two disks were stuck inside the beaker to reach the weight of (10 ± 2) g. The beaker was closed with one sealing ring, one aluminum foil, one glass plate, and one cooling plate. The aluminum foil was weighed before the test with an accuracy of ± 0.01 mg. The beaker was left inside the machine for 16 hours ± 10 minutes at a temperature of 100 ± 0.5 °C, after which the aluminum foil was dried in a desiccator with silica gel for 4 hours. The output was the difference in weight of the foil from before to after the test, which identifies the amount of condensable components in the specimen. The test was repeated six times for each set of GCP parameters.

## Results and discussion

Superficial Defects. For each value of gas counter pressure, 20 plates were photographed and analyzed, and the code's output was a graph with 300 values of standard deviation along the region of interest. From these outputs, a mean graph was created, as depicted in Fig. 4, where the values of global means are also reported in the areas they correspond to.
<figure><img src="image_2565.png" /><figcaption>Fig. 4 - Results of defects evaluation in terms of standard deviation. (a) GCP = 0 bar; (b) GCP = 15 bar; (c) GCP = 40 bar; (d) GCP = 60 bar. The global means are displayed in the corresponded areas.</figcaption></figure>

For the standard injection molding (GCP = 0 bar), the standard deviation computed as global mean 1 is equal to 4.29 in the region near the gate. This value rapidly decreases towards the end of the cavity, reaching its minimum at 3.33. The slope of the curve is high, indicating a heterogenous specimen in terms of color and, therefore, defects along its length. The defects are not distributed equally but are gathered in the first region after the gate and then fade towards a global mean 2 of 3.84 and a global mean 3 of 3.33. For the plates molded with gas pressure (15, 40, and 60 bar), the curve's trend is flatter, as they start from a lower value (3.21) and finish at around 3.00. This means that the defects are less present, and there is no great difference between the region near the gate and the end of the specimen.

The values of global mean 3 between the sets with GCP and the set with no GCP are almost comparable, and this result is representative of what can be seen in the plates, where the furthest region from the gate is clean from defects. The area near the gate is where the most silver streaks emerge because, when the bubbles created by the degraded contaminating substances reach the cavity, they expand for the lower pressure. The fountain flow then pushes them toward the walls, where they explode and form the defect. Gas counter pressure has a positive effect on the superficial appearance of the specimens because it communicates an opposite pressure to the flow front and makes the bubbles implode and close before they can reach the surface of the product.

From Fig. 4 it is also possible to notice that the results remain unvaried regarding standard deviation increasing the pressure level from 15 to 40 to 60 bar. Therefore, there is no need to use
<figure><img src="image_2558.png" /><figcaption>Fig. 4 - Results of defects evaluation in terms of standard deviation. (a) GCP = 0 bar; (b) GCP = 15 bar; (c) GCP = 40 bar; (d) GCP = 60 bar. The global means are displayed in the corresponded areas.</figcaption></figure>

For the standard injection molding (GCP = 0 bar), the standard deviation computed as global mean 1 is equal to 4.29 in the region near the gate. This value rapidly decreases towards the end of the cavity, reaching its minimum at 3.33. The slope of the curve is high, indicating a heterogenous specimen in terms of color and, therefore, defects along its length. The defects are not distributed equally but are gathered in the first region after the gate and then fade towards a global mean 2 of 3.84 and a global mean 3 of 3.33. For the plates molded with gas pressure (15, 40, and 60 bar), the curve's trend is flatter, as they start from a lower value (3.21) and finish at around 3.00. This means that the defects are less present, and there is no great difference between the region near the gate and the end of the specimen.

The values of global mean 3 between the sets with GCP and the set with no GCP are almost comparable, and this result is representative of what can be seen in the plates, where the furthest region from the gate is clean from defects. The area near the gate is where the most silver streaks emerge because, when the bubbles created by the degraded contaminating substances reach the cavity, they expand for the lower pressure. The fountain flow then pushes them toward the walls, where they explode and form the defect. Gas counter pressure has a positive effect on the superficial appearance of the specimens because it communicates an opposite pressure to the flow front and makes the bubbles implode and close before they can reach the surface of the product.

From Fig. 4 it is also possible to notice that the results remain unvaried regarding standard deviation increasing the pressure level from 15 to 40 to 60 bar. Therefore, there is no need to use
high nitrogen levels to reach good results for the surface appearance. From an economic point of view, it is preferable to use the lowest possible values.

Mold Contamination. For each set of parameters, Fig. 5 reports the grayscale cut image, the thresholded image, and a pie chart with the percentage of white pixels (indicating the dirt) in comparison to the black ones (indicating the clean mold surface).

<figure><img src="image_2566.png" /><figcaption>Fig. 5 - Results of mold contamination. The pie charts indicate the area occupied by the dirt in the image (white pixels). (a) GCP = 0 bar, (b) GCP = 15 bar, (C) GCP = 40 bar, (d) GCP = 60 bar.</figcaption></figure>

After molding 50 plates with a no GCP injection molding process, the dirt accumulated on the cavity surface could be seen with the naked eye and corresponded to an area of 56% of the analyzed images. It presented itself with the same shape and distribution of the silver streaks on the specimen: elongated along the flow direction, more intense near the gate, and slowly fading. Therefore, the dirt appears on the cavity surface where the bubbles of contaminants explode; the fewer silver streaks on the surface of the specimens, the cleaner the mold will be. In this particular case, the streaks of dirt had an orange nuance. Using gas counter pressure at 15 bar there was a significant 17 % difference from the previous case: the dirty area was less expanded and it had a grey/white color. The results with 40 and 60 bar showed a slight improvement of a few percentage points, as can be seen by the images and the graphs (Fig. 5).

The results show that using gas counter pressure, the accumulation of dirt on the mold cavity surface decreases significantly by around 17%. Therefore, gas counter pressure can solve both the superficial defects and the mold contamination simultaneously, with a proportional effect between the two. The difference between 15, 40, and 60 bar is minimal (1-2%), which is congruent to the
high nitrogen levels to reach good results for the surface appearance. From an economic point of view, it is preferable to use the lowest possible values.

Mold Contamination. For each set of parameters, Fig. 5 reports the grayscale cut image, the thresholded image, and a pie chart with the percentage of white pixels (indicating the dirt) in comparison to the black ones (indicating the clean mold surface).

<figure><img src="image_2559.png" /><figcaption>Fig. 5 - Results of mold contamination. The pie charts indicate the area occupied by the dirt in the image (white pixels). (a) GCP = 0 bar, (b) GCP = 15 bar, (C) GCP = 40 bar, (d) GCP = 60 bar.</figcaption></figure>

After molding 50 plates with a no GCP injection molding process, the dirt accumulated on the cavity surface could be seen with the naked eye and corresponded to an area of 56% of the analyzed images. It presented itself with the same shape and distribution of the silver streaks on the specimen: elongated along the flow direction, more intense near the gate, and slowly fading. Therefore, the dirt appears on the cavity surface where the bubbles of contaminants explode; the fewer silver streaks on the surface of the specimens, the cleaner the mold will be. In this particular case, the streaks of dirt had an orange nuance. Using gas counter pressure at 15 bar there was a significant 17 % difference from the previous case: the dirty area was less expanded and it had a grey/white color. The results with 40 and 60 bar showed a slight improvement of a few percentage points, as can be seen by the images and the graphs (Fig. 5).

The results show that using gas counter pressure, the accumulation of dirt on the mold cavity surface decreases significantly by around 17%. Therefore, gas counter pressure can solve both the superficial defects and the mold contamination simultaneously, with a proportional effect between the two. The difference between 15, 40, and 60 bar is minimal (1-2%), which is congruent to the
effect of GCP on the silver streaks, where the global mean 1 of the different nitrogen levels was the same (3.21).

It is important to report that even after cleaning the mold cavity surface with an acetone-based solvent, a ring of dirt remained on it. This ring affected the results from Python, which included it in the white pixels areas, even if it was not dirty and oily. The improvement of the cleanliness of the cavity surface could potentially be higher than the 15/20 % obtained from these results.

Emissions. The output is the difference in the weight of the aluminum foil between after and before the test. The test was repeated six times for each set of parameters, and a mean value was calculated from the six output values. The two means are displayed in Fig. 6 with their standard deviation, which represents the error of the test.

<figure><img src="image_2567.png" /><figcaption>Fig. 6 - Results of fogging test. The error band is the standard deviation of the values of the six tests.</figcaption></figure>

What can be observed from this graph is that the use of the gas counter pressure has no benefit on the plastic odor, as the weight of the aluminum foil varies from 2.71 mg to 2.66 mg, but the error bands overlap. It is reasonable to say that gas counter pressure may be able to stop the contaminating substances from emerging to the surface and limit their manifestation as silver streaks or dirt. However, the odorous compounds remain in the heart of the specimen. Even if the contaminating volatile substances are enclosed inside the product, they can reach the environment and disperse in it because of the high permeability of the polypropylene.

## Conclusions

In this work, a new application of gas counter pressure was investigated with the aim of obtaining high-quality injection molded products with recycled polypropylene. The experiments showed that gas counter pressure using nitrogen can:

- eliminate silver streaks from a visual point of view and decrease the color non-uniformity of 21% in the gate area, computed as standard deviation with image analysis;

- decrease mold contamination by around 20% when analyzed through image thresholding.

On the other hand, the emissions of volatile substances (VOCs) inside the plastic could not be reduced using GCP: the results of the fogging test showed the same quantity of emissions for the parameters studied.

To summarize, results suggest that employing a relatively low GCP value near the established threshold is advisable for the following reasons:

- the reduced usage of nitrogen makes the technology more cost-effective and more suitable for a possible scale-up in a real production line;
effect of GCP on the silver streaks, where the global mean 1 of the different nitrogen levels was the same (3.21).

It is important to report that even after cleaning the mold cavity surface with an acetone-based solvent, a ring of dirt remained on it. This ring affected the results from Python, which included it in the white pixels areas, even if it was not dirty and oily. The improvement of the cleanliness of the cavity surface could potentially be higher than the 15/20 % obtained from these results.

Emissions. The output is the difference in the weight of the aluminum foil between after and before the test. The test was repeated six times for each set of parameters, and a mean value was calculated from the six output values. The two means are displayed in Fig. 6 with their standard deviation, which represents the error of the test.

<figure><img src="image_2560.png" /><figcaption>Fig. 6 - Results of fogging test. The error band is the standard deviation of the values of the six tests.</figcaption></figure>

What can be observed from this graph is that the use of the gas counter pressure has no benefit on the plastic odor, as the weight of the aluminum foil varies from 2.71 mg to 2.66 mg, but the error bands overlap. It is reasonable to say that gas counter pressure may be able to stop the contaminating substances from emerging to the surface and limit their manifestation as silver streaks or dirt. However, the odorous compounds remain in the heart of the specimen. Even if the contaminating volatile substances are enclosed inside the product, they can reach the environment and disperse in it because of the high permeability of the polypropylene.

## Conclusions

In this work, a new application of gas counter pressure was investigated with the aim of obtaining high-quality injection molded products with recycled polypropylene. The experiments showed that gas counter pressure using nitrogen can:

- eliminate silver streaks from a visual point of view and decrease the color non-uniformity of 21% in the gate area, computed as standard deviation with image analysis;

- decrease mold contamination by around 20% when analyzed through image thresholding.

On the other hand, the emissions of volatile substances (VOCs) inside the plastic could not be reduced using GCP: the results of the fogging test showed the same quantity of emissions for the parameters studied.

To summarize, results suggest that employing a relatively low GCP value near the established threshold is advisable for the following reasons:

- the reduced usage of nitrogen makes the technology more cost-effective and more suitable for a possible scale-up in a real production line;
- on the specimens' surface, no discernible difference could be found between low- or high-pressure values.

These results can be a starting point to improve the processability of rPP and to obtain a high-quality product that can be used for aesthetic applications. Further studies need to be conducted to solve the problem regarding odor emissions, which could open many industrial sectors to using recycled plastics.

## References

[1] European Parliament, Plastic Waste and Recycling in the EU: numbers and figures, 2018.

[2] Plastics Europe and EPRO, Plastics - the Facts 2022, 2022.

[3] J. Hopewell, R. Dvorak, and E. Kosior, Plastics recycling: Challenges and opportunities, Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 364, no. 1526. Royal Society, pp. 2115-2126, Jul. 27, 2009. https://doi.org/10.1098/rstb.2008.0311

[4] M. K. Eriksen, A. Damgaard, A. Boldrin, and T. F. Astrup, Quality Assessment and Circularity Potential of Recovery Systems for Household Plastic Waste, J Ind Ecol, vol. 23, no. 1, pp. 156-168, Feb. 2019. https://doi.org/10.1111/jiec.12822

[5] K. Ragaert, L. Delva, and K. Van Geem, Mechanical and chemical recycling of solid plastic waste, Waste Management, vol. 69. Elsevier Ltd, pp. 24-58, Nov. 01, 2017. https://doi.org/10.1016/j.wasman.2017.07.044

[6] A. Schulte, B. Kampmann, and C. Galafton, Measuring the Circularity and Impact Reduction Potential of Post-Industrial and Post-Consumer Recycled Plastics, Sustainability, vol. 15, no. 16, p. 12242, Aug. 2023. https://doi.org/10.3390/su151612242

[7] H. Dahlbo, V. Poliakova, V. Mylläri, O. Sahimaa, and R. Anderson, Recycling potential of post-consumer plastic packaging waste in Finland, Waste Management, vol. 71, pp. 52-61, Jan. 2018. https://doi.org/10.1016/j.wasman.2017.10.033

[8] X. Zhao et al., Plastic waste upcycling toward a circular economy, Chemical Engineering Journal, vol. 428. Elsevier B.V., Jan. 15, 2022. doi: 10.1016/j.cej.2021.131928.

[9] Z. O. G. Schyns and M. P. Shaver, Mechanical Recycling of Packaging Plastics: A Review, Macromolecular Rapid Communications, vol. 42, no. 3. Wiley-VCH Verlag, Feb. 01, 2021. https://doi.org/10.1002/marc.202000415

[10] A. K. Undas, M. Groenen, R. J. B. Peters, and S. P. J. van Leeuwen, Safety of recycled plastics and textiles: Review on the detection, identification and safety assessment of contaminants, Chemosphere, vol. 312, Jan. 2023. https://doi.org/10.1016/j.chemosphere.2022.137175

[11] W. Camacho and S. Karlsson, Quality-determination of recycled plastic packaging waste by identification of contaminants by GC-MS after microwave assisted extraction (MAE), Polym Degrad Stab, vol. 71, no. 1, pp. 123-134, Jan. 2000. https://doi.org/10.1016/S0141-3910(00)00163-4

[12] X. Zhao, B. Boruah, K. F. Chin, M. Đokić, J. M. Modak, and H. Sen Soo, Upcycling to Sustainably Reuse Plastics, Advanced Materials, vol. 34, no. 25. John Wiley and Sons Inc, Jun. 01, 2022. https://doi.org/10.1002/adma.202100843

[13] J. Hou, G. Zhao, G. Wang, G. Dong, and J. Xu, A novel gas-assisted microcellular injection molding method for preparing lightweight foams with superior surface appearance and enhanced mechanical performance, Mater Des, vol. 127, pp. 115-125, Aug. 2017. https://doi.org/10.1016/j.matdes.2017.04.073
- on the specimens' surface, no discernible difference could be found between low- or high-pressure values.

These results can be a starting point to improve the processability of rPP and to obtain a high-quality product that can be used for aesthetic applications. Further studies need to be conducted to solve the problem regarding odor emissions, which could open many industrial sectors to using recycled plastics.

## References

[1] European Parliament, Plastic Waste and Recycling in the EU: numbers and figures, 2018.

[2] Plastics Europe and EPRO, Plastics - the Facts 2022, 2022.

[3] J. Hopewell, R. Dvorak, and E. Kosior, Plastics recycling: Challenges and opportunities, Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 364, no. 1526. Royal Society, pp. 2115-2126, Jul. 27, 2009. https://doi.org/10.1098/rstb.2008.0311

[4] M. K. Eriksen, A. Damgaard, A. Boldrin, and T. F. Astrup, Quality Assessment and Circularity Potential of Recovery Systems for Household Plastic Waste, J Ind Ecol, vol. 23, no. 1, pp. 156-168, Feb. 2019. https://doi.org/10.1111/jiec.12822

[5] K. Ragaert, L. Delva, and K. Van Geem, Mechanical and chemical recycling of solid plastic waste, Waste Management, vol. 69. Elsevier Ltd, pp. 24-58, Nov. 01, 2017. https://doi.org/10.1016/j.wasman.2017.07.044

[6] A. Schulte, B. Kampmann, and C. Galafton, Measuring the Circularity and Impact Reduction Potential of Post-Industrial and Post-Consumer Recycled Plastics, Sustainability, vol. 15, no. 16, p. 12242, Aug. 2023. https://doi.org/10.3390/su151612242

[7] H. Dahlbo, V. Poliakova, V. Mylläri, O. Sahimaa, and R. Anderson, Recycling potential of post-consumer plastic packaging waste in Finland, Waste Management, vol. 71, pp. 52-61, Jan. 2018. https://doi.org/10.1016/j.wasman.2017.10.033

[8] X. Zhao et al., Plastic waste upcycling toward a circular economy, Chemical Engineering Journal, vol. 428. Elsevier B.V., Jan. 15, 2022. doi: 10.1016/j.cej.2021.131928.

[9] Z. O. G. Schyns and M. P. Shaver, Mechanical Recycling of Packaging Plastics: A Review, Macromolecular Rapid Communications, vol. 42, no. 3. Wiley-VCH Verlag, Feb. 01, 2021. https://doi.org/10.1002/marc.202000415

[10] A. K. Undas, M. Groenen, R. J. B. Peters, and S. P. J. van Leeuwen, Safety of recycled plastics and textiles: Review on the detection, identification and safety assessment of contaminants, Chemosphere, vol. 312, Jan. 2023. https://doi.org/10.1016/j.chemosphere.2022.137175

[11] W. Camacho and S. Karlsson, Quality-determination of recycled plastic packaging waste by identification of contaminants by GC-MS after microwave assisted extraction (MAE), Polym Degrad Stab, vol. 71, no. 1, pp. 123-134, Jan. 2000. https://doi.org/10.1016/S0141-3910(00)00163-4

[12] X. Zhao, B. Boruah, K. F. Chin, M. Đokić, J. M. Modak, and H. Sen Soo, Upcycling to Sustainably Reuse Plastics, Advanced Materials, vol. 34, no. 25. John Wiley and Sons Inc, Jun. 01, 2022. https://doi.org/10.1002/adma.202100843

[13] J. Hou, G. Zhao, G. Wang, G. Dong, and J. Xu, A novel gas-assisted microcellular injection molding method for preparing lightweight foams with superior surface appearance and enhanced mechanical performance, Mater Des, vol. 127, pp. 115-125, Aug. 2017. https://doi.org/10.1016/j.matdes.2017.04.073
[14] H. Yokoi, N. Masuda, and H. Mitsuhata, Visualization analysis of flow front behavior during filling process of injection mold cavity by two-axis tracking system, J Mater Process Technol, vol. 130-131, pp. 328-333, Dec. 2002. https://doi.org/10.1016/S0924-0136(02)00742-2

[15] S. C. Chen, Y. W. Lin, R. Der Chien, and H. M. Li, Variable mold temperature to improve surface quality of microcellular injection molded parts using induction heating technology, in Advances in Polymer Technology, 2008, pp. 224-232. https://doi.org/10.1002/adv.20133

[16] J. Ren, L. Lin, J. Jiang, Q. Li, and S. S. Hwang, Effect of Gas Counter Pressure on the Surface Roughness, Morphology, and Tensile Strength between Microcellular and Conventional Injection-Molded PP Parts, Polymers (Basel), vol. 14, no. 6, Mar. 2022. https://doi.org/10.3390/polym14061078

[17] S. C. Chen, P. S. Hsu, and S. S. Hwang, The effects of gas counter pressure and mold temperature variation on the surface quality and morphology of the microcellular polystyrene foams, J Appl Polym Sci, vol. 127, no. 6, pp. 4769-4776, Mar. 2013. https://doi.org/10.1002/app.37994

[18] F. A. Shutov, Integral/Structural Polymer Foams. Springer Berlin Heidelberg, 1986. https://doi.org/10.1007/978-3-662-02486-7

[19] M. Sorgato, F. Zanini, D. Masato, and G. Lucchetta, Submicron laser-textured vents for self-cleaning injection molds, J Appl Polym Sci, vol. 137, no. 42, Nov. 2020. https://doi.org/10.1002/app.49280

[20] M. Roosen et al., Tracing the origin of VOCs in post-consumer plastic film bales, Chemosphere, vol. 324, May 2023. https://doi.org/10.1016/j.chemosphere.2023.138281

[21] K. S. Prado et al., Odor characterization of post-consumer and recycled automotive polypropylene by different sensory evaluation methods and instrumental analysis, Waste Management, vol. 115, pp. 36-46, Sep. 2020. https://doi.org/10.1016/j.wasman.2020.07.021

[22] I. Mikonsaari, E. van de Walle, and K. Moser, Physical Recycling of Plastics - Providing Recyclates with Reduced Emissions, Kunststoffe international, vol. 8, 2022, Accessed: Oct. 16, 2023. [Online]. Available: https://publica.fraunhofer.de/handle/publica/430119

[23] Fraunhofer, Extractive extrusion process performed with all provided material classes, 2021. Available: www createrproject eu

[24] A. Cabanes, F. J. Valdés, and A. Fullana, A review on VOCs from recycled plastics, Sustainable Materials and Technologies, vol. 25. Elsevier B.V., Sep. 01, 2020. https://doi.org/10.1016/j.susmat.2020.e00179

[25] N. Otsu, "A Threshold Selection Method from Gray-Level Histograms," IEEE Transactions on Systems, Man, and Cybernetics, vol. 9, no. 1, pp. 62-66, Jan. 1979. https://doi.org/10.1109/TSMC.1979.4310076
[14] H. Yokoi, N. Masuda, and H. Mitsuhata, Visualization analysis of flow front behavior during filling process of injection mold cavity by two-axis tracking system, J Mater Process Technol, vol. 130-131, pp. 328-333, Dec. 2002. https://doi.org/10.1016/S0924-0136(02)00742-2

[15] S. C. Chen, Y. W. Lin, R. Der Chien, and H. M. Li, Variable mold temperature to improve surface quality of microcellular injection molded parts using induction heating technology, in Advances in Polymer Technology, 2008, pp. 224-232. https://doi.org/10.1002/adv.20133

[16] J. Ren, L. Lin, J. Jiang, Q. Li, and S. S. Hwang, Effect of Gas Counter Pressure on the Surface Roughness, Morphology, and Tensile Strength between Microcellular and Conventional Injection-Molded PP Parts, Polymers (Basel), vol. 14, no. 6, Mar. 2022. https://doi.org/10.3390/polym14061078

[17] S. C. Chen, P. S. Hsu, and S. S. Hwang, The effects of gas counter pressure and mold temperature variation on the surface quality and morphology of the microcellular polystyrene foams, J Appl Polym Sci, vol. 127, no. 6, pp. 4769-4776, Mar. 2013. https://doi.org/10.1002/app.37994

[18] F. A. Shutov, Integral/Structural Polymer Foams. Springer Berlin Heidelberg, 1986. https://doi.org/10.1007/978-3-662-02486-7

[19] M. Sorgato, F. Zanini, D. Masato, and G. Lucchetta, Submicron laser-textured vents for self-cleaning injection molds, J Appl Polym Sci, vol. 137, no. 42, Nov. 2020. https://doi.org/10.1002/app.49280

[20] M. Roosen et al., Tracing the origin of VOCs in post-consumer plastic film bales, Chemosphere, vol. 324, May 2023. https://doi.org/10.1016/j.chemosphere.2023.138281

[21] K. S. Prado et al., Odor characterization of post-consumer and recycled automotive polypropylene by different sensory evaluation methods and instrumental analysis, Waste Management, vol. 115, pp. 36-46, Sep. 2020. https://doi.org/10.1016/j.wasman.2020.07.021

[22] I. Mikonsaari, E. van de Walle, and K. Moser, Physical Recycling of Plastics - Providing Recyclates with Reduced Emissions, Kunststoffe international, vol. 8, 2022, Accessed: Oct. 16, 2023. [Online]. Available: https://publica.fraunhofer.de/handle/publica/430119

[23] Fraunhofer, Extractive extrusion process performed with all provided material classes, 2021. Available: www createrproject eu

[24] A. Cabanes, F. J. Valdés, and A. Fullana, A review on VOCs from recycled plastics, Sustainable Materials and Technologies, vol. 25. Elsevier B.V., Sep. 01, 2020. https://doi.org/10.1016/j.susmat.2020.e00179

[25] N. Otsu, "A Threshold Selection Method from Gray-Level Histograms," IEEE Transactions on Systems, Man, and Cybernetics, vol. 9, no. 1, pp. 62-66, Jan. 1979. https://doi.org/10.1109/TSMC.1979.4310076
# Design optimization of filament wound cylinder by considering process induced residual stresses

PALMIERI Barbara<sup>1,2,a*</sup>, BIANCHI Iacopo<sup>3,b</sup>, DE PRISCO Nello<sup>2,c</sup>, FORCELLESE Archimede<sup>3,d</sup>, MANCIA Tommaso<sup>3,e</sup>, SIMONCINI Michela<sup>3,f</sup>, DE TOMMASO Giuseppe<sup>2,g</sup>, PETRICCIONE A.<sup>2,h</sup> and MARTONE Alfonso<sup>1,i</sup>

<sup>1</sup>CNR-IPCB Institute for Polymers and Composites, P.le E Fermi, 80055 Portici (NA) - Italy

<sup>2</sup>Advanced Tools and Moulds, S.r.l., Stab. 13 Z.i. Aversa Nord, Gricignao di Aversa (CE) - Italy

<sup>3</sup>Università Politecnica delle Marche, Via Brecce Bianche 12, 60123 Ancona, Italy

<sup>a</sup>barbara.palmieri@ipcb.cnr.it, <sup>b</sup>i.bianchi@pm.univpm.it, <sup>c</sup>nellodeprisco@atmsrl.com,

<sup>d</sup>a.forcellese@pm.univpm.it, <sup>e</sup>t.mancia@pm.univpm.it, <sup>f</sup>m.simoncini@pm.univpm.it,

<sup>h</sup>angelo.petriccione@atmsrl.com, <sup>i</sup>alfonso.martone@cnr.it

**Keywords:** Cure Kinetics, Multi-Physics, CFRP, Viscoelastic

**Abstract.** The manufacturing process has a significant influence on the product quality of filament wound composite parts. During the filament winding process, a large tensile load to the fibre was applied and maintained during resin curing, resulting in residual stress. This residual stress gradually relaxes due to the fibres' slippage, the matrix's crosslinking, and different coefficients of thermal expansion between composite parts and mandrels. As a result, increasing the number of layers becomes more problematic. In this work, a multiphysics analysis has been carried out to study the effect of the viscoelastic behaviour of the material on the rise of residual stress on thick cylinders. The multiphysics model was developed in COMSOL to predict the temperature distribution and the degree of polymerization during the consolidation process. The optimal cure profile was identified as a function of process parameters to minimize the thermal gradient within the composite element.

**Introduction**

Thanks to their high stiffness-to-weight ratios, corrosion resistance, and excellent design flexibility, filament wound cylindrical composite parts find extensive applications in the aerospace industry, offshore pipes, underwater vehicles, and high-pressure gas storage [1–4]. For this class of components, the manufacturing process would induce the rise of residual stresses, especially in case of the autoclave curing cycle, unavoidable residual stresses have been extensively documented as a potential hazard to composite structures [5–7]. Upon demoulding, part of these residual stresses is released, resulting in process-induced distortions. This can affect the dimensional accuracy of the composite part, and cause assembly issues, that could even result in the rejection of parts. In some applications the presence of an initial stress state can contribute to relief the working loads, therefore a tension state is applied during the winding process to induce a controlled prestress state. This prestress gradually relaxes as effect of chemical relaxation due to resin curing, and thermal relaxation depending on the temperature profile experienced during the process itself.

For thick composite cylindrical structures, decoupling these factors aids in understanding the quantitative relationship between prestress and residual stress. In fact, the exothermic reaction of resin during the cross-linking process and the low thermal conductivity of material usually lead to an overshoot temperature peak and nonuniform distribution of temperature for thick laminate, resulting in residual stress, possible degradation of the composite and matrix cracks [8,9]. Generally, the manufacturer's recommended cure cycle may not be applicable for thick laminates,

<figure><img src="image_2568.png" /></figure>
# Design optimization of filament wound cylinder by considering process induced residual stresses

PALMIERI Barbara<sup>1,2,a*</sup>, BIANCHI Iacopo<sup>3,b</sup>, DE PRISCO Nello<sup>2,c</sup>, FORCELLESE Archimede<sup>3,d</sup>, MANCIA Tommaso<sup>3,e</sup>, SIMONCINI Michela<sup>3,f</sup>, DE TOMMASO Giuseppe<sup>2,g</sup>, PETRICCIONE A.<sup>2,h</sup> and MARTONE Alfonso<sup>1,i</sup>

<sup>1</sup>CNR-IPCB Institute for Polymers and Composites, P.le E Fermi, 80055 Portici (NA) - Italy

<sup>2</sup>Advanced Tools and Moulds, S.r.l., Stab. 13 Z.i. Aversa Nord, Gricignao di Aversa (CE) - Italy

<sup>3</sup>Università Politecnica delle Marche, Via Brecce Bianche 12, 60123 Ancona, Italy

aBarbara.palmieri@ipcb.cnr.it, bI.bianchi@pm.univpm.it, cNellodeprisco@atmsrl.com,

da.forcellese@pm.univpm.it, eT.mancia@pm.univpm.it, fm.simoncini@pm.univpm.it,

hAngelo.petriccione@atmsrl.com, iAlfonso.martone@cnr.it

**Keywords:** Cure Kinetics, Multi-Physics, CFRP, Viscoelastic

**Abstract.** The manufacturing process has a significant influence on the product quality of filament wound composite parts. During the filament winding process, a large tensile load to the fibre was applied and maintained during resin curing, resulting in residual stress. This residual stress gradually relaxes due to the fibres' slippage, the matrix's crosslinking, and different coefficients of thermal expansion between composite parts and mandrels. As a result, increasing the number of layers becomes more problematic. In this work, a multiphysics analysis has been carried out to study the effect of the viscoelastic behaviour of the material on the rise of residual stress on thick cylinders. The multiphysics model was developed in COMSOL to predict the temperature distribution and the degree of polymerization during the consolidation process. The optimal cure profile was identified as a function of process parameters to minimize the thermal gradient within the composite element.

**Introduction**

Thanks to their high stiffness-to-weight ratios, corrosion resistance, and excellent design flexibility, filament wound cylindrical composite parts find extensive applications in the aerospace industry, offshore pipes, underwater vehicles, and high-pressure gas storage [1–4]. For this class of components, the manufacturing process would induce the rise of residual stresses, especially in case of the autoclave curing cycle, unavoidable residual stresses have been extensively documented as a potential hazard to composite structures [5–7]. Upon demoulding, part of these residual stresses is released, resulting in process-induced distortions. This can affect the dimensional accuracy of the composite part, and cause assembly issues, that could even result in the rejection of parts. In some applications the presence of an initial stress state can contribute to relief the working loads, therefore a tension state is applied during the winding process to induce a controlled prestress state. This prestress gradually relaxes as effect of chemical relaxation due to resin curing, and thermal relaxation depending on the temperature profile experienced during the process itself.

For thick composite cylindrical structures, decoupling these factors aids in understanding the quantitative relationship between prestress and residual stress. In fact, the exothermic reaction of resin during the cross-linking process and the low thermal conductivity of material usually lead to an overshoot temperature peak and nonuniform distribution of temperature for thick laminate, resulting in residual stress, possible degradation of the composite and matrix cracks [8,9]. Generally, the manufacturer's recommended cure cycle may not be applicable for thick laminates,

<figure><img src="image_2561.png" /></figure>
therefore knowing the effect of the cure cycle on residual stress is necessary to reduce residual stresses and increase the mechanical performance of composite parts. Several studies have been conducted to predict the residual stresses in composite by numerical model, but many of these only focus on the material properties in the glassy state [7,10–12].

In this paper, the cure kinetic properties of an epoxy TowPreg have been included in a multiphysics analysis for predicting residual stress. The proposed methodology involves two step analysis, the resin reaction during the cure including the exothermic heat generation and the thermomechanical behaviour when the resin is fully cured. An optimal cure profile has been finally identified by introducing two different dwells to retain the temperature overshoot below the degradation and to avoid temperature/degree of cure mismatches within the domain.

## Heat Transfer and Exothermic Cure Modelling

A thermal model was developed to study the time variation of temperature and the degree of cure (DoC) of the thermosetting resin used to impregnate the carbon tow. The Equation governing heat transfer in the resin during the manufacturing process is [13]:

$$ \rho C_p \frac{\partial T}{\partial t} = \frac{1}{r} \frac{\partial}{\partial r} (k_r \frac{\partial T}{\partial r}) + \frac{\partial}{\partial z} (k_z \frac{\partial T}{\partial z}) + \rho \Delta H_{\text{tot}} \frac{\partial \alpha}{\partial t} (1 - V_f) \quad (1) $$

Where T is the temperature, t is the time, ρ and C<sub>p</sub>, are the composite material's density and specific heat; k<sub>r</sub> and k<sub>z</sub> are the thermal conductivity in r and z direction, respectively. The third term of the equation (1) refers to the internal volumetric heat generation linked to the polymerization of the resin. ΔH<sub>tot</sub> and V<sub>f</sub> indicates the total reaction enthalpy and the fibre volume fraction, while ∂α/∂t is the polymerization's rate, which depends on the DoC (degree of Cure) and temperature (Eq.(2), Kamal and Sourour equation [14]. To resolve the time derivative of the DoC, an ordinary differential equation (ODEs) and differential algebraical equations (DAEs) nodes have been added to the heat transfer one.

$$ \frac{\partial \alpha}{\partial t} = k_1 * (1 - \alpha)^n + k_2 * \alpha^m * (1 - \alpha)^n \quad (2) $$

Where n and m are the reaction orders of the four parameters model, while k<sub>1</sub> and k<sub>2</sub> are the rate constants defined by the Arrhenius expression:

$$ k_1(T) = A_1 e^{-\frac{E_1}{RT}} ; k_2(T) = A_2 e^{-\frac{E_2}{RT}} \quad (3) $$

<table><caption>Table 1. Kinetic Parameters estimated for the epoxy system considered.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>A<sub>1</sub></td><td>1.9e3</td><td>1/s</td></tr><tr><td>A<sub>2</sub></td><td>1.5</td><td>1/s</td></tr><tr><td>E<sub>1</sub></td><td>4.34e4</td><td>J/mol</td></tr><tr><td>E<sub>2</sub></td><td>7.5e5</td><td>J/mol</td></tr><tr><td>n</td><td>1.42</td><td></td></tr><tr><td>m</td><td>1.2</td><td></td></tr><tr><td>ΔH<sub>tot</sub></td><td>350</td><td>kJ/kg</td></tr><tr><td>R</td><td>8.314</td><td>J/(mol·K)</td></tr></tbody></table>

E is the activation energy, R is the gas constant (8.314 J/mol K), T is the absolute temperature (K), and A is the pre-exponential factor. The parameters m, n, A<sub>1</sub>, A<sub>2</sub>, E<sub>1</sub>, E<sub>2</sub> have been identified experimentally through Differential Scanning Calorimetry (DSC) tests on the material and reported in Table 1.

In the ODE node, the resin kinetics (Eq.(2)) is represented by the equation (4):
therefore knowing the effect of the cure cycle on residual stress is necessary to reduce residual stresses and increase the mechanical performance of composite parts. Several studies have been conducted to predict the residual stresses in composite by numerical model, but many of these only focus on the material properties in the glassy state [7,10–12].

In this paper, the cure kinetic properties of an epoxy TowPreg have been included in a multiphysics analysis for predicting residual stress. The proposed methodology involves two step analysis, the resin reaction during the cure including the exothermic heat generation and the thermomechanical behaviour when the resin is fully cured. An optimal cure profile has been finally identified by introducing two different dwells to retain the temperature overshoot below the degradation and to avoid temperature/degree of cure mismatches within the domain.

## Heat Transfer and Exothermic Cure Modelling

A thermal model was developed to study the time variation of temperature and the degree of cure (DoC) of the thermosetting resin used to impregnate the carbon tow. The Equation governing heat transfer in the resin during the manufacturing process is [13]:

$$ \rho C_p \frac{\partial T}{\partial t} = \frac{1}{r} \frac{\partial}{\partial r} (k_r \frac{\partial T}{\partial r}) + \frac{\partial}{\partial z} (k_z \frac{\partial T}{\partial z}) + \rho \Delta H_{\text{tot}} \frac{\partial \alpha}{\partial t} (1 - V_f) \quad (1) $$

Where T is the temperature, t is the time, ρ and C<sub>p</sub>, are the composite material's density and specific heat; k<sub>r</sub> and k<sub>z</sub> are the thermal conductivity in r and z direction, respectively. The third term of the equation (1) refers to the internal volumetric heat generation linked to the polymerization of the resin. ΔH<sub>tot</sub> and V<sub>f</sub> indicates the total reaction enthalpy and the fibre volume fraction, while ∂α/∂t is the polymerization's rate, which depends on the DoC (degree of Cure) and temperature (Eq.(2), Kamal and Sourour equation [14]. To resolve the time derivative of the DoC, an ordinary differential equation (ODEs) and differential algebraical equations (DAEs) nodes have been added to the heat transfer one.

$$ \frac{\partial \alpha}{\partial t} = k_1 * (1 - \alpha)^n + k_2 * \alpha^m * (1 - \alpha)^n \quad (2) $$

Where n and m are the reaction orders of the four parameters model, while k<sub>1</sub> and k<sub>2</sub> are the rate constants defined by the Arrhenius expression:

$$ k_1(T) = A_1 e^{-\frac{E_1}{RT}} ; k_2(T) = A_2 e^{-\frac{E_2}{RT}} \quad (3) $$

<table><caption>Table 1. Kinetic Parameters estimated for the epoxy system considered.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>A<sub>1</sub></td><td>1.9e3</td><td>1/s</td></tr><tr><td>A<sub>2</sub></td><td>1.5</td><td>1/s</td></tr><tr><td>E<sub>1</sub></td><td>4.34e4</td><td>J/mol</td></tr><tr><td>E<sub>2</sub></td><td>7.5e5</td><td>J/mol</td></tr><tr><td>n</td><td>1.42</td><td></td></tr><tr><td>m</td><td>1.2</td><td></td></tr><tr><td>ΔH<sub>tot</sub></td><td>350</td><td>kJ/kg</td></tr><tr><td>R</td><td>8.314</td><td>J/(mol·K)</td></tr></tbody></table>

E is the activation energy, R is the gas constant (8.314 J/mol K), T is the absolute temperature (K), and A is the pre-exponential factor. The parameters m, n, A<sub>1</sub>, A<sub>2</sub>, E<sub>1</sub>, E<sub>2</sub> have been identified experimentally through Differential Scanning Calorimetry (DSC) tests on the material and reported in Table 1.

In the ODE node, the resin kinetics (Eq.(2)) is represented by the equation (4):
$$f = e_a \frac{\partial^2 \alpha}{\partial t^2} + d_a \frac{\partial \alpha}{\partial t} \qquad (4)$$

Where $d_a$ is the damping term and is unity, while $e_a$ is the mass coefficient and is zero, indicating that the material is modelled starting from the uncured state.

A 2D finite element model of the TowPreg polymerisation process for the autoclave cure cycle has been developed by the Comsol Multiphysics software. The following assumptions were considered in the model, both for the workpiece and the mandrel: (i) the density, the specific heat and the thermal conductivity were assumed constant; (ii) the material was set homogenous and transversely isotropic, and (iii) the heat transfer between the workpiece and the mandrel was taken into account.

The CFRP and mandrel properties used in the FE model are listed in Table 2. The density of the CFRP and the thermal capacity were obtained from data reported in the literature [15,16], while the thermal conductivity was obtained by the mixture rule:

$$\frac{1}{k_c} = \frac{V_f}{k_f} + \frac{V_m}{k_m} \qquad (5)$$

$$k_c = k_f V_f + k_m V_m \qquad (6)$$

Where $k_c$, $k_f$ and $k_m$ indicate, respectively, the composite's, fibres, and matrix thermal conductivity.

<table><caption>Table 2. Thermal properties of the CFRP component and aluminium mandrel used in the thermomechanical simulation.</caption><thead><tr><th>Material</th><th>Parameter</th><th>Value</th><th>Unit</th><th>Description</th></tr></thead><tbody><tr><td rowspan="5">Aluminum</td><td>ρ<sub>Al</sub></td><td>2700</td><td>kg/m<sup>3</sup></td><td>Density</td></tr><tr><td>C<sub>pAl</sub></td><td>900</td><td>J/(kg·K)</td><td>Specific Heat</td></tr><tr><td>k<sub>r,Al</sub>= k<sub>z,Al</sub></td><td>1.2e-5</td><td>W/(m·K)</td><td>Thermal conductivity</td></tr><tr><td>E<sub>Al</sub></td><td>69</td><td>GPa</td><td>Young modulus</td></tr><tr><td>v<sub>Al</sub></td><td>0.3</td><td>-</td><td>Poisson modulus</td></tr><tr><td rowspan="7">CFRP</td><td>ρ<sub>C</sub></td><td>1820</td><td>kg/m<sup>3</sup></td><td>Density</td></tr><tr><td>C<sub>pC</sub></td><td>1200</td><td>J/(kg·K)</td><td>Specific Heat</td></tr><tr><td>k<sub>r,C</sub></td><td>1</td><td>W/(m·K)</td><td>Thermal conductivity</td></tr><tr><td>k<sub>z,C</sub></td><td>200</td><td>W/(m·K)</td><td>Thermal conductivity</td></tr><tr><td>E<sub>r,C</sub></td><td>8</td><td>GPa</td><td>Young modulus, radial axis</td></tr><tr><td>E<sub>z,C</sub></td><td>94</td><td>GPa</td><td>Young modulus, z axis</td></tr><tr><td>v<sub>C</sub></td><td>0.3</td><td>-</td><td>Poisson modulus</td></tr></tbody></table>

Figure 1 shows the surfaces where thermal boundary conditions have been applied in the model. All the external surfaces of the mould and the part were exposed to the autoclave flux and temperature with an initial condition of $T_{room}$ at 20°C. The convective coefficient within the autoclave was set up according to the literature available data [17,18]. The mandrel is plugged by the rack holder therefore the air inside could be considered in no flow condition.
$$f = e_a \frac{\partial^2 \alpha}{\partial t^2} + d_a \frac{\partial \alpha}{\partial t} \qquad (4)$$

Where $d_a$ is the damping term and is unity, while $e_a$ is the mass coefficient and is zero, indicating that the material is modelled starting from the uncured state.

A 2D finite element model of the TowPreg polymerisation process for the autoclave cure cycle has been developed by the Comsol Multiphysics software. The following assumptions were considered in the model, both for the workpiece and the mandrel: (i) the density, the specific heat and the thermal conductivity were assumed constant; (ii) the material was set homogenous and transversely isotropic, and (iii) the heat transfer between the workpiece and the mandrel was taken into account.

The CFRP and mandrel properties used in the FE model are listed in Table 2. The density of the CFRP and the thermal capacity were obtained from data reported in the literature [15,16], while the thermal conductivity was obtained by the mixture rule:

$$\frac{1}{k_c} = \frac{V_f}{k_f} + \frac{V_m}{k_m} \qquad (5)$$

$$k_c = k_f V_f + k_m V_m \qquad (6)$$

Where $k_c$, $k_f$ and $k_m$ indicate, respectively, the composite's, fibres, and matrix thermal conductivity.

<table><caption>Table 2. Thermal properties of the CFRP component and aluminium mandrel used in the thermomechanical simulation.</caption><thead><tr><th>Material</th><th>Parameter</th><th>Value</th><th>Unit</th><th>Description</th></tr></thead><tbody><tr><td rowspan="5">Aluminum</td><td>ρ<sub>Al</sub></td><td>2700</td><td>kg/m<sup>3</sup></td><td>Density</td></tr><tr><td>C<sub>pAl</sub></td><td>900</td><td>J/(kg·K)</td><td>Specific Heat</td></tr><tr><td>k<sub>r,Al</sub>= k<sub>z,Al</sub></td><td>1.2e-5</td><td>W/(m·K)</td><td>Thermal conductivity</td></tr><tr><td>E<sub>Al</sub></td><td>69</td><td>GPa</td><td>Young modulus</td></tr><tr><td>v<sub>Al</sub></td><td>0.3</td><td>-</td><td>Poisson modulus</td></tr><tr><td rowspan="7">CFRP</td><td>ρ<sub>C</sub></td><td>1820</td><td>kg/m<sup>3</sup></td><td>Density</td></tr><tr><td>C<sub>pC</sub></td><td>1200</td><td>J/(kg·K)</td><td>Specific Heat</td></tr><tr><td>k<sub>r,C</sub></td><td>1</td><td>W/(m·K)</td><td>Thermal conductivity</td></tr><tr><td>k<sub>z,C</sub></td><td>200</td><td>W/(m·K)</td><td>Thermal conductivity</td></tr><tr><td>E<sub>r,C</sub></td><td>8</td><td>GPa</td><td>Young modulus, radial axis</td></tr><tr><td>E<sub>z,C</sub></td><td>94</td><td>GPa</td><td>Young modulus, z axis</td></tr><tr><td>v<sub>C</sub></td><td>0.3</td><td>-</td><td>Poisson modulus</td></tr></tbody></table>

Figure 1 shows the surfaces where thermal boundary conditions have been applied in the model. All the external surfaces of the mould and the part were exposed to the autoclave flux and temperature with an initial condition of $T_{room}$ at 20°C. The convective coefficient within the autoclave was set up according to the literature available data [17,18]. The mandrel is plugged by the rack holder therefore the air inside could be considered in no flow condition.
Autoclave flow

<figure><img src="image_2569.png" /></figure>

$$h_{\infty} = 5 \text{ W/(K m}^2\text{)}$$

<caption>Figure 1. Boundary Conditions for the Thermal Analysis.</caption>

In order to take into account, the heating generated by the polymerisation process, an additional heat source has been considered for the composite part. Two different temperature profiles were investigated to optimize the curing cycle to minimize the residual stress occurring in the workpiece. The first one, shown in Figure 2a, consists of a heating ramp from Troom to 120°C at 1.5°C min and a dwell time of 120 minutes, and then a cooling ramp of 2°C/min. The optimized curing cycle consists of an initial temperature of 20 °C and DoC of 0.0001. Then the temperature increases to 90°C with a temperature raising rate of 1.5°C/min. Then, a first holding stage of 120 min is applied.

After the dwell, the part is heated at 1.5 °C/min to 120°C to the second holding stage. After that, the laminate is heated at 120°C for 60 min. At last, the temperature drops to 20°C at 2 C°/min. Figure 2 shows the thermal cycle considered.

<figure><img src="image_2570.png" /><figcaption>Figure 2. a) Standard thermal cure cycle; b) Optimized thermal cure cycle</figcaption></figure>

## Coupled Heat Transfer and Mechanical Analysis

Thermo-mechanical properties of composite material are influenced by the interaction between fibres and matrix. In the present analysis, the thermo-mechanical properties have been characterized by experimental tests on the composite ply. Constitutive equation was therefore written at macro-level homogenized scale. To calculate the temporal evolution of the stress, the mechanical equilibrium equations have been imposed on the whole laminate,

$$\nabla \cdot \mathbf{S} + \mathbf{b} = 0 \qquad (7)$$

Where **b** is the body force vector, neglected in the present analysis. In cylindrical coordinates, the mechanical equilibrium equations, considering also the axial symmetric conditions, are given by:
Autoclave flow

<figure><img src="image_2562.png" /></figure>

$$h_{\infty} \frac{5 \text{ W}}{(\text{K m}^2)}$$

<caption>Figure 1. Boundary Conditions for the Thermal Analysis.</caption>

In order to take into account, the heating generated by the polymerisation process, an additional heat source has been considered for the composite part. Two different temperature profiles were investigated to optimize the curing cycle to minimize the residual stress occurring in the workpiece. The first one, shown in Figure 2a, consists of a heating ramp from Troom to 120°C at 1.5°C min and a dwell time of 120 minutes, and then a cooling ramp of 2°C/min. The optimized curing cycle consists of an initial temperature of 20 °C and DoC of 0.0001. Then the temperature increases to 90°C with a temperature raising rate of 1.5°C/min. Then, a first holding stage of 120 min is applied.

After the dwell, the part is heated at 1.5 °C/min to 120°C to the second holding stage. After that, the laminate is heated at 120°C for 60 min. At last, the temperature drops to 20°C at 2 C°/min. Figure 2 shows the thermal cycle considered.

<figure><img src="image_2563.png" /><figcaption>Figure 2. a) Standard thermal cure cycle; b) Optimized thermal cure cycle</figcaption></figure>

## Coupled Heat Transfer and Mechanical Analysis

Thermo-mechanical properties of composite material are influenced by the interaction between fibres and matrix. In the present analysis, the thermo-mechanical properties have been characterized by experimental tests on the composite ply. Constitutive equation was therefore written at macro-level homogenized scale. To calculate the temporal evolution of the stress, the mechanical equilibrium equations have been imposed on the whole laminate,

$$\nabla \cdot \mathbf{S} + \mathbf{b} = 0 \qquad (7)$$

Where **b** is the body force vector, neglected in the present analysis. In cylindrical coordinates, the mechanical equilibrium equations, considering also the axial symmetric conditions, are given by:
$$ \frac{\partial \sigma_r}{\partial r} + \frac{\partial \tau_{rz}}{\partial z} + \frac{\sigma_r - \sigma_\theta}{r} = 0 \qquad (8) $$

$$ \frac{\partial \tau_{r\theta}}{\partial r} + \frac{\partial \tau_{\theta z}}{\partial z} + 2 \frac{\tau_{r\theta}}{r} = 0 \qquad (9) $$

$$ \frac{\partial \tau_{rz}}{\partial r} + \frac{\partial \sigma_z}{\partial z} + \frac{\tau_{rz}}{r} = 0 \qquad (10) $$

Boundary conditions require radial stress to be the opposite of autoclave chamber environmental pressure $p(t)$ and absence of tangential stress on the external laminate surface:

$$ \sigma_r(R_{ext}^e, t) = -p(t), \quad \tau_{r\theta}(R_{ext}^e, t) = 0, \quad \tau_{rz}(R_{ext}^e, t) = 0 \qquad (11) $$

Where $R_{ext}^e$ is the external radius of the composite part. A scheme of the mechanical boundary conditions imposed is reported in Figure 3.

These boundary conditions are then coupled with the thermal fields evaluated according to the previous paragraph. The mechanical analysis (eq. 7-8) is run coupled with the thermal analysis (eq.1) during the cooling stage by assuming as boundary condition the temperature distribution at the end of dwell stage at 120°C.

<figure><img src="image_2571.png" /><figcaption>Figure 3. Mechanical boundary conditions</figcaption></figure>

## Results and Discussion

The standard cure cycle consists of a warmup to 120°C at 1.5 °C/min and a dwell time of 120 minutes, Figure 4 shows the temperature profile predicted by the model. Epoxy exothermic reaction results in temperature overshoots; the analysis of three different sections th=0, th=7.5 and th=15, namely the mandrel CFRP interface, the middle section and the external surface, shows temperature higher than the autoclave ambient profile. In addition, there is a temperature gradient within the cylinder, inside the CFRP part (between outer and inner radius) a difference of 20°C has been evaluated, with an average overshoot of 30°C with respect to the nominal temperature.

Overshooting is the typical behaviour of thick thermoset composite cylinders since high thickness slows down heat dissipation due to the low thermal conductivity of the composite [19]. Even if the temperature reaches a uniform distribution after 30 minutes, a dwell time of 120 min is needed to achieve the complete conversion all over the cylinder (Figure 4a). Figure 4a shows the trend of the DoC ($\alpha$) vs the thermal cycle. At the end of the curing cycle, the resin reaches a value of $\alpha$ = 0.95 (vitrification state), which is conventionally indicated as the complete conversion of the material. Nonetheless, due to the different temperature distribution the inner and outer surfaces of the part show a different DoC that leads to the stresses built up. Internal stresses developed inside the part are a consequence of coupling chemistry, thermal distribution, and local stiffness.
$$ \frac{\partial \sigma_r}{\partial r} + \frac{\partial \tau_{rz}}{\partial z} + \frac{\sigma_r - \sigma_\theta}{r} = 0 \qquad (8) $$

$$ \frac{\partial \tau_{r\theta}}{\partial r} + \frac{\partial \tau_{\theta z}}{\partial z} + 2 \frac{\tau_{r\theta}}{r} = 0 \qquad (9) $$

$$ \frac{\partial \tau_{rz}}{\partial r} + \frac{\partial \sigma_z}{\partial z} + \frac{\tau_{rz}}{r} = 0 \qquad (10) $$

Boundary conditions require radial stress to be the opposite of autoclave chamber environmental pressure $p(t)$ and absence of tangential stress on the external laminate surface:

$$ \sigma_r(R_{ext}^e, t) = -p(t), \quad \tau_{r\theta}(R_{ext}^e, t) = 0, \quad \tau_{rz}(R_{ext}^e, t) = 0 \qquad (11) $$

Where $R_{ext}^e$ is the external radius of the composite part. A scheme of the mechanical boundary conditions imposed is reported in Figure 3.

These boundary conditions are then coupled with the thermal fields evaluated according to the previous paragraph. The mechanical analysis (eq. 7-8) is run coupled with the thermal analysis (eq.1) during the cooling stage by assuming as boundary condition the temperature distribution at the end of dwell stage at 120°C.

<figure><img src="image_2564.png" /><figcaption>Figure 3. Mechanical boundary conditions</figcaption></figure>

## Results and Discussion

The standard cure cycle consists of a warmup to 120°C at 1.5 °C/min and a dwell time of 120 minutes, Figure 4 shows the temperature profile predicted by the model. Epoxy exothermic reaction results in temperature overshoots; the analysis of three different sections th=0, th=7.5 and th=15, namely the mandrel CFRP interface, the middle section and the external surface, shows temperature higher than the autoclave ambient profile. In addition, there is a temperature gradient within the cylinder, inside the CFRP part (between outer and inner radius) a difference of 20°C has been evaluated, with an average overshoot of 30°C with respect to the nominal temperature.

Overshooting is the typical behaviour of thick thermoset composite cylinders since high thickness slows down heat dissipation due to the low thermal conductivity of the composite [19]. Even if the temperature reaches a uniform distribution after 30 minutes, a dwell time of 120 min is needed to achieve the complete conversion all over the cylinder (Figure 4a). Figure 4a shows the trend of the DoC ($\alpha$) vs the thermal cycle. At the end of the curing cycle, the resin reaches a value of $\alpha$ = 0.95 (vitrification state), which is conventionally indicated as the complete conversion of the material. Nonetheless, due to the different temperature distribution the inner and outer surfaces of the part show a different DoC that leads to the stresses built up. Internal stresses developed inside the part are a consequence of coupling chemistry, thermal distribution, and local stiffness.
The polymers start to transfer loads when gelation occurs. A DoC in the range of 0.5 and 0.7 identifies gelation and vitrification respectively.

<figure><img src="image_2572.png" /><figcaption>Figure 4. a) Degree of Cure (α) vs thermal cycle for point at different radii; b) Temperature profile vs thermal cycle at different radii (th=0 mm, th =7.5 mm and th= 15 mm).</figcaption></figure>

As reported in Figure 4 within the part there is a variation in DoC, which leads to the formation of a differential stress field inside the part raising residual stresses at the end of the cycle.

Figure 5, reproduces the DoC map at 40 minutes, which identifies the critical situation when each point inside the part can carry loads (all the domain reached vitrification Doc>0.7) but with functionally graded properties, the maximum difference between points at different degrees of cure is:

$$ \Delta = DoC_{max} - DoC_{min} \approx 0.174 \qquad (12) $$

<figure><img src="image_2573.png" /><figcaption>Figure 5. DoC distribution within the domain (adimensional axis) The x-axis indicates the adimensional axial length of the CFRP cylinder (l= y/250 mm), while the y-axis indicates the adimensional thickness (th = x/15 mm).</figcaption></figure>

Figure 6 reproduces the stress distribution along the cooling stage, evaluated by coupling thermal and mechanical analysis. The temperature superimposed in each graph is related to the interface between mandrel and CFRP, while stresses are estimated at different sections: th=0 mm, th=7.5 mm, th=15 mm corresponding to different radius, namely th=0 is the interface between mandrel and CFRP; th=15 is the external surface of the CFRP.
The polymers start to transfer loads when gelation occurs. A DoC in the range of 0.5 and 0.7 identifies gelation and vitrification respectively.

<figure><img src="image_2565.png" /><figcaption>Figure 4. a) Degree of Cure (α) vs thermal cycle for point at different radii; b) Temperature profile vs thermal cycle at different radii (th=0 mm, th =7.5 mm and th= 15 mm).</figcaption></figure>

As reported in Figure 4 within the part there is a variation in DoC, which leads to the formation of a differential stress field inside the part raising residual stresses at the end of the cycle.

Figure 5, reproduces the DoC map at 40 minutes, which identifies the critical situation when each point inside the part can carry loads (all the domain reached vitrification Doc>0.7) but with functionally graded properties, the maximum difference between points at different degrees of cure is:

$$ \Delta = DoC_{max} - DoC_{min} \approx 0.174 \qquad (12) $$

<figure><img src="image_2566.png" /><figcaption>Figure 5. DoC distribution within the domain (adimensional axis) The x-axis indicates the adimensional axial length of the CFRP cylinder (l= y/250 mm), while the y-axis indicates the adimensional thickness (th = x/15 mm).</figcaption></figure>

Figure 6 reproduces the stress distribution along the cooling stage, evaluated by coupling thermal and mechanical analysis. The temperature superimposed in each graph is related to the interface between mandrel and CFRP, while stresses are estimated at different sections: th=0 mm, th=7.5 mm, th=15 mm corresponding to different radius, namely th=0 is the interface between mandrel and CFRP; th=15 is the external surface of the CFRP.
<figure><img src="image_2574.png" /><figcaption>Figure 6. Stress and Temperature evolution at different radii, a) hoop, b) axial, c) radial.</figcaption></figure>

The initial stress state at the precompression on the axial and tangential relaxes during the cooling stage of the axial stresses (Figure 6b).

Aiming to reduce the chance of residual stress formation, a different cure profile has been set. The rationale for defining the new profile is to minimize the degree of cure gap among the CFRP part (Δ function). A second constraint included in the optimal profile search is to minimize the temperature overshot to avoid the system reaching degradation stages.

Figure 7 depicts the DoC variation and the Temperature fields related to a double-stage cure, where a first dwell is set at 90°C for 2 hours and 30 minutes at 120°C. Numerical predictions indicate a lower overshoot (15°C) in the first dwell, and all over the cylinder, the maximum temperature reached is below the nominal cure temperature of the material (120°C).
<figure><img src="image_2567.png" /><figcaption>Figure 6. Stress and Temperature evolution at different radii, a) hoop, b) axial, c) radial.</figcaption></figure>

The initial stress state at the precompression on the axial and tangential relaxes during the cooling stage of the axial stresses (Figure 6b).

Aiming to reduce the chance of residual stress formation, a different cure profile has been set. The rationale for defining the new profile is to minimize the degree of cure gap among the CFRP part (Δ function). A second constraint included in the optimal profile search is to minimize the temperature overshot to avoid the system reaching degradation stages.

Figure 7 depicts the DoC variation and the Temperature fields related to a double-stage cure, where a first dwell is set at 90°C for 2 hours and 30 minutes at 120°C. Numerical predictions indicate a lower overshoot (15°C) in the first dwell, and all over the cylinder, the maximum temperature reached is below the nominal cure temperature of the material (120°C).
<figure><img src="image_2575.png" /><figcaption>Figure 7. a) Degree of cure (α) and (b) Temperature profile vs thermal cycle optimized at different radii of the CFRP part (th=0 mm, th= 7.5 mm and th= 15 mm)</figcaption></figure>

In addition, the DoC gradient inside the material is negligible, resulting in a reduction of properties mismatching (Figure 8).

<figure><img src="image_2576.png" /><figcaption>Figure 8. DoC distribution within the domain (adimensional axis). The x-axis indicates the adimensional axial length of the CFRP cylinder (l= y/250 mm), while the y-axis indicates the adimensional thickness (th = x/15 mm).</figcaption></figure>

The comparison between stress distribution related to the standard cure cycle and the optional one led to a reduction in hoop stresses. The two step cure led to a smooth stresses gradient during the cure since a homogenous state of cure is achieved during the cycle. The hoop stress at the end of the cycle results in a precompression in the winding direction which should be balanced by prestressing the fiber during manufacturing. The study of axial stresses related to the standard cycle shows a risk of delamination since the maximum stresses are achieved inside the CFRP cylinder (shear stresses in the plan z, theta).
<figure><img src="image_2568.png" /><figcaption>Figure 7. a) Degree of cure (α) and (b) Temperature profile vs thermal cycle optimized at different radii of the CFRP part (th=0 mm, th= 7.5 mm and th= 15 mm)</figcaption></figure>

In addition, the DoC gradient inside the material is negligible, resulting in a reduction of properties mismatching (Figure 8).

<figure><img src="image_2569.png" /><figcaption>Figure 8. DoC distribution within the domain (adimensional axis). The x-axis indicates the adimensional axial length of the CFRP cylinder (l= y/250 mm), while the y-axis indicates the adimensional thickness (th = x/15 mm).</figcaption></figure>

The comparison between stress distribution related to the standard cure cycle and the optional one led to a reduction in hoop stresses. The two step cure led to a smooth stresses gradient during the cure since a homogenous state of cure is achieved during the cycle. The hoop stress at the end of the cycle results in a precompression in the winding direction which should be balanced by prestressing the fiber during manufacturing. The study of axial stresses related to the standard cycle shows a risk of delamination since the maximum stresses are achieved inside the CFRP cylinder (shear stresses in the plan z, theta).
<figure><img src="image_2577.png" /><figcaption>Figure 9. Stress and Temperature evolution at different radii, a) hoop, b) axial, c) radial.</figcaption></figure>

The new cycle implies a reduction of interlaminar stresses, and an increase of compression is predicted at the interface between CFRP and mandrel. The latter phenomenon could depend on the boundary conditions and additional work should be addressed for overcoming the no-slip condition at the interface.

## Conclusion

During thermo-set composites manufacturing, highly exothermic polymerization reaction and low heat dissipation rate due to material, lead to the development of thermal and residual stresses, especially in thick laminates, where non-uniform cure degree due to thermal gradients may also reduce material final effectiveness. In the present work, a numerical model to analyze the autoclave composite cylinder manufacturing process was developed and embedded in multiphysics software. Based on the Finite Element Method (FEM), the model considers temperature and cure dependent viscoelastic anisotropic behaviour of composite material and tool-composite interaction. Heat transfer analysis based on cure kinetics of the employed matrix was performed to assign thermal load for structural simulations. Experimental characterization of the thermal properties of the employed matrix was carried out by performing typical DSC tests.

In this paper, a multistep analysis, for predicting stress formation during the cure cycle of thick composite cylinders, was carried out. The thermal analysis was set to include the cure kinetics of the epoxy and to study the cure evolution within the domain. Subsequent analysis is executed by accounting for the thermomechanical properties during the cooling stage accounting for final stresses.
<figure><img src="image_2570.png" /><figcaption>Figure 9. Stress and Temperature evolution at different radii, a) hoop, b) axial, c) radial.</figcaption></figure>

The new cycle implies a reduction of interlaminar stresses, and an increase of compression is predicted at the interface between CFRP and mandrel. The latter phenomenon could depend on the boundary conditions and additional work should be addressed for overcoming the no-slip condition at the interface.

## Conclusion

During thermo-set composites manufacturing, highly exothermic polymerization reaction and low heat dissipation rate due to material, lead to the development of thermal and residual stresses, especially in thick laminates, where non-uniform cure degree due to thermal gradients may also reduce material final effectiveness. In the present work, a numerical model to analyze the autoclave composite cylinder manufacturing process was developed and embedded in multiphysics software. Based on the Finite Element Method (FEM), the model considers temperature and cure dependent viscoelastic anisotropic behaviour of composite material and tool-composite interaction. Heat transfer analysis based on cure kinetics of the employed matrix was performed to assign thermal load for structural simulations. Experimental characterization of the thermal properties of the employed matrix was carried out by performing typical DSC tests.

In this paper, a multistep analysis, for predicting stress formation during the cure cycle of thick composite cylinders, was carried out. The thermal analysis was set to include the cure kinetics of the epoxy and to study the cure evolution within the domain. Subsequent analysis is executed by accounting for the thermomechanical properties during the cooling stage accounting for final stresses.
An optimal cure cycle has been identified by minimizing the Δ function which represents the maximum DoC difference within the domain. The optimal cycle led to a reduction in temperature overshoot and dramatically reduced the risk of delamination inside the CFRP cylinder.

## Acknowledgement

This research was carried out in the framework of the project SMART TOW WINDING CUP, founded by the Ministry of University and Research, grant number ARS01_00871, PON "Ricerca e Innovazione" 2014 – 2020 Azione II – Obiettivo Specifico 1b.

## Reference

[1] Liu, C.; Shi, Y. Design optimization for filament wound cylindrical composite internal pressure vessels considering process-induced residual stresses. *Compos. Struct.* **2020**, *235*, 111755. https://doi.org/10.1016/j.compstruct.2019.111755

[2] Kim, S.J.; Hayat, K.; Nasir, S.U.; Ha, S.K. Design and fabrication of hybrid composite hubs for a multi-rim flywheel energy storage system. *Compos. Struct.* **2014**, *107*, 19–29. https://doi.org/10.1016/j.compstruct.2013.07.032

[3] Yin, D.; Li, B.; Xiao, H. Analysis for the residual prestress of composite barrel for railgun with tension winding. *Def. Technol.* **2020**, *16*, 893–899. https://doi.org/10.1016/j.dt.2019.11.008

[4] Chen, X.; Li, Y.; Huan, D.; Wang, W.; Jiao, Y. Influence of resin curing cycle on the deformation of filament wound composites by in situ strain monitoring. *High Perform. Polym.* **2021**, *33*, 1141–1152. https://doi.org/10.1177/09540083211026359

[5] Hisada, S.; Minakuchi, S.; Takeda, N. Cure-induced strain and failure in deltoid of composite T-joints. *Compos. Part A Appl. Sci. Manuf.* **2021**, *141*, 106210. https://doi.org/10.1016/j.compositesa.2020.106210

[6] Benavente, M.; Marcin, L.; Courtois, A.; Lévesque, M.; Ruiz, E. Numerical analysis of viscoelastic process-induced residual distortions during manufacturing and post-curing. *Compos. Part A Appl. Sci. Manuf.* **2018**, *107*, 205–216. https://doi.org/10.1016/j.compositesa.2018.01.005

[7] Shokrieh, M.M.; Akbari, S.; Daneshvar, A. A comparison between the slitting method and the classical lamination theory in determination of macro-residual stresses in laminated composites. *Compos. Struct.* **2013**, *96*, 708–715. https://doi.org/10.1016/j.compstruct.2012.10.001

[8] Sorrentino, L.; Esposito, L.; Bellini, C. A new methodology to evaluate the influence of curing overheating on the mechanical properties of thick FRP laminates. *Compos. Part B Eng.* **2017**, *109*, 187–196. https://doi.org/10.1016/j.compositesb.2016.10.064

[9] He, H.-W.; Li, K.-X. Effect of Processing Parameters on the Interlaminar Shear Strength of Carbon Fiber/Epoxy Composites. *J. Macromol. Sci. Part B* **2014**, *53*, 1050–1058. https://doi.org/10.1080/00222348.2014.882249

[10] Abou Msallem, Y.; Jacquemin, F.; Boyard, N.; Poitou, A.; Delaunay, D.; Chatel, S. Material characterization and residual stresses simulation during the manufacturing process of epoxy matrix composites. *Compos. Part A Appl. Sci. Manuf.* **2010**, *41*, 108–115. https://doi.org/10.1016/j.compositesa.2009.09.025

[11] Zhang, M.; Zhang, S.; Xie, H.; Li, S. Micromechanical Analysis and Experimental Studies of Thermal Residual Stress Forming Mechanism in FRP Composites. *Appl. Compos. Mater.* **2021**, *28*, 1945–1957. https://doi.org/10.1007/s10443-021-09943-6

[12] Hu, H.; Cao, D.; Pavier, M.; Zhong, Y.; Zu, L.; Liu, L.; Li, S. Investigation of non-uniform gelation effects on residual stresses of thick laminates based on tailed FBG sensor. *Compos. Struct.* **2018**, *202*, 1361–1372. https://doi.org/10.1016/j.compstruct.2018.06.074
An optimal cure cycle has been identified by minimizing the Δ function which represents the maximum DoC difference within the domain. The optimal cycle led to a reduction in temperature overshoot and dramatically reduced the risk of delamination inside the CFRP cylinder.

## Acknowledgement

This research was carried out in the framework of the project SMART TOW WINDING CUP, founded by the Ministry of University and Research, grant number ARS01_00871, PON "Ricerca e Innovazione" 2014 – 2020 Azione II – Obiettivo Specifico 1b.

## Reference

[1] Liu, C.; Shi, Y. Design optimization for filament wound cylindrical composite internal pressure vessels considering process-induced residual stresses. *Compos. Struct.* **2020**, *235*, 111755. https://doi.org/10.1016/j.compstruct.2019.111755

[2] Kim, S.J.; Hayat, K.; Nasir, S.U.; Ha, S.K. Design and fabrication of hybrid composite hubs for a multi-rim flywheel energy storage system. *Compos. Struct.* **2014**, *107*, 19–29. https://doi.org/10.1016/j.compstruct.2013.07.032

[3] Yin, D.; Li, B.; Xiao, H. Analysis for the residual prestress of composite barrel for railgun with tension winding. *Def. Technol.* **2020**, *16*, 893–899. https://doi.org/10.1016/j.dt.2019.11.008

[4] Chen, X.; Li, Y.; Huan, D.; Wang, W.; Jiao, Y. Influence of resin curing cycle on the deformation of filament wound composites by in situ strain monitoring. *High Perform. Polym.* **2021**, *33*, 1141–1152. https://doi.org/10.1177/09540083211026359

[5] Hisada, S.; Minakuchi, S.; Takeda, N. Cure-induced strain and failure in deltoid of composite T-joints. *Compos. Part A Appl. Sci. Manuf.* **2021**, *141*, 106210. https://doi.org/10.1016/j.compositesa.2020.106210

[6] Benavente, M.; Marcin, L.; Courtois, A.; Lévesque, M.; Ruiz, E. Numerical analysis of viscoelastic process-induced residual distortions during manufacturing and post-curing. *Compos. Part A Appl. Sci. Manuf.* **2018**, *107*, 205–216. https://doi.org/10.1016/j.compositesa.2018.01.005

[7] Shokrieh, M.M.; Akbari, S.; Daneshvar, A. A comparison between the slitting method and the classical lamination theory in determination of macro-residual stresses in laminated composites. *Compos. Struct.* **2013**, *96*, 708–715. https://doi.org/10.1016/j.compstruct.2012.10.001

[8] Sorrentino, L.; Esposito, L.; Bellini, C. A new methodology to evaluate the influence of curing overheating on the mechanical properties of thick FRP laminates. *Compos. Part B Eng.* **2017**, *109*, 187–196. https://doi.org/10.1016/j.compositesb.2016.10.064

[9] He, H.-W.; Li, K.-X. Effect of Processing Parameters on the Interlaminar Shear Strength of Carbon Fiber/Epoxy Composites. *J. Macromol. Sci. Part B* **2014**, *53*, 1050–1058. https://doi.org/10.1080/00222348.2014.882249

[10] Abou Msallem, Y.; Jacquemin, F.; Boyard, N.; Poitou, A.; Delaunay, D.; Chatel, S. Material characterization and residual stresses simulation during the manufacturing process of epoxy matrix composites. *Compos. Part A Appl. Sci. Manuf.* **2010**, *41*, 108–115. https://doi.org/10.1016/j.compositesa.2009.09.025

[11] Zhang, M.; Zhang, S.; Xie, H.; Li, S. Micromechanical Analysis and Experimental Studies of Thermal Residual Stress Forming Mechanism in FRP Composites. *Appl. Compos. Mater.* **2021**, *28*, 1945–1957. https://doi.org/10.1007/s10443-021-09943-6

[12] Hu, H.; Cao, D.; Pavier, M.; Zhong, Y.; Zu, L.; Liu, L.; Li, S. Investigation of non-uniform gelation effects on residual stresses of thick laminates based on tailed FBG sensor. *Compos. Struct.* **2018**, *202*, 1361–1372. https://doi.org/10.1016/j.compstruct.2018.06.074
[13] Palmieri, B.; Petriccione, A.; De Tommaso, G.; Giordano, M.; Martone, A. An efficient thermal cure profile for thick parts made by reactive processing of acrylic thermoplastic composites. *J. Compos. Sci.* **2021**, *5*. https://doi.org/10.3390/jcs5090229

[14] Kamal, M.R.; Sourour, S. Kinetics and thermal characterization of thermoset cure. *Polym. Eng. Sci.* **1973**, *13*, 59–64. https://doi.org/10.1002/pen.760130110

[15] Patnaik, A.; Abdula; hyarani Biswas; Satapathy, A. Thermal conductivity of particulate filled polymer composites.; 2009.

[16] Macias, J.D.; Bante-Guerra, J.; Cervantes-Alvarez, F.; Rodríguez-Gattorno, G.; Arés-Muzio, O.; Romero-Paredes, H.; Arancibia-Bulnes, C.A.; Ramos-Sánchez, V.; Villafán-Vidales, H.I.; Ordonez-Miranda, J.; et al. Thermal Characterization of Carbon Fiber-Reinforced Carbon Composites. *Appl. Compos. Mater.* **2019**, *26*, 321–337. https://doi.org/10.1007/s10443-018-9694-0

[17] Antonucci, V.; Giordano, M.; Inserraimparato, S.; Nicolais, L. Analysis of heat transfer in autoclave technology. *Polym. Compos.* **2001**, *22*, 613–620. https://doi.org/10.1002/pc.10564

[18] N. Slesinger, T. Shimizu, A. Arafath, A.P. HEAT TRANSFER COEFFICIENT DISTRIBUTION INSIDE AN AUTOCLAVE.

[19] Zhou, Y.; Li, M.; Cheng, Q.; Wang, S.; Gu, Y.; Chen, X. Quantitative relations between curing processes and local properties within thick composites based on simulation and machine learning. *Mater. Des.* **2023**, *226*, 111686. https://doi.org/10.1016/j.matdes.2023.111686
[13] Palmieri, B.; Petriccione, A.; De Tommaso, G.; Giordano, M.; Martone, A. An efficient thermal cure profile for thick parts made by reactive processing of acrylic thermoplastic composites. *J. Compos. Sci.* **2021**, *5*. https://doi.org/10.3390/jcs5090229

[14] Kamal, M.R.; Sourour, S. Kinetics and thermal characterization of thermoset cure. *Polym. Eng. Sci.* **1973**, *13*, 59–64. https://doi.org/10.1002/pen.760130110

[15] Patnaik, A.; Abdula; hyarani Biswas; Satapathy, A. Thermal conductivity of particulate filled polymer composites.; 2009.

[16] Macias, J.D.; Bante-Guerra, J.; Cervantes-Alvarez, F.; Rodríguez-Gattorno, G.; Arés-Muzio, O.; Romero-Paredes, H.; Arancibia-Bulnes, C.A.; Ramos-Sánchez, V.; Villafán-Vidales, H.I.; Ordonez-Miranda, J.; et al. Thermal Characterization of Carbon Fiber-Reinforced Carbon Composites. *Appl. Compos. Mater.* **2019**, *26*, 321–337. https://doi.org/10.1007/s10443-018-9694-0

[17] Antonucci, V.; Giordano, M.; Inserraimparato, S.; Nicolais, L. Analysis of heat transfer in autoclave technology. *Polym. Compos.* **2001**, *22*, 613–620. https://doi.org/10.1002/pc.10564

[18] N. Slesinger, T. Shimizu, A. Arafath, A.P. HEAT TRANSFER COEFFICIENT DISTRIBUTION INSIDE AN AUTOCLAVE.

[19] Zhou, Y.; Li, M.; Cheng, Q.; Wang, S.; Gu, Y.; Chen, X. Quantitative relations between curing processes and local properties within thick composites based on simulation and machine learning. *Mater. Des.* **2023**, *226*, 111686. https://doi.org/10.1016/j.matdes.2023.111686
# Influence of the use of mechanically recycled pet in injection stretch blow moulding process (ISBM)

VIORA Laurianne¹,ª, BOUVARD Jean-Luc¹,ᵇ and COMBEAUD Christelle¹,ᶜ*

¹MINES Paris, Université PSL, Centre de Mise en Forme des Matériaux (CEMEF), CNRS UMR 7635, Sophia, Antipolis, France

ªlaurianne.viora@minesparis.psl.eu, ᵇjean-luc.bouvard@minesparis.psl.eu,

ᶜchristelle.combeaud@minesparis.psl.eu

**Keywords:** Mechanically Recycled PET, Stretchability, Blow Moulding Process

**Abstract.** Different mechanically recycled PET issuing from different countries of origin have been studied and compared to a neat one, as a reference. Stretchability above glass transition temperature was explored towards uni-axial tensile experiments or injection stretch blow moulding (ISBM) tests. It has been shown in that study that rPETs and virgin PET present global mechanical behaviours. This similar trend is obvious either in low or large deformations domains. Master curves built for the 5 grades indicated equivalent behaviour between the grades from the glassy to the rubbery state. A controlled stretching campaign confirmed that all grades present visco-hyperelastic behaviours that are similar until the deformation for which the materials start to strain-harden. Uni-axial tensile tests were proved to be efficient to discriminate all grades especially regarding the Natural Draw Ratio (NDR) onset of all grades. The virgin PET does present a lower NDR that comforts the fact that strain-induced crystallization can be easier in the virgin case. This test campaign analysis is confirmed by the injected preforms blowing process where the virgin case grade develops lower blowing volumes because of a sooner NDR. It highlights the fact that forming behaviours of rPET must be slightly adapted compared to virgin PET. For rPET, the effects of loss of molar mass combined with the presence of contaminants could be at the origin of these discrepancies.

**Introduction**

In Europe, the use of PET has generated more than 4 million tons of waste in 2019 [1]. The “Single-Use Plastics” (SUP) European directive sets a target of collecting 90% of plastic bottles by 2029. The second objective will be to incorporate, from 2025, 25 % of recycled PET in bottles, and 30 % of recycled plastic in all plastic bottles [2]. PET accounted for 8% of plastic consumption in 2007 (15 MT) and only 4.5 MT were recovered, of which 3.6 MT were converted into flakes for recycling. PET used for bottles is the best recycled, however, it is estimated that half of these are not collected and only 7% are collected to make new bottles [3]. There are two main ways to recycle PET, mechanical and chemical. Mechanical recycling is not the most efficient way to recycle PET but is currently the most environmentally friendly [4]. To isolate PET from other polymers upstream of the recycling routes, it is first shredded. Then, PET is separated from other polymers such as polypropylene (PP), polyethylene (PE) and polyvinyl chloride (PVC).

Mechanical recycling of PET consists of regrinding, i.e., crushing, cleaning, melting, homogenizing, a second cleaning of contaminants, and extrusion filtration, all in one circuit. It is inexpensive but the quality is reduced [5]. It is traditionally done in a twin-screw extruder based on shear flow and requiring a long residence time. This results in severe degradation of the polymer [6]. Many impurities have to be removed from labels, adhesives or dust, metals etc. The first cleaning is not sufficient and therefore filtration of the melt is a key step. The removal of impurities must be controlled, especially those from PVC (contained in labels and adhesives) [7]. Finally, a last step called “post-condensation polymerization” at the solid state has to be included most of

<figure><img src="image_2578.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
# Influence of the use of mechanically recycled pet in injection stretch blow moulding process (ISBM)

VIORA Laurianne¹,ª, BOUVARD Jean-Luc¹,ᵇ and COMBEAUD Christelle¹,ᶜ*

¹MINES Paris, Université PSL, Centre de Mise en Forme des Matériaux (CEMEF), CNRS UMR 7635, Sophia, Antipolis, France

ªlaurianne.viora@minesparis.psl.eu, ᵇjean-luc.bouvard@minesparis.psl.eu,

ᶜchristelle.combeaud@minesparis.psl.eu

**Keywords:** Mechanically Recycled PET, Stretchability, Blow Moulding Process

**Abstract.** Different mechanically recycled PET issuing from different countries of origin have been studied and compared to a neat one, as a reference. Stretchability above glass transition temperature was explored towards uni-axial tensile experiments or injection stretch blow moulding (ISBM) tests. It has been shown in that study that rPETs and virgin PET present global mechanical behaviours. This similar trend is obvious either in low or large deformations domains. Master curves built for the 5 grades indicated equivalent behaviour between the grades from the glassy to the rubbery state. A controlled stretching campaign confirmed that all grades present visco-hyperelastic behaviours that are similar until the deformation for which the materials start to strain-harden. Uni-axial tensile tests were proved to be efficient to discriminate all grades especially regarding the Natural Draw Ratio (NDR) onset of all grades. The virgin PET does present a lower NDR that comforts the fact that strain-induced crystallization can be easier in the virgin case. This test campaign analysis is confirmed by the injected preforms blowing process where the virgin case grade develops lower blowing volumes because of a sooner NDR. It highlights the fact that forming behaviours of rPET must be slightly adapted compared to virgin PET. For rPET, the effects of loss of molar mass combined with the presence of contaminants could be at the origin of these discrepancies.

**Introduction**

In Europe, the use of PET has generated more than 4 million tons of waste in 2019 [1]. The “Single-Use Plastics” (SUP) European directive sets a target of collecting 90% of plastic bottles by 2029. The second objective will be to incorporate, from 2025, 25 % of recycled PET in bottles, and 30 % of recycled plastic in all plastic bottles [2]. PET accounted for 8% of plastic consumption in 2007 (15 MT) and only 4.5 MT were recovered, of which 3.6 MT were converted into flakes for recycling. PET used for bottles is the best recycled, however, it is estimated that half of these are not collected and only 7% are collected to make new bottles [3]. There are two main ways to recycle PET, mechanical and chemical. Mechanical recycling is not the most efficient way to recycle PET but is currently the most environmentally friendly [4]. To isolate PET from other polymers upstream of the recycling routes, it is first shredded. Then, PET is separated from other polymers such as polypropylene (PP), polyethylene (PE) and polyvinyl chloride (PVC).

Mechanical recycling of PET consists of regrinding, i.e., crushing, cleaning, melting, homogenizing, a second cleaning of contaminants, and extrusion filtration, all in one circuit. It is inexpensive but the quality is reduced [5]. It is traditionally done in a twin-screw extruder based on shear flow and requiring a long residence time. This results in severe degradation of the polymer [6]. Many impurities have to be removed from labels, adhesives or dust, metals etc. The first cleaning is not sufficient and therefore filtration of the melt is a key step. The removal of impurities must be controlled, especially those from PVC (contained in labels and adhesives) [7]. Finally, a last step called “post-condensation polymerization” at the solid state has to be included most of

<figure><img src="image_2571.png" /></figure>
the time so as to increase molar mass of the chains that have been degraded over the previous steps.
The pellets issuing from this re-processing can be used again to produce new bottles or fibers.

It is necessary that the recycled PET (rPET) retains sufficient mechanical properties but also
that it does not contain any hazardous substances. The latter can be derived from the degradation
of PET or be unintentionally added substances (NIAS). Apart from their possible danger to human
health, they can modify the properties of PET (mechanical, optical, thermal and/or crystalline).

Depending on the end use, from reuse to manufacture other bottles to downcycling (use for less demanding objects), the mechanical properties as well as the contamination of rPET must meet certain requirements. Some of them are listed below [8]: presence of metals (less than 3ppm), presence of polyolefins (less than 10 ppm), intrinsic viscosity (higher than 0.7 dl.g⁻¹), yellowing (less than 20)...

The presence of contaminants is regulated especially if the polymer has to be in contact with a
food product. The mechanical properties must be sufficient for the recycled object to fulfill the
same role as its counterpart made from virgin material. During the recycling cycle, PET comes
into contact with degradation agents such as oxygen, light, mechanical stress, temperature and
water. These can cause breaks in the chains and alter the formability and properties of the polymer
[9].

The challenge of PET recycling appears today urgent: industrial issues must be understood from
the synthesis of polymer to their re-processing, involving recycling steps. PET is a really good
candidate for chemical and mechanical recycling. Nevertheless, the presence of contaminants in
mechanically recycled PET, added to a possible loss of molar mass, tend to open new scientific
and technological questions. The present study purpose is clearly in phase with such a current
industrial context. Is stretch ability of these polymers, largely deformed above their glass transition
is impacted by recycling? How can a process like Injection Stretch Blow Moulding (ISBM) be
optimized regarding the use of recycled PET?

Materials

Two different mechanically recycled PET (rPET) have been chosen for this work. Pellets supplied by two manufacturers Ecolor® and Barik®, issuing either from Europe (named 100R1) or from outside Europe (named 100R2) were considered. The rPET used are transparent rPET. A comparison with a neat PET from Indorama®, acting as a reference, has also been proposed. Blends of both neat and recycled PET have been realized on half to half mass proportion. The blends are referred as “50R1” and “50R2”, involving either the rPET from Ecolor® (R1) or Barik® (R2). Pellets have been injected into square plates of 100x100 millimetres with a thickness of 3 millimetres. Preforms basically used for ISBM process were also injected. All the injection conditions were chosen to ensure the amorphous state of the PET. These conditions were identical for all the five grades (Virgin, 50R1, 100R1, 50R2 and 100R2), arguing on the fact that the rheological behaviour of all grades are very similar.

Results and discussion

In a first time, viscoelastic properties of the five grades were measured by DMTA. Master curves
of the storage modulus (E') were built at a reference temperature of 85 °C for the five materials.
They are presented in Figure 1.
the time so as to increase molar mass of the chains that have been degraded over the previous steps.
The pellets issuing from this re-processing can be used again to produce new bottles or fibers.

It is necessary that the recycled PET (rPET) retains sufficient mechanical properties but also
that it does not contain any hazardous substances. The latter can be derived from the degradation
of PET or be unintentionally added substances (NIAS). Apart from their possible danger to human
health, they can modify the properties of PET (mechanical, optical, thermal and/or crystalline).

Depending on the end use, from reuse to manufacture other bottles to downcycling (use for less demanding objects), the mechanical properties as well as the contamination of rPET must meet certain requirements. Some of them are listed below [8]: presence of metals (less than 3ppm), presence of polyolefins (less than 10 ppm), intrinsic viscosity (higher than 0.7 dl.g⁻¹), yellowing (less than 20)...

The presence of contaminants is regulated especially if the polymer has to be in contact with a
food product. The mechanical properties must be sufficient for the recycled object to fulfill the
same role as its counterpart made from virgin material. During the recycling cycle, PET comes
into contact with degradation agents such as oxygen, light, mechanical stress, temperature and
water. These can cause breaks in the chains and alter the formability and properties of the polymer
[9].

The challenge of PET recycling appears today urgent: industrial issues must be understood from
the synthesis of polymer to their re-processing, involving recycling steps. PET is a really good
candidate for chemical and mechanical recycling. Nevertheless, the presence of contaminants in
mechanically recycled PET, added to a possible loss of molar mass, tend to open new scientific
and technological questions. The present study purpose is clearly in phase with such a current
industrial context. Is stretch ability of these polymers, largely deformed above their glass transition
is impacted by recycling? How can a process like Injection Stretch Blow Moulding (ISBM) be
optimized regarding the use of recycled PET?

Materials

Two different mechanically recycled PET (rPET) have been chosen for this work. Pellets supplied by two manufacturers Ecolor® and Barik®, issuing either from Europe (named 100R1) or from outside Europe (named 100R2) were considered. The rPET used are transparent rPET. A comparison with a neat PET from Indorama®, acting as a reference, has also been proposed. Blends of both neat and recycled PET have been realized on half to half mass proportion. The blends are referred as “50R1” and “50R2”, involving either the rPET from Ecolor® (R1) or Barik® (R2). Pellets have been injected into square plates of 100x100 millimetres with a thickness of 3 millimetres. Preforms basically used for ISBM process were also injected. All the injection conditions were chosen to ensure the amorphous state of the PET. These conditions were identical for all the five grades (Virgin, 50R1, 100R1, 50R2 and 100R2), arguing on the fact that the rheological behaviour of all grades are very similar.

Results and discussion

In a first time, viscoelastic properties of the five grades were measured by DMTA. Master curves
of the storage modulus (E') were built at a reference temperature of 85 °C for the five materials.
They are presented in Figure 1.
<figure><img src="image_2579.png" /><figcaption>Fig. 1: Master curves of elastic modulus (E'), built at a reference temperature of 85 °C, for virgin, 50R1, 100R1, 50R2 and 100R2 PETs.</figcaption></figure>

The five curves are very similar to each other, taking 85°C as a reference temperature. This reference is a temperature close to the α-transition temperature of each material, taken at the maximum of Tan (δ) peak, at a frequency of 1 Hz. To compare all grades, the rubbery plateau height cannot be used. All grades present an obvious transition from a rubbery behavior to a glassy one at the same equivalent frequency or reduced frequency. It is clear, considering all grades having the same inflexion point, that all materials should be sensitive to double effects of the temperature/strain rate couple with the same manner. For higher temperatures explored, it was observed that recycled PETs were able to crystallize easier in quiescent conditions than virgin PET. Lower molar mass combined with the presence of contaminants acting as nucleating agents may explain this phenomenon. The ability to develop strain-induced crystallization (SIC) in dynamic conditions was then investigated towards uni-axial tensile tests, as presented in the following paragraphs.

An equivalent frequency or equivalent strain rate ($\dot{\varepsilon}_{eq}$) was chosen at $10^{-3} \text{ s}^{-1}$ to explore the mechanical behaviour of the pure grades (Virgin, 100R1 and 100R2) in the large deformations domain. At the end of the rubbery-like plateau, the red dashed line illustrates the position selected, for which the material should be in a rubbery-like state. For this purpose, tensile tests were carried out for a controlled couple of temperature and strain rate associated to an equivalent strain rate of $10^{-3} \text{ s}^{-1}$. Figure 2 presents the true stress strain curves obtained for the three neat materials.
<figure><img src="image_2572.png" /><figcaption>Fig. 1: Master curves of elastic modulus (E'), built at a reference temperature of 85 °C, for virgin, 50R1, 100R1, 50R2 and 100R2 PETs.</figcaption></figure>

The five curves are very similar to each other, taking 85°C as a reference temperature. This reference is a temperature close to the α-transition temperature of each material, taken at the maximum of Tan (δ) peak, at a frequency of 1 Hz. To compare all grades, the rubbery plateau height cannot be used. All grades present an obvious transition from a rubbery behavior to a glassy one at the same equivalent frequency or reduced frequency. It is clear, considering all grades having the same inflexion point, that all materials should be sensitive to double effects of the temperature/strain rate couple with the same manner. For higher temperatures explored, it was observed that recycled PETs were able to crystallize easier in quiescent conditions than virgin PET. Lower molar mass combined with the presence of contaminants acting as nucleating agents may explain this phenomenon. The ability to develop strain-induced crystallization (SIC) in dynamic conditions was then investigated towards uni-axial tensile tests, as presented in the following paragraphs.

An equivalent frequency or equivalent strain rate ($\dot{\varepsilon}_{eq}$) was chosen at $10^{-3} \text{ s}^{-1}$ to explore the mechanical behaviour of the pure grades (Virgin, 100R1 and 100R2) in the large deformations domain. At the end of the rubbery-like plateau, the red dashed line illustrates the position selected, for which the material should be in a rubbery-like state. For this purpose, tensile tests were carried out for a controlled couple of temperature and strain rate associated to an equivalent strain rate of $10^{-3} \text{ s}^{-1}$. Figure 2 presents the true stress strain curves obtained for the three neat materials.
<figure><img src="image_2580.png" /><figcaption>Fig. 2: True stress as a function of the true strain for an equivalent strain rate ($\dot{\epsilon}_{eq}$) of $10^{-3}$ s$^{-1}$ for the three grades (Virgin, 100R1 and 100R2).</figcaption></figure>

For the three grades presented, true stress strain curves illustrate the visco-hyperelastic response of PET, taken in its rubbery-like state. As expected, the induced crystallization begins at the slope change, and it corresponds to the natural draw ratio (NDR). Before the NDR, all responses are very well-superimposed testifying on the same ability of the three materials in being largely deformed. The stretching conditions that have been selected correspond to the same couple of temperature and strain rate, from a material to another. Equivalent mechanical behaviours that were obvious in the low deformations domain are clearly confirmed in the large deformations domain. As observed from DMTA analysis, the sensitivity to both temperature and strain rate remains equivalent from a grade to another. Moreover, as the $\alpha$-transition temperature identified in the low deformations domain is the same from a grade to another, it appears that the physical state of the material is the same and clearly rules mechanical response either in low or large deformations domain. The gap from the $\alpha$-transition is then crucial.

Nevertheless, differences appear for the three grades at the NDR onset. The NDR values are respectively of 1.38, 1.43 and 1.46 for the virgin, 100R2 and 100R1 PETs. Virgin PET is the first to strain-harden followed by 100R2. The last to strain-harden is the 100R1 grade. The dynamic crystallization kinetics that are ruling the strain-hardening are faster and more efficient in the case of the virgin material. Moreover, for deformations higher than the NDR, PETs do not behave in a similar manner. Strain-hardening which is involved by microstructural development such as strain induced crystallization (SIC) presents slight discrepancies as the slope decreases between the virgin, the 100R2 and 100R1. As SIC tends to be disturbed by thermal relaxation, it is possible to observe slight decreases of the strain-hardening slope as it is the case for the 100R1 grade. This behavior is observed when the relaxation phenomenon speed is comparable to the induced crystallization. SIC kinetics involved in 100R1 are obviously lower. Two main reasons may explain this phenomenon. The presence of contaminants or hetero elements can affect PET local chains organization necessary for SIC development. Another reason can be relative to the slight loss of molar mass and possible entanglements density necessary for molecular orientation and stretching.

To complete tensile tests performed at the laboratory scale, blowing tests were performed thanks to a prototype developed at Cemef allowing free blowing of injected preforms, in controlled conditions of temperature. Temperature measurements were carried out on the preform surface,
<figure><img src="image_2573.png" /><figcaption>Fig. 2: True stress as a function of the true strain for an equivalent strain rate ($\dot{\epsilon}_{eq}$) of $10^{-3}$ s$^{-1}$ for the three grades (Virgin, 100R1 and 100R2).</figcaption></figure>

For the three grades presented, true stress strain curves illustrate the visco-hyperelastic response of PET, taken in its rubbery-like state. As expected, the induced crystallization begins at the slope change, and it corresponds to the natural draw ratio (NDR). Before the NDR, all responses are very well-superimposed testifying on the same ability of the three materials in being largely deformed. The stretching conditions that have been selected correspond to the same couple of temperature and strain rate, from a material to another. Equivalent mechanical behaviours that were obvious in the low deformations domain are clearly confirmed in the large deformations domain. As observed from DMTA analysis, the sensitivity to both temperature and strain rate remains equivalent from a grade to another. Moreover, as the $\alpha$-transition temperature identified in the low deformations domain is the same from a grade to another, it appears that the physical state of the material is the same and clearly rules mechanical response either in low or large deformations domain. The gap from the $\alpha$-transition is then crucial.

Nevertheless, differences appear for the three grades at the NDR onset. The NDR values are respectively of 1.38, 1.43 and 1.46 for the virgin, 100R2 and 100R1 PETs. Virgin PET is the first to strain-harden followed by 100R2. The last to strain-harden is the 100R1 grade. The dynamic crystallization kinetics that are ruling the strain-hardening are faster and more efficient in the case of the virgin material. Moreover, for deformations higher than the NDR, PETs do not behave in a similar manner. Strain-hardening which is involved by microstructural development such as strain induced crystallization (SIC) presents slight discrepancies as the slope decreases between the virgin, the 100R2 and 100R1. As SIC tends to be disturbed by thermal relaxation, it is possible to observe slight decreases of the strain-hardening slope as it is the case for the 100R1 grade. This behavior is observed when the relaxation phenomenon speed is comparable to the induced crystallization. SIC kinetics involved in 100R1 are obviously lower. Two main reasons may explain this phenomenon. The presence of contaminants or hetero elements can affect PET local chains organization necessary for SIC development. Another reason can be relative to the slight loss of molar mass and possible entanglements density necessary for molecular orientation and stretching.

To complete tensile tests performed at the laboratory scale, blowing tests were performed thanks to a prototype developed at Cemef allowing free blowing of injected preforms, in controlled conditions of temperature. Temperature measurements were carried out on the preform surface,