<figure><img src="image_2406.png" /></figure>

<table><caption>Fig 5. Correlation between maximum depth changes and temperature changes of studied paperboards in Line 1.</caption><thead><tr><th>Trial</th><th>Average of Sample depth (mm)</th><th>Average of Temperature change (°C)</th></tr></thead><tbody><tr><td>Paperboard 1- 90°C,3 sec, 1 bar</td><td>10,92 ± 0,55</td><td>42,57 ± 3,29</td></tr><tr><td>Paperboard 1- 110°C,3 sec, 1 bar</td><td>11,16 ± 0,28</td><td>54,83 ± 0,76</td></tr><tr><td>Paperboard 1- 110°C,3 sec, 2 bars</td><td>11,42 ± 0,25</td><td>56,13 ± 3,30</td></tr><tr><td>Paperboard 1- 110°C,5 sec, 1 bar</td><td>11,66 ± 0,06</td><td>59,97 ± 0,35</td></tr><tr><td>Paperboard 2- 110°C,3 sec, 1 bar</td><td>9,84 ± 0,5</td><td>4,47 ± 0,90</td></tr><tr><td>Paperboard 3- 110°C,3 sec, 1 bar</td><td>7,71 ± 0,2</td><td>7,70 ± 0,57</td></tr></tbody></table>

For further validation of the abovementioned correlation, the depth of the grooves was measured along the Line 2 (Fig. 2) from the shape profile, and the corresponding temperature difference was measured from the thermal profiles. A representative example of such measurement for Paperboard 1 under the reference forming conditions is shown in Fig. 6. Next, a statistical analysis of all the data points is presented in Fig. 7. The regression analysis yet revealed another strong correlation, further verifying the established relationship.

Nevertheless, from the regression coefficients displayed in Figures 5 and 7, it is evident that there is no exact linear relationship. This may be attributed to the spring-back and gradual recovery of a viscoelastic component over time, which materials like paper undergo [16]. The current shape measurements were taken on samples removed from the forming process and allowed some rest time. Due to the time gap between thermoforming and measurement, there may be a slight variation in the linear relationship between immediate temperature change after the process and depth change measured later. Notably, Line 2 shows higher regression coefficients than Line 1, possibly due to a higher rate of spring-back occurring as material contacts with mold. Analysis of temperature imaging indicates lack of contact with grooves in blue or dark green color areas; however, for Line 1 cases show material reaching bottom of mold at times. A previous study revealed contact with a cold mold being a contributing factor to spring-back in fiber-based structures [4]. Consequently, there might be a higher rate of spring-back over time in Line 1 where material contacted the mold compared to Line 2 where those not contacting the mold.

Overall, the significance of the correlations presented lies in their potential to optimize production process in real-time. Obtaining reference data that covers temperature changes, shape and depth values allows for the prediction of subsequent trials in real time. By doing so, the need for post-production analysis can be substantially reduced. It is nevertheless important to recognize that, despite the validation of this analysis focusing on depth and contact areas, other aspects of formability might still need to be examined post-production.
<figure><img src="image_2416.png" /><figcaption>Fig 6. Correlation between depth changes and temperature changes of studied paperboards in region 2.</figcaption></figure>

<figure><img src="image_2417.png" /></figure>

<table><caption>Fig 7. Correlation between depth changes and temperature changes of studied paperboards in Line 2.</caption><thead><tr><th>Trial</th><th>Average of groove depth (mm)</th><th>Average of Temperature change (°C)</th></tr></thead><tbody><tr><td>Paperboard 1- 90°C,3 sec, 1 bar</td><td>1,48 ± 0,12</td><td>39,77 ± 2,00</td></tr><tr><td>Paperboard 1- 110 °C,3 sec, 1 bar</td><td>1,87 ± 0,05</td><td>53,97 ± 1,72</td></tr><tr><td>Paperboard 1- 110°C,3 sec, 2 bars</td><td>2,20 ± 0,04</td><td>54,33 ± 2,83</td></tr><tr><td>Paperboard 1- 110°C,5 sec, 1 bar</td><td>1,80 ± 0,12</td><td>57,10 ± 1,06</td></tr><tr><td>Paperboard 2- 110°C,3 sec, 1 bar</td><td>1,01 ± 0,00</td><td>27,45 ± 0,64</td></tr><tr><td>Paperboard 3- 110°C,3 sec, 1 bar</td><td>0,63 ± 0,05</td><td>19,30 ± 0,85</td></tr></tbody></table>

## Conclusions

The purpose of this study was to investigate the potential of thermal imaging in thermoformability analysis of plastic-coated paperboards as a mean to optimize real-time production processes. For this purpose, three paperboards underwent vacuum and air pressure thermoforming, and their temperature distributions were recorded under different forming conditions. Microscopic shape profile measurements were conducted on studied paperboards to establish a relationship between
<figure><img src="image_2407.png" /><figcaption>Fig 6. Correlation between depth changes and temperature changes of studied paperboards in region 2.</figcaption></figure>

<figure><img src="image_2408.png" /></figure>

<table><caption>Fig 7. Correlation between depth changes and temperature changes of studied paperboards in Line 2.</caption><thead><tr><th>Trial</th><th>Average of groove depth (mm)</th><th>Average of Temperature change (°C)</th></tr></thead><tbody><tr><td>Paperboard 1- 90°C,3 sec, 1 bar</td><td>1,48 ± 0,12</td><td>39,77 ± 2,00</td></tr><tr><td>Paperboard 1- 110 °C,3 sec, 1 bar</td><td>1,87 ± 0,05</td><td>53,97 ± 1,72</td></tr><tr><td>Paperboard 1- 110°C,3 sec, 2 bars</td><td>2,20 ± 0,04</td><td>54,33 ± 2,83</td></tr><tr><td>Paperboard 1- 110°C,5 sec, 1 bar</td><td>1,80 ± 0,12</td><td>57,10 ± 1,06</td></tr><tr><td>Paperboard 2- 110°C,3 sec, 1 bar</td><td>1,01 ± 0,00</td><td>27,45 ± 0,64</td></tr><tr><td>Paperboard 3- 110°C,3 sec, 1 bar</td><td>0,63 ± 0,05</td><td>19,30 ± 0,85</td></tr></tbody></table>

## Conclusions

The purpose of this study was to investigate the potential of thermal imaging in thermoformability analysis of plastic-coated paperboards as a mean to optimize real-time production processes. For this purpose, three paperboards underwent vacuum and air pressure thermoforming, and their temperature distributions were recorded under different forming conditions. Microscopic shape profile measurements were conducted on studied paperboards to establish a relationship between
temperature distributions, thermal profiles, and shape conformability. The study indicates the
following main findings:

* By analyzing thermal images directly, accurate measurements could be made of the contact areas between the mold and the material. This involved mapping the cold regions in the images that have acquired the mold temperature. This result suggest that measurements of contact areas can be conducted quantitatively using any image measurement software, eliminating the need for more complex analyses of produced samples, such as microscopic inspections.

* Regardless of the type of material or forming condition, the temperature distribution and corresponding thermal profiles of the formed samples were closely related to the shape profiles, particularly with the depth achieved. The findings revealed that temperature changes reflected the rate of material stretching, which might be due to exothermic response of the studied materials in the induced stretching process.

* The data obtained in this study can be integrated in real-time to assess thermoformability of plastic-coated paperboards and improve shape conformability by strategically selecting process parameters that yield an optimal temperature profile.

## Acknowledgement

The authors thank Mr. Roman Lev for their invaluable feedback on this work.

## References

[1] Matthews, S., Tanninen, P., Afshariantorghabeh, S., Toghyan, A., Leminen, V. and Varis, J., 2024, January. Geometrical evaluation of thermoformed bioplastic tray packages. In *AIP Conference Proceedings* (Vol. 2989, No. 1). AIP Publishing. https://doi.org/10.1063/5.0191920

[2] S. Afshariantorghabeh, T. Kärki, and V. Leminen, “Three-dimensional forming of plastic-coated fibre-based materials using a thermoforming process,” *Packaging Technology and Science*, vol. 35, no. 7, pp. 543–555, 2022. https://doi.org/10.1002/pts.2650

[3] Vishtal A. Formability of Paper and Its Improvement. Doctoral thesis. VTT; 2015.

[4] Afshariantorghabeh, S., Pesonen, A., Kärki, T. and Leminen, V., 2023. Effects of thermoforming operation and tooling on the thermoformability of plastic-coated fibre-based materials. *Packaging Technology and Science*, 36(10), pp.855-871. https://doi.org/10.1002/pts.2762

[5] Chrysochoos, A., Huon, V., Jourdan, F., Muracciole, J.M., Peyroux, R. and Wattrisse, B., 2010. Use of full-field digital image correlation and infrared thermography measurements for the thermomechanical analysis of material behaviour. *Strain*, 46(1), pp.117-130. https://doi.org/10.1111/j.1475-1305.2009.00635.x

[6] Bagavathiappan, S., Lahiri, B.B., Saravanan, T., Philip, J. and Jayakumar, T., 2013. Infrared thermography for condition monitoring–A review. *Infrared Physics & Technology*, 60, pp.35-55. https://doi.org/10.1016/j.infrared.2013.03.006

[7] Le Maoult, Y. and Schmidt, F., 2016. Infrared radiation applied to polymer processes. *Heat Transfer in Polymer Composite Materials: Forming Processes*, pp.385-423. https://doi.org/10.1002/9781119116288.ch13

[8] Patil, J.P., Nandedkar, V., Mishra, S. and Saha, S.K., 2021. Transient thermal analysis of close pressure thermoforming process. *Journal of Manufacturing Processes*, 62, pp.513-522. https://doi.org/10.1016/j.jmapro.2020.12.057
temperature distributions, thermal profiles, and shape conformability. The study indicates the
following main findings:

* By analyzing thermal images directly, accurate measurements could be made of the contact areas between the mold and the material. This involved mapping the cold regions in the images that have acquired the mold temperature. This result suggest that measurements of contact areas can be conducted quantitatively using any image measurement software, eliminating the need for more complex analyses of produced samples, such as microscopic inspections.

* Regardless of the type of material or forming condition, the temperature distribution and corresponding thermal profiles of the formed samples were closely related to the shape profiles, particularly with the depth achieved. The findings revealed that temperature changes reflected the rate of material stretching, which might be due to exothermic response of the studied materials in the induced stretching process.

* The data obtained in this study can be integrated in real-time to assess thermoformability of plastic-coated paperboards and improve shape conformability by strategically selecting process parameters that yield an optimal temperature profile.

## Acknowledgement

The authors thank Mr. Roman Lev for their invaluable feedback on this work.

## References

[1] Matthews, S., Tanninen, P., Afshariantorghabeh, S., Toghyan, A., Leminen, V. and Varis, J., 2024, January. Geometrical evaluation of thermoformed bioplastic tray packages. In *AIP Conference Proceedings* (Vol. 2989, No. 1). AIP Publishing. https://doi.org/10.1063/5.0191920

[2] S. Afshariantorghabeh, T. Kärki, and V. Leminen, “Three-dimensional forming of plastic-coated fibre-based materials using a thermoforming process,” *Packaging Technology and Science*, vol. 35, no. 7, pp. 543–555, 2022. https://doi.org/10.1002/pts.2650

[3] Vishtal A. Formability of Paper and Its Improvement. Doctoral thesis. VTT; 2015.

[4] Afshariantorghabeh, S., Pesonen, A., Kärki, T. and Leminen, V., 2023. Effects of thermoforming operation and tooling on the thermoformability of plastic-coated fibre-based materials. *Packaging Technology and Science*, 36(10), pp.855-871. https://doi.org/10.1002/pts.2762

[5] Chrysochoos, A., Huon, V., Jourdan, F., Muracciole, J.M., Peyroux, R. and Wattrisse, B., 2010. Use of full-field digital image correlation and infrared thermography measurements for the thermomechanical analysis of material behaviour. *Strain*, 46(1), pp.117-130. https://doi.org/10.1111/j.1475-1305.2009.00635.x

[6] Bagavathiappan, S., Lahiri, B.B., Saravanan, T., Philip, J. and Jayakumar, T., 2013. Infrared thermography for condition monitoring–A review. *Infrared Physics & Technology*, 60, pp.35-55. https://doi.org/10.1016/j.infrared.2013.03.006

[7] Le Maoult, Y. and Schmidt, F., 2016. Infrared radiation applied to polymer processes. *Heat Transfer in Polymer Composite Materials: Forming Processes*, pp.385-423. https://doi.org/10.1002/9781119116288.ch13

[8] Patil, J.P., Nandedkar, V., Mishra, S. and Saha, S.K., 2021. Transient thermal analysis of close pressure thermoforming process. *Journal of Manufacturing Processes*, 62, pp.513-522. https://doi.org/10.1016/j.jmapro.2020.12.057
[9] Marchal, N., Ducloud, G., Agazzi, A. and Le Goff, R., 2023. Data-based model applied to thermoforming process control. *The International Journal of Advanced Manufacturing Technology*, pp.1-12. https://doi.org/10.1007/s00170-023-12404-y

[10] Afshariantorghabeh, S., Kärki, T. and Leminen, V., 2023. Thermoformability study of wood flour-HDPE composites with variations in wood content under vacuum forming. *Heliyon*, 9(11). https://doi.org/10.1016/j.heliyon.2023.e22174

[11] C. Yi Wen, D. Xinying, T. Le Quan Ngoc, T. Long Bin, and T. Wern Sze, “IR-thermoforming window design via a thermal approach: For CFRTP and Hybrid Thermoplastic Composites,” *Asian Society for Precision Engineering and Nanotechnology (ASPEN 2022)*, 2022. doi:10.3850/978-981-18-6021-8_or-13-0026.html

[12] Hyll, C., 2012. *Infrared Emittance of Paper: Method Development, Measurements and Application* (Doctoral dissertation, KTH Royal Institute of Technology).

[13] Klein, P., 2022. *Fundamentals of plastics thermoforming*. Springer Nature. https://doi.org/10.1007/978-3-031-02392-7

[14] Arango-Restrepo, A., Rubi, J.M. and Pradhan, S., 2021. A Thermodynamic Framework for Stretching Processes in Fiber Materials. *Frontiers in Physics*, 9, p.642754. https://doi.org/10.3389/fphy.2021.642754

[15] Zimin, B.A., Sventitskaya, V.E.E., Smirnov, I.V.E. and Sud'enkov, Y.V., 2018. Influence of strain rate on heat release under quasi-static stretching of metals. Experiment. *Physics of the Solid State*, 60, pp.758-763. https://doi.org/10.1134/S1063783418040352

[16] Paetow R, Rauhut M, Göttsching L. Strain behaviour of paper. Das Papier. 1991;45(6):287-296.
[9] Marchal, N., Ducloud, G., Agazzi, A. and Le Goff, R., 2023. Data-based model applied to thermoforming process control. *The International Journal of Advanced Manufacturing Technology*, pp.1-12. https://doi.org/10.1007/s00170-023-12404-y

[10] Afshariantorghabeh, S., Kärki, T. and Leminen, V., 2023. Thermoformability study of wood flour-HDPE composites with variations in wood content under vacuum forming. *Heliyon*, 9(11). https://doi.org/10.1016/j.heliyon.2023.e22174

[11] C. Yi Wen, D. Xinying, T. Le Quan Ngoc, T. Long Bin, and T. Wern Sze, “IR-thermoforming window design via a thermal approach: For CFRTP and Hybrid Thermoplastic Composites,” *Asian Society for Precision Engineering and Nanotechnology (ASPEN 2022)*, 2022. doi:10.3850/978-981-18-6021-8_or-13-0026.html

[12] Hyll, C., 2012. *Infrared Emittance of Paper: Method Development, Measurements and Application* (Doctoral dissertation, KTH Royal Institute of Technology).

[13] Klein, P., 2022. *Fundamentals of plastics thermoforming*. Springer Nature. https://doi.org/10.1007/978-3-031-02392-7

[14] Arango-Restrepo, A., Rubi, J.M. and Pradhan, S., 2021. A Thermodynamic Framework for Stretching Processes in Fiber Materials. *Frontiers in Physics*, 9, p.642754. https://doi.org/10.3389/fphy.2021.642754

[15] Zimin, B.A., Sventitskaya, V.E.E., Smirnov, I.V.E. and Sud'enkov, Y.V., 2018. Influence of strain rate on heat release under quasi-static stretching of metals. Experiment. *Physics of the Solid State*, 60, pp.758-763. https://doi.org/10.1134/S1063783418040352

[16] Paetow R, Rauhut M, Göttsching L. Strain behaviour of paper. Das Papier. 1991;45(6):287-296.
# Analysis of thermal behavior in 3D printing of continuous fiber reinforced polymer composites

LI Shixian¹,*, CORREIA J.P.M.¹,ᵇ, WANG Kui²,ᶜ and AHZI Said¹,ᵈ

¹ICUBE Laboratory – CNRS, University of Strasbourg, Strasbourg 67000, France

²Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic & Transportation Engineering, Central South University, Changsha, 410075, China

ᵃshixian.li@etu.unistra.fr, ᵇjpm.correia@unistra.fr, ᶜkui.wang@csu.edu.cn, ᵈahzi@unistra.fr

**Keywords:** 3D Printing, Continuous Fiber, Thermal Behavior, Interfacial Bonding

**Abstract.** Fused filament fabrication (FFF) as an additive manufacturing process, is a thermal driven method used to produce continuous fiber reinforced composites for engineering applications. Interlayer delamination is a significant concern for composites manufactured by FFF process. To address the problem of interlayer delamination and enhance the macro-mechanical properties of FFF fiber composites, it is necessary to study the thermal behavior of continuous fiber filled composites during the deposition process. A thermal simulation model with the consideration of continuous fiber was proposed. The numerical simulations reproduce the trends of experimental temperature evolution. When the continuous fiber phase is omitted from the heat transfer model, the predicted reheating temperature at the interface is lower compared to the temperature measured via IR monitoring. This result highlights the critical necessity of developing a numerical model that takes the continuous fiber phase into account in order to accurately predict the reheating temperature at the interface. Such a model is essential for deeper exploration into the adhesion mechanisms between adjacent layers and adjacent filaments.

**Introduction**

Continuous fiber reinforced polymer composites (CFRPCs) have garnered significant interest from both the academic research community and industrial sectors. This is primarily due to their ability to offer a combination of low weight, high strength, and stiffness that outperforms traditional metals and alloys [1, 2]. The production of composites filled with continuous fibers to depend on molding techniques, resulting in high expenses, limited adaptability, and impracticality for producing small batches. These limitations and disadvantages have hindered the capacity of CFRPCs to be utilized in novel structural applications.

The emergence of additive manufacturing (AM), often known as 3D printing, presents a promising resolution for engineering fiber composites. This technology enables the production of components with intricate geometries, attaining remarkable performance levels, and realizing cost savings [3, 4]. As a result, complex components can be quickly manufactured with reduced expenses and without the requirement for specialized equipment [5]. 3D printing is mainly conducted by stereolithography (SLA), fused filament fabrication (FFF), laminated object manufacturing (LOM), selective laser sintering (SLS), selective laser melting (SLM), etc. One of the most commonly employed AM processes is FFF, which manufactures composites layer-by-layer deposition of extruded molten material [6-8]. Specifically, due to the FFF continuous processing characteristics, adjacent strands come into touch with one another and create a bonding interface that is typically weak and prone to failure [9, 10]. Therefore, an essential issue in printing materials with good mechanical properties is the bonding quality between the solidified strands [11-14].

<figure><img src="image_2418.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.
# Analysis of thermal behavior in 3D printing of continuous fiber reinforced polymer composites

LI Shixian¹,*, CORREIA J.P.M.¹,ᵇ, WANG Kui²,ᶜ and AHZI Said¹,ᵈ

¹ICUBE Laboratory – CNRS, University of Strasbourg, Strasbourg 67000, France

²Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic & Transportation Engineering, Central South University, Changsha, 410075, China

ªshixian.li@etu.unistra.fr, ᵇjpm.correia@unistra.fr, ᶜkui.wang@csu.edu.cn, ᵈahzi@unistra.fr

**Keywords:** 3D Printing, Continuous Fiber, Thermal Behavior, Interfacial Bonding

**Abstract.** Fused filament fabrication (FFF) as an additive manufacturing process, is a thermal driven method used to produce continuous fiber reinforced composites for engineering applications. Interlayer delamination is a significant concern for composites manufactured by FFF process. To address the problem of interlayer delamination and enhance the macro-mechanical properties of FFF fiber composites, it is necessary to study the thermal behavior of continuous fiber filled composites during the deposition process. A thermal simulation model with the consideration of continuous fiber was proposed. The numerical simulations reproduce the trends of experimental temperature evolution. When the continuous fiber phase is omitted from the heat transfer model, the predicted reheating temperature at the interface is lower compared to the temperature measured via IR monitoring. This result highlights the critical necessity of developing a numerical model that takes the continuous fiber phase into account in order to accurately predict the reheating temperature at the interface. Such a model is essential for deeper exploration into the adhesion mechanisms between adjacent layers and adjacent filaments.

**Introduction**

Continuous fiber reinforced polymer composites (CFRPCs) have garnered significant interest from both the academic research community and industrial sectors. This is primarily due to their ability to offer a combination of low weight, high strength, and stiffness that outperforms traditional metals and alloys [1, 2]. The production of composites filled with continuous fibers to depend on molding techniques, resulting in high expenses, limited adaptability, and impracticality for producing small batches. These limitations and disadvantages have hindered the capacity of CFRPCS to be utilized in novel structural applications.

The emergence of additive manufacturing (AM), often known as 3D printing, presents a promising resolution for engineering fiber composites. This technology enables the production of components with intricate geometries, attaining remarkable performance levels, and realizing cost savings [3, 4]. As a result, complex components can be quickly manufactured with reduced expenses and without the requirement for specialized equipment [5]. 3D printing is mainly conducted by stereolithography (SLA), fused filament fabrication (FFF), laminated object manufacturing (LOM), selective laser sintering (SLS), selective laser melting (SLM), etc. One of the most commonly employed AM processes is FFF, which manufactures composites layer-by-layer deposition of extruded molten material [6-8]. Specifically, due to the FFF continuous processing characteristics, adjacent strands come into touch with one another and create a bonding interface that is typically weak and prone to failure [9, 10]. Therefore, an essential issue in printing materials with good mechanical properties is the bonding quality between the solidified strands [11-14].

<figure><img src="image_2409.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.
Bellehumeur et al. [15] proposed that the merging of continuous filament segments occurred through a series of stages including contact, wetting, and neck growth. These phases were induced through the sintering or thermal diffusion of adjacent layers, necessitating temperatures surpassing the material's glass-transition temperature (Tg). Moreover, as presented in [16, 17], the arrangement and evolution of temperature distribution during the FFF process for polymer composites proved to be a pivotal element influencing diverse attributes including geometric precision, surface finish, mechanical strength, and macro and micro-porosity. These characteristics were impacted by the chosen process parameters, encompassing factors like the material being printed, nozzle temperature, printing speed, infill design, deposition order, and layer thickness. Consequently, the thermal history of the printed composite holds importance in determining the ultimate mechanical performance of the end product.

To obtain optimal process conditions, numerous experiments are needed to investigate and optimize the process parameters within given machines and processes by using contact sensors or non-contact sensors [18-20]. Montecon et al. [21] investigated the effect of the interlayer cooling and consequent bonding behavior in printed PLA-based composites by using the thermal imaging method and tensile tests. In [21], it was found that the additional waiting times did not present significant differences in the interfacial bonding properties of printed composites. Fen et al. [22] studied the influence of nozzle temperature and bed temperature on the thermal and mechanical attributes of 3D-printed continuous carbon fiber-reinforced composites. They employed K-type thermocouples (contact sensors) for real-time in-situ thermal assessments. In [22], the nozzle temperature was elevated from 180 to 220 °C, the diameter of the bonding neck expanded from 0.29 to 0.34 mm, leading to a decline in cross-sectional porosity from 5.48 % to 3.22 %.

However, it is rather time-consuming and expensive to produce components with sound geometric configuration and good mechanical properties using FDM by a trial-and-error approach. Hamid Reza et al. [23] employed a 1D heat transfer model to predict temperature variations in a single PLA filament and a vertical PLA wall. In a subsequent study [24], they introduced the finite volume method to describe the overall heat transfer phenomena occurring during the manufacturing sequence. This approach considered three potential mechanisms: conduction between filaments, conduction between filament and support, and free convection with the environment. The predicted results demonstrated a satisfactory agreement when compared to the recorded temperature variations at the interface of adjacent filaments in a printed PLA vertical wall. In [25, 26], researchers also built a 2D or 3D heat transfer modeling to predict temperature evolution of PEKK and ABS, respectively. The recent studies most focus on the thermal prediction of pure polymer matrix materials in FFF process, with insufficient attention given to continuous fiber composites. However, the introduction of continuous fibers in printing brings about alterations in physical parameters during heat transfer and shrinkage, consequently influencing the resin diffusion process on the base and the size of the bonding neck between the printing raster.

In this study, a polypropylene based composite with continuous ramie fiber reinforcement was manufactured by the FFF method. The thermal behavior was investigated by using an in-situ thermal behavior monitoring platform, consisting of an infrared camera, laptop and printed composites. A novel thermal simulation model with the consideration of continuous fiber was proposed. Effect of layer thickness on effective reheating temperature and weld time in continuous ramie fiber-reinforced PP-based composites were investigated.

# Experimental Methodology

## Materials

In this study, Polypropylene (PP) filaments (grade 9025, Sabic, Saudi Arabia) were selected as the thermoplastic matrix material for continuous ramie fiber-reinforced PP-based composites (CRFRPCs). The reinforcement chosen for CRFRPCs in this study are continuous ramie fiber filaments sourced from Hunan Huasheng Dongting Ramie Textile Co., Ltd, Hunan, China. The
Bellehumeur et al. [15] proposed that the merging of continuous filament segments occurred through a series of stages including contact, wetting, and neck growth. These phases were induced through the sintering or thermal diffusion of adjacent layers, necessitating temperatures surpassing the material's glass-transition temperature (Tg). Moreover, as presented in [16, 17], the arrangement and evolution of temperature distribution during the FFF process for polymer composites proved to be a pivotal element influencing diverse attributes including geometric precision, surface finish, mechanical strength, and macro and micro-porosity. These characteristics were impacted by the chosen process parameters, encompassing factors like the material being printed, nozzle temperature, printing speed, infill design, deposition order, and layer thickness. Consequently, the thermal history of the printed composite holds importance in determining the ultimate mechanical performance of the end product.

To obtain optimal process conditions, numerous experiments are needed to investigate and optimize the process parameters within given machines and processes by using contact sensors or non-contact sensors [18-20]. Montecon et al. [21] investigated the effect of the interlayer cooling and consequent bonding behavior in printed PLA-based composites by using the thermal imaging method and tensile tests. In [21], it was found that the additional waiting times did not present significant differences in the interfacial bonding properties of printed composites. Fen et al. [22] studied the influence of nozzle temperature and bed temperature on the thermal and mechanical attributes of 3D-printed continuous carbon fiber-reinforced composites. They employed K-type thermocouples (contact sensors) for real-time in-situ thermal assessments. In [22], the nozzle temperature was elevated from 180 to 220 °C, the diameter of the bonding neck expanded from 0.29 to 0.34 mm, leading to a decline in cross-sectional porosity from 5.48 % to 3.22 %.

However, it is rather time-consuming and expensive to produce components with sound geometric configuration and good mechanical properties using FDM by a trial-and-error approach. Hamid Reza et al. [23] employed a 1D heat transfer model to predict temperature variations in a single PLA filament and a vertical PLA wall. In a subsequent study [24], they introduced the finite volume method to describe the overall heat transfer phenomena occurring during the manufacturing sequence. This approach considered three potential mechanisms: conduction between filaments, conduction between filament and support, and free convection with the environment. The predicted results demonstrated a satisfactory agreement when compared to the recorded temperature variations at the interface of adjacent filaments in a printed PLA vertical wall. In [25, 26], researchers also built a 2D or 3D heat transfer modeling to predict temperature evolution of PEKK and ABS, respectively. The recent studies most focus on the thermal prediction of pure polymer matrix materials in FFF process, with insufficient attention given to continuous fiber composites. However, the introduction of continuous fibers in printing brings about alterations in physical parameters during heat transfer and shrinkage, consequently influencing the resin diffusion process on the base and the size of the bonding neck between the printing raster.

In this study, a polypropylene based composite with continuous ramie fiber reinforcement was manufactured by the FFF method. The thermal behavior was investigated by using an in-situ thermal behavior monitoring platform, consisting of an infrared camera, laptop and printed composites. A novel thermal simulation model with the consideration of continuous fiber was proposed. Effect of layer thickness on effective reheating temperature and weld time in continuous ramie fiber-reinforced PP-based composites were investigated.

# Experimental Methodology

## Materials

In this study, Polypropylene (PP) filaments (grade 9025, Sabic, Saudi Arabia) were selected as the thermoplastic matrix material for continuous ramie fiber-reinforced PP-based composites (CRFRPCs). The reinforcement chosen for CRFRPCs in this study are continuous ramie fiber filaments sourced from Hunan Huasheng Dongting Ramie Textile Co., Ltd, Hunan, China. The
composition of the ramie yarn, assessed through the Van Soest method, revealed the following components: 73.6% cellulose, 13.8% hemicellulose, 3.5% pectin, 1.9% lignin, and 7.2% other constituents [27]. Before the FFF process, the ramie yarns underwent a drying procedure in an oven at 80 °C for a duration of two hours.

## Manufacturing

3D-printed composites incorporating continuous ramie fibers were fabricated using an in-situ impregnation desk printer, specifically the Combot-200 from Fibertech in Shanxi, China. The printer utilized a single flat-head nozzle with a diameter of 1.3 mm. The experimental setup of the printing process is illustrated in Fig. 1 (a).

<figure><img src="image_2419.png" /><figcaption>Fig. 1 Schematic representation of the (a) in-situ impregnation process in FFF for continuous fiber filled composites, (b) of the setup for in-situ thermal behavior monitoring platform during FFF. (c) Optical image by camera and (d) thermal image captured by IR camera during FFF process.</figcaption></figure>

In this process, the thermoplastic PP matrix was raised to a temperature exceeding its melting point within the nozzle. Concurrently, the dry continuous ramie fibers underwent pre-heating within the heated die. Subsequently, the impregnated ramie fiber yarns and the molten PP matrix were extruded together from the nozzle and promptly deposited. This facilitated the in-situ impregnation of the ramie yarns with the PP matrix. The deposition was systematically placed onto the printing platform, gradually forming each component layer by layer. Key parameters governing the process, including layer thickness, printing speed, nozzle temperature, and bed temperature, were configured as follows: 0.3 mm, 100 mm/min, 190 °C, and 50 °C, respectively [28, 29].

## Differential scanning calorimetry test

Differential Scanning Calorimetry (TG/DSC1, Mettler-Toledo) was employed to determine the crystallization and melting temperatures of the CRFRPCs after the completion of the printing process. The experiment was carried out in a nitrogen atmosphere, with a sample weighing (5.9 ± 0.8) mg. The sample underwent heating from room temperature to 200°C at a consistent rate of 10 °C per minute [30] and cooling back to room temperature naturally. It could be measured that the crystallization temperature (Tc) and melting temperature (Tm) of sample was 121.45 °C and 152.05 °C in this range of study, as shown in Fig. 2.
composition of the ramie yarn, assessed through the Van Soest method, revealed the following components: 73.6% cellulose, 13.8% hemicellulose, 3.5% pectin, 1.9% lignin, and 7.2% other constituents [27]. Before the FFF process, the ramie yarns underwent a drying procedure in an oven at 80 °C for a duration of two hours.

## Manufacturing

3D-printed composites incorporating continuous ramie fibers were fabricated using an in-situ impregnation desk printer, specifically the Combot-200 from Fibertech in Shanxi, China. The printer utilized a single flat-head nozzle with a diameter of 1.3 mm. The experimental setup of the printing process is illustrated in Fig. 1 (a).

<figure><img src="image_2410.png" /><figcaption>Fig. 1 Schematic representation of the (a) in-situ impregnation process in FFF for continuous fiber filled composites, (b) of the setup for in-situ thermal behavior monitoring platform during FFF. (c) Optical image by camera and (d) thermal image captured by IR camera during FFF process.</figcaption></figure>

In this process, the thermoplastic PP matrix was raised to a temperature exceeding its melting point within the nozzle. Concurrently, the dry continuous ramie fibers underwent pre-heating within the heated die. Subsequently, the impregnated ramie fiber yarns and the molten PP matrix were extruded together from the nozzle and promptly deposited. This facilitated the in-situ impregnation of the ramie yarns with the PP matrix. The deposition was systematically placed onto the printing platform, gradually forming each component layer by layer. Key parameters governing the process, including layer thickness, printing speed, nozzle temperature, and bed temperature, were configured as follows: 0.3 mm, 100 mm/min, 190 °C, and 50 °C, respectively [28, 29].

## Differential scanning calorimetry test

Differential Scanning Calorimetry (TG/DSC1, Mettler-Toledo) was employed to determine the crystallization and melting temperatures of the CRFRPCs after the completion of the printing process. The experiment was carried out in a nitrogen atmosphere, with a sample weighing (5.9 ± 0.8) mg. The sample underwent heating from room temperature to 200°C at a consistent rate of 10 °C per minute [30] and cooling back to room temperature naturally. It could be measured that the crystallization temperature (Tc) and melting temperature (Tm) of sample was 121.45 °C and 152.05 °C in this range of study, as shown in Fig. 2.
<figure><img src="image_2420.png" /><figcaption>Fig. 2 DSC curves for printed CRFRPCs specimen</figcaption></figure>

## Thermography

For this study, an infrared (IR) camera, specifically the Mengchen MCDC-310 from Hunan Ruoxin Co., Ltd in China, was chosen. The IR camera operates within a wavelength range of 7.5-14 µm, has a sampling frequency of 50 Hz, an optical resolution of 384×288 pixels, spatial resolution of 17 µm/pixel, and a working distance ranging from 50 to 90 cm. Fig. 1 (b) depicts the schematic representation of the in-situ thermal behavior monitoring platform.

The geometry of the single wall-shaped composites measured 60×2.2×50 mm, as illustrated in Fig. 1 (b). When the object was oriented along the machine's Cartesian system, the IR camera captured the evolution of temperature over time within the object's frontal x-z plane. This process recorded temporal temperature variations within the object's frontal plane, specifically monitoring temperature fluctuations at a designated position (xᵢ, zₖ). For example, this observation encompassed both primary reheating, resulting from the deposition of the upper neighbor (xᵢ, zₖ+1), and secondary reheating, stemming from the deposition of the subsequent neighbor (xᵢ, zₖ+2), ..., and nth times reheating, induced by the deposition of the nth neighbor (xᵢ, zₖ+n).

## Theoretical Methodology

### Heat transfer modeling for FFF process

This section introduces the modeling of heat transfer model in the filament during the FFF process. And assumptions of isotropic thermal behavior of materials and constant heat exchange coefficient values are used in this model. The fixed domain utilized is illustrated in Fig. 3, representing a vertical wall constructed with a single filament in the thickness. FFF is purely a thermal process that is explained by the heat transfer governing equation [31, 32] given by Eq. (1):

$$ \rho C_p \frac{\partial T}{\partial t} = k \nabla^2 T + \dot{q} \qquad (1) $$

where T, ρ, Cₚ, k, ḳ are temperature, density, specific heat, thermal conductivity, and the internal heat generated of part due to the heated nozzle. The initial temperature (Tinitial) is imposed by the extruder. Subsequently, the filament undergoes cooling through convection and radiation interactions with the surrounding air at Tenvironment (representing ② and Ω in Fig. 3 (a). Additionally, it experiences cooling through conduction with the previously extruded filament (indicated as boundary ③ in Fig. 3 (a)). The support plate is kept at Tplate and the filaments were reheating by plate with conductive transfer (corresponding to ① in Fig. 3 (a)). It's worth noting that thermal contact resistances between filaments play a role in influencing the conductive transfer, particularly along boundaries ① and ③ as depicted in Fig. 3 (a). The initial and boundary condition are described as follows:

$$ T(t = 0) = T_{initial} = T_{extrusion} \qquad (2) $$

$$ q_{convective} = h(T - T_{environment}) \qquad (3) $$

$$ q_{radiative} = \varepsilon \sigma (T^4 - T_{environment}^4) \qquad (4) $$
<figure><img src="image_2411.png" /><figcaption>Fig. 2 DSC curves for printed CRFRPCs specimen</figcaption></figure>

## Thermography

For this study, an infrared (IR) camera, specifically the Mengchen MCDC-310 from Hunan Ruoxin Co., Ltd in China, was chosen. The IR camera operates within a wavelength range of 7.5-14 µm, has a sampling frequency of 50 Hz, an optical resolution of 384×288 pixels, spatial resolution of 17 µm/pixel, and a working distance ranging from 50 to 90 cm. Fig. 1 (b) depicts the schematic representation of the in-situ thermal behavior monitoring platform.

The geometry of the single wall-shaped composites measured 60×2.2×50 mm, as illustrated in Fig. 1 (b). When the object was oriented along the machine's Cartesian system, the IR camera captured the evolution of temperature over time within the object's frontal x-z plane. This process recorded temporal temperature variations within the object's frontal plane, specifically monitoring temperature fluctuations at a designated position (xᵢ, zₖ). For example, this observation encompassed both primary reheating, resulting from the deposition of the upper neighbor (xᵢ, zₖ+1), and secondary reheating, stemming from the deposition of the subsequent neighbor (xᵢ, zₖ+2), ..., and nth times reheating, induced by the deposition of the nth neighbor (xᵢ, zₖ+n).

## Theoretical Methodology

### Heat transfer modeling for FFF process

This section introduces the modeling of heat transfer model in the filament during the FFF process. And assumptions of isotropic thermal behavior of materials and constant heat exchange coefficient values are used in this model. The fixed domain utilized is illustrated in Fig. 3, representing a vertical wall constructed with a single filament in the thickness. FFF is purely a thermal process that is explained by the heat transfer governing equation [31, 32] given by Eq. (1):

$$ \rho C_p \frac{\partial T}{\partial t} = k \nabla^2 T + \dot{q} \qquad (1) $$

where T, ρ, Cₚ, k, ḳ are temperature, density, specific heat, thermal conductivity, and the internal heat generated of part due to the heated nozzle. The initial temperature (Tinitial) is imposed by the extruder. Subsequently, the filament undergoes cooling through convection and radiation interactions with the surrounding air at Tenvironment (representing ② and Ω in Fig. 3 (a). Additionally, it experiences cooling through conduction with the previously extruded filament (indicated as boundary ③ in Fig. 3 (a)). The support plate is kept at Tplate and the filaments were reheating by plate with conductive transfer (corresponding to ① in Fig. 3 (a)). It's worth noting that thermal contact resistances between filaments play a role in influencing the conductive transfer, particularly along boundaries ① and ③ as depicted in Fig. 3 (a). The initial and boundary condition are described as follows:

$$ T(t = 0) = T_{initial} = T_{extrusion} \qquad (2) $$

$$ q_{convective} = h(T - T_{environment}) \qquad (3) $$

$$ q_{radiative} = \varepsilon \sigma (T^4 - T_{environment}^4) \qquad (4) $$
where $q_{convective}$, $q_{radiative}$, $h$, $T_{environment}$, $\varepsilon$, $\sigma$ represent heat flux due to convection, heat flux due to radiation, heat convection coefficient, environment temperature of the surrounding air, material's emissivity, and the Stefan-Boltzmann constant, respectively.

<figure><img src="image_2421.png" /><figcaption>Fig. 3 (a) Geometry and boundary conditions applied in the heat transfer model. (b) Polymer printability rules for FFF process</figcaption></figure>

As depicted in Fig. 3 (b), maintaining an adequately elevated temperature is crucial to facilitate effective healing at the filament interfaces. However, it is equally essential to ensure that this temperature remains within an optimal range to prevent structural collapse, which can result from excessively low viscosity or the potential risks of thermal degradation or chemical aging of the extruded polymer. Additionally, the adhesive bonding between adjacent layers is significantly influenced by the thermal behavior of the printed composites, given the layer-by-layer deposition method [11]. Therefore, a detailed investigation into how thermal properties impact interfacial bonding performance was necessary. Specifically, focusing on the effective temperature range between the $T_c$ at 121.45 °C and the $T_m$ at 152.05 °C of semi-crystalline polymers emerged as a crucial consideration during the FFF process.

Finite Element Simulation Model

To analysis the FFF process including heat transfer, a transient heat transfer model was solved using the commercial finite element (FE) software Abaqus in this study as shown in Fig. 3 (a) and Fig. 4. The geometry of the polymer filaments' model is a stack of rectangles with rounded corners, and of the continuous fiber yarn' model is an ellipse, mirroring the structure of the printed object during the FFF process. The height and width of polymer filament are 0.3 mm and 1.0 mm, respectively. The fiber's height is defined as 0.1 mm, and the width is 0.26 mm. The cross-sectional size, and position of the continuous fiber yarns in each layer are based on [33]. To facilitate comparison with pyrometer measurements, the simulated temperature was evaluated at a specific point situated on interface between adjacent layers, as illustrated in Fig. 3 (a).

The FE simulation incorporates the deposition of each filament, resulting in a dynamic alteration of geometry and boundary conditions in the numerical model for every new filament. Convective heat transfer and radiative heat transfer are modeled on all interfaces interacting with the air. A consistent temperature is enforced at the bottom boundary of the heating plate. Thermal contact resistance is applied with a constant value at the plate-filament interface and another constant value at the filament-filament interface. The temperature of newly deposited filaments is set to $T_{extrusion}$, as depicted in Fig. 4 (b). The convective coefficients $h$ and material's emissivity coefficient $\varepsilon$ are 150 W/(m²·°C) and 0.96, respectively, in the current range of study [34]. The interaction between fiber yarn and polymer matrix, as well as the interaction between adjacent polymer matrix filaments are defined as low contact (100 W/(m²·°C)) and perfect contact (10⁶ W/(m²·°C)) based on [33, 34].
where $q_{convective}$, $q_{radiative}$, $h$, $T_{environment}$, $\varepsilon$, $\sigma$ represent heat flux due to convection, heat flux due to radiation, heat convection coefficient, environment temperature of the surrounding air, material's emissivity, and the Stefan-Boltzmann constant, respectively.

<figure><img src="image_2412.png" /><figcaption>Fig. 3 (a) Geometry and boundary conditions applied in the heat transfer model. (b) Polymer printability rules for FFF process</figcaption></figure>

As depicted in Fig. 3 (b), maintaining an adequately elevated temperature is crucial to facilitate effective healing at the filament interfaces. However, it is equally essential to ensure that this temperature remains within an optimal range to prevent structural collapse, which can result from excessively low viscosity or the potential risks of thermal degradation or chemical aging of the extruded polymer. Additionally, the adhesive bonding between adjacent layers is significantly influenced by the thermal behavior of the printed composites, given the layer-by-layer deposition method [11]. Therefore, a detailed investigation into how thermal properties impact interfacial bonding performance was necessary. Specifically, focusing on the effective temperature range between the $T_c$ at 121.45 °C and the $T_m$ at 152.05 °C of semi-crystalline polymers emerged as a crucial consideration during the FFF process.

Finite Element Simulation Model

To analysis the FFF process including heat transfer, a transient heat transfer model was solved using the commercial finite element (FE) software Abaqus in this study as shown in Fig. 3 (a) and Fig. 4. The geometry of the polymer filaments' model is a stack of rectangles with rounded corners, and of the continuous fiber yarn' model is an ellipse, mirroring the structure of the printed object during the FFF process. The height and width of polymer filament are 0.3 mm and 1.0 mm, respectively. The fiber's height is defined as 0.1 mm, and the width is 0.26 mm. The cross-sectional size, and position of the continuous fiber yarns in each layer are based on [33]. To facilitate comparison with pyrometer measurements, the simulated temperature was evaluated at a specific point situated on interface between adjacent layers, as illustrated in Fig. 3 (a).

The FE simulation incorporates the deposition of each filament, resulting in a dynamic alteration of geometry and boundary conditions in the numerical model for every new filament. Convective heat transfer and radiative heat transfer are modeled on all interfaces interacting with the air. A consistent temperature is enforced at the bottom boundary of the heating plate. Thermal contact resistance is applied with a constant value at the plate-filament interface and another constant value at the filament-filament interface. The temperature of newly deposited filaments is set to $T_{extrusion}$, as depicted in Fig. 4 (b). The convective coefficients $h$ and material's emissivity coefficient $\varepsilon$ are 150 W/(m²·°C) and 0.96, respectively, in the current range of study [34]. The interaction between fiber yarn and polymer matrix, as well as the interaction between adjacent polymer matrix filaments are defined as low contact (100 W/(m²·°C)) and perfect contact (10⁶ W/(m²·°C)) based on [33, 34].
<figure><img src="image_2422.png" /><figcaption>Fig. 4 Model representation, (a) interaction definition between different parts, and (b) with boundary conditions for each new layer deposition.</figcaption></figure>

The thermal properties of PP and ramie fiber were taken from literature [35-39], as shown in table 1. And the process parameters representatives of experimental conditions are reported in the table 2. The component was configured with a mesh comprising 8-nodes linear heat transfer brick elements, specifically DC3D8, and the mesh was incorporated refinement at the corners of the rectangles.

<table><caption>Table 1. Thermal properties used in simulations [35-39].</caption><thead><tr><td>Properties</td><td>PP</td><td>Ramie fiber</td><td>Heating plate</td></tr></thead><tbody><tr><td>Density(kg/m³)</td><td>900</td><td>1450</td><td>2210</td></tr><tr><td>Specific heat Cp (J.kg⁻¹K⁻¹)</td><td>1580</td><td>1422</td><td>730</td></tr><tr><td>Thermal conductivity k (W.m⁻¹K⁻¹)</td><td>0.27</td><td>1.46</td><td>1.40</td></tr></tbody></table>

<table><caption>Table 2. Process parameters used for simulations.</caption><thead><tr><td>Parameters</td><td>PP</td><td>Ramie fiber</td></tr></thead><tbody><tr><td>Extrusion temperature (°C)</td><td>190</td><td>190</td></tr><tr><td>Heating plate temperature (°C)</td><td>50</td><td>50</td></tr><tr><td>Environment temperature (°C)</td><td>25</td><td>25</td></tr><tr><td>Time between 2 filaments deposition (s)</td><td>40</td><td>40</td></tr><tr><td>Layer thickness h (mm)</td><td>0.30</td><td>0.10</td></tr><tr><td>Layer width w (mm)</td><td>1.00</td><td>0.26</td></tr></tbody></table>

# Results and discussion

## Simulation results

The temperature predicted at different times is shown in Fig. 5. The simulation outcomes reveal temperature heterogeneity within the filament. Unlike numerous heat transfer models in existing literature that assume a small Biot number, such an assumption is not validated in our case. The interface temperature significantly differs from that observed on the surface through camera monitoring. This reinforces the necessity for a numerical model to accurately estimate the interface temperature.
<figure><img src="image_2413.png" /><figcaption>Fig. 4 Model representation, (a) interaction definition between different parts, and (b) with boundary conditions for each new layer deposition.</figcaption></figure>

The thermal properties of PP and ramie fiber were taken from literature [35-39], as shown in table 1. And the process parameters representatives of experimental conditions are reported in the table 2. The component was configured with a mesh comprising 8-nodes linear heat transfer brick elements, specifically DC3D8, and the mesh was incorporated refinement at the corners of the rectangles.

<table><caption>Table 1. Thermal properties used in simulations [35-39].</caption><thead><tr><td>Properties</td><td>PP</td><td>Ramie fiber</td><td>Heating plate</td></tr></thead><tbody><tr><td>Density(kg/m³)</td><td>900</td><td>1450</td><td>2210</td></tr><tr><td>Specific heat Cp (J.kg⁻¹K⁻¹)</td><td>1580</td><td>1422</td><td>730</td></tr><tr><td>Thermal conductivity k (W.m⁻¹K⁻¹)</td><td>0.27</td><td>1.46</td><td>1.40</td></tr></tbody></table>

<table><caption>Table 2. Process parameters used for simulations.</caption><thead><tr><td>Parameters</td><td>PP</td><td>Ramie fiber</td></tr></thead><tbody><tr><td>Extrusion temperature (°C)</td><td>190</td><td>190</td></tr><tr><td>Heating plate temperature (°C)</td><td>50</td><td>50</td></tr><tr><td>Environment temperature (°C)</td><td>25</td><td>25</td></tr><tr><td>Time between 2 filaments deposition (s)</td><td>40</td><td>40</td></tr><tr><td>Layer thickness h (mm)</td><td>0.30</td><td>0.10</td></tr><tr><td>Layer width w (mm)</td><td>1.00</td><td>0.26</td></tr></tbody></table>

# Results and discussion

## Simulation results

The temperature predicted at different times is shown in Fig. 5. The simulation outcomes reveal temperature heterogeneity within the filament. Unlike numerous heat transfer models in existing literature that assume a small Biot number, such an assumption is not validated in our case. The interface temperature significantly differs from that observed on the surface through camera monitoring. This reinforces the necessity for a numerical model to accurately estimate the interface temperature.
<figure><img src="image_2423.png" /><figcaption>Fig. 5 ABAQUS numerical predictions of temperature (°C) for CRFRPCs during the FFF process.</figcaption></figure>

## Validation by experimental results

To validate the thermal results derived from the Abaqus FE model, the evolution of temperature data is compared with that obtained from an IR camera, as detailed in section 2.4. Fig. 6 shows the comparison between simulated and experimental temperature evolutions of layer 1 in CRFRPCs. In Fig. 6, for post-processing analysis, the temperature measurement signals are synchronized at t=0 with reference to the moment of the first temperature peak, considering the highest measured value as the reference at t=0. The curve illustrated in Fig. 6 exhibits a distinct decline after each peak followed by an ascent leading to the subsequent peak. This phenomenon is likely attributed to the reheating effect. Specifically, during the printing process, when a new filament is deposited, the preceding one undergoes a significant cooling phase before being reheated. In literatures [40], the effective reheating peaks, especially for the first reheating processes, were more important for strong interfacial bonding than those of the rest of the reheating peaks. When the temperature of deposited filaments decreases below Tc, the growth of the bonding neck between filaments ceases. Therefore, it is necessary to focus on the first reheating peak whether is within the effective reheating temperature range, to better study the degree of bonding between adjacent layers. Specifically, the predicted value of the first reheating temperature is 127.3 °C, compared with the measured value of 127.9 °C, the difference between each other is small. The numerical simulations reproduce the experimental trends in temperature variation. However, the Abaqus FE model exhibits a faster and more consistent cooling process, potentially attributed to factors such as ideal operating conditions (environment temperature and bed temperature), and limitations in accurately reflecting the material's crystallization behavior within the model.

<figure><img src="image_2424.png" /><figcaption>Fig. 6 Comparison of experimental and simulated temperature evolutions of layer 1.</figcaption></figure>
<figure><img src="image_2414.png" /><figcaption>Fig. 5 ABAQUS numerical predictions of temperature (°C) for CRFRPCs during the FFF process.</figcaption></figure>

## Validation by experimental results

To validate the thermal results derived from the Abaqus FE model, the evolution of temperature data is compared with that obtained from an IR camera, as detailed in section 2.4. Fig. 6 shows the comparison between simulated and experimental temperature evolutions of layer 1 in CRFRPCs. In Fig. 6, for post-processing analysis, the temperature measurement signals are synchronized at t=0 with reference to the moment of the first temperature peak, considering the highest measured value as the reference at t=0. The curve illustrated in Fig. 6 exhibits a distinct decline after each peak followed by an ascent leading to the subsequent peak. This phenomenon is likely attributed to the reheating effect. Specifically, during the printing process, when a new filament is deposited, the preceding one undergoes a significant cooling phase before being reheated. In literatures [40], the effective reheating peaks, especially for the first reheating processes, were more important for strong interfacial bonding than those of the rest of the reheating peaks. When the temperature of deposited filaments decreases below Tc, the growth of the bonding neck between filaments ceases. Therefore, it is necessary to focus on the first reheating peak whether is within the effective reheating temperature range, to better study the degree of bonding between adjacent layers. Specifically, the predicted value of the first reheating temperature is 127.3 °C, compared with the measured value of 127.9 °C, the difference between each other is small. The numerical simulations reproduce the experimental trends in temperature variation. However, the Abaqus FE model exhibits a faster and more consistent cooling process, potentially attributed to factors such as ideal operating conditions (environment temperature and bed temperature), and limitations in accurately reflecting the material's crystallization behavior within the model.

<figure><img src="image_2415.png" /><figcaption>Fig. 6 Comparison of experimental and simulated temperature evolutions of layer 1.</figcaption></figure>
Fig. 7 shows the numerical predictions with and without considering the presence of continuous fiber. For the model without considering the continuous fiber, the predicted first reheating temperature value (102.2°C) is much lower than that of the model with considering the presence of continuous fiber phase and lower compared to the value measured by experiment. Thus, we conclude that the presence of fiber may increase the degree of reheating.

<figure><img src="image_2425.png" /><figcaption>Fig. 7 Simulated results without/with considering the presence of fiber in heat transfer model.</figcaption></figure>

## Conclusion

Fused Filament Fabrication (FFF), an additive manufacturing process driven by thermal mechanisms, is employed for the production of continuous fiber-reinforced composites in various engineering applications. Face to the challenge posed by interlayer delamination of FFF composites, improved adhesive bonding is required to improve the macro-mechanical properties of material extrusion 3D printed fiber composites. It is necessary to study the thermal behavior of continuous fiber filled composites in the manufacturing process. This study introduces a novel thermal simulation FE model, incorporating continuous fiber considerations, for heat transfer modeling.

The numerical simulations reproduce the experimental trends in temperature variation. The effective reheating temperature of model is 127.3 °C, compared with the measured value of 127.9 °C. When continuous fiber phase is not considered into the heat transfer model, the reheating temperature at the interface is lower than that of the temperature observed via IR monitoring. This finding underscores the imperative need for a numerical model to precisely estimate the interface's reheating temperature by considering with fiber phase, to further investigate the adhesion between adjacent layers and filaments.

## References

[1] Naser M, Hawileh R, Abdalla J. Fiber-reinforced polymer composites in strengthening reinforced concrete structures: A critical review. Engineering Structures. 2019;198:109542. https://doi.org/10.1016/j.engstruct.2019.109542

[2] Bakis CE, Bank LC, Brown V, Cosenza E, Davalos J, Lesko J, et al. Fiber-reinforced polymer composites for construction—State-of-the-art review. Journal of composites for construction. 2002;6(2):73-87. https://doi.org/10.1061/(ASCE)1090-0268(2002)6:2(73)

[3] Chacón J, Caminero M, Núñez P, García-Plaza E, García-Moreno I, Reverte J. Additive manufacturing of continuous fibre reinforced thermoplastic composites using fused deposition modelling: Effect of process parameters on mechanical properties. Composites science and technology. 2019;181:107688. https://doi.org/10.1016/j.compscitech.2019.107688

[4] Ngo TD, Kashani A, Imbalzano G, Nguyen KT, Hui D. Additive manufacturing (3D printing): A review of materials, methods, applications and challenges. Composites Part B: Engineering. 2018;143:172-96. https://doi.org/10.1016/j.compositesb.2018.02.012
Fig. 7 shows the numerical predictions with and without considering the presence of continuous fiber. For the model without considering the continuous fiber, the predicted first reheating temperature value (102.2°C) is much lower than that of the model with considering the presence of continuous fiber phase and lower compared to the value measured by experiment. Thus, we conclude that the presence of fiber may increase the degree of reheating.

<figure><img src="image_2416.png" /><figcaption>Fig. 7 Simulated results without/with considering the presence of fiber in heat transfer model.</figcaption></figure>

## Conclusion

Fused Filament Fabrication (FFF), an additive manufacturing process driven by thermal mechanisms, is employed for the production of continuous fiber-reinforced composites in various engineering applications. Face to the challenge posed by interlayer delamination of FFF composites, improved adhesive bonding is required to improve the macro-mechanical properties of material extrusion 3D printed fiber composites. It is necessary to study the thermal behavior of continuous fiber filled composites in the manufacturing process. This study introduces a novel thermal simulation FE model, incorporating continuous fiber considerations, for heat transfer modeling.

The numerical simulations reproduce the experimental trends in temperature variation. The effective reheating temperature of model is 127.3 °C, compared with the measured value of 127.9 °C. When continuous fiber phase is not considered into the heat transfer model, the reheating temperature at the interface is lower than that of the temperature observed via IR monitoring. This finding underscores the imperative need for a numerical model to precisely estimate the interface's reheating temperature by considering with fiber phase, to further investigate the adhesion between adjacent layers and filaments.

## References

[1] Naser M, Hawileh R, Abdalla J. Fiber-reinforced polymer composites in strengthening reinforced concrete structures: A critical review. Engineering Structures. 2019;198:109542. https://doi.org/10.1016/j.engstruct.2019.109542

[2] Bakis CE, Bank LC, Brown V, Cosenza E, Davalos J, Lesko J, et al. Fiber-reinforced polymer composites for construction—State-of-the-art review. Journal of composites for construction. 2002;6(2):73-87. https://doi.org/10.1061/(ASCE)1090-0268(2002)6:2(73)

[3] Chacón J, Caminero M, Núñez P, García-Plaza E, García-Moreno I, Reverte J. Additive manufacturing of continuous fibre reinforced thermoplastic composites using fused deposition modelling: Effect of process parameters on mechanical properties. Composites science and technology. 2019;181:107688. https://doi.org/10.1016/j.compscitech.2019.107688

[4] Ngo TD, Kashani A, Imbalzano G, Nguyen KT, Hui D. Additive manufacturing (3D printing): A review of materials, methods, applications and challenges. Composites Part B: Engineering. 2018;143:172-96. https://doi.org/10.1016/j.compositesb.2018.02.012
[5] Cheng P, Peng Y, Li S, Rao Y, Le Duigou A, Wang K, et al. 3D printed continuous fiber reinforced composite lightweight structures: A review and outlook. Composites Part B: Engineering. 2023;250:110450. https://doi.org/10.1016/j.compositesb.2022.110450

[6] Rinaldi M, Ghidini T, Cecchini F, Brandao A, Nanni F. Additive layer manufacturing of poly (ether ether ketone) via FDM. Composites Part B: Engineering. 2018;145:162-72. https://doi.org/10.1016/j.compositesb.2018.03.029

[7] Cheng P, Peng Y, Wang K, Le Duigou A, Yao S, Chen C. Quasi-static penetration property of 3D printed woven-like ramie fiber reinforced biocomposites. Composite Structures. 2023;303:116313. https://doi.org/10.1016/j.compstruct.2022.116313

[8] Zhao H, Liu X, Zhao W, Wang G, Liu B. An Overview of Research on FDM 3D Printing Process of Continuous Fiber Reinforced Composites. Journal of Physics: Conference Series: IOP Publishing; 2019. p. 052037. https://doi.org/10.1088/1742-6596/1213/5/052037

[9] Seppala JE, Migler KD. Infrared thermography of welding zones produced by polymer extrusion additive manufacturing. Additive manufacturing. 2016;12:71-6. https://doi.org/10.1016/j.addma.2016.06.007

[10] Zhou M, Zhou X, Si L, Chen P, Li M, Zhang Y, et al. Modeling of bonding strength for Fused Filament Fabrication considering bonding interface evolution and molecular diffusion. Journal of Manufacturing Processes. 2021;68:1485-94. https://doi.org/10.1016/j.jmapro.2021.06.064

[11] Seppala JE, Han SH, Hillgartner KE, Davis CS, Migler KB. Weld formation during material extrusion additive manufacturing. Soft matter. 2017;13(38):6761-9. https://doi.org/10.1039/C7SM00950J

[12] Sun Q, Rizvi G, Bellehumeur C, Gu P. Effect of processing conditions on the bonding quality of FDM polymer filaments. Rapid prototyping journal. 2008. https://doi.org/10.1108/13552540810862028

[13] Costa S, Duarte F, Covas J. Estimation of filament temperature and adhesion development in fused deposition techniques. Journal of Materials Processing Technology. 2017;245:167-79. https://doi.org/10.1016/j.jmatprotec.2017.02.026

[14] Touchard F, Chocinski-Arnault L, Fournier T, Magro C, Lafitte A, Caradec A. Interfacial adhesion quality in 3D printed continuous CF/PA6 composites at filament/matrix and interlaminar scales. Composites Part B: Engineering. 2021;218:108891. https://doi.org/10.1016/j.compositesb.2021.108891

[15] Bellehumeur C, Li L, Sun Q, Gu P. Modeling of bond formation between polymer filaments in the fused deposition modeling process. Journal of manufacturing processes. 2004;6(2):170-8. https://doi.org/10.1016/S1526-6125(04)70071-7

[16] Vanaei H, Deligant M, Shirinbayan M, Raissi K, Fitoussi J, Khelladi S, et al. A comparative in-process monitoring of temperature profile in fused filament fabrication. Polymer Engineering & Science. 2021;61(1):68-76. https://doi.org/10.1002/pen.25555

[17] Roy M, Yavari R, Zhou C, Wodo O, Rao P. Prediction and experimental validation of part thermal history in the fused filament fabrication additive manufacturing process. Journal of Manufacturing Science and Engineering. 2019;141(12). https://doi.org/10.1115/1.4045056

[18] Wang K, Li S, Rao Y, Wu Y, Peng Y, Yao S, et al. Flexure Behaviors of ABS-Based Composites Containing Carbon and Kevlar Fibers by Material Extrusion 3D Printing. Polymers. 2019;11(11):1878. https://doi.org/10.3390/polym11111878
[5] Cheng P, Peng Y, Li S, Rao Y, Le Duigou A, Wang K, et al. 3D printed continuous fiber reinforced composite lightweight structures: A review and outlook. Composites Part B: Engineering. 2023;250:110450. https://doi.org/10.1016/j.compositesb.2022.110450

[6] Rinaldi M, Ghidini T, Cecchini F, Brandao A, Nanni F. Additive layer manufacturing of poly (ether ether ketone) via FDM. Composites Part B: Engineering. 2018;145:162-72. https://doi.org/10.1016/j.compositesb.2018.03.029

[7] Cheng P, Peng Y, Wang K, Le Duigou A, Yao S, Chen C. Quasi-static penetration property of 3D printed woven-like ramie fiber reinforced biocomposites. Composite Structures. 2023;303:116313. https://doi.org/10.1016/j.compstruct.2022.116313

[8] Zhao H, Liu X, Zhao W, Wang G, Liu B. An Overview of Research on FDM 3D Printing Process of Continuous Fiber Reinforced Composites. Journal of Physics: Conference Series: IOP Publishing; 2019. p. 052037. https://doi.org/10.1088/1742-6596/1213/5/052037

[9] Seppala JE, Migler KD. Infrared thermography of welding zones produced by polymer extrusion additive manufacturing. Additive manufacturing. 2016;12:71-6. https://doi.org/10.1016/j.addma.2016.06.007

[10] Zhou M, Zhou X, Si L, Chen P, Li M, Zhang Y, et al. Modeling of bonding strength for Fused Filament Fabrication considering bonding interface evolution and molecular diffusion. Journal of Manufacturing Processes. 2021;68:1485-94. https://doi.org/10.1016/j.jmapro.2021.06.064

[11] Seppala JE, Han SH, Hillgartner KE, Davis CS, Migler KB. Weld formation during material extrusion additive manufacturing. Soft matter. 2017;13(38):6761-9. https://doi.org/10.1039/C7SM00950J

[12] Sun Q, Rizvi G, Bellehumeur C, Gu P. Effect of processing conditions on the bonding quality of FDM polymer filaments. Rapid prototyping journal. 2008. https://doi.org/10.1108/13552540810862028

[13] Costa S, Duarte F, Covas J. Estimation of filament temperature and adhesion development in fused deposition techniques. Journal of Materials Processing Technology. 2017;245:167-79. https://doi.org/10.1016/j.jmatprotec.2017.02.026

[14] Touchard F, Chocinski-Arnault L, Fournier T, Magro C, Lafitte A, Caradec A. Interfacial adhesion quality in 3D printed continuous CF/PA6 composites at filament/matrix and interlaminar scales. Composites Part B: Engineering. 2021;218:108891. https://doi.org/10.1016/j.compositesb.2021.108891

[15] Bellehumeur C, Li L, Sun Q, Gu P. Modeling of bond formation between polymer filaments in the fused deposition modeling process. Journal of manufacturing processes. 2004;6(2):170-8. https://doi.org/10.1016/S1526-6125(04)70071-7

[16] Vanaei H, Deligant M, Shirinbayan M, Raissi K, Fitoussi J, Khelladi S, et al. A comparative in-process monitoring of temperature profile in fused filament fabrication. Polymer Engineering & Science. 2021;61(1):68-76. https://doi.org/10.1002/pen.25555

[17] Roy M, Yavari R, Zhou C, Wodo O, Rao P. Prediction and experimental validation of part thermal history in the fused filament fabrication additive manufacturing process. Journal of Manufacturing Science and Engineering. 2019;141(12). https://doi.org/10.1115/1.4045056

[18] Wang K, Li S, Rao Y, Wu Y, Peng Y, Yao S, et al. Flexure Behaviors of ABS-Based Composites Containing Carbon and Kevlar Fibers by Material Extrusion 3D Printing. Polymers. 2019;11(11):1878. https://doi.org/10.3390/polym11111878
[19] Heidari-Rarani M, Rafiee-Afarani M, Zahedi A. Mechanical characterization of FDM 3D printing of continuous carbon fiber reinforced PLA composites. Composites Part B: Engineering. 2019;175:107147. https://doi.org/10.1016/j.compositesb.2019.107147

[20] Cui H, Thomson D, Pellegrino A, Wiegand J, Petrinic N. Effect of strain rate and fibre rotation on the in-plane shear response of±45° laminates in tension and compression tests. Composites Science and Technology. 2016;135:106-15. https://doi.org/10.1016/j.compscitech.2016.09.016

[21] Mantecón R, Rufo-Martín C, Castellanos R, Diaz-Alvarez J. Experimental assessment of thermal gradients and layout effects on the mechanical performance of components manufactured by fused deposition modeling. Rapid Prototyping Journal. 2022. https://doi.org/10.1108/RPJ-12-2021-0329

[22] Fan C, Shan Z, Zou G, Zhan L, Yan D. Interfacial bonding mechanism and mechanical performance of continuous fiber reinforced composites in additive manufacturing. Chinese Journal of Mechanical Engineering. 2021;34(1):1-11. https://doi.org/10.1186/s10033-021-00538-7

[23] Vanaei HR, Shirinbayan M, Costa SF, Duarte FM, Covas JA, Deligant M, et al. Experimental study of PLA thermal behavior during fused filament fabrication. Journal of Applied Polymer Science. 2021;138(4):49747. https://doi.org/10.1002/app.49747

[24] Vanaei HR, Khelladi S, Deligant M, Shirinbayan M, Tcharkhtchi A. Numerical Prediction for Temperature Profile of Parts Manufactured using Fused Filament Fabrication. Journal of Manufacturing Processes. 2022;76:548-58. https://doi.org/10.1016/j.jmapro.2022.02.042

[25] Lepoivre A, Boyard N, Levy A, Sobotka V. Methodology to assess interlayer quality in the material extrusion process: A temperature and adhesion prediction on a high performance polymer. Additive Manufacturing. 2022;60:103167. https://doi.org/10.1016/j.addma.2022.103167

[26] Mahmoud Y, Lyu J, Akhavan J, Xu K, Manoochehri S. Thermal history based prediction of interlayer bond strength in parts manufactured by material extrusion additive manufacturing. The International Journal of Advanced Manufacturing Technology. 2023:1-17. https://doi.org/10.21203/rs.3.rs-2413996/v1

[27] Van Soest Pv, Robertson JB, Lewis BA. Methods for dietary fiber, neutral detergent fiber, and nonstarch polysaccharides in relation to animal nutrition. Journal of dairy science. 1991;74(10):3583-97. https://doi.org/10.3168/jds.S0022-0302(91)78551-2

[28] Lei L, Yao Z, Zhou J, Wei B, Fan H. 3D printing of carbon black/polypropylene composites with excellent microwave absorption performance. Composites Science and Technology. 2020;200:108479. https://doi.org/10.1016/j.compscitech.2020.108479

[29] Morales MA, Atencio Martinez CL, Maranon A, Hernandez C, Michaud V, Porras A. Development and characterization of rice husk and recycled polypropylene composite filaments for 3D printing. Polymers. 2021;13(7):1067. https://doi.org/10.3390/polym13071067

[30] Vanaei H, Shirinbayan M, Deligant M, Raissi K, Fitoussi J, Khelladi S, et al. Influence of process parameters on thermal and mechanical properties of polylactic acid fabricated by fused filament fabrication. Polymer Engineering & Science. 2020;60(8):1822-31. https://doi.org/10.1002/pen.25419

[31] Nath P, Olson JD, Mahadevan S, Lee Y-TT. Optimization of fused filament fabrication process parameters under uncertainty to maximize part geometry accuracy. Additive manufacturing. 2020;35:101331. https://doi.org/10.1016/j.addma.2020.101331

[32] Xu D, Zhang Y, Pigeonneau F. Thermal analysis of the fused filament fabrication printing process: Experimental and numerical investigations. International Journal of Material Forming. 2021;14:763-76. https://doi.org/10.1007/s12289-020-01591-8
[19] Heidari-Rarani M, Rafiee-Afarani M, Zahedi A. Mechanical characterization of FDM 3D printing of continuous carbon fiber reinforced PLA composites. Composites Part B: Engineering. 2019;175:107147. https://doi.org/10.1016/j.compositesb.2019.107147

[20] Cui H, Thomson D, Pellegrino A, Wiegand J, Petrinic N. Effect of strain rate and fibre rotation on the in-plane shear response of±45° laminates in tension and compression tests. Composites Science and Technology. 2016;135:106-15. https://doi.org/10.1016/j.compscitech.2016.09.016

[21] Mantecón R, Rufo-Martín C, Castellanos R, Diaz-Alvarez J. Experimental assessment of thermal gradients and layout effects on the mechanical performance of components manufactured by fused deposition modeling. Rapid Prototyping Journal. 2022. https://doi.org/10.1108/RPJ-12-2021-0329

[22] Fan C, Shan Z, Zou G, Zhan L, Yan D. Interfacial bonding mechanism and mechanical performance of continuous fiber reinforced composites in additive manufacturing. Chinese Journal of Mechanical Engineering. 2021;34(1):1-11. https://doi.org/10.1186/s10033-021-00538-7

[23] Vanaei HR, Shirinbayan M, Costa SF, Duarte FM, Covas JA, Deligant M, et al. Experimental study of PLA thermal behavior during fused filament fabrication. Journal of Applied Polymer Science. 2021;138(4):49747. https://doi.org/10.1002/app.49747

[24] Vanaei HR, Khelladi S, Deligant M, Shirinbayan M, Tcharkhtchi A. Numerical Prediction for Temperature Profile of Parts Manufactured using Fused Filament Fabrication. Journal of Manufacturing Processes. 2022;76:548-58. https://doi.org/10.1016/j.jmapro.2022.02.042

[25] Lepoivre A, Boyard N, Levy A, Sobotka V. Methodology to assess interlayer quality in the material extrusion process: A temperature and adhesion prediction on a high performance polymer. Additive Manufacturing. 2022;60:103167. https://doi.org/10.1016/j.addma.2022.103167

[26] Mahmoud Y, Lyu J, Akhavan J, Xu K, Manoochehri S. Thermal history based prediction of interlayer bond strength in parts manufactured by material extrusion additive manufacturing. The International Journal of Advanced Manufacturing Technology. 2023:1-17. https://doi.org/10.21203/rs.3.rs-2413996/v1

[27] Van Soest Pv, Robertson JB, Lewis BA. Methods for dietary fiber, neutral detergent fiber, and nonstarch polysaccharides in relation to animal nutrition. Journal of dairy science. 1991;74(10):3583-97. https://doi.org/10.3168/jds.S0022-0302(91)78551-2

[28] Lei L, Yao Z, Zhou J, Wei B, Fan H. 3D printing of carbon black/polypropylene composites with excellent microwave absorption performance. Composites Science and Technology. 2020;200:108479. https://doi.org/10.1016/j.compscitech.2020.108479

[29] Morales MA, Atencio Martinez CL, Maranon A, Hernandez C, Michaud V, Porras A. Development and characterization of rice husk and recycled polypropylene composite filaments for 3D printing. Polymers. 2021;13(7):1067. https://doi.org/10.3390/polym13071067

[30] Vanaei H, Shirinbayan M, Deligant M, Raissi K, Fitoussi J, Khelladi S, et al. Influence of process parameters on thermal and mechanical properties of polylactic acid fabricated by fused filament fabrication. Polymer Engineering & Science. 2020;60(8):1822-31. https://doi.org/10.1002/pen.25419

[31] Nath P, Olson JD, Mahadevan S, Lee Y-TT. Optimization of fused filament fabrication process parameters under uncertainty to maximize part geometry accuracy. Additive manufacturing. 2020;35:101331. https://doi.org/10.1016/j.addma.2020.101331

[32] Xu D, Zhang Y, Pigeonneau F. Thermal analysis of the fused filament fabrication printing process: Experimental and numerical investigations. International Journal of Material Forming. 2021;14:763-76. https://doi.org/10.1007/s12289-020-01591-8
[33] Cheng P, Wang K, Chen X, Wang J, Peng Y, Ahzi S, et al. Interfacial and mechanical properties of continuous ramie fiber reinforced biocomposites fabricated by in-situ impregnated 3D printing. Industrial Crops and Products. 2021;170:113760. https://doi.org/10.1016/j.indcrop.2021.113760

[34] Costa S, Duarte F, Covas J. Thermal conditions affecting heat transfer in FDM/FFE: a contribution towards the numerical modelling of the process: This paper investigates convection, conduction and radiation phenomena in the filament deposition process. Virtual and Physical Prototyping. 2015;10(1):35-46. https://doi.org/10.1080/17452759.2014.984042

[35] Lepoivre A, Boyard N, Levy A, Sobotka V. Heat transfer and adhesion study for the FFF additive manufacturing process. Procedia manufacturing. 2020;47:948-55. https://doi.org/10.1016/j.promfg.2020.04.291

[36] Patti A, Acierno D. Thermal conductivity of polypropylene-based materials. Polypropylene—Polymerization And Characterization Of Mechanical And Thermal Properties. 2020. https://doi.org/10.5772/intechopen.84477

[37] Weidenfeller B, Höfer M, Schilling FR. Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene. Composites Part A: applied science and manufacturing. 2004;35(4):423-9. https://doi.org/10.1016/j.compositesa.2003.11.005

[38] Lodha P, Netravali AN. Characterization of interfacial and mechanical properties of “green” composites with soy protein isolate and ramie fiber. Journal of materials science. 2002;37:3657-65. https://doi.org/10.1023/A:1016557124372

[39] Maddah HA. Polypropylene as a promising plastic: A review. Am J Polym Sci. 2016;6(1):1-11.

[40] Basgul C, Thieringer FM, Kurtz SM. Heat transfer-based non-isothermal healing model for the interfacial bonding strength of fused filament fabricated polyetheretherketone. Additive Manufacturing. 2021;46:102097. https://doi.org/10.1016/j.addma.2021.102097
[33] Cheng P, Wang K, Chen X, Wang J, Peng Y, Ahzi S, et al. Interfacial and mechanical properties of continuous ramie fiber reinforced biocomposites fabricated by in-situ impregnated 3D printing. Industrial Crops and Products. 2021;170:113760. https://doi.org/10.1016/j.indcrop.2021.113760

[34] Costa S, Duarte F, Covas J. Thermal conditions affecting heat transfer in FDM/FFE: a contribution towards the numerical modelling of the process: This paper investigates convection, conduction and radiation phenomena in the filament deposition process. Virtual and Physical Prototyping. 2015;10(1):35-46. https://doi.org/10.1080/17452759.2014.984042

[35] Lepoivre A, Boyard N, Levy A, Sobotka V. Heat transfer and adhesion study for the FFF additive manufacturing process. Procedia manufacturing. 2020;47:948-55. https://doi.org/10.1016/j.promfg.2020.04.291

[36] Patti A, Acierno D. Thermal conductivity of polypropylene-based materials. Polypropylene—Polymerization And Characterization Of Mechanical And Thermal Properties. 2020. https://doi.org/10.5772/intechopen.84477

[37] Weidenfeller B, Höfer M, Schilling FR. Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene. Composites Part A: applied science and manufacturing. 2004;35(4):423-9. https://doi.org/10.1016/j.compositesa.2003.11.005

[38] Lodha P, Netravali AN. Characterization of interfacial and mechanical properties of “green” composites with soy protein isolate and ramie fiber. Journal of materials science. 2002;37:3657-65. https://doi.org/10.1023/A:1016557124372

[39] Maddah HA. Polypropylene as a promising plastic: A review. Am J Polym Sci. 2016;6(1):1-11.

[40] Basgul C, Thieringer FM, Kurtz SM. Heat transfer-based non-isothermal healing model for the interfacial bonding strength of fused filament fabricated polyetheretherketone. Additive Manufacturing. 2021;46:102097. https://doi.org/10.1016/j.addma.2021.102097
# Optimization of the temperature profile of PET preform via a 3D modelling of the Infrared Heating and ventilation

LUO Yun-Mei¹,ᵃ*, CHEVALIER Luc¹,ᵇ, NGUYEN Thanh Tung¹,ᶜ

¹Université Gustave Eiffel, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77545 Marne-la-Vallée, France

ᵃyun-mei.luo@univ-eiffel.fr, ᵇluc.chevalier@univ-eiffel.fr, ᶜthanh-tung.nguyen@univ-eiffel.fr

**Keywords:** Infrared Heating, Numerical Simulation, Ventilation Effect, Optimization

**Abstract.** Thermal effect has important influence during the stretch blow moulding (SBM) process of PET bottle. Setting the heating condition in an industrial context is a complex task. A 3D simplified modelling of the heating stage during this process is proposed. In this numerical approach, the radiation source is simulated by using a model for intensity of the incident radiation and the Beer Lambert's law. On the other hand, the ventilation effect under industrial condition is taken into account by a modelling of the forced convection around a cylinder. The IR flux and ventilation effects are implemented as thermal boundary conditions in COMSOL for a 3D computation of the thermal problem for the preform only. Based on this simplified approach to achieve quickly the numerical simulation of the preform heating, an optimization procedure is proposed to adjust the settings of the infrared lamps by comparing our simulation results to the target temperature profile. This optimization tool provides quickly a first set of parameters to help industrial to obtain the desired temperature profile.

**Introduction**

The stretch blow moulding (SBM) process is a manufacturing process which is widely used to produce the plastic bottles and containers. In this process, a tube like preform is heated in front of infrared (IR) lamps, stretched, and then blown into the desired bottle shape within a mold. There have been numerous researches on the experimental approach and on the numerical one over the last 30 years [1-7]. However, the performance requirements of material PET and of the final bottle regularly increase, that leads to an upgraded investigation on the thermal and mechanical response of the process.

The temperature distribution of the preform before the blowing stage and thermal effect have important influence during the SBM process of PET bottle [8-10]. They plays an important role in the final thickness distribution and induced properties [11]. Numerous works have been carried out to obtain accurately the temperature distribution of the heating stage and to improve the design of infrared-ovens [11-13]. In author's previous works [10,14], the thermal properties of PET have been firstly identified from injected sheet. The IR heating flux was calculated by using radiative laws adapted to the test geometry in a semi-analytic way. For the preform case, the radiation source is simulated by using same model for intensity of the incident radiation and the Beer Lambert's law. On the other hand, in order to simulate a more realistic ventilation effect under industrial condition, we consider a simplified modelling of forced convection. The IR flux and ventilation effects are implemented as thermal boundary conditions in COMSOL for a 3D computation of the thermal problem for the preform only. The numerical temperature distribution of the external surface of the preform is compared to the measured internal and external temperature of preforms from THERMOscan device [15] in order to validate the approach. This device is provided by Blow Moulding Technologies Ltd. (BMT) company in Belfast. It measures simultaneously the internal and external preform temperature profile.

<figure><img src="image_2426.png" /></figure>
# Optimization of the temperature profile of PET preform via a 3D modelling of the Infrared Heating and ventilation

LUO Yun-Mei¹,ᵃ*, CHEVALIER Luc¹,ᵇ, NGUYEN Thanh Tung¹,ᶜ

¹Université Gustave Eiffel, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77545 Marne-la-Vallée, France

ᵃyun-mei.luo@univ-eiffel.fr, ᵇluc.chevalier@univ-eiffel.fr, ᶜthanh-tung.nguyen@univ-eiffel.fr

**Keywords:** Infrared Heating, Numerical Simulation, Ventilation Effect, Optimization

**Abstract.** Thermal effect has important influence during the stretch blow moulding (SBM) process of PET bottle. Setting the heating condition in an industrial context is a complex task. A 3D simplified modelling of the heating stage during this process is proposed. In this numerical approach, the radiation source is simulated by using a model for intensity of the incident radiation and the Beer Lambert's law. On the other hand, the ventilation effect under industrial condition is taken into account by a modelling of the forced convection around a cylinder. The IR flux and ventilation effects are implemented as thermal boundary conditions in COMSOL for a 3D computation of the thermal problem for the preform only. Based on this simplified approach to achieve quickly the numerical simulation of the preform heating, an optimization procedure is proposed to adjust the settings of the infrared lamps by comparing our simulation results to the target temperature profile. This optimization tool provides quickly a first set of parameters to help industrial to obtain the desired temperature profile.

**Introduction**

The stretch blow moulding (SBM) process is a manufacturing process which is widely used to produce the plastic bottles and containers. In this process, a tube like preform is heated in front of infrared (IR) lamps, stretched, and then blown into the desired bottle shape within a mold. There have been numerous researches on the experimental approach and on the numerical one over the last 30 years [1-7]. However, the performance requirements of material PET and of the final bottle regularly increase, that leads to an upgraded investigation on the thermal and mechanical response of the process.

The temperature distribution of the preform before the blowing stage and thermal effect have important influence during the SBM process of PET bottle [8-10]. They plays an important role in the final thickness distribution and induced properties [11]. Numerous works have been carried out to obtain accurately the temperature distribution of the heating stage and to improve the design of infrared-ovens [11-13]. In author's previous works [10,14], the thermal properties of PET have been firstly identified from injected sheet. The IR heating flux was calculated by using radiative laws adapted to the test geometry in a semi-analytic way. For the preform case, the radiation source is simulated by using same model for intensity of the incident radiation and the Beer Lambert's law. On the other hand, in order to simulate a more realistic ventilation effect under industrial condition, we consider a simplified modelling of forced convection. The IR flux and ventilation effects are implemented as thermal boundary conditions in COMSOL for a 3D computation of the thermal problem for the preform only. The numerical temperature distribution of the external surface of the preform is compared to the measured internal and external temperature of preforms from THERMOscan device [15] in order to validate the approach. This device is provided by Blow Moulding Technologies Ltd. (BMT) company in Belfast. It measures simultaneously the internal and external preform temperature profile.

<figure><img src="image_2417.png" /></figure>
The objective of this paper is to provide an optimization procedure in order to adjust the settings of the heating steps by comparing our simulation results to the temperature profile target.

The simulation from the simplified modelling takes only a few minutes and is the elementary brick of the optimization procedure. The study of the elementary contribution of each lamp on the temperature distribution in different regions of the preform is carried out. On the other hand, the effect of the accumulation of sub-steps on the temperature distribution of the preform is also studied. Based on the results of the elementary increase of temperature for each lamp and the target temperature, a system of linear equations related to the three different regions (bottom, middle and neck) can be written. The optimization procedure can be achieved by minimizing the residual of the three equations using different setting of lamps on each sub-step.

## Heating system presentation

Figure 1 presents the heating system including two series of ten infrared lamps. A preform transport chain including a rotation system for the preforms to turn around their axis when passing in front of the lamps, reflectors on the opposed side of the lamps to provide a radiative flux on the rear part of the preforms and a ventilation system composed of three fan turbines is used to cool the neck of the preform to make sure it does not deforms during the blowing process. It also helps to regulate the temperature in the thickness of the preform.

<figure><img src="image_2427.png" /><figcaption>Figure 1: The heating system presentation with architecture of lamps and preform. The figure is partially blurred for confidentiality reasons [14].</figcaption></figure>

One can control the power of each IR lamp to obtain a required temperature distribution in the height of the preform. Figure 2 shows the four steps and eight sub-steps of the heating stage:

(i) from 0 to 6s the preform is heated through the first set of IR lamps and ventilation;

(ii) from 6 to 19s, air stabilization step to reduce the difference between the outside and the inside temperature of the preform;

(iii) from 19 to 25s, the preform is heated again through the second set of lamps;

(iv) from 25 to 38s the preform is transferred in the mold.

The duration of the two heating steps (i) and (iii) is 6s each. Three sets of lamps are to be adjusted for each step, the preform passes 2s in front of each set. Consequently, in order to obtain the best temperature profile, the 8 lamps have to be turned on or off during the 6 sub-steps of 2s each. With the 2 air stabilization step, one highlights 8 sub-steps in the Fig. 2.

During the first step, the temperature of the outside of the preform is more important than the inside one. During the second step, the temperature of the external surface decreases while the internal temperature keeps rising by conduction from the outside. Therefore, the temperature becomes more homogeneous in the thickness during this step. After the IR heating of the third step, the difference of temperature through the thickness increases again. The last step is a second
The objective of this paper is to provide an optimization procedure in order to adjust the settings of the heating steps by comparing our simulation results to the temperature profile target.

The simulation from the simplified modelling takes only a few minutes and is the elementary brick of the optimization procedure. The study of the elementary contribution of each lamp on the temperature distribution in different regions of the preform is carried out. On the other hand, the effect of the accumulation of sub-steps on the temperature distribution of the preform is also studied. Based on the results of the elementary increase of temperature for each lamp and the target temperature, a system of linear equations related to the three different regions (bottom, middle and neck) can be written. The optimization procedure can be achieved by minimizing the residual of the three equations using different setting of lamps on each sub-step.

## Heating system presentation

Figure 1 presents the heating system including two series of ten infrared lamps. A preform transport chain including a rotation system for the preforms to turn around their axis when passing in front of the lamps, reflectors on the opposed side of the lamps to provide a radiative flux on the rear part of the preforms and a ventilation system composed of three fan turbines is used to cool the neck of the preform to make sure it does not deforms during the blowing process. It also helps to regulate the temperature in the thickness of the preform.

<figure><img src="image_2418.png" /><figcaption>Figure 1: The heating system presentation with architecture of lamps and preform. The figure is partially blurred for confidentiality reasons [14].</figcaption></figure>

One can control the power of each IR lamp to obtain a required temperature distribution in the height of the preform. Figure 2 shows the four steps and eight sub-steps of the heating stage:

(i) from 0 to 6s the preform is heated through the first set of IR lamps and ventilation;

(ii) from 6 to 19s, air stabilization step to reduce the difference between the outside and the inside temperature of the preform;

(iii) from 19 to 25s, the preform is heated again through the second set of lamps;

(iv) from 25 to 38s the preform is transferred in the mold.

The duration of the two heating steps (i) and (iii) is 6s each. Three sets of lamps are to be adjusted for each step, the preform passes 2s in front of each set. Consequently, in order to obtain the best temperature profile, the 8 lamps have to be turned on or off during the 6 sub-steps of 2s each. With the 2 air stabilization step, one highlights 8 sub-steps in the Fig. 2.

During the first step, the temperature of the outside of the preform is more important than the inside one. During the second step, the temperature of the external surface decreases while the internal temperature keeps rising by conduction from the outside. Therefore, the temperature becomes more homogeneous in the thickness during this step. After the IR heating of the third step, the difference of temperature through the thickness increases again. The last step is a second
homogenization period for the temperature to become uniform through the thickness while the preform is transported from the oven to the mold. One must notice that for this specific preform, only 8 lamps (from 1 to 8) are used. The target temperature profile is given in Fig.3. This is the average temperature between the external and the internal one which is provide by Sidel group. One can notice that the target temperature is only given from just under the neck to the bottom of the preform. To preserve the cap the temperature must be under 50°C and the air duct neck addresses this. The mid height of the preform needs to be less heated than the top or bottom regions: this is necessary to obtain the best thickness distribution after blowing.

<figure><img src="image_2428.png" /><figcaption>Figure 2: The path of the preform in the heating oven. 3 heating sub-steps followed by an homogenization step and then 3 more heating sub-steps and a final homogenization step before stretching and blowing [14]</figcaption></figure>

<figure><img src="image_2429.png" /><figcaption>Figure 3: Target temperature profile</figcaption></figure>

IR heating and ventilation

In previous work of authors [10,14], we developed a simplified method to calculate the IR heating flux. A quasi-analytical model is performed to quantify the intensity of the incident radiation. This model together with Beer Lambert's law, can simulate the radiation source term in the heating equation. The model has been used here to characterize the contribution of each of the 8 lamps as shown in Fig. 4. Table 1 gives the characteristics of the lamps used for the simulation. The IR radiation flux is calculated on cylindrical coordinates (r,θ,z) on the preform surface and interpolated by an exponential function where coefficient a to f are determined for each lamp contribution. Table 2 summarizes the 8 sets of identified values of the coefficients in Eq.1a.

$$q_{\text{flux}} = a \exp(b\theta^2 + c\theta + dz^2 + ez + f) \qquad (1a)$$
homogenization period for the temperature to become uniform through the thickness while the preform is transported from the oven to the mold. One must notice that for this specific preform, only 8 lamps (from 1 to 8) are used. The target temperature profile is given in Fig.3. This is the average temperature between the external and the internal one which is provide by Sidel group. One can notice that the target temperature is only given from just under the neck to the bottom of the preform. To preserve the cap the temperature must be under 50°C and the air duct neck addresses this. The mid height of the preform needs to be less heated than the top or bottom regions: this is necessary to obtain the best thickness distribution after blowing.

<figure><img src="image_2419.png" /><figcaption>Figure 2: The path of the preform in the heating oven. 3 heating sub-steps followed by an homogenization step and then 3 more heating sub-steps and a final homogenization step before stretching and blowing [14]</figcaption></figure>

<figure><img src="image_2420.png" /><figcaption>Figure 3: Target temperature profile</figcaption></figure>

IR heating and ventilation

In previous work of authors [10,14], we developed a simplified method to calculate the IR heating flux. A quasi-analytical model is performed to quantify the intensity of the incident radiation. This model together with Beer Lambert's law, can simulate the radiation source term in the heating equation. The model has been used here to characterize the contribution of each of the 8 lamps as shown in Fig. 4. Table 1 gives the characteristics of the lamps used for the simulation. The IR radiation flux is calculated on cylindrical coordinates (r,θ,z) on the preform surface and interpolated by an exponential function where coefficient a to f are determined for each lamp contribution. Table 2 summarizes the 8 sets of identified values of the coefficients in Eq.1a.

$$q_{\text{flux}} = a \exp(b\theta^2 + c\theta + dz^2 + ez + f) \qquad (1a)$$
Considering the geometry of preform, the intensity of internal radiation is considered as one-dimensional (through thickness) and quantified by Beer Lambert's law. For the preform case, one can adapt to the geometry as follows:

$$ \vec{q}_r = q_{\text{flux}} e^{-k_{\lambda}(R-r)} (-\vec{e}_r) \qquad (1b) $$

This can lead to the source term that writes:

$$ \begin{aligned} \mathrm{div}(\vec{q}_r) &= \frac{\partial u}{\partial r} + \frac{u}{r} = -k_{\lambda} q_{\text{flux}} e^{-k_{\lambda}(R-r)} + \frac{q_{\text{flux}} e^{-k_{\lambda}(R-r)}}{r} \\ \Rightarrow \mathrm{div}(\vec{q}_r) &= \left(\frac{1}{r} - k_{\lambda}\right) q_{\text{flux}} e^{-k_{\lambda}(R-r)} \end{aligned} \qquad (1c) $$

where r is the classic current radius, R is external radius and $k_{\lambda}$ is the spectral absorption coefficient for the PET material. The absorption is maximum for the wavelength between 5 and 15 µm and varies from $1.10^4 - 7.10^4$ m$^{-1}$. Here, we choose $3.10^4$ m$^{-1}$. There is no influence on the simulation since $k_{\lambda}$ is above 500m-1: the value of this parameter has no much influence on the result. The expression of Eq. 1c will be considered in the heat equation for the simulation in the following.

<table><caption>Table 1: Different heating characteristics</caption><thead><tr><td>T of filament (K)</td><td>Number of lamps and global height</td><td>Distance between lamps and preform</td><td>Length of lamps</td></tr></thead><tbody><tr><td>2700</td><td>8 lamps<br>172.5 mm</td><td>30 mm</td><td>306 mm</td></tr></tbody></table>

<figure><img src="image_2430.png" /></figure>

<figure><img src="image_2431.png" /></figure>
Considering the geometry of preform, the intensity of internal radiation is considered as one-dimensional (through thickness) and quantified by Beer Lambert's law. For the preform case, one can adapt to the geometry as follows:

$$ \vec{q}_r = q_{\text{flux}} e^{-k_{\lambda}(R-r)} (-\vec{e}_r) \qquad (1b) $$

This can lead to the source term that writes:

$$ \begin{gathered} \mathrm{div}(\vec{q}_r) = \frac{\partial u}{\partial r} + \frac{u}{r} = -k_{\lambda} q_{\text{flux}} e^{-k_{\lambda}(R-r)} + \frac{q_{\text{flux}} e^{-k_{\lambda}(R-r)}}{r} \qquad (1c) \\ \Rightarrow \mathrm{div}(\vec{q}_r) = \left(\frac{1}{r} - k_{\lambda}\right) q_{\text{flux}} e^{-k_{\lambda}(R-r)} \end{gathered} $$

where r is the classic current radius, R is external radius and $k_λ$ is the spectral absorption coefficient for the PET material. The absorption is maximum for the wavelength between 5 and 15 µm and varies from $1.10^4 - 7.10^4$ m⁻¹. Here, we choose $3.10^4$ m⁻¹. There is no influence on the simulation since $k_λ$ is above 500m-1: the value of this parameter has no much influence on the result. The expression of Eq. 1c will be considered in the heat equation for the simulation in the following.

<table><caption>Table 1: Different heating characteristics</caption><thead><tr><th>T of filament (K)</th><th>Number of lamps and global height</th><th>Distance between lamps and preform</th><th>Length of lamps</th></tr></thead><tbody><tr><td>2700</td><td>8 lamps<br>172.5 mm</td><td>30 mm</td><td>306 mm</td></tr></tbody></table>

<figure><img src="image_2421.png" /></figure>

<figure><img src="image_2422.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_2423.png" /></figure>

<figure><img src="image_2424.png" /></figure>
<figure><img src="image_2432.png" /><figcaption>Figure 4:: (a) IR radiation flux calculated preform from lamp 1; (b) interpolated function of z and θ for each lamp</figcaption></figure>

<table><caption>Table 2: Identified values of the coefficients in Eq. 1 for each lamp with θ expressed in rad and z in mm</caption><thead><tr><th></th><th>Lamp 1</th><th>Lamp 2</th><th>Lamp 3</th><th>Lamp 4</th><th>Lamp 5</th><th>Lamp 6</th><th>Lamp 7</th><th>Lamp 8</th></tr></thead><tbody><tr><th>a (W/m²)</th><td>1.487</td><td>10.286</td><td>12.808</td><td>11.805</td><td>12.553</td><td>12.086</td><td>2.154</td><td>1.693</td></tr><tr><th>b</th><td>-0.719</td><td>-0.702</td><td>-0.723</td><td>-0.74</td><td>-0.757</td><td>-0.771</td><td>-0.772</td><td>-0.772</td></tr><tr><th>c</th><td>-0.0138</td><td>-0.0025</td><td>-0.0058</td><td>-0.0082</td><td>-0.0103</td><td>-0.117</td><td>-0.0202</td><td>-0.0112</td></tr><tr><th>d(m⁻²)</th><td>-50.45</td><td>-64.09</td><td>-64.67</td><td>-66.9</td><td>-72.5</td><td>-68.46</td><td>-56.19</td><td>-60.19</td></tr><tr><th>e(m⁻¹)</th><td>19.28</td><td>8.68</td><td>5.364</td><td>1.864</td><td>-1.737</td><td>-5.265</td><td>-11.62</td><td>-15.62</td></tr><tr><th>f</th><td>7.735</td><td>6.534</td><td>6.534</td><td>6.732</td><td>6.674</td><td>6.609</td><td>7.89</td><td>7.99</td></tr></tbody></table>
<figure><img src="image_2425.png" /><figcaption>Figure 4:: (a) IR radiation flux calculated preform from lamp 1; (b) interpolated function of z and θ for each lamp</figcaption></figure>

<table><caption>Table 2: Identified values of the coefficients in Eq. 1 for each lamp with θ expressed in rad and z in mm</caption><thead><tr><th></th><th>Lamp 1</th><th>Lamp 2</th><th>Lamp 3</th><th>Lamp 4</th><th>Lamp 5</th><th>Lamp 6</th><th>Lamp 7</th><th>Lamp 8</th></tr></thead><tbody><tr><th>a (W/m²)</th><td>1.487</td><td>10.286</td><td>12.808</td><td>11.805</td><td>12.553</td><td>12.086</td><td>2.154</td><td>1.693</td></tr><tr><th>b</th><td>-0.719</td><td>-0.702</td><td>-0.723</td><td>-0.74</td><td>-0.757</td><td>-0.771</td><td>-0.772</td><td>-0.772</td></tr><tr><th>c</th><td>-0.0138</td><td>-0.0025</td><td>-0.0058</td><td>-0.0082</td><td>-0.0103</td><td>-0.117</td><td>-0.0202</td><td>-0.0112</td></tr><tr><th>d(m⁻²)</th><td>-50.45</td><td>-64.09</td><td>-64.67</td><td>-66.9</td><td>-72.5</td><td>-68.46</td><td>-56.19</td><td>-60.19</td></tr><tr><th>e(m⁻¹)</th><td>19.28</td><td>8.68</td><td>5.364</td><td>1.864</td><td>-1.737</td><td>-5.265</td><td>-11.62</td><td>-15.62</td></tr><tr><th>f</th><td>7.735</td><td>6.534</td><td>6.534</td><td>6.732</td><td>6.674</td><td>6.609</td><td>7.89</td><td>7.99</td></tr></tbody></table>
## Optimization procedure

For the convective exchange with the airflow around the preform, we considered a simple model by consuming the preform as a cylinder [14]. Based on the IR flux and the air convection coming from the ventilation as two turning boundary conditions, one can manage fast thermal simulation with Comsol. The 3D thermal simulation of PET preform using finite element method is carried out with the following characteristics:

- Thermal conductivity of PET: $k = 0.4$ (W/m.K)

- Density of PET: $\rho = 1.20$ (g/(cm³))

- Heat capacity: $C_p = \Delta C_p \arctan(\alpha(T - T_g)) + C_{p1}$ with $\Delta C_p = 220J/kg.K$, $\alpha = 0.1$, $T_g = 87°C$, $C_{p1} = 1400J/kg.K$

- $h$ is the exchange convection parameter that is related to the Nusselt number by: $Nu = \frac{hL_c}{k}$ with $k$ the thermal conductivity of the air and $L_c$ a characteristic length of the preform. The ventilation system leads to the air velocity that is near 8m/s when blowing on the neck, and only 1.3m/s in the cylindrical region of the preform. Consequently we can estimate the Reynolds number $Re = 2800$ for this case. The Nusselt number can be extrapolated from $Re$.

In order to get the target temperature (Fig. 3), at first, a simulation is managed with the 8 lamps turned on to test the order of magnitude of the increase of temperature. Four situations are considered: lamps on at sub-step 3 only, at sub-step 7 only (these two are chosen because they are followed by a homogenization step), at sub-step 3 and 7 together and finally at sub-step 3, 6 and 7 together. In all four cases, the initial temperature is 30°C on the entire preform and the final temperature profile is almost uniform. The mean increases of temperature are respectively: 32°C, 33°C, 60°C and 82°C. It is to be noticed that for the last case (3, 6 and 7 turned on) the final mean temperature is equal to 82+30=112°C that is too high for the central zone target. We can observe that the increase of temperature is more or less 30°C for each supplementary series of lamps. Considering this semi additivity of the lamp contribution, one is interested to study the contribution of each lamp.

Under the condition which sub-steps 3 and 7 are turned on all the 8 lamps, it remains 35°C near the bottom and almost 30°C near the neck of the preform to increase in order to obtain the target temperature. It remains only 4 lines and 8 lamps: 32 calculations. We define three indicators that are the mean temperature near the bottom of the preform, in the middle region and near the top. For each case, a simulation is carried out and Fig.5 summarizes the final temperature for the three regions. One can see that: (i) the sub-step has a very small influence on the final temperature ; (ii) lamps on position 6, 7, 8 have the highest contribution near the bottom, while lamps 4, 5 and 6 have contribution in the middle, because of the boundary condition, the contribution is not so clear for lamp 1, 2 and 3 ; (iii) elementary contribution of each lamp never exceed 4°C. Because of observation (i) we will consider, in the following, the mean increase of temperature illustrated by the red line in Fig.5. The numerical values of the elementary increase of temperature are given in Table 3.
## Optimization procedure

For the convective exchange with the airflow around the preform, we considered a simple model by consuming the preform as a cylinder [14]. Based on the IR flux and the air convection coming from the ventilation as two turning boundary conditions, one can manage fast thermal simulation with Comsol. The 3D thermal simulation of PET preform using finite element method is carried out with the following characteristics:

- Thermal conductivity of PET: $k = 0.4$ (W/m.K)

- Density of PET: $\rho = 1.20$ (g/(cm³))

- Heat capacity: $C_p = \Delta C_p \arctan(\alpha(T - T_g)) + C_{p1}$ with $\Delta C_p = 220J/kg.K$, $\alpha = 0.1$, $T_g = 87°C$, $C_{p1} = 1400J/kg.K$

- $h$ is the exchange convection parameter that is related to the Nusselt number by: $Nu = \frac{hL_c}{k}$ with $k$ the thermal conductivity of the air and $L_c$ a characteristic length of the preform. The ventilation system leads to the air velocity that is near 8m/s when blowing on the neck, and only 1.3m/s in the cylindrical region of the preform. Consequently we can estimate the Reynolds number $Re = 2800$ for this case. The Nusselt number can be extrapolated from $Re$.

In order to get the target temperature (Fig. 3), at first, a simulation is managed with the 8 lamps turned on to test the order of magnitude of the increase of temperature. Four situations are considered: lamps on at sub-step 3 only, at sub-step 7 only (these two are chosen because they are followed by a homogenization step), at sub-step 3 and 7 together and finally at sub-step 3, 6 and 7 together. In all four cases, the initial temperature is 30°C on the entire preform and the final temperature profile is almost uniform. The mean increases of temperature are respectively: 32°C, 33°C, 60°C and 82°C. It is to be noticed that for the last case (3, 6 and 7 turned on) the final mean temperature is equal to 82+30=112°C that is too high for the central zone target. We can observe that the increase of temperature is more or less 30°C for each supplementary series of lamps. Considering this semi additivity of the lamp contribution, one is interested to study the contribution of each lamp.

Under the condition which sub-steps 3 and 7 are turned on all the 8 lamps, it remains 35°C near the bottom and almost 30°C near the neck of the preform to increase in order to obtain the target temperature. It remains only 4 lines and 8 lamps: 32 calculations. We define three indicators that are the mean temperature near the bottom of the preform, in the middle region and near the top. For each case, a simulation is carried out and Fig.5 summarizes the final temperature for the three regions. One can see that: (i) the sub-step has a very small influence on the final temperature ; (ii) lamps on position 6, 7, 8 have the highest contribution near the bottom, while lamps 4, 5 and 6 have contribution in the middle, because of the boundary condition, the contribution is not so clear for lamp 1, 2 and 3 ; (iii) elementary contribution of each lamp never exceed 4°C. Because of observation (i) we will consider, in the following, the mean increase of temperature illustrated by the red line in Fig.5. The numerical values of the elementary increase of temperature are given in Table 3.
<table><caption>Table 3: Mean influence of each lamp on the different region of the preform</caption><thead><tr><th>Lamp position</th><th>8</th><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th></tr></thead><tbody><tr><td>Mean increase of T bottom (°C)</td><td>3.694</td><td>3.432</td><td>2.898</td><td>3.097</td><td>2.742</td><td>0.8</td><td>0.727</td><td>0.649</td></tr><tr><td>Mean increase of T middle (°C)</td><td>2.154</td><td>2.218</td><td>2.155</td><td>3.222</td><td>3.275</td><td>1.575</td><td>1.658</td><td>1.681</td></tr><tr><td>Mean increase of T neck (°C)</td><td>0.764</td><td>0.965</td><td>1.118</td><td>2.494</td><td>3.045</td><td>2.63</td><td>3.247</td><td>3.651</td></tr></tbody></table>

<figure><img src="image_2433.png" /><figcaption>Figure 5. Contribution of each lamp: increase of temperature in °C as a function of the lamp number and the sub-step when the lamp is turned on</figcaption></figure>

The last series of calculations focus on the effect of the accumulation of sub-steps. For each lamp, we simulate the heating of the preform when it is turned on during sub-step 1, then 1 and 2 then 1, 2, 5 and finally 1, 2, 5 and 6: totally 8X3 =24 calculations.

Figure 6 summarizes the results of these simulations. One can observe the quasi-linearity of the accumulation. For example, if lamp 8 is only turned on during sub-step 1, the increase of temperature is 3.6°C, when the same lamp is turned on in the four sub-steps 1, 2, 5 and 6, the increase is 14.5°C that is almost equal 4 times 3.6.

Thanks to the quasi-linearity of the accumulation, we propose the following method to set the entire lamps. First, we evaluate the difference between the preliminary calculation when the 8 lamps are turned on during sub-steps 3 and 7 and the target temperature in each zone. It appears that 32.2°C are needed in the bottom region, 29.1°C in the neck region and only 23.9°C in the middle one as shown in Table 4.
<table><caption>Table 3: Mean influence of each lamp on the different region of the preform</caption><thead><tr><th>Lamp position</th><th>8</th><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th></tr></thead><tbody><tr><td>Mean increase of T bottom (°C)</td><td>3.694</td><td>3.432</td><td>2.898</td><td>3.097</td><td>2.742</td><td>0.8</td><td>0.727</td><td>0.649</td></tr><tr><td>Mean increase of T middle (°C)</td><td>2.154</td><td>2.218</td><td>2.155</td><td>3.222</td><td>3.275</td><td>1.575</td><td>1.658</td><td>1.681</td></tr><tr><td>Mean increase of T neck (°C)</td><td>0.764</td><td>0.965</td><td>1.118</td><td>2.494</td><td>3.045</td><td>2.63</td><td>3.247</td><td>3.651</td></tr></tbody></table>

<figure><img src="image_2426.png" /><figcaption>Figure 5. Contribution of each lamp: increase of temperature in °C as a function of the lamp number and the sub-step when the lamp is turned on</figcaption></figure>

The last series of calculations focus on the effect of the accumulation of sub-steps. For each lamp, we simulate the heating of the preform when it is turned on during sub-step 1, then 1 and 2 then 1, 2, 5 and finally 1, 2, 5 and 6: totally 8X3 =24 calculations.

Figure 6 summarizes the results of these simulations. One can observe the quasi-linearity of the accumulation. For example, if lamp 8 is only turned on during sub-step 1, the increase of temperature is 3.6°C, when the same lamp is turned on in the four sub-steps 1, 2, 5 and 6, the increase is 14.5°C that is almost equal 4 times 3.6.

Thanks to the quasi-linearity of the accumulation, we propose the following method to set the entire lamps. First, we evaluate the difference between the preliminary calculation when the 8 lamps are turned on during sub-steps 3 and 7 and the target temperature in each zone. It appears that 32.2°C are needed in the bottom region, 29.1°C in the neck region and only 23.9°C in the middle one as shown in Table 4.
<figure><img src="image_2434.png" /><figcaption>Figure 6. Effect of the accumulation of sub-steps for each lamp on the final temperature</figcaption></figure>

<table><caption>Table 4. Increase of temperature needed in the three regions of the preform</caption><thead><tr><th></th><th>T mean Zone bottom (°C)</th><th>T mean Zone middle (°C)</th><th>T mean Zone neck (°C)</th></tr></thead><tbody><tr><td>Numerical simulation with 8 lamps at sub-steps 3 and 7</td><td>89.35</td><td>88.74</td><td>90.03</td></tr><tr><td>Target temperatures on the 3 regions</td><td>121.35</td><td>112.54</td><td>119.83</td></tr><tr><td>Increase of temperature needed</td><td>32.0</td><td>23.8</td><td>29.8</td></tr></tbody></table>

We consider the indicator $X_i$ where $i$ is the number of the lamp and that can equal to 1, 2, 3 or 4 when the lamp $i$ is on, respectively in one to four sub-steps. $X_i$ is equal to 0 when the lamp is off. It is then possible to take advantage of the quasi linearity to write the following system based on results of Tables 3 and 4:

$$ 
\begin{aligned}
3.694X_8 + 3.4318X_7 + 2.898X_6 + 3.097X_5 + 2.742X_4 + 0.8X_3 + 0.727X_2 + 0.649X_1 &= 32.0 \\
2.1541X_8 + 2.218X_7 + 2.1545X_6 + 3.222X_5 + 3.275X_4 + 1.575X_3 + 1.658X_2 + 1.681X_1 &= 23.8 \\
0.7635X_8 + 0.965X_7 + 1.118X_6 + 2.494X_5 + 3.045X_4 + 2.630X_3 + 3.247X_2 + 3.651X_1 &= 29.8
\end{aligned}
\quad (2) $$

Because each of the 8 indicators $X_i$ can take 5 integer values, this leads to 58 possibilities for the $X_i$. It is very fast to compute the 390 625 cases and to look at the residual difference defined by Eq.3 where the 3 functions are the left hand terms of Eq.2:

$$ \text{error} = |f_{\text{bottom}}(X_i) - 32.0| + |f_{\text{middle}}(X_i) - 23.8| + |f_{\text{neck}}(X_i) - 29.8| \quad (3) $$

Table 5 gives the optimized choice of each lamp for the entire 8 sub-steps.
<figure><img src="image_2427.png" /><figcaption>Figure 6. Effect of the accumulation of sub-steps for each lamp on the final temperature</figcaption></figure>

<table><caption>Table 4. Increase of temperature needed in the three regions of the preform</caption><thead><tr><th></th><th>T mean Zone bottom (°C)</th><th>T mean Zone middle (°C)</th><th>T mean Zone neck (°C)</th></tr></thead><tbody><tr><td>Numerical simulation with 8 lamps at sub-steps 3 and 7</td><td>89.35</td><td>88.74</td><td>90.03</td></tr><tr><td>Target temperatures on the 3 regions</td><td>121.35</td><td>112.54</td><td>119.83</td></tr><tr><td>Increase of temperature needed</td><td>32.0</td><td>23.8</td><td>29.8</td></tr></tbody></table>

We consider the indicator $X_i$ where $i$ is the number of the lamp and that can equal to 1, 2, 3 or 4 when the lamp $i$ is on, respectively in one to four sub-steps. $X_i$ is equal to 0 when the lamp is off. It is then possible to take advantage of the quasi linearity to write the following system based on results of Tables 3 and 4:

$$ 
\begin{aligned}
3.694X_8 + 3.4318X_7 + 2.898X_6 + 3.097X_5 + 2.742X_4 + 0.8X_3 + 0.727X_2 + 0.649X_1 &= 32.0 \\
2.1541X_8 + 2.218X_7 + 2.1545X_6 + 3.222X_5 + 3.275X_4 + 1.575X_3 + 1.658X_2 + 1.681X_1 &= 23.8 \\
0.7635X_8 + 0.965X_7 + 1.118X_6 + 2.494X_5 + 3.045X_4 + 2.630X_3 + 3.247X_2 + 3.651X_1 &= 29.8
\end{aligned}
\quad (2) $$

Because each of the 8 indicators $X_i$ can take 5 integer values, this leads to 58 possibilities for the $X_i$. It is very fast to compute the 390 625 cases and to look at the residual difference defined by Eq.3 where the 3 functions are the left hand terms of Eq.2:

$$ \text{error} = |f_{\text{bottom}}(X_i) - 32.0| + |f_{\text{middle}}(X_i) - 23.8| + |f_{\text{neck}}(X_i) - 29.8| \quad (3) $$

Table 5 gives the optimized choice of each lamp for the entire 8 sub-steps.
<table><caption>Table 5. The optimal lamps configuration for the target temperature profile.</caption><thead><tr><th></th><th>Lamp →</th><th>8</th><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th></tr></thead><tbody><tr><td>Sub-step 1</td><td>0-2s</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Sub-step 2</td><td>2-4s</td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td>X</td><td>X</td></tr><tr><td>Sub-step 3</td><td>4-6s</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Sub-step 4</td><td>6-19s</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="10">Stabilization</td></tr><tr><td>Sub-step 5</td><td>19-21s</td><td>X</td><td>X</td><td></td><td></td><td>X</td><td></td><td>X</td><td>X</td></tr><tr><td>Sub-step 6</td><td>21-23s</td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td>X</td><td>X</td></tr><tr><td>Sub-step 7</td><td>23-25s</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Sub-step 8</td><td>25-38s</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Figure 7 compares this prediction with the target. One can see that the prediction is very good for the bottom region where the temperature is 3°C lower than the target. In the middle region, the prediction is 2°C higher than the target and the neck region is the quite good except the curvature that cannot be simulated correctly because of the boundary condition in the finite element simulation. That leads to the mean temperature in this region about 1°C higher than the target. To provide a better simulation in this region, one should also simulate the screw of the preform. Furthermore, if one divides the preform in more regions, the simulations and the optimization could be more accurate. This would not lead to more finite element simulations, the only difference would more relations to satisfy in Eq.2 and this would not take a higher CPU time.

Figure 8 presents the temperature evolution over time for the three different zones. The red curves show the temperature evolution of the outside surface: the temperature increases in sub-steps 1, 2, 3 and 5, 6, 7, decreases in sub-steps 4 and 8. The blue curves show the evolution of temperature of the inside surface of the preform. This last increases during the whole heating stage because of the thermal conduction that homogenizes the temperature in the thickness during the sub-steps 4 and 8.

<figure><img src="image_2435.png" /><figcaption>Figure 7. Comparison of the best final temperature (red and blue) with the target profile</figcaption></figure>
<table><caption>Table 5. The optimal lamps configuration for the target temperature profile.</caption><thead><tr><th></th><th>Lamp →</th><th>8</th><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th></tr></thead><tbody><tr><td>Sub-step 1</td><td>0-2s</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Sub-step 2</td><td>2-4s</td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td>X</td><td>X</td></tr><tr><td>Sub-step 3</td><td>4-6s</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Sub-step 4</td><td>6-19s</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="10">Stabilization</td></tr><tr><td>Sub-step 5</td><td>19-21s</td><td>X</td><td>X</td><td></td><td></td><td>X</td><td></td><td>X</td><td>X</td></tr><tr><td>Sub-step 6</td><td>21-23s</td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td>X</td><td>X</td></tr><tr><td>Sub-step 7</td><td>23-25s</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Sub-step 8</td><td>25-38s</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Figure 7 compares this prediction with the target. One can see that the prediction is very good for the bottom region where the temperature is 3°C lower than the target. In the middle region, the prediction is 2°C higher than the target and the neck region is the quite good except the curvature that cannot be simulated correctly because of the boundary condition in the finite element simulation. That leads to the mean temperature in this region about 1°C higher than the target. To provide a better simulation in this region, one should also simulate the screw of the preform. Furthermore, if one divides the preform in more regions, the simulations and the optimization could be more accurate. This would not lead to more finite element simulations, the only difference would more relations to satisfy in Eq.2 and this would not take a higher CPU time.

Figure 8 presents the temperature evolution over time for the three different zones. The red curves show the temperature evolution of the outside surface: the temperature increases in sub-steps 1, 2, 3 and 5, 6, 7, decreases in sub-steps 4 and 8. The blue curves show the evolution of temperature of the inside surface of the preform. This last increases during the whole heating stage because of the thermal conduction that homogenizes the temperature in the thickness during the sub-steps 4 and 8.

<figure><img src="image_2428.png" /><figcaption>Figure 7. Comparison of the best final temperature (red and blue) with the target profile</figcaption></figure>
<figure><img src="image_2436.png" /><figcaption>Figure 8. Temperature evolution (a) in the neck zone; (b) in the middle zone; (c) in the bottom zone</figcaption></figure>

**Conclusion and discussion**

A simplified modelling of the heating stage during SBM process under the industrial condition has been proposed and managed in our previous work. This simulation takes only a few minutes and is the elementary brick of the optimization procedure. In this study, eight lamps are chosen to heat the preform. The heating system involves three heating sub-steps followed by an homogenization step and then three more heating sub-steps and a final homogenization step before stretching and blowing.

In the numerical simulation, the intensity of the incident radiation for each lamp is calculated by a quasi-analytical model. The study of the elementary contribution of each lamp on the temperature distribution in the bottom, middle and neck region of the preform is carried out. Thanks to the low thermal conductivity of the PET, effect of each lamp remains localized in the area of the height of the lamp. The mean influence of each lamp on the different region of the preform is obtained. On the other hand, the effect of the accumulation of sub-steps on the temperature distribution of the preform is almost linear.

Based on the results of the elementary increase of temperature for each lamp and the target temperature, three linear equations related to the three different regions (bottom, middle and neck) can be written. The optimization procedure can be achieved by minimizing the residual of the three equations using different integer values Xi related with the number of sub-steps where the lamps are turned on or off. This optimization tool allows to get quickly a first set of heating lamps, with a good representation of the target temperature.

**Acknowledgement**

The authors thank Sidel group that provided measurements during the blow moulding process.

**References**

[1] Luo Y.-M., Chevalier L. On induced properties and self heating during free blowing of PET preform. (2019) International Polymer Processing, 34 (3), p. 330 - 338.
https://doi.org/10.3139/217.3759

[2] G.H. Menary, C.G. Armstrong, R.J. Crawford, J.P. McEvoy. (2000). Modelling of poly(ethylene terephthalate) in injection stretch-blow moulding, Plastics, Rubber and Composites, 29:7, 360-370. https://doi.org/10.1179/146580100101541166

[3] N. Billon, M. Picard, E. Gorlier. (2014). Stretch blow moulding of PET; structure development and constitutive model. Int J Mater Form 7, 369-378. https://doi.org/10.1007/s12289-013-1131-1
<figure><img src="image_2429.png" /><figcaption>Figure 8. Temperature evolution (a) in the neck zone; (b) in the middle zone; (c) in the bottom zone</figcaption></figure>

## Conclusion and discussion

A simplified modelling of the heating stage during SBM process under the industrial condition has been proposed and managed in our previous work. This simulation takes only a few minutes and is the elementary brick of the optimization procedure. In this study, eight lamps are chosen to heat the preform. The heating system involves three heating sub-steps followed by an homogenization step and then three more heating sub-steps and a final homogenization step before stretching and blowing.

In the numerical simulation, the intensity of the incident radiation for each lamp is calculated by a quasi-analytical model. The study of the elementary contribution of each lamp on the temperature distribution in the bottom, middle and neck region of the preform is carried out. Thanks to the low thermal conductivity of the PET, effect of each lamp remains localized in the area of the height of the lamp. The mean influence of each lamp on the different region of the preform is obtained. On the other hand, the effect of the accumulation of sub-steps on the temperature distribution of the preform is almost linear.

Based on the results of the elementary increase of temperature for each lamp and the target temperature, three linear equations related to the three different regions (bottom, middle and neck) can be written. The optimization procedure can be achieved by minimizing the residual of the three equations using different integer values Xi related with the number of sub-steps where the lamps are turned on or off. This optimization tool allows to get quickly a first set of heating lamps, with a good representation of the target temperature.

## Acknowledgement

The authors thank Sidel group that provided measurements during the blow moulding process.

## References

[1] Luo Y.-M., Chevalier L. On induced properties and self heating during free blowing of PET preform. (2019) International Polymer Processing, 34 (3), p. 330 - 338. https://doi.org/10.3139/217.3759

[2] G.H. Menary, C.G. Armstrong, R.J. Crawford, J.P. McEvoy. (2000). Modelling of poly(ethylene terephthalate) in injection stretch-blow moulding, Plastics, Rubber and Composites, 29:7, 360-370. https://doi.org/10.1179/146580100101541166

[3] N. Billon, M. Picard, E. Gorlier. (2014). Stretch blow moulding of PET; structure development and constitutive model. Int J Mater Form 7, 369-378. https://doi.org/10.1007/s12289-013-1131-1
[4] F.M. Schmidt, J.F. Agassant, M. Bellet. (1998). Experimental study and numerical simulation of the injection stretch/blow molding process. Polym Eng Sci, 38: 1399-1412.
https://doi.org/10.1002/pen.10310

[5] Luo Y.-M., Chevalier L., Monteiro E., Utheza F. Numerical simulation of self heating during stretch blow moulding of PET: viscohyperelastic modelling versus experimental results (2021) International Journal of Material Forming, 14 (4), p. 703 - 714, 10.1007/s12289-020-01565-w

[6] Timur, M. The Effect of Temperature, Pressure and Stretch Bar on Product Quality in Production of 0.5 L Pet Bottle. Int. J. Precis. Eng. Manuf. (2023). https://doi.org/10.1007/s12541-023-00899-0

[7] H. Groot, C.G. Giannopapa, R.M.M. Mattheij. A Computer Simulation Model for the Stretch Blow Moulding Process of Polymer Containers. Proceedings of the ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASME 2010 Pressure Vessels and Piping Conference: Volume 5. Bellevue, Washington, USA. July 18-22, 2010. pp. 567-576. ASME. https://doi.org/10.1115/PVP2010-25710

[8] Y.M. Luo, L. Chevalier, F. Utheza. X. Nicolas. Simplified Modelling of the Infrared Heating Involving the Air Convection Effect before the Injection Stretch Blowing Moulding of PET Preform. Material Forming ESAFORM 2014, May 2014, Espoo, Finland. Jari Larkiola, 611 - 612, pp.844-851, 2014. DOI: 10.4028/www.scientific.net/KEM.611-612.844

[9] Venkateswaran G., Cameron M.R., Jabarin S.A. Effects of temperature profiles through preform thickness on the properties of reheat-blown PET containers. Adv. Polym. Technol., 17 (3) (1998), pp. 237-249, 10.1002/(SICI)1098-2329(199823)17:3

[10] Y. M. Luo, L. Chevalier, F. Utheza, X. Nicolas. Simplified modeling of the convection and radiation heat transfers during the infrared heating of PET sheets and preforms Nomenclature. International Polymer Processing, 2015, 30 (5), pp.554-565. https://doi.org/10.3139/217.3092

[11] Z.q. Yang, W. Naeem, G. Menary, J. Deng, K. Li. (2014). Advanced Modelling and Optimization of Infared Oven in Injection Stretch Blow-moulding for Energy Saving, IFAC Proceedings Volumes, Volume 47, Issue 3, Pages 766-771, ISSN 1474-6670, https://doi.org/10.3182/20140824-6-ZA-1003.01191

[12] M. Bordival, F. M. Schmidt, Y. Le Maoult and V. Velay. (2009). Optimisation of preform temperature distribution for the stretch-blow moulding of PET bottles: Infrared heating and blowing modelling, Polymer Engineering and Science, vol. 49, no. 4, pp. 783-793.
DOI:10.1007/s12289-008-0232-8

[13] Z.q. Yang, W. Naeem, G. Menary, J. Deng, K. Li. (2014). Advanced Modelling and Optimization of Infared Oven in Injection Stretch Blow-moulding for Energy Saving, IFAC Proceedings Volumes, Volume 47, Issue 3, Pages 766-771, ISSN 1474-6670, https://doi.org/10.3182/20140824-6-ZA-1003.01191

[14] Nguyen, T.T., Luo, YM., Chevalier, L. et al. Numerical Simulation of Infrared Heating and Ventilation before Stretch Blow Molding of PET Bottles. Int J Mater Form 16, 37 (2023).
https://doi.org/10.1007/s12289-023-01763-2

[15] Nixon J, Menary G. H., Yan S. (2017). Assessing the Stretch-blow Moulding FE Simulation of PET over a Large Process Window. AIP Conference Proceedings 1896, 060008; https://doi.org/10.1063/1.5008071
[4] F.M. Schmidt, J.F. Agassant, M. Bellet. (1998). Experimental study and numerical simulation of the injection stretch/blow molding process. Polym Eng Sci, 38: 1399-1412.
https://doi.org/10.1002/pen.10310

[5] Luo Y.-M., Chevalier L., Monteiro E., Utheza F. Numerical simulation of self heating during stretch blow moulding of PET: viscohyperelastic modelling versus experimental results (2021) International Journal of Material Forming, 14 (4), p. 703 - 714, 10.1007/s12289-020-01565-w

[6] Timur, M. The Effect of Temperature, Pressure and Stretch Bar on Product Quality in Production of 0.5 L Pet Bottle. Int. J. Precis. Eng. Manuf. (2023). https://doi.org/10.1007/s12541-023-00899-0

[7] H. Groot, C.G. Giannopapa, R.M.M. Mattheij. A Computer Simulation Model for the Stretch Blow Moulding Process of Polymer Containers. Proceedings of the ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASME 2010 Pressure Vessels and Piping Conference: Volume 5. Bellevue, Washington, USA. July 18-22, 2010. pp. 567-576. ASME. https://doi.org/10.1115/PVP2010-25710

[8] Y.M. Luo, L. Chevalier, F. Utheza. X. Nicolas. Simplified Modelling of the Infrared Heating Involving the Air Convection Effect before the Injection Stretch Blowing Moulding of PET Preform. Material Forming ESAFORM 2014, May 2014, Espoo, Finland. Jari Larkiola, 611 - 612, pp.844-851, 2014. DOI: 10.4028/www.scientific.net/KEM.611-612.844

[9] Venkateswaran G., Cameron M.R., Jabarin S.A. Effects of temperature profiles through preform thickness on the properties of reheat-blown PET containers. Adv. Polym. Technol., 17 (3) (1998), pp. 237-249, 10.1002/(SICI)1098-2329(199823)17:3

[10] Y. M. Luo, L. Chevalier, F. Utheza, X. Nicolas. Simplified modeling of the convection and radiation heat transfers during the infrared heating of PET sheets and preforms Nomenclature. International Polymer Processing, 2015, 30 (5), pp.554-565. https://doi.org/10.3139/217.3092

[11] Z.q. Yang, W. Naeem, G. Menary, J. Deng, K. Li. (2014). Advanced Modelling and Optimization of Infared Oven in Injection Stretch Blow-moulding for Energy Saving, IFAC Proceedings Volumes, Volume 47, Issue 3, Pages 766-771, ISSN 1474-6670, https://doi.org/10.3182/20140824-6-ZA-1003.01191

[12] M. Bordival, F. M. Schmidt, Y. Le Maoult and V. Velay. (2009). Optimisation of preform temperature distribution for the stretch-blow moulding of PET bottles: Infrared heating and blowing modelling, Polymer Engineering and Science, vol. 49, no. 4, pp. 783-793.
DOI:10.1007/s12289-008-0232-8

[13] Z.q. Yang, W. Naeem, G. Menary, J. Deng, K. Li. (2014). Advanced Modelling and Optimization of Infared Oven in Injection Stretch Blow-moulding for Energy Saving, IFAC Proceedings Volumes, Volume 47, Issue 3, Pages 766-771, ISSN 1474-6670, https://doi.org/10.3182/20140824-6-ZA-1003.01191

[14] Nguyen, T.T., Luo, YM., Chevalier, L. et al. Numerical Simulation of Infrared Heating and Ventilation before Stretch Blow Molding of PET Bottles. Int J Mater Form 16, 37 (2023).
https://doi.org/10.1007/s12289-023-01763-2

[15] Nixon J, Menary G. H., Yan S. (2017). Assessing the Stretch-blow Moulding FE Simulation of PET over a Large Process Window. AIP Conference Proceedings 1896, 060008; https://doi.org/10.1063/1.5008071
# Experimental and numerical investigation of the light scattering of the 3D printed parts

NGUYEN Thi-Ha-Xuyen¹,ᵃ, AKUÉ ASSÉKO André Chateau¹,ᵇ, LE Anh-Duc¹ and COSSON Benoît¹,ᶜ

¹IMT Nord Europe, Institut Mines Télécom, University of Lille, Centre for Materials and Processes, Lille, F-59653 Villeneuve d'Ascq, France

ᵃthi-ha-xuyen.nguyen@imt-nord-europe.fr, ᵇandre.chateau.akue@imt-nord-europe.fr, ᶜbenoit.cosson@imt-nord-europe.fr

**Keywords:** Transmission Laser Welding (TLW), 3D-Printed Thermoplastic Parts, Light Scattering, X-Ray Tomography Images, Ray-Tracing Simulation

**Abstract.** Anisoprint is a forefront technology in the realm of 3D printing and has ushered in a transformative era in composite material fabrication. The synergistic fusion of Anisoprint's 3D printing technology with laser transmission welding has enabled the creation of complex structures featuring carbon fiber reinforcements along all three spatial axes. This innovative amalgamation empowers the production of components distinguished by their unparalleled strength and precision. In the pursuit of this objective, the integration of transparent thermoplastic windows within 3D-printed components has been employed as conduits for laser beams during the welding process. Nevertheless, the interaction between laser beams and these transparent windows introduces a phenomenon characterized by beam diffusion, primarily attributed to the intrinsic porosity inherent in the 3D printing process. Within the scope of this study, an in-depth examination of laser beam diffusion within 3D-printed carbon fiber components is undertaken. This endeavor encompasses the application of micro-tomography to meticulously construct a comprehensive mesh representing the microstructural intricacies of the transparent section. Leveraging this mesh, ray tracing simulations are conducted to elucidate laser beam behavior. Subsequently, a comparative analysis is conducted between these numerical outcomes and experimental observations, involving the scrutiny of laser beam photographs as they traverse the printed component. This research aspires to enhance our comprehension of the intricate dynamics governing laser beam interactions within Anisoprinted structures. Ultimately, this will contribute to the refinement of laser welding processes and foster the advancement of more efficient and dependable manufacturing methodologies for composite materials.

## Introduction

Three-dimensional (3D) printing is one of the potential and major manufacturing processes for fabricating 3D advanced composite parts in more flexible ways than those using molds, thus meeting the expectations of the industry of the future [4,19,20]. Using this advanced fabrication additive, various types of materials are used layer by layer according to given digital CAD data to fabricate complex and personal geometry pieces in a bottom-up manner [5]. 3D printing of continuous carbon fiber reinforced composites (CCFRCs) has demonstrated impressive capabilities in delivering superior mechanical properties and creating lightweight structures [13,15]. In the family of 3D-printed technologies, you can find the technology of Material Extrusion (MEX - Fig. 1). However, these processes for continuous fiber composite parts are also limited by the orientation of the fibers remaining in the printing plane, thus allowing high mechanical performance only in this fiber direction. One way to address this technological challenge is to utilize a hybrid approach that combines method 3D printing and Transmission Laser Welding (TLW). The hybrid method aims to create structural parts with high mechanical

<figure><img src="image_2437.png" /></figure>
# Experimental and numerical investigation of the light scattering of the 3D printed parts

NGUYEN Thi-Ha-Xuyen¹,ᵃ, AKUÉ ASSÉKO André Chateau¹,ᵇ, LE Anh-Duc¹ and COSSON Benoît¹,ᶜ

¹IMT Nord Europe, Institut Mines Télécom, University of Lille, Centre for Materials and Processes, Lille, F-59653 Villeneuve d'Ascq, France

ᵃthi-ha-xuyen.nguyen@imt-nord-europe.fr, ᵇandre.chateau.akue@imt-nord-europe.fr, ᶜbenoit.cosson@imt-nord-europe.fr

**Keywords:** Transmission Laser Welding (TLW), 3D-Printed Thermoplastic Parts, Light Scattering, X-Ray Tomography Images, Ray-Tracing Simulation

**Abstract.** Anisoprint is a forefront technology in the realm of 3D printing and has ushered in a transformative era in composite material fabrication. The synergistic fusion of Anisoprint's 3D printing technology with laser transmission welding has enabled the creation of complex structures featuring carbon fiber reinforcements along all three spatial axes. This innovative amalgamation empowers the production of components distinguished by their unparalleled strength and precision. In the pursuit of this objective, the integration of transparent thermoplastic windows within 3D-printed components has been employed as conduits for laser beams during the welding process. Nevertheless, the interaction between laser beams and these transparent windows introduces a phenomenon characterized by beam diffusion, primarily attributed to the intrinsic porosity inherent in the 3D printing process. Within the scope of this study, an in-depth examination of laser beam diffusion within 3D-printed carbon fiber components is undertaken. This endeavor encompasses the application of micro-tomography to meticulously construct a comprehensive mesh representing the microstructural intricacies of the transparent section. Leveraging this mesh, ray tracing simulations are conducted to elucidate laser beam behavior. Subsequently, a comparative analysis is conducted between these numerical outcomes and experimental observations, involving the scrutiny of laser beam photographs as they traverse the printed component. This research aspires to enhance our comprehension of the intricate dynamics governing laser beam interactions within Anisoprinted structures. Ultimately, this will contribute to the refinement of laser welding processes and foster the advancement of more efficient and dependable manufacturing methodologies for composite materials.

**Introduction**

Three-dimensional (3D) printing is one of the potential and major manufacturing processes for fabricating 3D advanced composite parts in more flexible ways than those using molds, thus meeting the expectations of the industry of the future [4,19,20]. Using this advanced fabrication additive, various types of materials are used layer by layer according to given digital CAD data to fabricate complex and personal geometry pieces in a bottom-up manner [5]. 3D printing of continuous carbon fiber reinforced composites (CCFRCs) has demonstrated impressive capabilities in delivering superior mechanical properties and creating lightweight structures [13,15]. In the family of 3D-printed technologies, you can find the technology of Material Extrusion (MEX - Fig. 1). However, these processes for continuous fiber composite parts are also limited by the orientation of the fibers remaining in the printing plane, thus allowing high mechanical performance only in this fiber direction. One way to address this technological challenge is to utilize a hybrid approach that combines method 3D printing and Transmission Laser Welding (TLW). The hybrid method aims to create structural parts with high mechanical

<figure><img src="image_2430.png" /></figure>
properties, which is impossible with 3D printing of thermoplastics, even when filled with short staple fibers.

<figure><img src="image_2438.png" /><figcaption>Fig. 1 ANISOPRINT 3D Printing solution for continuous fiber composites</figcaption></figure>

In TLW, two components are used: one is transparent (semi-transparent) at the laser wavelength and the other is an absorbent part at the same wavelength. Before the welding process starts, the components are aligned together. Then, the laser beam energy passes through the transparent (semi-transparent) material and gets absorbed into the interface of both materials (Fig. 2). This heats up the interface of the substrate and triggers the melting and fusion of the materials, resulting in a bond creation between the two parts when the temperature is greater than the melting point in this area. The well-established bonding strength between welded parts depends on both an optimal temperature distribution within the heat-affected zone and a controlled welding time.

<figure><img src="image_2439.png" /><figcaption>Fig. 2 Transmission Laser Welding (TLW)</figcaption></figure>

Achieving the success of TLW of two components requires careful control of the laser beam profile within the materials and the welding interface. Accurate estimation of the laser beam profile is essential to determine the heat source reaching the interface and to predict the temperature field during the TLW. This temperature is affected by multiple factors, including the optical and thermal properties of the components being welded using the TLW process [2,3,12]. As the laser beam propagates through highly heterogeneous and anisotropic materials, it introduces a new challenge. Due to the 3D-printed component that contains a substantial amount of voids, new phenomena are involved in parallel: uneven transmission and light scattering. This occurrence results in laser beam scattering, which decreases the amount of transmitted energy reaching the weld interface [10]. As a consequence, it directly impacted the quality of welds because of an energy reduction.

It has been demonstrated that the transmissivity and scattering behavior of thermoplastic 3D-printed components are a function of 3D printing process parameters [11]. In this study, we aim to comprehensively investigate the impact of light scattering on the 3D-printed parts. We propose to utilize X-ray micro-tomography to meticulously construct a comprehensive mesh representing the 3D-printed microstructures (Fig. 3) and a ray-tracing model to simulate the optical paths of the laser beam through the 3D-printed part[16,18]. Using this model, it is possible to predict the
properties, which is impossible with 3D printing of thermoplastics, even when filled with short staple fibers.

<figure><img src="image_2431.png" /><figcaption>Fig. 1 ANISOPRINT 3D Printing solution for continuous fiber composites</figcaption></figure>

In TLW, two components are used: one is transparent (semi-transparent) at the laser wavelength and the other is an absorbent part at the same wavelength. Before the welding process starts, the components are aligned together. Then, the laser beam energy passes through the transparent (semi-transparent) material and gets absorbed into the interface of both materials (Fig. 2). This heats up the interface of the substrate and triggers the melting and fusion of the materials, resulting in a bond creation between the two parts when the temperature is greater than the melting point in this area. The well-established bonding strength between welded parts depends on both an optimal temperature distribution within the heat-affected zone and a controlled welding time.

<figure><img src="image_2432.png" /><figcaption>Fig. 2 Transmission Laser Welding (TLW)</figcaption></figure>

Achieving the success of TLW of two components requires careful control of the laser beam profile within the materials and the welding interface. Accurate estimation of the laser beam profile is essential to determine the heat source reaching the interface and to predict the temperature field during the TLW. This temperature is affected by multiple factors, including the optical and thermal properties of the components being welded using the TLW process [2,3,12]. As the laser beam propagates through highly heterogeneous and anisotropic materials, it introduces a new challenge. Due to the 3D-printed component that contains a substantial amount of voids, new phenomena are involved in parallel: uneven transmission and light scattering. This occurrence results in laser beam scattering, which decreases the amount of transmitted energy reaching the weld interface [10]. As a consequence, it directly impacted the quality of welds because of an energy reduction.

It has been demonstrated that the transmissivity and scattering behavior of thermoplastic 3D-printed components are a function of 3D printing process parameters [11]. In this study, we aim to comprehensively investigate the impact of light scattering on the 3D-printed parts. We propose to utilize X-ray micro-tomography to meticulously construct a comprehensive mesh representing the 3D-printed microstructures (Fig. 3) and a ray-tracing model to simulate the optical paths of the laser beam through the 3D-printed part[16,18]. Using this model, it is possible to predict the
changes in the laser heat source distribution at the welded interface, which directly elucidates the impact of the light-scattering effect within the microstructure of the parts.

<figure><img src="image_2440.png" /><figcaption>Fig. 3 Schema of the process using the X-ray tomography</figcaption></figure>

Different engineering aspects have been presented with X-ray CT to provide the three-dimensional evaluation of defects inside of the structure in one process [14]. In the actual context, several examples are shown and described utilizing micro CT in the evaluation of 3D-printed components using images of the cross-section of composite materials with micron-sized resolution. Yu et al. [21] performed high-resolution X-ray microscopy and microstructural analysis to study the structure and mechanical properties of 3D-printed fiber-reinforced PLA composites. Chen et al. [6] presented the characterization of air-void systems in 3D-printed cementitious materials using image scanning and X-ray computed tomography. These investigations have researched the influence of the microstructure of the 3D-printed components on the mechanical properties of the materials.

As a first step, the microstructure of the samples printed under different printing parameters will be examined by micro CT. According to the microstructure analysis, the numerical RVEs of the samples will be generated. Subsequently, ray-tracing simulations will be performed to model the diffusion patterns of light scattering through the samples. Then, the transmitted laser beam distributions will be generated at the weld interface and compared for different samples. Finally, a 3D transient thermal model of the TLW process will be conducted using the FEM software COMSOL Multiphysics®. The thermal model will be able to confirm the influence of the scattering effect on the temperature field during the TLW process and the quality of the weld could be predicted.

# Experimental section

## Materials and processing

The specimens used for the experimental X-ray micro-tomography in this study were produced using an extrusion-based fused filament fabrication process, as illustrated in Fig. 1, which depicts the MEX process. The filaments were composed of Polyethylene terephthalate Glycol (PETG) and carbon fiber-reinforced polymer composites. Polymaker™ supplied the materials in the form of 1.75mm diameter filaments. According to the supplier, the material is characterized by a density
changes in the laser heat source distribution at the welded interface, which directly elucidates the impact of the light-scattering effect within the microstructure of the parts.

<figure><img src="image_2433.png" /><figcaption>Fig. 3 Schema of the process using the X-ray tomography</figcaption></figure>

Different engineering aspects have been presented with X-ray CT to provide the three-dimensional evaluation of defects inside of the structure in one process [14]. In the actual context, several examples are shown and described utilizing micro CT in the evaluation of 3D-printed components using images of the cross-section of composite materials with micron-sized resolution. Yu et al. [21] performed high-resolution X-ray microscopy and microstructural analysis to study the structure and mechanical properties of 3D-printed fiber-reinforced PLA composites. Chen et al. [6] presented the characterization of air-void systems in 3D-printed cementitious materials using image scanning and X-ray computed tomography. These investigations have researched the influence of the microstructure of the 3D-printed components on the mechanical properties of the materials.

As a first step, the microstructure of the samples printed under different printing parameters will be examined by micro CT. According to the microstructure analysis, the numerical RVEs of the samples will be generated. Subsequently, ray-tracing simulations will be performed to model the diffusion patterns of light scattering through the samples. Then, the transmitted laser beam distributions will be generated at the weld interface and compared for different samples. Finally, a 3D transient thermal model of the TLW process will be conducted using the FEM software COMSOL Multiphysics®. The thermal model will be able to confirm the influence of the scattering effect on the temperature field during the TLW process and the quality of the weld could be predicted.

# Experimental section

## Materials and processing

The specimens used for the experimental X-ray micro-tomography in this study were produced using an extrusion-based fused filament fabrication process, as illustrated in Fig. 1, which depicts the MEX process. The filaments were composed of Polyethylene terephthalate Glycol (PETG) and carbon fiber-reinforced polymer composites. Polymaker™ supplied the materials in the form of 1.75mm diameter filaments. According to the supplier, the material is characterized by a density
of 1.25g/cm³ and a glass transition temperature of 81°C. The recommended nozzle temperature ranges from 230°C to 260°C. The 3D CAD models that were employed to manufacture the welding specimens have a rectangular bar shape with dimensions of 60 × 40 × 4mm³. The nozzle temperature was set to Tn = 240°C, and the bed temperature was set to Tb = 75°C. Except for the parameters listed in Table 1, all other printing parameters were kept constant, with the layer thickness varied between 0.2mm and 0.4mm. For the sample used for tomography, we cut the samples to size 60 × 4 × 4mm³.

<table><caption>Table 1 MEX processing parameters used in this study</caption><thead><tr><td>Processing parameters</td><td>Values</td></tr></thead><tbody><tr><td>Nozzle temperature [°C]</td><td>240</td></tr><tr><td>Nozzle diameter [mm]</td><td>0.4</td></tr><tr><td>Bed temperature °C</td><td>75</td></tr><tr><td>Print speed [mm/s]</td><td>30</td></tr><tr><td>Layer thickness [mm]</td><td>0.2 – 0.4</td></tr><tr><td>Infill pattern</td><td>Line</td></tr><tr><td>Infill percentage [%]</td><td>100</td></tr><tr><td>Extrusion multiplier</td><td>1</td></tr></tbody></table>

## Sample microstructures investigation

The microstructural rendering of the droplet-based 3D printing process is evaluated using a 3D imaging technique based on X-ray micro-tomography. Image acquisition is performed using the X ISIS4D (In Situ Innovative Set-ups) equipment, with the following acquisition parameters: a 230 kV X-ray source, a variable detector, that can produce a voxel size ranging from 0.4 to 120 µm. For this study, the voxel size is 5 µm for all scans. The resolution is obtained with the high power source. We obtained 2D images corresponding to each cross-section, as illustrated in Fig. 3.

<table><caption>Table 2 Step by step to construct 3D mesh</caption><tr><td>1.</td><td>Preprocessing – Separation of the individual voxelized porosity of each sample using the software GIMP</td></tr><tr><td>2.</td><td>Using a MATLAB algorithm to clearly generate a binary image that separates two zones representing porosity and PETG (Fig. 4)</td></tr><tr><td>3.</td><td>Constructing a 3D mesh using the COMSOL Multiphysics software</td></tr><tr><td>3.1</td><td>Importing the binary image</td></tr><tr><td>3.2</td><td>Running a curve to reconstruct the contour of each porosity</td></tr><tr><td>3.3</td><td>Using the function ‘extrude’ to construct a 3D contour of porosity</td></tr><tr><td>3.4</td><td>Constructing a cube around all porosity to create a 3D model (Fig. 5). Thanks to this 3D model, it is easy to generate a 3D mesh</td></tr><tr><td>4.</td><td>Exporting the mesh.mphtxt file to import this mesh into the ray-tracing simulation to predict the laser distribution at the interface</td></tr></table>

To describe the microstructure of the 3D printed part, we used a cross section of the tomography results. Idealized astroid-shaped and half astroid-shaped voids are considered to represent four typical sample types (I, II, and III), each with variable layer thicknesses of e = 0.2mm, e = 0.3mm, and e = 0.4mm, respectively. The form of the voids is computed based on the measured porosity from experimental tomography images as shown in Table 2 (see Fig. 4). The data used in this study are listed in Table 3.
of 1.25g/cm³ and a glass transition temperature of 81°C. The recommended nozzle temperature ranges from 230°C to 260°C. The 3D CAD models that were employed to manufacture the welding specimens have a rectangular bar shape with dimensions of 60 × 40 × 4mm³. The nozzle temperature was set to Tn = 240°C, and the bed temperature was set to Tb = 75°C. Except for the parameters listed in Table 1, all other printing parameters were kept constant, with the layer thickness varied between 0.2mm and 0.4mm. For the sample used for tomography, we cut the samples to size 60 × 4 × 4mm³.

<table><caption>Table 1 MEX processing parameters used in this study</caption><thead><tr><td>Processing parameters</td><td>Values</td></tr></thead><tbody><tr><td>Nozzle temperature [°C]</td><td>240</td></tr><tr><td>Nozzle diameter [mm]</td><td>0.4</td></tr><tr><td>Bed temperature °C</td><td>75</td></tr><tr><td>Print speed [mm/s]</td><td>30</td></tr><tr><td>Layer thickness [mm]</td><td>0.2 – 0.4</td></tr><tr><td>Infill pattern</td><td>Line</td></tr><tr><td>Infill percentage [%]</td><td>100</td></tr><tr><td>Extrusion multiplier</td><td>1</td></tr></tbody></table>

## Sample microstructures investigation

The microstructural rendering of the droplet-based 3D printing process is evaluated using a 3D imaging technique based on X-ray micro-tomography. Image acquisition is performed using the X ISIS4D (In Situ Innovative Set-ups) equipment, with the following acquisition parameters: a 230 kV X-ray source, a variable detector, that can produce a voxel size ranging from 0.4 to 120 µm. For this study, the voxel size is 5 µm for all scans. The resolution is obtained with the high power source. We obtained 2D images corresponding to each cross-section, as illustrated in Fig. 3.

<table><caption>Table 2 Step by step to construct 3D mesh</caption><tr><td>1.</td><td>Preprocessing – Separation of the individual voxelized porosity of each sample using the software GIMP</td></tr><tr><td>2.</td><td>Using a MATLAB algorithm to clearly generate a binary image that separates two zones representing porosity and PETG (Fig. 4)</td></tr><tr><td>3.</td><td>Constructing a 3D mesh using the COMSOL Multiphysics software</td></tr><tr><td>3.1</td><td>Importing the binary image</td></tr><tr><td>3.2</td><td>Running a curve to reconstruct the contour of each porosity</td></tr><tr><td>3.3</td><td>Using the function ‘extrude’ to construct a 3D contour of porosity</td></tr><tr><td>3.4</td><td>Constructing a cube around all porosity to create a 3D model (Fig. 5). Thanks to this 3D model, it is easy to generate a 3D mesh</td></tr><tr><td>4.</td><td>Exporting the mesh.mphtxt file to import this mesh into the ray-tracing simulation to predict the laser distribution at the interface</td></tr></table>

To describe the microstructure of the 3D printed part, we used a cross section of the tomography results. Idealized astroid-shaped and half astroid-shaped voids are considered to represent four typical sample types (I, II, and III), each with variable layer thicknesses of e = 0.2mm, e = 0.3mm, and e = 0.4mm, respectively. The form of the voids is computed based on the measured porosity from experimental tomography images as shown in Table 2 (see Fig. 4). The data used in this study are listed in Table 3.
<table><caption>Table 3 Size of the voids</caption><thead><tr><th>Samples</th><th>Layer thickness [mm]</th><th>Composition of the sample</th><th>Porosity (%)</th><th>Volume fraction of the filament PETG (V<sub>f</sub> [%])</th></tr></thead><tbody><tr><td>Type I</td><td>0.2</td><td>PETG, Air</td><td>1.88</td><td>98.12</td></tr><tr><td>Type II</td><td>0.3</td><td>PETG, Air</td><td>7.01</td><td>92.99</td></tr><tr><td>Type III</td><td>0.4</td><td>PETG, Air</td><td>5.39</td><td>94.61</td></tr></tbody></table>

<figure><img src="image_2441.png" /><figcaption>Fig. 4 Void morphology of the 3D printed parts and image analysis procedure to find the void fraction. (a, c, and e) Unprocessed tomography images (b, d, and f) Post-processed images</figcaption></figure>

<figure><img src="image_2442.png" /><figcaption>Fig. 5 Generation of the microstructure of the 3D printed parts (I 1x1x1 mm³; II 1.5x1.5x1.5 mm³; III 1.2x1.2x1.2 mm³)</figcaption></figure>

## Numerical section

### Ray-tracing simulation

According to the description of the interaction between the laser beam and the 3D-printed part, the ray-tracing method is chosen. This method allows us to follow the propagation of the laser beam into a complex structure. In previous studies, the ray-tracing method has been successfully employed to simulate the transmission laser welding (TLW) through the thermoplastic glass fiber composite (polymer + continuous glass fibers) [7,8]. In this method, the laser beam is discretized into a set of rays, and then the path of each ray is followed in the model geometry. Therefore, the ray-tracing method is able to take-into-account the different optical effects of light through the materials, such as refraction, and absorption. In the case of semi-transparent 3D-printed parts, the laser beam diffuses through the complex heterogeneous microstructure due to the numerous refractions occurring at the matrix/void interfaces.

In a complex structure, the propagation of laser beams can be simulated using the ray-tracing method which is based on a Snell-Descartes law [17]:
<table><caption>Table 3 Size of the voids</caption><thead><tr><th>Samples</th><th>Layer thickness [mm]</th><th>Composition of the sample</th><th>Porosity (%)</th><th>Volume fraction of the filament PETG (V<sub>f</sub> [%])</th></tr></thead><tbody><tr><td>Type I</td><td>0.2</td><td>PETG, Air</td><td>1.88</td><td>98.12</td></tr><tr><td>Type II</td><td>0.3</td><td>PETG, Air</td><td>7.01</td><td>92.99</td></tr><tr><td>Type III</td><td>0.4</td><td>PETG, Air</td><td>5.39</td><td>94.61</td></tr></tbody></table>

<figure><img src="image_2434.png" /><figcaption>Fig. 4 Void morphology of the 3D printed parts and image analysis procedure to find the void fraction. (a, c, and e) Unprocessed tomography images (b, d, and f) Post-processed images</figcaption></figure>

<figure><img src="image_2435.png" /><figcaption>Fig. 5 Generation of the microstructure of the 3D printed parts (I 1x1x1 mm³; II 1.5x1.5x1.5 mm³; III 1.2x1.2x1.2 mm³)</figcaption></figure>

## Numerical section

### Ray-tracing simulation

According to the description of the interaction between the laser beam and the 3D-printed part, the ray-tracing method is chosen. This method allows us to follow the propagation of the laser beam into a complex structure. In previous studies, the ray-tracing method has been successfully employed to simulate the transmission laser welding (TLW) through the thermoplastic glass fiber composite (polymer + continuous glass fibers) [7,8]. In this method, the laser beam is discretized into a set of rays, and then the path of each ray is followed in the model geometry. Therefore, the ray-tracing method is able to take-into-account the different optical effects of light through the materials, such as refraction, and absorption. In the case of semi-transparent 3D-printed parts, the laser beam diffuses through the complex heterogeneous microstructure due to the numerous refractions occurring at the matrix/void interfaces.

In a complex structure, the propagation of laser beams can be simulated using the ray-tracing method which is based on a Snell-Descartes law [17]:
$$n_1 \sin \theta_1 = n_2 \sin \theta_2 \qquad (1)$$

where $n_i$ and $\theta_i$ are the refractive indices of the medium i and the angle formed by ray and normal at the interface (see Fig. 6). The refractive indices of the polymer and the voids are respectively $n_m = 1.49$ and $n_v = 1$. The reflection of light at the diopter is considered to be negligible in front of refraction [8].

<figure><img src="image_2443.png" /><figcaption>Fig. 6 Transmission of a laser beam through two different media</figcaption></figure>

<figure><img src="image_2444.png" /><figcaption>Fig. 7 Path of a ray projection in semi-transparent part</figcaption></figure>

Generally, laser energy absorption is considered only at the weld interface and in the absorbent part. These analytical approaches take into account the Beer-Lambert law to calculate the intensity profile during the laser propagation through the semi-transparent part [22]:

$$I = I_0 e^{-K_h \times d_h} \qquad (2)$$

Where $I_0$ is the initial intensity of the laser beam, $K_h$ is the absorption coefficient (mm⁻¹) of the 3D-printed thermoplastic part, $d_A$ represents the ray path length, and I is the lase the final laser intensity at the weld interface.

The ray-tracing simulations are carried out with a focused beam having a focal angle as seen in the welding machine. Fig. 7 shows an example of the path of a ray that is traveling through the thickness of the semi-transparent part. The distance traveled by each ray in every macro-element is calculated during the ray-tracing simulation. For each macro-element, the Beer-Lambert theory is applied to determine the attenuation of the laser intensity of every ray when it propagates through each macro-element. When Beer-Lambert law is applied to a macro-element n, the intensity of a ray after traveling through the macro-element can be written as:
$$n_1 \sin \theta_1 = n_2 \sin \theta_2 \qquad (1)$$

where $n_i$ and $\theta_i$ are the refractive indices of the medium i and the angle formed by ray and normal at the interface (see Fig. 6). The refractive indices of the polymer and the voids are respectively $n_m = 1.49$ and $n_v = 1$. The reflection of light at the diopter is considered to be negligible in front of refraction [8].

<figure><img src="image_2436.png" /><figcaption>Fig. 6 Transmission of a laser beam through two different media</figcaption></figure>

<figure><img src="image_2437.png" /><figcaption>Fig. 7 Path of a ray projection in semi-transparent part</figcaption></figure>

Generally, laser energy absorption is considered only at the weld interface and in the absorbent part. These analytical approaches take into account the Beer-Lambert law to calculate the intensity profile during the laser propagation through the semi-transparent part [22]:

$$I = I_0 e^{-K_h \times d_h} \qquad (2)$$

Where $I_0$ is the initial intensity of the laser beam, $K_h$ is the absorption coefficient (mm⁻¹) of the 3D-printed thermoplastic part, $d_A$ represents the ray path length, and I is the lase the final laser intensity at the weld interface.

The ray-tracing simulations are carried out with a focused beam having a focal angle as seen in the welding machine. Fig. 7 shows an example of the path of a ray that is traveling through the thickness of the semi-transparent part. The distance traveled by each ray in every macro-element is calculated during the ray-tracing simulation. For each macro-element, the Beer-Lambert theory is applied to determine the attenuation of the laser intensity of every ray when it propagates through each macro-element. When Beer-Lambert law is applied to a macro-element n, the intensity of a ray after traveling through the macro-element can be written as:
$$I_n = I_{n-1} \times e^{Kh_d h} \qquad (3)$$

The difference in intensity in every macro-element is given by (see Fig. 7):

$$I_{a,n} = I_{n-1} - I_n \qquad (4)$$

In this work, the ray-tracing simulations are carried with a focused beam having a focal angle in the welding machine. The beam is discretized into 2400 rays.

### Thermal simulation

The temperature field will vary depending on the applied radiative source. This discrepancy arises due to the distinct surface characteristics of intensity distribution between the two cases.

COMSOL Multiphysics® software is a solver for multiphysics simulations using finite elements. This software is used to model heat transfer during transmission laser welding. The heat transfer in the interface of the solid COMSOL is used to model heat transfer in solids by conduction, convection, and radiation. In this study, transmission laser welding is modeled by a radiation source to show the key role of the distribution.

A 3D thermal model of TLW is considered to obtain the temperature field at the interface by solving the energy balance equation [9,12]:

$$\rho C_p \frac{\partial T}{\partial t} = -\nabla \cdot (-k \vec{\nabla} T) + Q \qquad (5)$$

where $\rho$ is the material density, $C_p$ is the specific heat, $T$ is the temperature, $t$ is the time, $k$ is the thermal conductivity, $Q$ is the heat source and $\nabla$ is the gradient operator.

<figure><img src="image_2445.png" /><figcaption>Fig. 8 The heat source of the welded interface during TLW</figcaption></figure>

The laser irradiation is modeled by volume heat source in the absorbent part with the following equation [1] (see Fig. 8):

$$Q(x, y, z) = I(x, y, z) \times K_A \times e^{-K_A \times z} \qquad (6)$$

where $z$ is the distance from the interface to the semi-transparent part and $K_A$ is the homogenized absorption coefficient of the 3D printed thermoplastic part. $I(x, y, z)$ is the intensity profile given by the ray-tracing model.
$$I_n = I_{n-1} \times e^{Kh_d h} \qquad (3)$$

The difference in intensity in every macro-element is given by (see Fig. 7):

$$I_{a,n} = I_{n-1} - I_n \qquad (4)$$

In this work, the ray-tracing simulations are carried with a focused beam having a focal angle in the welding machine. The beam is discretized into 2400 rays.

### Thermal simulation

The temperature field will vary depending on the applied radiative source. This discrepancy arises due to the distinct surface characteristics of intensity distribution between the two cases.

COMSOL Multiphysics® software is a solver for multiphysics simulations using finite elements. This software is used to model heat transfer during transmission laser welding. The heat transfer in the interface of the solid COMSOL is used to model heat transfer in solids by conduction, convection, and radiation. In this study, transmission laser welding is modeled by a radiation source to show the key role of the distribution.

A 3D thermal model of TLW is considered to obtain the temperature field at the interface by solving the energy balance equation [9,12]:

$$\rho C_p \frac{\partial T}{\partial t} = -\nabla \cdot (-k \vec{\nabla} T) + Q \qquad (5)$$

where $\rho$ is the material density, $C_p$ is the specific heat, $T$ is the temperature, $t$ is the time, $k$ is the thermal conductivity, $Q$ is the heat source and $\nabla$ is the gradient operator.

<figure><img src="image_2438.png" /><figcaption>Fig. 8 The heat source of the welded interface during TLW</figcaption></figure>

The laser irradiation is modeled by volume heat source in the absorbent part with the following equation [1] (see Fig. 8):

$$Q(x, y, z) = I(x, y, z) \times K_A \times e^{-K_A \times z} \qquad (6)$$

where $z$ is the distance from the interface to the semi-transparent part and $K_A$ is the homogenized absorption coefficient of the 3D printed thermoplastic part. $I(x, y, z)$ is the intensity profile given by the ray-tracing model.
<figure><img src="image_2446.png" /><figcaption>Fig. 9 Numerical model geometry with a surface heat source for thermal simulations</figcaption></figure>

<table><caption>Table 4 Thermal properties of PETG</caption><thead><tr><td>Thermal properties</td><td>Filament PETG</td></tr></thead><tbody><tr><td>Thermal conductivity (k) [W/m.K]</td><td>0.2</td></tr><tr><td>Density (ρ) [Kg/m³]</td><td>1250</td></tr><tr><td>Heat capacity (C<sub>p</sub>) [J/kg.K]</td><td>1800</td></tr></tbody></table>

The material properties of $C_p$), ρ, and k are input for semi-transparent material properties. The thermal properties of the absorbent part are that of pure PETG, as seen in

Table 4. All the exposed surfaces are prescribed a convective heat flux boundary condition, with a heat transfer coefficient of $h = 10[W/(m².K)]$.

The initial value for temperature is taken as the default room temperature, 23°C. Thermal insulation is applied on all the faces of the components except the interface. The heat source (Eq.(6), is determined by the beam laser distribution through 3D printed parts using the ray-tracing simulations. The intensity distribution data is applied as a function depending on the volume of the semi-transparent part and the area of the weld interface. This intensity is applied using a LiveLink™ for MATLAB® (see Fig. 9). That is the radiation source to simulate the temperature field in the COMSOL thanks to equation (5).

The displacement of the laser beam is considered parallel to the printing direction. In this case, that is perpendicular to the welding direction, the diffusion will affect strongly the temperature field.

## Results and Discussion

### Influence of void shape

This section uses the intensity distribution simulation at the interface obtained from the ray-tracing models. The ray tracing simulation (geometrical optic) are done with the mesh shown in Fig. 10. This mesh is used as RVE to carry out the paving of the overall sample geometry. Fig. 10 shows the intensity distribution of the laser beam before and after passing through the sample. The light scattering within the sample causes a redistribution of the laser intensity, leading to the formation of small slits where the laser intensity is significantly reduced. These slits are formed at locations where there are void grooves in the sample and are the results of the multiple refractions of the laser light at the air-matrix interfaces. In contrast, areas of the sample with no void grooves
<figure><img src="image_2439.png" /><figcaption>Fig. 9 Numerical model geometry with a surface heat source for thermal simulations</figcaption></figure>

<table><caption>Table 4 Thermal properties of PETG</caption><thead><tr><td>Thermal properties</td><td>Filament PETG</td></tr></thead><tbody><tr><td>Thermal conductivity (k) [W/m.K]</td><td>0.2</td></tr><tr><td>Density (ρ) [Kg/m³]</td><td>1250</td></tr><tr><td>Heat capacity (C<sub>p</sub>) [J/kg.K]</td><td>1800</td></tr></tbody></table>

The material properties of $C_p$), $\rho$), and k are input for semi-transparent material properties. The thermal properties of the absorbent part are that of pure PETG, as seen in

Table 4. All the exposed surfaces are prescribed a convective heat flux boundary condition, with a heat transfer coefficient of $h = 10[W/(m^2.K)]$.

The initial value for temperature is taken as the default room temperature, 23°C. Thermal insulation is applied on all the faces of the components except the interface. The heat source (Eq.(6), is determined by the beam laser distribution through 3D printed parts using the ray-tracing simulations. The intensity distribution data is applied as a function depending on the volume of the semi-transparent part and the area of the weld interface. This intensity is applied using a LiveLink™ for MATLAB® (see Fig. 9). That is the radiation source to simulate the temperature field in the COMSOL thanks to equation (5).

The displacement of the laser beam is considered parallel to the printing direction. In this case, that is perpendicular to the welding direction, the diffusion will affect strongly the temperature field.

## Results and Discussion

### Influence of void shape

This section uses the intensity distribution simulation at the interface obtained from the ray-tracing models. The ray tracing simulation (geometrical optic) are done with the mesh shown in Fig. 10. This mesh is used as RVE to carry out the paving of the overall sample geometry. Fig. 10 shows the intensity distribution of the laser beam before and after passing through the sample. The light scattering within the sample causes a redistribution of the laser intensity, leading to the formation of small slits where the laser intensity is significantly reduced. These slits are formed at locations where there are void grooves in the sample and are the results of the multiple refractions of the laser light at the air-matrix interfaces. In contrast, areas of the sample with no void grooves
allow the laser light to pass along straight paths with no scattering. In addition, these areas also receive intensities from the scattered zones, resulting in concentrated areas of laser light. Overall, the sample's microstructure influences the laser beam behavior and can result in complex intensity patterns that depend on the presence or absence of the void grooves. It can also be seen in Fig. 10a, b, and c that the ray-tracing model effectively simulates this feature.

<figure><img src="image_2447.png" /><figcaption>Fig. 10 Comparison of simulated laser intensity for three sample types</figcaption></figure>

The influence of the void shape on the intensity distribution map of the laser beam at the weld interface is shown in Fig. 10. It is observed that the size of the slits, where the laser intensity is reduced, is a function of the voids' form. As a result, the ones observed that the laser beam distribution of the sample type I is more concentrated than samples II and III are for sample II. Accordingly, for the sample II, the light scattering in concentrated areas reaches higher peaks (Fig. 10).

<figure><img src="image_2448.png" /><figcaption>Fig. 11 The intensity distribution at the interface of three results</figcaption></figure>
allow the laser light to pass along straight paths with no scattering. In addition, these areas also receive intensities from the scattered zones, resulting in concentrated areas of laser light. Overall, the sample's microstructure influences the laser beam behavior and can result in complex intensity patterns that depend on the presence or absence of the void grooves. It can also be seen in Fig. 10a, b, and c that the ray-tracing model effectively simulates this feature.

<figure><img src="image_2440.png" /><figcaption>Fig. 10 Comparison of simulated laser intensity for three sample types</figcaption></figure>

The influence of the void shape on the intensity distribution map of the laser beam at the weld interface is shown in Fig. 10. It is observed that the size of the slits, where the laser intensity is reduced, is a function of the voids' form. As a result, the ones observed that the laser beam distribution of the sample type I is more concentrated than samples II and III are for sample II. Accordingly, for the sample II, the light scattering in concentrated areas reaches higher peaks (Fig. 10).

<figure><img src="image_2441.png" /><figcaption>Fig. 11 The intensity distribution at the interface of three results</figcaption></figure>
Influence of the scattering effect on the weld quality

<figure><img src="image_2449.png" /><figcaption>Fig. 12 Comparison of simulated maximum temperature profiles</figcaption></figure>

For the sake of comparison, Fig. 12 shows the thermal simulations for two different types the sample types I and II with a thickness 2mm. Based on the results, observing the orange line, we can see that the energy distribution reaching the weld interface is more diffused compared to the blue line. It means that the quality of the weld seam is directly influenced by the porosity of the 3D printing process during the welding process. This confirms that the non-homogenization of the intensity distribution due to the scattering effect. Consequently, the weld quality along the seam line width is seriously impacted.

Conclusion

The structural layer-by-layer process of the 3D printing procedure results in a complex heterogeneous microstructure with a larger amount of porosity within the 3D printed parts. Consequently, laser intensity is subjected to scattering effects when propagating through the thickness of the 3D-printed components during the TLW process. Clearly, understanding the effects of light scattering allows for the control of the interface weld temperature to achieve high-quality assembly.

In this study, we have explored the influence of 3D printing process parameters on the microstructure, specifically the void shape, of 3D printed thermoplastic parts. Subsequently, we have investigated three types of void morphologies in 3D-oriented parts to examine the light-scattering effects of each sample type.

We have introduced a ray-tracing model capable of simulating light-scattering phenomena during the transmission of laser intensity through a semi-transparent sample. This proposed model can predict the laser beam reaching the interface during TLW, allowing for the consideration of differences in the microstructure among various sample types. The influence of void shape is also examined, demonstrating the growing impact of light-scattering effects with variable voids.

To assess the influence of the scattering effect on weld quality, 3D thermal simulations are conducted to predict the temperature field during the TLW process. Results indicate a noticeable reduction in weld quality due to the scattering effect.

Future work will involve using the ray-tracing model coupled with a FEM model to simulate the temperature field during the TLW process of 3D CCFRCs.

Acknowledgments

The authors extend their sincere appreciation to the National French Research Agency's ANR JCJC program for funding the SHORYUKEN project (Grant agreement n° ANR-21-CE10-0007-01) through AAPG 2021—CE10 "Industrie et Usine du Futur: Homme, Organisation, Technologies" initiative. Without their support, this work would not have been possible.
Influence of the scattering effect on the weld quality

<figure><img src="image_2442.png" /><figcaption>Fig. 12 Comparison of simulated maximum temperature profiles</figcaption></figure>

For the sake of comparison, Fig. 12 shows the thermal simulations for two different types the sample types I and II with a thickness 2mm. Based on the results, observing the orange line, we can see that the energy distribution reaching the weld interface is more diffused compared to the blue line. It means that the quality of the weld seam is directly influenced by the porosity of the 3D printing process during the welding process. This confirms that the non-homogenization of the intensity distribution due to the scattering effect. Consequently, the weld quality along the seam line width is seriously impacted.

Conclusion

The structural layer-by-layer process of the 3D printing procedure results in a complex heterogeneous microstructure with a larger amount of porosity within the 3D printed parts. Consequently, laser intensity is subjected to scattering effects when propagating through the thickness of the 3D-printed components during the TLW process. Clearly, understanding the effects of light scattering allows for the control of the interface weld temperature to achieve high-quality assembly.

In this study, we have explored the influence of 3D printing process parameters on the microstructure, specifically the void shape, of 3D printed thermoplastic parts. Subsequently, we have investigated three types of void morphologies in 3D-oriented parts to examine the light-scattering effects of each sample type.

We have introduced a ray-tracing model capable of simulating light-scattering phenomena during the transmission of laser intensity through a semi-transparent sample. This proposed model can predict the laser beam reaching the interface during TLW, allowing for the consideration of differences in the microstructure among various sample types. The influence of void shape is also examined, demonstrating the growing impact of light-scattering effects with variable voids.

To assess the influence of the scattering effect on weld quality, 3D thermal simulations are conducted to predict the temperature field during the TLW process. Results indicate a noticeable reduction in weld quality due to the scattering effect.

Future work will involve using the ray-tracing model coupled with a FEM model to simulate the temperature field during the TLW process of 3D CCFRCs.

Acknowledgments

The authors extend their sincere appreciation to the National French Research Agency's ANR JCJC program for funding the SHORYUKEN project (Grant agreement n° ANR-21-CE10-0007-01) through AAPG 2021—CE10 "Industrie et Usine du Futur: Homme, Organisation, Technologies" initiative. Without their support, this work would not have been possible.
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