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# Two-step forging of polyimide powders into small-/medium-sized gears with and without carbon fiber reinforcement

AIZAWA Tatsuhiko¹,ª*, MIYATA Tomohiro²,ᵇ and ENDO Kiyoyuki³,ᶜ

¹³-15-10 Minami-Rokugo, Ota-City, Tokyo 144-0045, Japan

²215-1 Monden Industrial Park, Aizu-Wakamatu, Fukushima 965-0846, Japan

³4-1-5 Sannoh, Ota-City, Tokyo 143-0023, Japan

ªtaizawa@sic.shibaura-it.ac.jp, ᵇaizu5@marutaka-ind.co.jp, ᶜendo@igma.co.jp

**Keywords:** Polyimide Powder Feed Stock, Green Preform, Sinter-Forging, Carbon Reinforcement

**Abstract.** A green polyimide cylindrical preform with short carbon fibers was prepared for two-step forging processes. Each preform was hot-forged at 623 K above the glass transition temperature of polyimide for near-net shaping of fifteen-teeth module-1.0 gear, and sinter-forged at 673 K below its melting point for densification. SEM and X-ray computer tomography were employed to make destructive and non-destructive diagnoses on the carbon fiber orientation during hot forging. Micro-hardness testing and gear-grade balancing were utilized to evaluate the engineering durability and dimensional accuracy of sinter-forged gears.

## Introduction

Light weight and high stiffness have become an essential key item for mechanical gears in the reducers of the robotics and electrical vehicles [1]. Minimization of gear volume without change of loading capacity and mechanical constraints is the first approach to reduce the weight of mechanical parts and elements [2]. In case of the gear design, the weight can be reduced only with the decrease of stiffness [3]. The light weight metals, alloys and plastics are employed as the second approach to decrease the weight without loss of stiffness [4]. The carbon fiber reinforced gears and screws could provide the solution [5]; the long carbon fibers are difficult to be aligned after plastic flow into the gear matrix [6]. In addition, the polymer matrix property has often less engineering durability in severe conditions with heating up on the contact interface. New approach is necessary to satisfy the light weight, the high stiffness and the engineering toughness as a gear to be working even in severe situation [7-8].

Authors proposed the super-engineering plastic gears with the higher melting point than 700 K, the higher strength and toughness than the conventional CFRP (Carbon Fiber reinforced plastics) and CFRTP (Carbon Fiber Reinforced Thermo-Plastics) [9-10]. Two step PM (Powder Metallurgy) procedure was also developed to make a gear-shaped green compact and to sinter-forge this green compact to a net-shaped gear. This sinter-forged gear had a well-defined gear-grade balance; e.g., the cumulative pitch deviation was fixed into -10 µm to +10 µm. This deviation for fifteen teeth gear without finishing was classified into JIS-2 grade.

In the present study, the carbon fibers are included and mixed into the polyimide powders to build up the feedstock. This mixture powders are poured into a die cavity for cold compaction to a cylindrical green preform. This preform is hot forged above the glass transition temperature to a fifteen teeth gear model. During this viscous matrix flow, the carbon fibers are forced to orient along the plastically flowing directions of matrix. The hot forged model is further sinter-forged to a net-shaped fifteen teeth gear. SEM (Scanning Electron Microscopy) and>XCT (X-ray Computer Tomography) are utilized to make destructive and non-destructive diagnoses on the orientation of carbon fibers in the polyimide matrix during the hot forging of green compact. Micro-Vickers hardness testing was employed to measure the hardness of tooth top and bottom of sinter-forged

<figure><img src="image_2492.png" /></figure>
# Two-step forging of polyimide powders into small-/medium-sized gears with and without carbon fiber reinforcement

AIZAWA Tatsuhiko¹,ª*, MIYATA Tomohiro²,ᵇ and ENDO Kiyoyuki³,ᶜ

¹³-15-10 Minami-Rokugo, Ota-City, Tokyo 144-0045, Japan

²215-1 Monden Industrial Park, Aizu-Wakamatu, Fukushima 965-0846, Japan

³4-1-5 Sannoh, Ota-City, Tokyo 143-0023, Japan

ªtaizawa@sic.shibaura-it.ac.jp, ᵇaizu5@marutaka-ind.co.jp, ᶜendo@igma.co.jp

**Keywords:** Polyimide Powder Feed Stock, Green Preform, Sinter-Forging, Carbon Reinforcement

**Abstract.** A green polyimide cylindrical preform with short carbon fibers was prepared for two-step forging processes. Each preform was hot-forged at 623 K above the glass transition temperature of polyimide for near-net shaping of fifteen-teeth module-1.0 gear, and sinter-forged at 673 K below its melting point for densification. SEM and X-ray computer tomography were employed to make destructive and non-destructive diagnoses on the carbon fiber orientation during hot forging. Micro-hardness testing and gear-grade balancing were utilized to evaluate the engineering durability and dimensional accuracy of sinter-forged gears.

## Introduction

Light weight and high stiffness have become an essential key item for mechanical gears in the reducers of the robotics and electrical vehicles [1]. Minimization of gear volume without change of loading capacity and mechanical constraints is the first approach to reduce the weight of mechanical parts and elements [2]. In case of the gear design, the weight can be reduced only with the decrease of stiffness [3]. The light weight metals, alloys and plastics are employed as the second approach to decrease the weight without loss of stiffness [4]. The carbon fiber reinforced gears and screws could provide the solution [5]; the long carbon fibers are difficult to be aligned after plastic flow into the gear matrix [6]. In addition, the polymer matrix property has often less engineering durability in severe conditions with heating up on the contact interface. New approach is necessary to satisfy the light weight, the high stiffness and the engineering toughness as a gear to be working even in severe situation [7-8].

Authors proposed the super-engineering plastic gears with the higher melting point than 700 K, the higher strength and toughness than the conventional CFRP (Carbon Fiber reinforced plastics) and CFRTP (Carbon Fiber Reinforced Thermo-Plastics) [9-10]. Two step PM (Powder Metallurgy) procedure was also developed to make a gear-shaped green compact and to sinter-forge this green compact to a net-shaped gear. This sinter-forged gear had a well-defined gear-grade balance; e.g., the cumulative pitch deviation was fixed into -10 µm to +10 µm. This deviation for fifteen teeth gear without finishing was classified into JIS-2 grade.

In the present study, the carbon fibers are included and mixed into the polyimide powders to build up the feedstock. This mixture powders are poured into a die cavity for cold compaction to a cylindrical green preform. This preform is hot forged above the glass transition temperature to a fifteen teeth gear model. During this viscous matrix flow, the carbon fibers are forced to orient along the plastically flowing directions of matrix. The hot forged model is further sinter-forged to a net-shaped fifteen teeth gear. SEM (Scanning Electron Microscopy) and XCT (X-ray Computer Tomography) are utilized to make destructive and non-destructive diagnoses on the orientation of carbon fibers in the polyimide matrix during the hot forging of green compact. Micro-Vickers hardness testing was employed to measure the hardness of tooth top and bottom of sinter-forged

<figure><img src="image_2485.png" /></figure>
fifteen teeth gear. In the above three processes, CNC (Computer Numerical Control) stamper was commonly utilized with and without use of IH (Induction Heating) units to keep the specified holding temperature. The gear-grade evaluation is also performed to measure the dimensional deviations of tooth shape and geometry.

## Methods and Materials

The green compaction, the hot forging and the sinter forging processes are explained in detail to point out the processing parameters in each process.

**Green compaction to preforms.** The recycled long carbon fibers from the CFRP in-factory dusts, were used as a feed stock. These fibers were cut into chips with the length of 5 mm in average. Their weight was measured to determine their total mass for inclusion into the green compact.

<figure><img src="image_2493.png" /><figcaption>Figure 1. Green compaction process to consolidate the powder mixtures with carbon short fibers into a preform. a) Schematic view on the die-set for consolidation process, and b) a cylindrical preform of consolidated polyimide powders with short carbon fibers.</figcaption></figure>

The measured carbon fiber - polyimide powder mixture, was poured into a die cavity in the cold compaction die - punch unit in Fig. 1a. The load was applied by 3 kN to yield the green compact with the relative density of 70 to 80% for the true polyimide density.

<figure><img src="image_2494.png" /><figcaption>Figure 2. Hot forging of the preform to gear-shaped intermediates. a) Schematic view on the die-set for hot forging, and b) a gear-shaped product intermediate.</figcaption></figure>

**Two-step PM-forging processes.** PM-forging process consists of two steps. At first, the hot PM-forging is utilized to make near-net shaping of the preform to a gear model with fifteen teeth, module 1.0 above the glass-transition temperature of polyimide matrix. Through this viscous deformation and flow of polyimide matrix, the short carbon fibers are realigned from the original locations to the tooth tops together with this matrix flow. Fig. 2a illustrates the experimental setup
fifteen teeth gear. In the above three processes, CNC (Computer Numerical Control) stamper was commonly utilized with and without use of IH (Induction Heating) units to keep the specified holding temperature. The gear-grade evaluation is also performed to measure the dimensional deviations of tooth shape and geometry.

## Methods and Materials

The green compaction, the hot forging and the sinter forging processes are explained in detail to point out the processing parameters in each process.

**Green compaction to preforms.** The recycled long carbon fibers from the CFRP in-factory dusts, were used as a feed stock. These fibers were cut into chips with the length of 5 mm in average. Their weight was measured to determine their total mass for inclusion into the green compact.

<figure><img src="image_2486.png" /><figcaption>Figure 1. Green compaction process to consolidate the powder mixtures with carbon short fibers into a preform. a) Schematic view on the die-set for consolidation process, and b) a cylindrical preform of consolidated polyimide powders with short carbon fibers.</figcaption></figure>

The measured carbon fiber - polyimide powder mixture, was poured into a die cavity in the cold compaction die - punch unit in Fig. 1a. The load was applied by 3 kN to yield the green compact with the relative density of 70 to 80% for the true polyimide density.

<figure><img src="image_2487.png" /><figcaption>Figure 2. Hot forging of the preform to gear-shaped intermediates. a) Schematic view on the die-set for hot forging, and b) a gear-shaped product intermediate.</figcaption></figure>

**Two-step PM-forging processes.** PM-forging process consists of two steps. At first, the hot PM-forging is utilized to make near-net shaping of the preform to a gear model with fifteen teeth, module 1.0 above the glass-transition temperature of polyimide matrix. Through this viscous deformation and flow of polyimide matrix, the short carbon fibers are realigned from the original locations to the tooth tops together with this matrix flow. Fig. 2a illustrates the experimental setup
for this hot forging. IH-coil was used for heating and holding temperature after thermal transient program. The uniaxial compression load was applied during hot forging step. The holding time as well as the applied load were varied to investigate their effect on the plastic flow of polyimide matrix. Fig. 2b depicts the hot forged fifteen teeth, module 1.0 gear model.

<figure><img src="image_2495.png" /><figcaption>Figure 3. Sinter forging of the gear-shaped intermediates to the final product before polishing.
a) Schematic view on the die-set for sinter forging, and b) a gear-shaped product before polishing.</figcaption></figure>

The sinter-forging was utilized as the second step for densification below the melting point of polyimide matrix. Fig. 3a illustrates the similar setup to the hot forging. In practical operation, both forging steps were performed in the successive manner without ejection of forged sample. After the time schedule in the CNC stamping unit, the loading and temperature sequences were controlled in practice before cooling. Fig. 3b shows the final product with the outer diameter of 16.4 mm, the inner diameter of 11.9 mm and PCD of 14.2 mm after sinter-forging,

**Work materials.** The polyimide powders (Aurum; Mitsui Chemicals, Co., Ltd.) were shown in Fig. 4a. This Aurum-PD450 was a thermoplastic polyimide with $T_g$ (Glass transition temperature) of 518 K (or 245 °C), $T_m$ (Melting temperature) of 661 K (or 388 °C), and the density of 1.33 g/cm³. The carbon long fibers with the density of 2.0 g/cm³, were recycled from the CFRP (Carbon fiber reinforced plastic) in-factory dusts, as shown in Fig. 4b. These fibers were cut into short fibers with the length of 5 mm.

<figure><img src="image_2496.png" /><figcaption>Figure 4. Initial feedstock of work materials. a) Polyimide powders, and b) recycled carbon fibers from CFRP dusts.</figcaption></figure>

These short fibers were mixed with the polyimide powders to prepare the starting material for green compaction and successive forging processes. The mass fraction of carbon fibers was varied to be 1, 3 and 5 mass% against the polyimide powder mass.
for this hot forging. IH-coil was used for heating and holding temperature after thermal transient program. The uniaxial compression load was applied during hot forging step. The holding time as well as the applied load were varied to investigate their effect on the plastic flow of polyimide matrix. Fig. 2b depicts the hot forged fifteen teeth, module 1.0 gear model.

<figure><img src="image_2488.png" /><figcaption>Figure 3. Sinter forging of the gear-shaped intermediates to the final product before polishing.
a) Schematic view on the die-set for sinter forging, and b) a gear-shaped product before polishing.</figcaption></figure>

The sinter-forging was utilized as the second step for densification below the melting point of polyimide matrix. Fig. 3a illustrates the similar setup to the hot forging. In practical operation, both forging steps were performed in the successive manner without ejection of forged sample. After the time schedule in the CNC stamping unit, the loading and temperature sequences were controlled in practice before cooling. Fig. 3b shows the final product with the outer diameter of 16.4 mm, the inner diameter of 11.9 mm and PCD of 14.2 mm after sinter-forging,

**Work materials.** The polyimide powders (Aurum; Mitsui Chemicals, Co., Ltd.) were shown in Fig. 4a. This Aurum-PD450 was a thermoplastic polyimide with $T_g$ (Glass transition temperature) of 518 K (or 245 °C), $T_m$ (Melting temperature) of 661 K (or 388 °C), and the density of 1.33 g/cm³. The carbon long fibers with the density of 2.0 g/cm³, were recycled from the CFRP (Carbon fiber reinforced plastic) in-factory dusts, as shown in Fig. 4b. These fibers were cut into short fibers with the length of 5 mm.

<figure><img src="image_2489.png" /><figcaption>Figure 4. Initial feedstock of work materials. a) Polyimide powders, and b) recycled carbon fibers from CFRP dusts.</figcaption></figure>

These short fibers were mixed with the polyimide powders to prepare the starting material for green compaction and successive forging processes. The mass fraction of carbon fibers was varied to be 1, 3 and 5 mass% against the polyimide powder mass.
**Characterization.** The micro-Vickers hardness testing was employed to optimize the forging process parameters such as the alloyed load and loading duration. SEM (Scanning Electron Microscopy; JOEL, Tokyo, Japan) and SCT (X-ray Computer Tomography) were utilized for destructive and non-destructive diagnosis on the green compact and the sintered gears to describe the alignment of carbon fibers.

## Results

The green compaction is performed to prepare the preform for hot- and sinter-forging processes. This two-step forging is utilized to yield the carbon fiber reinforced polyimide gears with varying the carbon fiber contents.

**Polyimide – carbon fiber preform by green compaction.** The mixture polyimide powders with the short carbon fibers were consolidated to a green preform by cold compaction, as depicted in Fig. 1. The applied load was 3 kN and the constant velocity was 0.1 m/s. The cylindrical preform had the relative density of 70-80%. In addition to the destructive evaluation by SEM, the SCT was utilized to make nondestructive diagnosis on this preform.

<figure><img src="image_2497.png" /><figcaption>Figure 5. Non-destructive quantitative evaluation on the carbon alignment by X-ray tomography. a) Three dimensional images of preform, and b) half-sectional image of preform.</figcaption></figure>

Fig. 5a depicts the top and cross-sectional view images of green preform. No pores and cavities were detected in every cross-section of preform due to its high relative density. As shown in Fig. 5b, the polyimide powders were consolidated in everywhere.
**Characterization.** The micro-Vickers hardness testing was employed to optimize the forging process parameters such as the alloyed load and loading duration. SEM (Scanning Electron Microscopy; JOEL, Tokyo, Japan) and/XCT (X-ray Computer Tomography) were utilized for destructive and non-destructive diagnosis on the green compact and the sintered gears to describe the alignment of carbon fibers.

## Results

The green compaction is performed to prepare the preform for hot- and sinter-forging processes. This two-step forging is utilized to yield the carbon fiber reinforced polyimide gears with varying the carbon fiber contents.

**Polyimide – carbon fiber preform by green compaction.** The mixture polyimide powders with the short carbon fibers were consolidated to a green preform by cold compaction, as depicted in Fig. 1. The applied load was 3 kN and the constant velocity was 0.1 m/s. The cylindrical preform had the relative density of 70-80%. In addition to the destructive evaluation by SEM, the/XCT was utilized to make nondestructive diagnosis on this preform.

<figure><img src="image_2490.png" /><figcaption>Figure 5. Non-destructive quantitative evaluation on the carbon alignment by X-ray tomography.
a) Three dimensional images of preform, and b) half-sectional image of preform.</figcaption></figure>

Fig. 5a depicts the top and cross-sectional view images of green preform. No pores and cavities were detected in every cross-section of preform due to its high relative density. As shown in Fig. 5b, the polyimide powders were consolidated in everywhere.
**Sinter-forged polyimide – carbon fiber gear.** The preform in the above was fixed into the die-cavity with the shape of fifteen-teeth gear. At first, the preform was viscously deformed from a cylindrical shape to a fifteen-teeth gear during hot forging, as illustrated in Fig. 2. The holding die temperature was 623 K (350 °C), the duration was 180 s, and the applied load was 2 kN. After this hot forging, the die temperature is increased from 623 K to 693 K (420 °C) for sinter-forging. At this step, the applied load was varied to 1.5 kN, and the duration was also 180 s. As depicted in Fig. 3, the hot-forged gear model was net-shaped to a gear product.

<figure><img src="image_2498.png" /><figcaption>Measurement position:
Selected five points at each tooth.</figcaption></figure>

<caption>Figure 6. Measurement of Vickers hardness distribution at the tooth top of sinter-forged gear.</caption>

Micro-Vickers hardness testing was employed to evaluate the stiffness of sinter-forged gear. As depicted in Fig. 6, the hardness was measured at five positions in each tooth to deduce the average hardness of product. This average hardness reached 180 HV<sub>1N</sub> much higher than 30 to 50 HV<sub>1N</sub> for the sinter-forged polyimide gear, reported in [10]. This is because of the carbon fiber reinforcement even at the tops and roots of fifteen gears.

<figure><img src="image_2499.png" /><figcaption>Figure 7. Non-destructive quantitative evaluation on the carbon fiber alignment by X-ray computer tomography.</figcaption></figure>
**Sinter-forged polyimide – carbon fiber gear.** The preform in the above was fixed into the die-cavity with the shape of fifteen-teeth gear. At first, the preform was viscously deformed from a cylindrical shape to a fifteen-teeth gear during hot forging, as illustrated in Fig. 2. The holding die temperature was 623 K (350 °C), the duration was 180 s, and the applied load was 2 kN. After this hot forging, the die temperature is increased from 623 K to 693 K (420 °C) for sinter-forging. At this step, the applied load was varied to 1.5 kN, and the duration was also 180 s. As depicted in Fig. 3, the hot-forged gear model was net-shaped to a gear product.

<figure><img src="image_2491.png" /><figcaption>Measurement position:
Selected five points at each tooth.</figcaption></figure>

<caption>Figure 6. Measurement of Vickers hardness distribution at the tooth top of sinter-forged gear.</caption>

Micro-Vickers hardness testing was employed to evaluate the stiffness of sinter-forged gear. As depicted in Fig. 6, the hardness was measured at five positions in each tooth to deduce the average hardness of product. This average hardness reached 180 HV<sub>1N</sub> much higher than 30 to 50 HV<sub>1N</sub> for the sinter-forged polyimide gear, reported in [10]. This is because of the carbon fiber reinforcement even at the tops and roots of fifteen gears.

<figure><img src="image_2492.png" /><figcaption>Figure 7. Non-destructive quantitative evaluation on the carbon fiber alignment by X-ray computer tomography.</figcaption></figure>
XCT was also utilized to demonstrate this strengthening of gear teeth by the short carbon fiber reinforcement. Figure 7 also shows the top and cross-sectional view images of sinter-forged gear. Due to the difference of mass density between carbon and polyimide, the carbon fibers were detected as a black dot and a black line. In the top view in Fig. 7, black dots were distinguished in almost all the teeth of gear. This proves that the short-cut carbon fibers were filled into the die cavities together with the polyimide matrix. At the cross-sectional images in Fig. 7, the black dots and lines were also detected so that the whole teeth of gear were reinforced by the short carbon fibers. After SEM analysis, a few carbon fibers, aligning along the gear side surfaces, are detected as a black line and dot in this�.

<figure><img src="image_2500.png" /><figcaption>Figure 8. Cross-sectional view image of sinter-forged product by�.</figcaption></figure>

Fig. 8 depicts the cross-sectional view image of sinter-forged product. In correspondence to the black dots lines at the top and cross-sectional view image in Fig. 7, the gray-patterns were noticed in Fig. 8. This proves that a short carbon fiber distributes and orients by itself in the polyimide matrix of gear teeth.

**Carbon fiber mass-fraction effect on the forging process.** The green preform, the hot-forged gear model, and the sinter-forged product with the different mass fraction of carbon fibers are compared among them to investigate the carbon fiber mass-fraction effect on the two-step forging process,

<figure><img src="image_2501.png" /><figcaption>Figure 9. Green compact, hot-forged and sinter-forged gears including the carbon fibers by 1 mass% into polyimide powders. The white colored depots were residual solid lubricants of hBN (hexagonal boron nitride) powders.</figcaption></figure>

Fig. 9 depicts the green preform, the hot-forged gear model, the sinter-forged gear product, only including the carbon fibers with 1 mass%. As seen in the green compact, the short carbon fibers are detected as a black dot. This preform was forged at 623 K for 180 s under the applied load of
XCT was also utilized to demonstrate this strengthening of gear teeth by the short carbon fiber reinforcement. Figure 7 also shows the top and cross-sectional view images of sinter-forged gear. Due to the difference of mass density between carbon and polyimide, the carbon fibers were detected as a black dot and a black line. In the top view in Fig. 7, black dots were distinguished in almost all the teeth of gear. This proves that the short-cut carbon fibers were filled into the die cavities together with the polyimide matrix. At the cross-sectional images in Fig. 7, the black dots and lines were also detected so that the whole teeth of gear were reinforced by the short carbon fibers. After SEM analysis, a few carbon fibers, aligning along the gear side surfaces, are detected as a black line and dot in this�.

<figure><img src="image_2493.png" /><figcaption>Figure 8. Cross-sectional view image of sinter-forged product by�.</figcaption></figure>

Fig. 8 depicts the cross-sectional view image of sinter-forged product. In correspondence to the black dots lines at the top and cross-sectional view image in Fig. 7, the gray-patterns were noticed in Fig. 8. This proves that a short carbon fiber distributes and orients by itself in the polyimide matrix of gear teeth.

**Carbon fiber mass-fraction effect on the forging process.** The green preform, the hot-forged gear model, and the sinter-forged product with the different mass fraction of carbon fibers are compared among them to investigate the carbon fiber mass-fraction effect on the two-step forging process,

<figure><img src="image_2494.png" /><figcaption>Figure 9. Green compact, hot-forged and sinter-forged gears including the carbon fibers by 1 mass% into polyimide powders. The white colored depots were residual solid lubricants of hBN (hexagonal boron nitride) powders.</figcaption></figure>

Fig. 9 depicts the green preform, the hot-forged gear model, the sinter-forged gear product, only including the carbon fibers with 1 mass%. As seen in the green compact, the short carbon fibers are detected as a black dot. This preform was forged at 623 K for 180 s under the applied load of
2 kN. During this hot forging process, the polyimide matrix deforms visco-plastically to fill into the fifteen teeth cavities. Using the hBN as a solid lubricant at the elevated temperature, the hot forging process is free from adhesion of gear-model and gear-product onto the die surfaces.

Let us compare the effect of carbon mass fraction on the three-step process. As shown in Figs. 10 and 11, more black dots are detected on the surface of preform. When adding the carbon fraction by 3 mass%, every surface of hot-forged gear model and sinter-forged gear product is formed to be smooth with the highest accuracy in dimension. When increasing the fraction up to 5 mass%, some of fibers are located near the surface to roughen the finished surface and to increase the surface roughness of models and products. To be discussed in later, the loading sequence must be changed to an incremental loading with holding time.

<figure><img src="image_2502.png" /><figcaption>Figure 10. Green compact, hot-forged and sinter-forged gears including the carbon fibers by 3 mass% into polyimide powders.</figcaption></figure>

<figure><img src="image_2503.png" /><figcaption>Figure 11. Green compact, hot-forged and sinter-forged gears including the carbon fibers by 5 mass% into polyimide powders.</figcaption></figure>

## Discussion

The mechanical behavior of polyimide matrix as well as the orientation of short-cut carbon fibers are discussed in the powder compaction and the hot-/sinter-forging steps. During the compaction process, each polyimide powder is consolidated to a preform with high relative density of 70 to 80%. Since the initial alignment of short carbon fibers in matrix is fixed by blending and mixing processes before compaction, no essential change occurs in this consolidation. In the hot forging step, the polyimide matrix deforms and flows in the visco-plasticity above the glass-transition temperature. After suggested in [11], the fiber length, its aspect ratio and its geometry influences on the effective visco-plasticity of fiber-matrix composite. Hence, the upsetting and filling processes of polyimide – fiber mixture is driven by more viscous flow than the polyimide without fibers.

XCT images are used to describe the hot forging behavior together with SEM analysis. As shown in Fig. 7, the carbon fibers are seen to agglomerate at the top of teeth as black dots and
2 kN. During this hot forging process, the polyimide matrix deforms visco-plastically to fill into the fifteen teeth cavities. Using the hBN as a solid lubricant at the elevated temperature, the hot forging process is free from adhesion of gear-model and gear-product onto the die surfaces.

Let us compare the effect of carbon mass fraction on the three-step process. As shown in Figs. 10 and 11, more black dots are detected on the surface of preform. When adding the carbon fraction by 3 mass%, every surface of hot-forged gear model and sinter-forged gear product is formed to be smooth with the highest accuracy in dimension. When increasing the fraction up to 5 mass%, some of fibers are located near the surface to roughen the finished surface and to increase the surface roughness of models and products. To be discussed in later, the loading sequence must be changed to an incremental loading with holding time.

<figure><img src="image_2495.png" /><figcaption>Figure 10. Green compact, hot-forged and sinter-forged gears including the carbon fibers by 3 mass% into polyimide powders.</figcaption></figure>

<figure><img src="image_2496.png" /><figcaption>Figure 11. Green compact, hot-forged and sinter-forged gears including the carbon fibers by 5 mass% into polyimide powders.</figcaption></figure>

## Discussion

The mechanical behavior of polyimide matrix as well as the orientation of short-cut carbon fibers are discussed in the powder compaction and the hot-/sinter-forging steps. During the compaction process, each polyimide powder is consolidated to a preform with high relative density of 70 to 80%. Since the initial alignment of short carbon fibers in matrix is fixed by blending and mixing processes before compaction, no essential change occurs in this consolidation. In the hot forging step, the polyimide matrix deforms and flows in the visco-plasticity above the glass-transition temperature. After suggested in [11], the fiber length, its aspect ratio and its geometry influences on the effective visco-plasticity of fiber-matrix composite. Hence, the upsetting and filling processes of polyimide – fiber mixture is driven by more viscous flow than the polyimide without fibers.

XCT images are used to describe the hot forging behavior together with SEM analysis. As shown in Fig. 7, the carbon fibers are seen to agglomerate at the top of teeth as black dots and
lines. This implies that the short carbon fibers are massively pushed into the tooth-cavity of die. That is, the viscous mixtures are filled into the tooth-cavity of die by higher stress gradient from the center of preform to every end of tooth cavity. Relatively longer duration is necessary to this fill-filling of viscous mixture to die cavity.

In the sinter-forging step, the microstructure of hot-forged mixture is homogenized to fix the alignment of carbon fibers in the matrix and to increase the relative density. As depicted in Fig. 8, no porosities are seen in the cross-sectional XCT image; the microstructure becomes uniform without segregation of fibers.

The present XCT has a spatial resolution of 50 µm; local orientation of short carbon fibers is difficult to analyze the original images. In order to describe the local densification and stiffness, finer spatial resolution is necessary. At present, the XCT in the synchrotron-radiation imaging with the use of high intensity X-ray is planned to utilize for this measurement [12]. Under this fine XCT, the local alignment of each short carbon fiber can be analyzed to deduce each orientation of short carbon fiber in the polyimide matrix.

The homogenized finite element analysis [13] is useful to estimate the local stiffness tensor in correspondence to the unit-cell image of XCT-scanned three dimensional image. After [14-15], the unit cell model was determined from the real SEM image of composite materials such as iron ores to calculate its equivalent stiffness and stress distribution in it. This estimate on the homogenized local stiffness tensor is responsible for theoretical validation on the effect of the carbon mass fraction on the hardness.

The orientation of carbon fibers has essential influence on the stiffness and strength of carbon fiber reinforced plastic components. With respect to the reinforcement by the long fibers, the misorientation in the neighboring fibers mainly determines the stiffness of CFRP parts [16]. On the other hand, the statistical distribution of short carbon fibers has main contribution to the stiffness. The unit-cell model is useful in evaluation on the stiffness of CFRSEP gears to represent their elastic stiffness tensor with direct consideration of the microstructure measured by XCT imaging.

The in situ alignment of short-cut carbon fibers in the polyimide matrix during the hot-forging step is identified as a self-orientation process of fibers under the elastic constraint by matrix in the visco-plastic flow. The programmable schedule of external loading in the forging step must be controlled to assist this self-orientation process of fibers to align the fibers along the gear shape. As shown in Figs. 7 and 8, the image-tracing of black dots and lines by XCT enables to describe this self-orientation process with time in loading.

Let us reconsider the marketing of carbon fiber reinforced super-engineering plastic (CFRSEP) gears. The flexible and precise movement of joints in robotics needs the light-weight and small-sized gears with high engineering durability [15, 17]. Due to the carbon fiber reinforcement at the tooth top and root, the tooth-to-tooth traction transfer is put into practice by using the CFRSEP-gears. After early measurement on the gear-grade balancing, the JIS-3 to JIS-5 grades can be attained even in these CFRSEP-gear just like the super-engineering plastic gears in [18]. This dimensional accuracy is sustained even for miniature and mm-sized CFRSEP-gears. These gears must be suitable to micro-systems such as a mobile phone and a sensing micro-robots [19]. Mesoscopic and micro CFRSEP gears grow up to key elements of various micro-systems and devices used for transmitting power and/or motion due to their ultra-light weight, smaller size and compact, higher dimensional accuracy, better functional and operating characteristics, longer service life, zero backlash and ability to sustain their performance under risky ecological environments.

## Summary

A manufacturing methodology is proposed to fabricate the miniature carbon fiber reinforced super-engineering plastic gears in mm- to cm-range from the feedstock of polyimide matrix and short-
lines. This implies that the short carbon fibers are massively pushed into the tooth-cavity of die. That is, the viscous mixtures are filled into the tooth-cavity of die by higher stress gradient from the center of preform to every end of tooth cavity. Relatively longer duration is necessary to this fill-filling of viscous mixture to die cavity.

In the sinter-forging step, the microstructure of hot-forged mixture is homogenized to fix the alignment of carbon fibers in the matrix and to increase the relative density. As depicted in Fig. 8, no porosities are seen in the cross-sectional XCT image; the microstructure becomes uniform without segregation of fibers.

The present XCT has a spatial resolution of 50 µm; local orientation of short carbon fibers is difficult to analyze the original images. In order to describe the local densification and stiffness, finer spatial resolution is necessary. At present, the XCT in the synchrotron-radiation imaging with the use of high intensity X-ray is planned to utilize for this measurement [12]. Under this fine XCT, the local alignment of each short carbon fiber can be analyzed to deduce each orientation of short carbon fiber in the polyimide matrix.

The homogenized finite element analysis [13] is useful to estimate the local stiffness tensor in correspondence to the unit-cell image of XCT-scanned three dimensional image. After [14-15], the unit cell model was determined from the real SEM image of composite materials such as iron ores to calculate its equivalent stiffness and stress distribution in it. This estimate on the homogenized local stiffness tensor is responsible for theoretical validation on the effect of the carbon mass fraction on the hardness.

The orientation of carbon fibers has essential influence on the stiffness and strength of carbon fiber reinforced plastic components. With respect to the reinforcement by the long fibers, the misorientation in the neighboring fibers mainly determines the stiffness of CFRP parts [16]. On the other hand, the statistical distribution of short carbon fibers has main contribution to the stiffness. The unit-cell model is useful in evaluation on the stiffness of CFRSEP gears to represent their elastic stiffness tensor with direct consideration of the microstructure measured by XCT imaging.

The in situ alignment of short-cut carbon fibers in the polyimide matrix during the hot-forging step is identified as a self-orientation process of fibers under the elastic constraint by matrix in the visco-plastic flow. The programmable schedule of external loading in the forging step must be controlled to assist this self-orientation process of fibers to align the fibers along the gear shape. As shown in Figs. 7 and 8, the image-tracing of black dots and lines by XCT enables to describe this self-orientation process with time in loading.

Let us reconsider the marketing of carbon fiber reinforced super-engineering plastic (CFRSEP) gears. The flexible and precise movement of joints in robotics needs the light-weight and small-sized gears with high engineering durability [15, 17]. Due to the carbon fiber reinforcement at the tooth top and root, the tooth-to-tooth traction transfer is put into practice by using the CFRSEP-gears. After early measurement on the gear-grade balancing, the JIS-3 to JIS-5 grades can be attained even in these CFRSEP-gear just like the super-engineering plastic gears in [18]. This dimensional accuracy is sustained even for miniature and mm-sized CFRSEP-gears. These gears must be suitable to micro-systems such as a mobile phone and a sensing micro-robots [19]. Mesoscopic and micro CFRSEP gears grow up to key elements of various micro-systems and devices used for transmitting power and/or motion due to their ultra-light weight, smaller size and compact, higher dimensional accuracy, better functional and operating characteristics, longer service life, zero backlash and ability to sustain their performance under risky ecological environments.

## Summary

A manufacturing methodology is proposed to fabricate the miniature carbon fiber reinforced super-engineering plastic gears in mm- to cm-range from the feedstock of polyimide matrix and short-
cut recycled carbon fibers. At first, this feed stock is poured into a die cavity and consolidated to a green preform. In second, this cylindrical preform was fixed into a gear-shaped die cavity of die and hot forged at 623 K for 180 s to a gear model. In third, this mode is further sinter-forged to homogenize its microstructure and yield the gear product with nearly full density. SCT and SEM are utilized to characterize the microstructure of preform, model and product by nondestructive and destructive material evaluation. In particular, the orientation of short carbon fibers to the tooth root and top is detected in the SCT of gear-product. The surface hardness of 180 HV<sub>IN</sub> than the hardness of 30 HV<sub>IN</sub> in sintered polyimide gear, proves that carbon reinforcement at the tooth root and top is responsible for this strengthening,

XCT imaging works well to describe the in situ carbon self-orientation during the hot- and sinter-forging processes. Since the spatial resolution in the present SCT is limited by 50 µm, fine imaging on the local alignment of fibers is difficult to analyze in the present study. Only black dots and lines at every tooth in gear model and product, implies that short carbon fibers are placed at every tooth root and top. When increasing this spatial resolution by using the synchrotron-radiation imaging, fine local SCT image is yielded to deduce the unit cell model to represent the equivalent microstructure of CFRSEP-gear. Using the homogenized finite element analysis, the elastic stiffness tensor is calculated from this unit cell model to compare the major elastic moduli in this tensor with the measured hardness of sinter-forged gear product and to provide a way to control the orientation of carbon fibers toward the high stiff and hard gears.

## Acknowledgment

The authors would like to express their gratitude to S-I. Kurozumi (Nano-Film Coat, llc.) for his help in experiments.

## References

[1] Ando, K., Future prospects and current situation of the robot reduction gear. J. Robotics 33 (5) (2015) pp. 329-333. https://doi.org/10.7210/jrsj.33.329

[2] Souza T. S. G., de Souza M. M., Savoy J., Light-weight assembled gears: A green design solution for passenger and commercial vehicles. Gear Tech. 5 (2013) pp. 64-71.

[3] Z. Liu, Z. You, Z. Wang, Lightweight design of multistage gear reducer based on continuous variables and discrete neighborhood. Proc. ICMD 2017 (2017) 379-387. https://doi.org/10.1007/978-981-10-6553-8_26

[4] Politis D. J., Politis N. J., Lin J., Review of recent developments in manufacturing lightweight multi-metal gears. Production Eng. 15 (2021) pp. 235-262. https://doi.org/10.1007/s11740-020-01011-5

[5] Tatsuno D., Yoneyama T., Kuga M., Honda Y., Akaishi Y., Hashimoto H., Fiber deformation behavior of discontinuous CFRTP in gear forging. Int. J. Material Forming 14 (2021) pp. 947-960. https://doi.org/10.1007/s12289-021-01611-1

[6] Tatsuno D., Masukawa H., Forming of CFTRP screw. Proc. JSTP (November 17th, 2023) pp. 315-316.

[7] More C. V., Alsayed Z., Badawi M. S., Thabet A., Pawar P. P., Polymetric composite materials for radiation shielding: a review. Environmental Chemistry Letters 2021, 19, 2057-2090. https://doi.org/10.1007/s10311-021-01189-9

[8] Park S-A., Jeon H., Kim H., Shin S-H., Choy S., Hwang D. D., Koo J. M., Jegal J., Hwang S. Y., Park J., Oh D. X., Sustainable and recyclable super engineering thermoplastic from
cut recycled carbon fibers. At first, this feed stock is poured into a die cavity and consolidated to a green preform. In second, this cylindrical preform was fixed into a gear-shaped die cavity of die and hot forged at 623 K for 180 s to a gear model. In third, this mode is further sinter-forged to homogenize its microstructure and yield the gear product with nearly full density. SCT and SEM are utilized to characterize the microstructure of preform, model and product by nondestructive and destructive material evaluation. In particular, the orientation of short carbon fibers to the tooth root and top is detected in the SCT of gear-product. The surface hardness of 180 HV<sub>IN</sub> than the hardness of 30 HV<sub>IN</sub> in sintered polyimide gear, proves that carbon reinforcement at the tooth root and top is responsible for this strengthening,

XCT imaging works well to describe the in situ carbon self-orientation during the hot- and sinter-forging processes. Since the spatial resolution in the present SCT is limited by 50 µm, fine imaging on the local alignment of fibers is difficult to analyze in the present study. Only black dots and lines at every tooth in gear model and product, implies that short carbon fibers are placed at every tooth root and top. When increasing this spatial resolution by using the synchrotron-radiation imaging, fine local SCT image is yielded to deduce the unit cell model to represent the equivalent microstructure of CFRSEP-gear. Using the homogenized finite element analysis, the elastic stiffness tensor is calculated from this unit cell model to compare the major elastic moduli in this tensor with the measured hardness of sinter-forged gear product and to provide a way to control the orientation of carbon fibers toward the high stiff and hard gears.

## Acknowledgment

The authors would like to express their gratitude to S-I. Kurozumi (Nano-Film Coat, llc.) for his help in experiments.

## References

[1] Ando, K., Future prospects and current situation of the robot reduction gear. J. Robotics 33 (5) (2015) pp. 329-333. https://doi.org/10.7210/jrsj.33.329

[2] Souza T. S. G., de Souza M. M., Savoy J., Light-weight assembled gears: A green design solution for passenger and commercial vehicles. Gear Tech. 5 (2013) pp. 64-71.

[3] Z. Liu, Z. You, Z. Wang, Lightweight design of multistage gear reducer based on continuous variables and discrete neighborhood. Proc. ICMD 2017 (2017) 379-387. https://doi.org/10.1007/978-981-10-6553-8_26

[4] Politis D. J., Politis N. J., Lin J., Review of recent developments in manufacturing lightweight multi-metal gears. Production Eng. 15 (2021) pp. 235-262. https://doi.org/10.1007/s11740-020-01011-5

[5] Tatsuno D., Yoneyama T., Kuga M., Honda Y., Akaishi Y., Hashimoto H., Fiber deformation behavior of discontinuous CFRTP in gear forging. Int. J. Material Forming 14 (2021) pp. 947-960. https://doi.org/10.1007/s12289-021-01611-1

[6] Tatsuno D., Masukawa H., Forming of CFTRP screw. Proc. JSTP (November 17th, 2023) pp. 315-316.

[7] More C. V., Alsayed Z., Badawi M. S., Thabet A., Pawar P. P., Polymetric composite materials for radiation shielding: a review. Environmental Chemistry Letters 2021, 19, 2057-2090. https://doi.org/10.1007/s10311-021-01189-9

[8] Park S-A., Jeon H., Kim H., Shin S-H., Choy S., Hwang D. D., Koo J. M., Jegal J., Hwang S. Y., Park J., Oh D. X., Sustainable and recyclable super engineering thermoplastic from
biorenewable monomer. Nature Communications. 2919, 10, 2601.
https://doi.org/10.1038/s41467-019-10582-6

[9] Aizawa, T., Miyata, T., K. Endo, Two-step PM forging for precise fabrication of carbon fiber reinforced engineering plastic gears. Mater. Res. Proc. 28 (2023) pp. 1799-1808.
https://doi.org/10.21741/9781644902479-195

[10] Aizawa, T., Miyata, T., Endo, K., Fine sinter-forging of miniature super-engineering plastic gears for carbon fiber reinforcement design. Proc. 5th WCMNM (Chicago, USA; September 19th, 2023) pp. 1-5.

[11] Joung C. G., Phan-Thien N., Fan X. J., Viscosity of curved fibers in suspension. J. Non-Newtonian Fluid Mechanics 102 (1) (2002) pp. 1-17.
https://doi.org/10.1016/S0377-0257(01)00163-X

[12] Strotton M. C., Bodey A. J., Wanelik K., Darrow M. C., Medina E., Hobbs C., Rau C., Bradbury E. J., Optimising complementary soft tissue synchrotron X-ray microtomography for reversibly-stained central nervous system samples. Sci. Rep. 8 (2018) 12017.
https://doi.org/10.1038/s41598-018-30520-8

[13] Schenk D., Mathis A., Lippuner K., Zysset P., In vivo repeatability of homogenized finite element analysis based on multiple HR-pQCT sections for assessment of distal radius and tibia strength. Bone 141 (2020) 115575.
https://doi.org/10.1016/j.bone.2020.115575

[14] Aizawa T., Suwa Y., Muraishi S., Real microstructure modeling for stiffness and strength analyses of texture in ores. ISIJ-International 44 (12) (2004) pp. 2086-2092.
https://doi.org/10.2355/isijinternational.44.2086

[15] Aizawa T., Suwa Y., Meso-porous modeling for theoretical analysis of sinter ores by the phase-field, unit-cell method. ISIJ-International 45 (4) (2005) pp. 587-593.
https://doi.org/10.2355/isijinternational.45.587

[16] Lomov S. V., Fiber mis-orientation identified via XCT and structure tensor-based image analysis. ESAFORM2023-Webinar (September 20th, 2023).

[17] Hashimoto K., Mechanics of humanoid robot. Advanced Robotics 34 (21-22) (2020) pp. 1390-1397.
https://doi.org/10.1080/01691864.2020.1813624

[18] Aizawa T., Miyata T., Endoh K., Two-step PM-procedure for fabrication of super-engineering plastic gears. J. Machines (2024) (in press).
https://doi.org/10.3390/machines12030174

[19] Chaubey S. K., Jain B. K., State-of-art review of past research on manufacturing of meso and micro cylindrical gears. Precision Engineering 51 (2018) pp. 702-728.
https://doi.org/10.1016/j.precisioneng.2017.07.014
biorenewable monomer. Nature Communications. 2919, 10, 2601.
https://doi.org/10.1038/s41467-019-10582-6

[9] Aizawa, T., Miyata, T., K. Endo, Two-step PM forging for precise fabrication of carbon fiber reinforced engineering plastic gears. Mater. Res. Proc. 28 (2023) pp. 1799-1808.
https://doi.org/10.21741/9781644902479-195

[10] Aizawa, T., Miyata, T., Endo, K., Fine sinter-forging of miniature super-engineering plastic gears for carbon fiber reinforcement design. Proc. 5th WCMNM (Chicago, USA; September 19th, 2023) pp. 1-5.

[11] Joung C. G., Phan-Thien N., Fan X. J., Viscosity of curved fibers in suspension. J. Non-Newtonian Fluid Mechanics 102 (1) (2002) pp. 1-17.
https://doi.org/10.1016/S0377-0257(01)00163-X

[12] Strotton M. C., Bodey A. J., Wanelik K., Darrow M. C., Medina E., Hobbs C., Rau C., Bradbury E. J., Optimising complementary soft tissue synchrotron X-ray microtomography for reversibly-stained central nervous system samples. Sci. Rep. 8 (2018) 12017.
https://doi.org/10.1038/s41598-018-30520-8

[13] Schenk D., Mathis A., Lippuner K., Zysset P., In vivo repeatability of homogenized finite element analysis based on multiple HR-pQCT sections for assessment of distal radius and tibia strength. Bone 141 (2020) 115575.
https://doi.org/10.1016/j.bone.2020.115575

[14] Aizawa T., Suwa Y., Muraishi S., Real microstructure modeling for stiffness and strength analyses of texture in ores. ISIJ-International 44 (12) (2004) pp. 2086-2092.
https://doi.org/10.2355/isijinternational.44.2086

[15] Aizawa T., Suwa Y., Meso-porous modeling for theoretical analysis of sinter ores by the phase-field, unit-cell method. ISIJ-International 45 (4) (2005) pp. 587-593.
https://doi.org/10.2355/isijinternational.45.587

[16] Lomov S. V., Fiber mis-orientation identified via XCT and structure tensor-based image analysis. ESAFORM2023-Webinar (September 20th, 2023).

[17] Hashimoto K., Mechanics of humanoid robot. Advanced Robotics 34 (21-22) (2020) pp. 1390-1397.
https://doi.org/10.1080/01691864.2020.1813624

[18] Aizawa T., Miyata T., Endoh K., Two-step PM-procedure for fabrication of super-engineering plastic gears. J. Machines (2024) (in press).
https://doi.org/10.3390/machines12030174

[19] Chaubey S. K., Jain B. K., State-of-art review of past research on manufacturing of meso and micro cylindrical gears. Precision Engineering 51 (2018) pp. 702-728.
https://doi.org/10.1016/j.precisioneng.2017.07.014
# Rheological behavior of nanofillers enclosed multilayer systems under elongational flows: From microlayers to nanolayers

LI Jixiang¹,ª, MAAZOUZ Abderrahim¹,ᵇ and LAMNAWAR Khalid¹,ᶜ*

¹Université de Lyon, CNRS, UMR 5223, Ingénierie des Matériaux Polymères, INSA Lyon, F-69621, Villeurbanne, France

ªjixiang.li@insa-lyon.fr, ᵇabderrahim.maazouz@insa-lyon.fr, ᶜkhalid.lamnawar@insa-lyon.fr

**Keywords:** Polymer Nanocomposites, Multilayer, Forced Assembly, Elongational Flow

**Abstract.** The present work dedicated in the elongational behavior of multilayer polymer nanocomposites. CNTs were enclosed in a polypropylene with linear chain structure (PPC) and then co-extruded with another polypropylene (PPH) with long chain branching (LCB). By forced assembly, multilayer films with layer thickness from micro to nano were fabricated and the elongational rheology test was then conducted with the extension vertical to the film extrusion direction. Due to the LCB inside PPH, all multilayer films showed obvious strain hardening behavior despite linear PPC is a strain softening polymer. When the layer numbers were fewer, namely, the layer thickness was higher than the length of the CNTs, the strain hardening behavior of nanocomposite films was close to the multilayer system with neat polymers. With the layer numbers increasing, the layer thickness became lower than the length of the CNTs and the strain hardening behavior of nanocomposite films increased dramatically compared to the multilayer system with neat polymers. The reason for this kind behavior was because of the better orientation of CNTs via layer confinement when layer numbers increased, which thus making the strain hardening more significant.

**Introduction**

With the coming era of 5G, the demand of materials with higher efficiency for electromagnetic interference (EMI) shielding is growing rapidly. Enclosing conductive fillers into multilayer polymer films has been reported to enhance the EMI shielding properties dramatically[1–3]. Popular techniques of fabricating Multilayer films including layer-by-layer casting, spin coating or compression molding are often with many steps and hard to be industrialized[4]. Therefore, forced assembly co-extrusion seems to be a better solution for this problem as the process is continuous. During the forced assembly, the flow effects to the fillers dispersion and alignment can be crucial for the final properties.

Extensional rheology is a rapid developing technology[5] to study multilayer systems recently which can reflect chain entanglement in the interphase as well as interfacial slip and failure dramatically[6]. For example, Zhang et al. created a compatible multilayer film by combining poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) with a composition of 50% using layer-multiplying coextrusion[7]. Besides, elongational rheology also can be effective to detect the nanofillers behavior during melt state, which is rarely been studied.

In this context, polypropylenes with chain structure of linear (PPC) and long chain branching (PPH) were applied as the polymer pair for co-extrusion and carbon nanotubes (CNTs) as the conductive fillers enclosed in PPC. Multilayer films with different layer numbers from micro-layer to nano-layer thickness were fabricated. Extension rheology was then conducted to investigate the strain hardening behavior of PPH/PPC(CNTs) films and compared with PPH/PPC films and neat polymers to reflect the fillers alignment during forced assembly co-extrusion.

<figure><img src="image_2504.png" /></figure>
# Rheological behavior of nanofillers enclosed multilayer systems under elongational flows: From microlayers to nanolayers

LI Jixiang¹,ª, MAAZOUZ Abderrahim¹,ᵇ and LAMNAWAR Khalid¹,ᶜ*

¹Université de Lyon, CNRS, UMR 5223, Ingénierie des Matériaux Polymères, INSA Lyon, F-69621, Villeurbanne, France

ªjixiang.li@insa-lyon.fr, ᵇabderrahim.maazouz@insa-lyon.fr, ᶜkhalid.lamnawar@insa-lyon.fr

**Keywords:** Polymer Nanocomposites, Multilayer, Forced Assembly, Elongational Flow

**Abstract.** The present work dedicated in the elongational behavior of multilayer polymer nanocomposites. CNTs were enclosed in a polypropylene with linear chain structure (PPC) and then co-extruded with another polypropylene (PPH) with long chain branching (LCB). By forced assembly, multilayer films with layer thickness from micro to nano were fabricated and the elongational rheology test was then conducted with the extension vertical to the film extrusion direction. Due to the LCB inside PPH, all multilayer films showed obvious strain hardening behavior despite linear PPC is a strain softening polymer. When the layer numbers were fewer, namely, the layer thickness was higher than the length of the CNTs, the strain hardening behavior of nanocomposite films was close to the multilayer system with neat polymers. With the layer numbers increasing, the layer thickness became lower than the length of the CNTs and the strain hardening behavior of nanocomposite films increased dramatically compared to the multilayer system with neat polymers. The reason for this kind behavior was because of the better orientation of CNTs via layer confinement when layer numbers increased, which thus making the strain hardening more significant.

**Introduction**

With the coming era of 5G, the demand of materials with higher efficiency for electromagnetic interference (EMI) shielding is growing rapidly. Enclosing conductive fillers into multilayer polymer films has been reported to enhance the EMI shielding properties dramatically[1–3]. Popular techniques of fabricating Multilayer films including layer-by-layer casting, spin coating or compression molding are often with many steps and hard to be industrialized[4]. Therefore, forced assembly co-extrusion seems to be a better solution for this problem as the process is continuous. During the forced assembly, the flow effects to the fillers dispersion and alignment can be crucial for the final properties.

Extensional rheology is a rapid developing technology[5] to study multilayer systems recently which can reflect chain entanglement in the interphase as well as interfacial slip and failure dramatically[6]. For example, Zhang et al. created a compatible multilayer film by combining poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) with a composition of 50% using layer-multiplying coextrusion[7]. Besides, elongational rheology also can be effective to detect the nanofillers behavior during melt state, which is rarely been studied.

In this context, polypropylenes with chain structure of linear (PPC) and long chain branching (PPH) were applied as the polymer pair for co-extrusion and carbon nanotubes (CNTs) as the conductive fillers enclosed in PPC. Multilayer films with different layer numbers from micro-layer to nano-layer thickness were fabricated. Extension rheology was then conducted to investigate the strain hardening behavior of PPH/PPC(CNTs) films and compared with PPH/PPC films and neat polymers to reflect the fillers alignment during forced assembly co-extrusion.

<figure><img src="image_2497.png" /></figure>
## Experiment section

*Materials:* PPC (polypropylene, RD204CF, Borealis AG, Austria) and PPH (polypropylene, Daploy™ WB140HMS, Borealis AG, Austria) were chosen as the polymer matrices. The melt flow rate (MFR) of PPC was 8 g/10min and that of PPH was 2.1 g/10min. Multiwall Carbon Nanotubes (CNTs) were purchased from Nanocyl SA in Belgium and their properties are listed in Table 1.

<table><caption>Table 1 Physical properties of the CNTs</caption><thead><tr><td>Diameter (nm)</td><td>Average length (μm)</td><td>Surface Area (m²/g)</td></tr></thead><tbody><tr><td>7~20</td><td>1.5</td><td>250~300</td></tr></tbody></table>

*Sample preparation:* The CNTs were melt mixed with PPC in a twin-screw extruder to prepare masterbatches with a CNT amount of 2 wt% (PPC(CNTs)). PPH and PPC(CNTs) with volume fraction of 50/50 were then co-extruded via a homemade multilayer coextrusion setup as schemed in Figure 1. Two extruders were combined through a feedblock from where a series of layer multiplication dies were connected. The two different polymer melts first meet in the feedblock in a bilayer configuration, then, when going through the layer multiplication dies, the melt is successively split vertically and horizontally spread back to its original width before being stacked again, keeping the total film thickness constant. The final number of layers is determined by the number of multipliers used. During the coextrusion process, the melt temperature was set at 260°C for the extruders, multipliers, and die. The chill-roll temperature was set to 90°C and at certain speed to obtain a total film thickness of 500±50 µm. The stretching ratio was kept low as the focus is mainly set on the structuration due to the coextrusion and layer multiplication processes rather than chain orientation by drawing. The feedblock configuration used for the systems was a A/B/A configuration, where A and B correspond to the extruders displayed in Figure 1. A set of N multipliers leads to a final film of 2N+1 +1 layers. Neat PPH and PPC were also co-extruded as references. Multilayer films of neat PPH and PPC with volume fraction of 50/50 were also prepared similarly via the coextrusion setup as references. Besides, Neat polymers, the 50/50 volume fraction blend films of PPH/PPC and PPH/ PPC(CNTs) were also extruded by the setup where only extruder A was using.

<figure><img src="image_2505.png" /><figcaption>Figure 1 Schematic illustration of layer multiplication in the homemade multilayer coextrusion setup.</figcaption></figure>

All produced and studied multilayer films are listed in Table 2 with PPH combined with PPC or PPC(CNTs), where n is the number of multipliers and N the corresponding number of layers. The estimated nominal layer thickness for each layer with a A/B film configuration was calculated using Equation 1.

$$h_{nomA,B} = \varphi_{A,B} \frac{h_{total}}{2^n} \quad (1)$$
## Experiment section

*Materials:* PPC (polypropylene, RD204CF, Borealis AG, Austria) and PPH (polypropylene, Daploy™ WB140HMS, Borealis AG, Austria) were chosen as the polymer matrices. The melt flow rate (MFR) of PPC was 8 g/10min and that of PPH was 2.1 g/10min. Multiwall Carbon Nanotubes (CNTs) were purchased from Nanocyl SA in Belgium and their properties are listed in Table 1.

<table><caption>Table 1 Physical properties of the CNTs</caption><thead><tr><td>Diameter (nm)</td><td>Average length (μm)</td><td>Surface Area (m²/g)</td></tr></thead><tbody><tr><td>7~20</td><td>1.5</td><td>250~300</td></tr></tbody></table>

*Sample preparation:* The CNTs were melt mixed with PPC in a twin-screw extruder to prepare masterbatches with a CNT amount of 2 wt% (PPC(CNTs)). PPH and PPC(CNTs) with volume fraction of 50/50 were then co-extruded via a homemade multilayer coextrusion setup as schemed in Figure 1. Two extruders were combined through a feedblock from where a series of layer multiplication dies were connected. The two different polymer melts first meet in the feedblock in a bilayer configuration, then, when going through the layer multiplication dies, the melt is successively split vertically and horizontally spread back to its original width before being stacked again, keeping the total film thickness constant. The final number of layers is determined by the number of multipliers used. During the coextrusion process, the melt temperature was set at 260°C for the extruders, multipliers, and die. The chill-roll temperature was set to 90°C and at certain speed to obtain a total film thickness of 500±50 µm. The stretching ratio was kept low as the focus is mainly set on the structuration due to the coextrusion and layer multiplication processes rather than chain orientation by drawing. The feedblock configuration used for the systems was a A/B/A configuration, where A and B correspond to the extruders displayed in Figure 1. A set of N multipliers leads to a final film of 2N+1 +1 layers. Neat PPH and PPC were also co-extruded as references. Multilayer films of neat PPH and PPC with volume fraction of 50/50 were also prepared similarly via the coextrusion setup as references. Besides, Neat polymers, the 50/50 volume fraction blend films of PPH/PPC and PPH/ PPC(CNTs) were also extruded by the setup where only extruder A was using.

<figure><img src="image_2498.png" /><figcaption>Figure 1 Schematic illustration of layer multiplication in the homemade multilayer coextrusion setup.</figcaption></figure>

All produced and studied multilayer films are listed in Table 2 with PPH combined with PPC or PPC(CNTs), where n is the number of multipliers and N the corresponding number of layers. The estimated nominal layer thickness for each layer with a A/B film configuration was calculated using Equation 1.

$$h_{nomA,B} = \varphi_{A,B} \frac{h_{total}}{2^n} \quad (1)$$
where $\phi_A$ and $\phi_B$ represent the volume fraction of A and B, respectively, $h_{total}$ the total film thickness and n the number of multipliers.

<table><caption>Table 2. Characteristics of the multilayered PPH/PPC and PPH/PPC(CNTs) films, where the $h_T$ represent the total thickness of the film and $h_N$ represent the thersitical layer thickness.</caption><thead><tr><th colspan="2">Polymer systems</th><th colspan="2">PPH/PPC</th><th colspan="2">PPH/PPC(CNTs)</th></tr><tr><th>no. of layers (N)</th><th>no. of multipliers (n)</th><th>h<sub>T</sub> (μm)</th><th>h<sub>N</sub></th><th>h<sub>T</sub> (μm)</th><th>h<sub>N</sub></th></tr></thead><tbody><tr><td>3L</td><td>0</td><td>518</td><td>259 μm</td><td>530</td><td>265 μm</td></tr><tr><td>17L</td><td>3</td><td>524</td><td>32.75 μm</td><td>541</td><td>33.81 μm</td></tr><tr><td>257L</td><td>6</td><td>486</td><td>1.89 μm</td><td>492</td><td>1.92 μm</td></tr><tr><td>1025L</td><td>9</td><td>526</td><td>510 nm</td><td>515</td><td>500 nm</td></tr></tbody></table>

**Size exclusion chromatography and multi-angle laser light scattering (SEC-MALLS):** The average molecular weights and the polymer chain microstructure were determined by SEC-MALLS which is a combination of SEC for separation with a multi-angle laser scattering (MALLS) for analysis. Both PP samples were run at 160°C with 1,2,4-trichlorobenzene (TCB) as the solvent and at a flow rate of 1 mL/min. The light scattering detector was placed in line between the SEC system and the refractive index detector. The absolute molecular weight and radius of gyration R<sub>g</sub> of both PPs used in this study were measured directly by the SEC-MALS technique, and as a result the long-chain branching distribution and content in the PPs could be determined by direct application of the Zimm-Stock approach[8].

**Uniaxial Extensional Rheology:** Uniaxial extensional rheology was carried out using a Sentmanat extensional rheometer fixture (SER-2, Xpansion Instruments, LLC) mounted on the DHR-2 rheometer.29,36 Samples from the extrusion process were cut into rectangular strips with the following dimensions: length, width, and thickness of 20 mm × 10 mm × 0.5 mm (width along the extrusion direction) for the extensional test. Each sample was preheated at the tested temperature for 120 s in the rheometer oven before tests and was observed with a built-in camera to ensure sagging did not occur. Extensional flow data were then collected with extension vertical to the film extrusion direction at a constant Hencky strain rate at 180 °C under nitrogen. All measurements were repeated at least three times.

## Results and discussion

The combination of SEC and MALLS is a versatile and reliable means of characterizing the polymer chain microstructure. In this study, the LCBs of PPH could be clearly reflected by analysis of the SEC-MALLS results. The molar mass distributions and radius of gyration ($R_g$) related to the molar mass of the two polymers are illustrated in Figure 2. The broader distribution of the molecular weight with two peaks of PPH was the first clue to the presence of LCBs. Meanwhile, the nonlinearity of $R_g$ for PPH related to molar mass also suggested a disparate polymer chain microstructure between PPC and PPH.

For PPC with linear chain structure, the curve of $R_g$ complied well with the linear reference of linear PP[9]. On the other hand, higher values of $R_g$ of the lower molecular weight PPH and a deviation from the linear reference PP curve in the higher molecular area indicated a probable branched or star-like chain structure in PPH[10]. This last feature is typical of LDPE and has also been found for electron beam irradiated polypropylenes[11,12].
where $\phi_A$ and $\phi_B$ represent the volume fraction of A and B, respectively, $h_{total}$ the total film thickness and n the number of multipliers.

<table><caption>Table 2. Characteristics of the multilayered PPH/PPC and PPH/PPC(CNTs) films, where the $h_T$ represent the total thickness of the film and $h_N$ represent the thersitical layer thickness.</caption><thead><tr><th colspan="2">Polymer systems</th><th colspan="2">PPH/PPC</th><th colspan="2">PPH/PPC(CNTs)</th></tr><tr><th>no. of layers (N)</th><th>no. of multipliers (n)</th><th>h<sub>T</sub> (μm)</th><th>h<sub>N</sub></th><th>h<sub>T</sub> (μm)</th><th>h<sub>N</sub></th></tr></thead><tbody><tr><td>3L</td><td>0</td><td>518</td><td>259 μm</td><td>530</td><td>265 μm</td></tr><tr><td>17L</td><td>3</td><td>524</td><td>32.75 μm</td><td>541</td><td>33.81 μm</td></tr><tr><td>257L</td><td>6</td><td>486</td><td>1.89 μm</td><td>492</td><td>1.92 μm</td></tr><tr><td>1025L</td><td>9</td><td>526</td><td>510 nm</td><td>515</td><td>500 nm</td></tr></tbody></table>

**Size exclusion chromatography and multi-angle laser light scattering (SEC-MALLS):** The average molecular weights and the polymer chain microstructure were determined by SEC-MALLS which is a combination of SEC for separation with a multi-angle laser scattering (MALLS) for analysis. Both PP samples were run at 160°C with 1,2,4-trichlorobenzene (TCB) as the solvent and at a flow rate of 1 mL/min. The light scattering detector was placed in line between the SEC system and the refractive index detector. The absolute molecular weight and radius of gyration Rg of both PPs used in this study were measured directly by the SEC-MALS technique, and as a result the long-chain branching distribution and content in the PPs could be determined by direct application of the Zimm-Stock approach[8].

**Uniaxial Extensional Rheology:** Uniaxial extensional rheology was carried out using a Sentmanat extensional rheometer fixture (SER-2, Xpansion Instruments, LLC) mounted on the DHR-2 rheometer.29,36 Samples from the extrusion process were cut into rectangular strips with the following dimensions: length, width, and thickness of 20 mm × 10 mm × 0.5 mm (width along the extrusion direction) for the extensional test. Each sample was preheated at the tested temperature for 120 s in the rheometer oven before tests and was observed with a built-in camera to ensure sagging did not occur. Extensional flow data were then collected with extension vertical to the film extrusion direction at a constant Hencky strain rate at 180 °C under nitrogen. All measurements were repeated at least three times.

## Results and discussion

The combination of SEC and MALLS is a versatile and reliable means of characterizing the polymer chain microstructure. In this study, the LCBs of PPH could be clearly reflected by analysis of the SEC-MALLS results. The molar mass distributions and radius of gyration ($R_g$) related to the molar mass of the two polymers are illustrated in Figure 2. The broader distribution of the molecular weight with two peaks of PPH was the first clue to the presence of LCBs. Meanwhile, the nonlinearity of $R_g$ for PPH related to molar mass also suggested a disparate polymer chain microstructure between PPC and PPH.

For PPC with linear chain structure, the curve of $R_g$ complied well with the linear reference of linear PP[9]. On the other hand, higher values of $R_g$ of the lower molecular weight PPH and a deviation from the linear reference PP curve in the higher molecular area indicated a probable branched or star-like chain structure in PPH[10]. This last feature is typical of LDPE and has also been found for electron beam irradiated polypropylenes[11,12].
<figure><img src="image_2506.png" /></figure>

<figure><img src="image_2507.png" /><figcaption>Figure 2 Size exclusion chromatography traces of the studied PP samples.</figcaption></figure>

More concrete evidence can be obtained by calculating the viscosity branching index *g*', the average number of branched points *B*<sub>n</sub> and the LCB frequency *λ*. The values of *B*<sub>n</sub> and *λ* between molecular weights of 3 × 10<sup>4</sup> and 1 × 10<sup>6</sup> g/mol are listed in Table 3. Although no great amount of LCBs was detected in PPH, there was already a significant influence on the viscoelastic properties compared with PPC with a linear chain structure.

<table><caption>Table 3 Long-chain branching characteristics. Viscosity branching index, average LCB per molecule and average branching frequency per 1000 units for PPH between 3 × 10<sup>4</sup> and 1 × 10<sup>6</sup> g/mol.</caption><thead><tr><td></td><td>g'</td><td>B<sub>n</sub> (LCB/molecule)</td><td>λ (LCB/1000 monomers)</td></tr></thead><tbody><tr><td>PPH</td><td>0.67</td><td>1.73</td><td>1.50</td></tr></tbody></table>

The extensional viscosities, $\eta_E^+$, of PPC and PPH melts as functions of time at constant Hencky strain rates, $\dot{\epsilon}_H$, ranging from 0.3 $S^{-1}$ to 10 $S^{-1}$, are presented in Figure 3. The linear viscoelastic (LVE) curves which corresponded very well with the threefold value of the linear viscosity ($3\eta_0^+$) [13] measured during startup shear in the range of linear deformation are also displayed. Apparently, PPC with linear chain structure is a strain softening polymer with very slight strain hardening observed at the $\dot{\epsilon}_H$ of 10 $S^{-1}$, which complies with other report[14]. By contrast, the phenomena that occurred for PPH were different. For all $\dot{\epsilon}_H$ tested in this work, the PPH samples showed obvious strain hardening behaviors. In fact, polymers with LCB resisted chain disentanglement[15], particularly in extension, wherefore the final collapse of the entanglement network was effectively postponed. Such behavior would be favorable for stable film blowing and fiber spinning. In summary, it can be suggested that the presence of LCB in PPH favored the more obvious strain hardening behaviors during the elongational experiments. In contrast, PPC with its linear structure showed less strain hardening.
<figure><img src="image_2499.png" /></figure>

<figure><img src="image_2500.png" /><figcaption>Figure 2 Size exclusion chromatography traces of the studied PP samples.</figcaption></figure>

More concrete evidence can be obtained by calculating the viscosity branching index *g*', the average number of branched points *B*<sub>n</sub> and the LCB frequency *λ*. The values of *B*<sub>n</sub> and *λ* between molecular weights of 3 × 10<sup>4</sup> and 1 × 10<sup>6</sup> g/mol are listed in Table 3. Although no great amount of LCBs was detected in PPH, there was already a significant influence on the viscoelastic properties compared with PPC with a linear chain structure.

<table><caption>Table 3 Long-chain branching characteristics. Viscosity branching index, average LCB per molecule and average branching frequency per 1000 units for PPH between 3 × 10<sup>4</sup> and 1 × 10<sup>6</sup> g/mol.</caption><thead><tr><td></td><td>g'</td><td>B<sub>n</sub> (LCB/molecule)</td><td>λ (LCB/1000 monomers)</td></tr></thead><tbody><tr><td>PPH</td><td>0.67</td><td>1.73</td><td>1.50</td></tr></tbody></table>

The extensional viscosities, $\eta_E^+$, of PPC and PPH melts as functions of time at constant Hencky strain rates, $\dot{\epsilon}_H$, ranging from 0.3 $S^{-1}$ to 10 $S^{-1}$, are presented in Figure 3. The linear viscoelastic (LVE) curves which corresponded very well with the threefold value of the linear viscosity ($3\eta_0^+$) [13] measured during startup shear in the range of linear deformation are also displayed. Apparently, PPC with linear chain structure is a strain softning polymer with very slight strain hardening observed at the $\dot{\epsilon}_H$ of 10 $S^{-1}$, which complies with other report[14]. By contrast, the phenomena that occurred for PPH were different. For all $\dot{\epsilon}_H$ tested in this work, the PPH samples showed obvious strain hardening behaviors. In fact, polymers with LCB resisted chain disentanglement[15], particularly in extension, wherefore the final collapse of the entanglement network was effectively postponed. Such behavior would be favorable for stable film blowing and fiber spinning. In summary, it can be suggested that the presence of LCB in PPH favored the more obvious strain hardening behaviors during the elongational experiments. In contrast, PPC with its linear structure showed less strain hardening.
<figure><img src="image_2508.png" /><figcaption>Figure 3 Elongation viscosity vs time at (a) 180 °C in startup uniaxial extension with constant Hencky strain rates ranging from 0.3 to 10.0 s⁻¹ for PPC and PPH</figcaption></figure>

The extensional viscosities of multilayer films with layer numbers of 17L and 1025L are shown in Figure 4. To clearer manifesting the tendency and comparing, extensional curves with $\dot{\epsilon}_H$ of only 0.3 S⁻¹ were presented. Blend and neat polymer films are also displayed as references. It can be suggested that except Neat PPC, all other films show strain hardening behavior indicating its sensitivity to the LCB[10,16]. Negative deviation of blend film curve with CNTs (CNTBlend) from neat polymer blend (Neat Blend) curve manifest the decrease of strain hardening due to the CNTs loading. The nanoparticles influence to the strain hardening behavior under elongational flow is reported to be complicated and may be related to the size, dispersion and attractive force between nanoparticles[17]. With the increased amounts of nanoparticles, the elongation viscosity often increased at lower $\dot{\epsilon}_H$ [18,19]. However, the strain hardening behavior at higher Hencky strain may disappeared or decreased. Elongation thinning may even happen at high $\dot{\epsilon}_H$ [20]. This is because at higher nanoparticles loading, especially higher than the percolation threshold, the aggregation of nanofillers form a rigid network making the film melt more solid like thus without extensibility[19]. In contrast, lower quantity of well dispersed nanofillers show less significant influence on the extensional viscosities of the system. In some cases, increased strain hardening may occur when enhancing the interaction between nano fillers and polymer chains[17]. Whereas, poor dispersed nanofillers inside the polymer matrix will lead to the disappear or decrease of strain hardening. In our blend cases, the CNTs were first dispersed in PPC and then mixed with PPH inside a single-screw extruder where the shear force is comparatively lower and the weight percentage of CNTs were only 1 wt%. Therefore, the dispersion of CNTs inside the blend films were not very well and these unconnected aggregates of CNTs may be the reason for the decrease of strain hardening compare to the neat polymer blend films.

For the multilayer films with neat polymers, the elongation viscosities are highly depended on the polymer pair properties and the number of layers, which were carefully studied by our previous work[21–23]. Generally, for multilayer system with two different polymers, a simple additivity rule can be applied to predict the elongational viscosity according to the elongational viscosities of the two neat polymers. Upon the uniaxial extension, the deformation rate for each layer in the multilayer structure is the same. The total force is the sum of the contributions of constituent layers and interphase/interlayer, which could be estimated with the following equation (2):

$$F(t) = \sigma_A A_A(t) + \sigma_B A_B(t) + \sigma_{int} A_{int}(t) \quad (2)$$
<figure><img src="image_2501.png" /><figcaption>Figure 3 Elongation viscosity vs time at (a) 180 °C in startup uniaxial extension with constant Hencky strain rates ranging from 0.3 to 10.0 s⁻¹ for PPC and PPH</figcaption></figure>

The extensional viscosities of multilayer films with layer numbers of 17L and 1025L are shown in Figure 4. To clearer manifesting the tendency and comparing, extensional curves with $\dot{\epsilon}_H$ of only 0.3 S⁻¹ were presented. Blend and neat polymer films are also displayed as references. It can be suggested that except Neat PPC, all other films show strain hardening behavior indicating its sensitivity to the LCB[10,16]. Negative deviation of blend film curve with CNTs (CNTBlend) from neat polymer blend (Neat Blend) curve manifest the decrease of strain hardening due to the CNTs loading. The nanoparticles influence to the strain hardening behavior under elongational flow is reported to be complicated and may be related to the size, dispersion and attractive force between nanoparticles[17]. With the increased amounts of nanoparticles, the elongation viscosity often increased at lower $\dot{\epsilon}_H$ [18,19]. However, the strain hardening behavior at higher Hencky strain may disappeared or decreased. Elongation thinning may even happen at high $\dot{\epsilon}_H$ [20]. This is because at higher nanoparticles loading, especially higher than the percolation threshold, the aggregation of nanofillers form a rigid network making the film melt more solid like thus without extensibility[19]. In contrast, lower quantity of well dispersed nanofillers show less significant influence on the extensional viscosities of the system. In some cases, increased strain hardening may occur when enhancing the interaction between nano fillers and polymer chains[17]. Whereas, poor dispersed nanofillers inside the polymer matrix will lead to the disappear or decrease of strain hardening. In our blend cases, the CNTs were first dispersed in PPC and then mixed with PPH inside a single-screw extruder where the shear force is comparatively lower and the weight percentage of CNTs were only 1 wt%. Therefore, the dispersion of CNTs inside the blend films were not very well and these unconnected aggregates of CNTs may be the reason for the decrease of strain hardening compare to the neat polymer blend films.

For the multilayer films with neat polymers, the elongation viscosities are highly depended on the polymer pair properties and the number of layers, which were carefully studied by our previous work[21–23]. Generally, for multilayer system with two different polymers, a simple additivity rule can be applied to predict the elongational viscosity according to the elongational viscosities of the two neat polymers. Upon the uniaxial extension, the deformation rate for each layer in the multilayer structure is the same. The total force is the sum of the contributions of constituent layers and interphase/interlayer, which could be estimated with the following equation (2):

$$F(t) = \sigma_A A_A(t) + \sigma_B A_B(t) + \sigma_{int} A_{int}(t) \quad (2)$$
where $\sigma_i(t)$ is the Cauchy stress of layer i (i denotes component layer A, B and the interphase/interlayer). $A_i(t)$ is the area of cross section parallel to the film coextrusion direction with $A_i(t) = W_i(t) \times H_i(t)$, where $W_i(t)$ and $H_i(t)$ are the time-dependent width and thickness of a layer i, respectively. Therefore, the transient extensional viscosity of the total multilayer structure including interphases can be described as:

$$ \eta_E^+(t) = \frac{F(t)}{\dot{\epsilon}_A(t)} = \phi_A \frac{\sigma_A(t)}{\dot{\epsilon}} + \phi_B \frac{\sigma_B(t)}{\dot{\epsilon}} + \phi_{int} \frac{\sigma_{int}(t)}{\dot{\epsilon}} = \phi_A \eta_{E,A}^+(t) + \phi_B \eta_{E,B}^+(t) + \phi_{int} \eta_{E,int}^+(t) \quad (3) $$

in which $\phi_i$ is the volume fraction of layer i with $\phi_i = A_i(t)/A_{total}(t) = H_i(t)/H_{total}(t)$.

Specifically, in the absence of an interphase layer, eq (4) can be simplified to rule as follows[24]:

$$ \eta_E^+(t) = \phi_A \eta_{E,A}^+(t) + \phi_B \eta_{E,B}^+(t) \quad (4) $$

During forced assembly, when the layer numbers are fewer, the contact time in the multiplier elements is less and the experimental data of elongational viscosity curve usually follows the prediction of additivity rule. When the layer numbers increased, the contact time increased with the numbers of multipliers. If the two polymers are miscible, interfacial diffusion would happen in case of films with high number of layers and would cause a positive deviation of experimental elongational viscosity curve from the simple additivity rule in absence of an interphase layer, which has been addressed in the study related to the multilayer system of PVDF and PMMA[22,23]. This is because of the increased chain entanglement between polymer-polymer interface. In addition, this kind of phenomenon may also happen when the polymer pairs are immiscible[25]. In our cases, as the polymer pairs are the same polymer with different chain structures, they are totally miscible thus causing the positive deviation of almost all the multilayer films from the calculated additivity rule using neat PPC and PPH (as the solid line shown in Figure 4 (a) and (b)). Therefore, the extensional behaviors of multilayer systems with neat PPC and PPH are close to the PPC/PPH blend films.

<figure><img src="image_2509.png" /><figcaption>Figure 4 Elongation viscosity vs time at 180 °C with constant Hencky strain rates of 0.5 s⁻¹ of neat polymer, blend and multilayer films where (a) 17L and (b) 1025L. All films were tested in the direction vertical to the extrusion direction. Solid line were calculated from additivity rule.</figcaption></figure>
where $\sigma_i(t)$ is the Cauchy stress of layer i (i denotes component layer A, B and the interphase/interlayer). $A_i(t)$ is the area of cross section parallel to the film coextrusion direction with $A_i(t) = W_i(t) \times H_i(t)$, where $W_i(t)$ and $H_i(t)$ are the time-dependent width and thickness of a layer i, respectively. Therefore, the transient extensional viscosity of the total multilayer structure including interphases can be described as:

$$ \eta_E^+(t) = \frac{F(t)}{\dot{\epsilon}A(t)} = \phi_A \frac{\sigma_A(t)}{\dot{\epsilon}} + \phi_B \frac{\sigma_B(t)}{\dot{\epsilon}} + \phi_{int} \frac{\sigma_{int}(t)}{\dot{\epsilon}} = \phi_A \eta_{E,A}^+(t) + \phi_B \eta_{E,B}^+(t) + \phi_{int} \eta_{E,int}^+(t) \quad (3) $$

in which $\phi_i$ is the volume fraction of layer i with $\phi_i = A_i(t)/A_{total}(t) = H_i(t)/H_{total}(t)$.

Specifically, in the absence of an interphase layer, eq (4) can be simplified to rule as follows[24]:

$$ \eta_E^+(t) = \phi_A \eta_{E,A}^+(t) + \phi_B \eta_{E,B}^+(t) \quad (4) $$

During forced assembly, when the layer numbers are fewer, the contact time in the multiplier elements is less and the experimental data of elongational viscosity curve usually follows the prediction of additivity rule. When the layer numbers increased, the contact time increased with the numbers of multipliers. If the two polymers are miscible, interfacial diffusion would happen in case of films with high number of layers and would cause a positive deviation of experimental elongational viscosity curve from the simple additivity rule in absence of an interphase layer, which has been addressed in the study related to the multilayer system of PVDF and PMMA[22,23]. This is because of the increased chain entanglement between polymer-polymer interface. In addition, this kind of phenomenon may also happen when the polymer pairs are immiscible[25]. In our cases, as the polymer pairs are the same polymer with different chain structures, they are totally miscible thus causing the positive deviation of almost all the multilayer films from the calculated additivity rule using neat PPC and PPH (as the solid line shown in Figure 4 (a) and (b)). Therefore, the extensional behaviors of multilayer systems with neat PPC and PPH are close to the PPC/PPH blend films.

<figure><img src="image_2502.png" /><figcaption>Figure 4 Elongation viscosity vs time at 180 °C with constant Hencky strain rates of 0.5 s⁻¹ of neat polymer, blend and multilayer films where (a) 17L and (b) 1025L. All films were tested in the direction vertical to the extrusion direction. Solid line were calculated from additivity rule.</figcaption></figure>
When adding CNTs into the PPC layer, the influence to the elongational viscosity of multilayer system with 17L was less significant as shown in Figure 4(a). Only a slight decrease of strain hardening was observed which is reasonable as the CNTs weight percentage was only 1 wt%. Conversely, when the layer number reached 1025, the strain hardening of multilayer system with CNTs was apparently enhanced compared with the film without CNTs. As the CNTs weight percentage was still 1wt%, we assumed to regard this phenomenon to the orientation of CNTs due to the layer confinement by PPH. In our previous work, we got the evidence that CNTs mobility inside a LCB polymer is restricted[26]. Therefore, during the forced assembly, CNTs are more pronounced to move with the flow inside PPC layer. With layer numbers increased, the nominal thickness of PPC layer decreased dramatically blow the length of CNTs as shown in Table 2 and the CNTs would be confined by the PPH layer causing a better orientation parallel to the extrusion direction as well as the layer interface as shown in Figure 5. As our extension direction was perpendicular to the extrusion direction, namely, it was also perpendicular to the CNTs orientation direction. The enhanced strain hardening is because of the increased force to change the CNTs orientation during stretching. The influence of strain hardening from the fillers orientation by flow was also reported by Yu wei et al where their tested fillers are glass fibers[27]. In our cases, it is the coordination of flow and layer confinement that enhanced the orientation of CNTs as well as the strain hardening of the loading films.
When adding CNTs into the PPC layer, the influence to the elongational viscosity of multilayer system with 17L was less significant as shown in Figure 4(a). Only a slight decrease of strain hardening was observed which is reasonable as the CNTs weight percentage was only 1 wt%. Conversely, when the layer number reached 1025, the strain hardening of multilayer system with CNTs was apparently enhanced compared with the film without CNTs. As the CNTs weight percentage was still 1wt%, we assumed to regard this phenomenon to the orientation of CNTs due to the layer confinement by PPH. In our previous work, we got the evidence that CNTs mobility inside a LCB polymer is restricted[26]. Therefore, during the forced assembly, CNTs are more pronounced to move with the flow inside PPC layer. With layer numbers increased, the nominal thickness of PPC layer decreased dramatically blow the length of CNTs as shown in Table 2 and the CNTs would be confined by the PPH layer causing a better orientation parallel to the extrusion direction as well as the layer interface as shown in Figure 5. As our extension direction was perpendicular to the extrusion direction, namely, it was also perpendicular to the CNTs orientation direction. The enhanced strain hardening is because of the increased force to change the CNTs orientation during stretching. The influence of strain hardening from the fillers orientation by flow was also reported by Yu wei et al where their tested fillers are glass fibers[27]. In our cases, it is the coordination of flow and layer confinement that enhanced the orientation of CNTs as well as the strain hardening of the loading films.
<figure><img src="image_2510.png" /><figcaption>Figure 5 Proposed schematic illustration displaying the increased strain hardening due to the CNTs orientation caused by layer confinement with layer numbers increased.</figcaption></figure>

## Conclusions

In summary, the elongation behaviors of polymer nanocomposites with multilayer structure were revealed in this work. Both blend films and multilayer films showed strain hardening behavior because of the LCB inside PPH, even though PPC alone was a strain softening polymer. The small amount of CNTs inside the films cause less significant influence to the films with fewer number of layers but strongly enhanced strain hardening to the films with a greater number of layers due to the better CNTs orientation which was beneficial from the coordination of extrusion flow and layer confinement.
<figure><img src="image_2503.png" /><figcaption>Figure 5 Proposed schematic illustration displaying the increased strain hardening due to the CNTs orientation caused by layer confinement with layer numbers increased.</figcaption></figure>

## Conclusions

In summary, the elongation behaviors of polymer nanocomposites with multilayer structure were revealed in this work. Both blend films and multilayer films showed strain hardening behavior because of the LCB inside PPH, even though PPC alone was a strain softening polymer. The small amount of CNTs inside the films cause less significant influence to the films with fewer number of layers but strongly enhanced strain hardening to the films with a greater number of layers due to the better CNTs orientation which was beneficial from the coordination of extrusion flow and layer confinement.
## References

[1] B. Zhou, Z. Zhang, Y. Li, G. Han, Y. Feng, B. Wang, D. Zhang, J. Ma, C. Liu, Flexible, Robust, and Multifunctional Electromagnetic Interference Shielding Film with Alternating Cellulose Nanofiber and MXene Layers, ACS Appl. Mater. Interfaces 12 (2020) 4895-4905. https://doi.org/10.1021/acsami.9b19768

[2] G. Yin, Y. Wang, W. Wang, D. Yu, Multilayer structured PANI/MXene/CF fabric for electromagnetic interference shielding constructed by layer-by-layer strategy, Colloids and Surfaces A: Physicochemical and Engineering Aspects 601 (2020) 125047. https://doi.org/10.1016/j.colsurfa.2020.125047

[3] L. He, Y. Shi, Q. Wang, D. Chen, J. Shen, S. Guo, Strategy for constructing electromagnetic interference shielding and flame retarding synergistic network in poly (butylene succinate) and thermoplastic polyurethane multilayered composites, Composites Science and Technology 199 (2020) 108324. https://doi.org/10.1016/j.compscitech.2020.108324

[4] X. Zhang, Y. Xu, X. Zhang, H. Wu, J. Shen, R. Chen, Y. Xiong, J. Li, S. Guo, Progress on the layer-by-layer assembly of multilayered polymer composites: Strategy, structural control and applications, Progress in Polymer Science 89 (2019) 76-107. https://doi.org/10.1016/j.progpolymsci.2018.10.002

[5] Q. Huang, When Polymer Chains Are Highly Aligned: A Perspective on Extensional Rheology, Macromolecules 55 (2022) 715-727. https://doi.org/10.1021/acs.macromol.1c02262.

[6] F. Gholami, L. Pakzad, E. Behzadfar, Morphological, interfacial and rheological properties in multilayer polymers: A review, Polymer 208 (2020) 122950. https://doi.org/10.1016/j.polymer.2020.122950

[7] H. Zhang, K. Lamnawar, A. Maazouz, J.M. Maia, A nonlinear shear and elongation rheological study of interfacial failure in compatible bilayer systems, Journal of Rheology 60 (2016) 1-23. https://doi.org/10.1122/1.4926492

[8] B.H. Zimm, W.H. Stockmayer, The dimensions of chain molecules containing branches and rings, The Journal of Chemical Physics 17 (1949) 1301-1314. https://doi.org/10.1063/1.1747157

[9] D. Auhl, J. Stange, H. Münstedt, B. Krause, D. Voigt, A. Lederer, U. Lappan, K. Lunkwitz, Long-Chain Branched Polypropylenes by Electron Beam Irradiation and Their Rheological Properties, Macromolecules 37 (2004) 9465-9472. https://doi.org/10.1021/ma030579w

[10] J. Stange, C. Uhl, H. Münstedt, Rheological behavior of blends from a linear and a long-chain branched polypropylene, Journal of Rheology 49 (2005) 1059-1079. https://doi.org/10.1122/1.2008297

[11] M. Sugimoto, T. Tanaka, Y. Masubuchi, J.-I. Takimoto, K. Koyama, Effect of chain structure on the melt rheology of modified polypropylene, Journal of Applied Polymer Science 73 (1999) 1493-1500. https://doi.org/10.1002/(SICI)1097-4628(19990822)73:8<1493::AID-APP18>3.0.CO;2-2

[12] S. Kurzbeck, F. Oster, H. Münstedt, T.Q. Nguyen, R. Gensler, Rheological properties of two polypropylenes with different molecular structure, Journal of Rheology 43 (1999) 359-374. https://doi.org/10.1122/1.551040

[13] F.T. Trouton, On the coefficient of viscous traction and its relation to that of viscosity, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 77 (1906) 426-440. https://doi.org/10.1098/rspa.1906.0038
## References

[1] B. Zhou, Z. Zhang, Y. Li, G. Han, Y. Feng, B. Wang, D. Zhang, J. Ma, C. Liu, Flexible, Robust, and Multifunctional Electromagnetic Interference Shielding Film with Alternating Cellulose Nanofiber and MXene Layers, ACS Appl. Mater. Interfaces 12 (2020) 4895-4905. https://doi.org/10.1021/acsami.9b19768

[2] G. Yin, Y. Wang, W. Wang, D. Yu, Multilayer structured PANI/MXene/CF fabric for electromagnetic interference shielding constructed by layer-by-layer strategy, Colloids and Surfaces A: Physicochemical and Engineering Aspects 601 (2020) 125047. https://doi.org/10.1016/j.colSURFA.2020.125047

[3] L. He, Y. Shi, Q. Wang, D. Chen, J. Shen, S. Guo, Strategy for constructing electromagnetic interference shielding and flame retarding synergistic network in poly (butylene succinate) and thermoplastic polyurethane multilayered composites, Composites Science and Technology 199 (2020) 108324. https://doi.org/10.1016/j.compscitech.2020.108324

[4] X. Zhang, Y. Xu, X. Zhang, H. Wu, J. Shen, R. Chen, Y. Xiong, J. Li, S. Guo, Progress on the layer-by-layer assembly of multilayered polymer composites: Strategy, structural control and applications, Progress in Polymer Science 89 (2019) 76-107. https://doi.org/10.1016/j.progpolymsci.2018.10.002

[5] Q. Huang, When Polymer Chains Are Highly Aligned: A Perspective on Extensional Rheology, Macromolecules 55 (2022) 715-727. https://doi.org/10.1021/acs.macromol.1c02262.

[6] F. Gholami, L. Pakzad, E. Behzadfar, Morphological, interfacial and rheological properties in multilayer polymers: A review, Polymer 208 (2020) 122950. https://doi.org/10.1016/j.polymer.2020.122950

[7] H. Zhang, K. Lamnawar, A. Maazouz, J.M. Maia, A nonlinear shear and elongation rheological study of interfacial failure in compatible bilayer systems, Journal of Rheology 60 (2016) 1-23. https://doi.org/10.1122/1.4926492

[8] B.H. Zimm, W.H. Stockmayer, The dimensions of chain molecules containing branches and rings, The Journal of Chemical Physics 17 (1949) 1301-1314. https://doi.org/10.1063/1.1747157

[9] D. Auhl, J. Stange, H. Münstedt, B. Krause, D. Voigt, A. Lederer, U. Lappan, K. Lunkwitz, Long-Chain Branched Polypropylenes by Electron Beam Irradiation and Their Rheological Properties, Macromolecules 37 (2004) 9465-9472. https://doi.org/10.1021/ma030579w

[10] J. Stange, C. Uhl, H. Münstedt, Rheological behavior of blends from a linear and a long-chain branched polypropylene, Journal of Rheology 49 (2005) 1059-1079. https://doi.org/10.1122/1.2008297

[11] M. Sugimoto, T. Tanaka, Y. Masubuchi, J.-I. Takimoto, K. Koyama, Effect of chain structure on the melt rheology of modified polypropylene, Journal of Applied Polymer Science 73 (1999) 1493-1500. https://doi.org/10.1002/(SICI)1097-4628(19990822)73:8<1493::AID-APP18>3.0.CO;2-2

[12] S. Kurzbeck, F. Oster, H. Münstedt, T.Q. Nguyen, R. Gensler, Rheological properties of two polypropylenes with different molecular structure, Journal of Rheology 43 (1999) 359-374. https://doi.org/10.1122/1.551040

[13] F.T. Trouton, On the coefficient of viscous traction and its relation to that of viscosity, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 77 (1906) 426-440. https://doi.org/10.1098/rspa.1906.0038
[14] J.M. Dealy, D.J. Read, R.G. Larson, Structure and Rheology of Molten Polymers, in: J.M. Dealy, D.J. Read, R.G. Larson (Eds.), Structure and Rheology of Molten Polymers (Second Edition), Hanser, 2018: p. I-XVII. https://doi.org/10.3139/9781569906125.fm

[15] G. Liu, H. Sun, S. Rangou, K. Ntetsikas, A. Avgeropoulos, S.-Q. Wang, Studying the origin of “strain hardening”: Basic difference between extension and shear, Journal of Rheology 57 (2013) 89–104. https://doi.org/10.1122/1.4763568

[16] M.H. Wagner, S. Kheirandish, M. Yamaguchi, Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends, Rheologica Acta 44 (2004) 198–218. https://doi.org/10.1007/s00397-004-0400-9

[17] K. Hagita, H. Morita, M. Doi, H. Takano, Coarse-Grained Molecular Dynamics Simulation of Filled Polymer Nanocomposites under Uniaxial Elongation, Macromolecules 49 (2016) 1972–1983. https://doi.org/10.1021/acs.macromol.5b02799

[18] A. Huegun, M. Fernández, M.E. Muñoz, A. Santamaría, Rheological properties and electrical conductivity of irradiated MWCNT/PP nanocomposites, Composites Science and Technology 72 (2012) 1602–1607. https://doi.org/10.1016/j.compscitech.2012.06.011

[19] M. Hoseini, A. Haghtalab, M.H.N. Family, Elongational behavior of silica nanoparticle-filled low-density polyethylene/polylactic acid blends and their morphology, Rheologica Acta 59 (2020) 621–630. https://doi.org/10.1007/s00397-020-01225-5

[20] M. Kong, Y. Huang, Y. Lv, Q. Yang, G. Li, R.G. Larson, Elongation thinning and morphology deformation of nanoparticle-filled polypropylene/polystyrene blends in elongational flow, Journal of Rheology 62 (2018) 11–23. https://doi.org/10.1122/1.5009195

[21] B. Lu, P. Alcouffe, G. Sudre, S. Pruvost, A. Serghei, C. Liu, A. Maazouz, K. Lamnawar, Unveiling the Effects of In Situ Layer–Layer Interfacial Reaction in Multilayer Polymer Films via Multilayered Assembly: From Microlayers to Nanolayers, Macromolecular Materials and Engineering 305 (2020) 2000076. https://doi.org/10.1002/mame.202000076

[22] H. Zhang, K. Lamnawar, A. Maazouz, J.M. Maia, A nonlinear shear and elongation rheological study of interfacial failure in compatible bilayer systems, Journal of Rheology 60 (2016) 1–23. https://doi.org/10.1122/1.4926492

[23] B. Lu, K. Lamnawar, A. Maazouz, G. Sudre, Critical Role of Interfacial Diffusion and Diffuse Interphases Formed in Multi-Micro-/Nanolayered Polymer Films Based on Poly(vinylidene fluoride) and Poly(methyl methacrylate), ACS Appl. Mater. Interfaces 10 (2018) 29019–29037. https://doi.org/10.1021/acsami.8b09064

[24] L. Levitt, C.W. Macosko, T. Schweizer, J. Meissner, Extensional rheometry of polymer multilayers: A sensitive probe of interfaces, Journal of Rheology 41 (1997) 671–685. https://doi.org/10.1122/1.550829

[25] A. Dmochowska, J. Peixinho, C. Sollogoub, G. Miquelard-Garnier, Extensional Viscosity of Immiscible Polymer Multi-Nanolayer Films: Signature of the Interphase, Macromolecules 56 (2023) 6222–6231. https://doi.org/10.1021/acs.macromol.3c00288

[26] J. Li, A. Maazouz, K. Lamnawar, Unveiling the restricted mobility of carbon nanotubes inside a long chain branched polymer matrix via probing the shear flow effects on the rheological and electrical properties of the filled systems, Soft Matter 19 (2023) 9146–9165. https://doi.org/10.1039/D3SM01311A

[27] J. Wang, W. Yu, C. Zhou, Y. Guo, W. Zoetelief, P. Steeman, Elongational rheology of glass fiber-filled polymer composites, Rheologica Acta 55 (2016) 833–845. https://doi.org/10.1007/s00397-016-0960-5
[14] J.M. Dealy, D.J. Read, R.G. Larson, Structure and Rheology of Molten Polymers, in: J.M. Dealy, D.J. Read, R.G. Larson (Eds.), Structure and Rheology of Molten Polymers (Second Edition), Hanser, 2018: p. I-XVII. https://doi.org/10.3139/9781569906125.fm

[15] G. Liu, H. Sun, S. Rangou, K. Ntetsikas, A. Avgeropoulos, S.-Q. Wang, Studying the origin of “strain hardening”: Basic difference between extension and shear, Journal of Rheology 57 (2013) 89–104. https://doi.org/10.1122/1.4763568

[16] M.H. Wagner, S. Kheirandish, M. Yamaguchi, Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends, Rheologica Acta 44 (2004) 198–218. https://doi.org/10.1007/s00397-004-0400-9

[17] K. Hagita, H. Morita, M. Doi, H. Takano, Coarse-Grained Molecular Dynamics Simulation of Filled Polymer Nanocomposites under Uniaxial Elongation, Macromolecules 49 (2016) 1972–1983. https://doi.org/10.1021/acs.macromol.5b02799

[18] A. Huegun, M. Fernández, M.E. Muñoz, A. Santamaría, Rheological properties and electrical conductivity of irradiated MWCNT/PP nanocomposites, Composites Science and Technology 72 (2012) 1602–1607. https://doi.org/10.1016/j.compscitech.2012.06.011

[19] M. Hoseini, A. Haghtalab, M.H.N. Family, Elongational behavior of silica nanoparticle-filled low-density polyethylene/polylactic acid blends and their morphology, Rheologica Acta 59 (2020) 621–630. https://doi.org/10.1007/s00397-020-01225-5

[20] M. Kong, Y. Huang, Y. Lv, Q. Yang, G. Li, R.G. Larson, Elongation thinning and morphology deformation of nanoparticle-filled polypropylene/polystyrene blends in elongational flow, Journal of Rheology 62 (2018) 11–23. https://doi.org/10.1122/1.5009195

[21] B. Lu, P. Alcouffe, G. Sudre, S. Pruvost, A. Serghei, C. Liu, A. Maazouz, K. Lamnawar, Unveiling the Effects of In Situ Layer–Layer Interfacial Reaction in Multilayer Polymer Films via Multilayered Assembly: From Microlayers to Nanolayers, Macromolecular Materials and Engineering 305 (2020) 2000076. https://doi.org/10.1002/mame.202000076

[22] H. Zhang, K. Lamnawar, A. Maazouz, J.M. Maia, A nonlinear shear and elongation rheological study of interfacial failure in compatible bilayer systems, Journal of Rheology 60 (2016) 1–23. https://doi.org/10.1122/1.4926492

[23] B. Lu, K. Lamnawar, A. Maazouz, G. Sudre, Critical Role of Interfacial Diffusion and Diffuse Interphases Formed in Multi-Micro-/Nanolayered Polymer Films Based on Poly(vinylidene fluoride) and Poly(methyl methacrylate), ACS Appl. Mater. Interfaces 10 (2018) 29019–29037. https://doi.org/10.1021/acsami.8b09064

[24] L. Levitt, C.W. Macosko, T. Schweizer, J. Meissner, Extensional rheometry of polymer multilayers: A sensitive probe of interfaces, Journal of Rheology 41 (1997) 671–685. https://doi.org/10.1122/1.550829

[25] A. Dmochowska, J. Peixinho, C. Sollogoub, G. Miquelard-Garnier, Extensional Viscosity of Immiscible Polymer Multi-Nanolayer Films: Signature of the Interphase, Macromolecules 56 (2023) 6222–6231. https://doi.org/10.1021/acs.macromol.3c00288

[26] J. Li, A. Maazouz, K. Lamnawar, Unveiling the restricted mobility of carbon nanotubes inside a long chain branched polymer matrix via probing the shear flow effects on the rheological and electrical properties of the filled systems, Soft Matter 19 (2023) 9146–9165. https://doi.org/10.1039/D3SM01311A

[27] J. Wang, W. Yu, C. Zhou, Y. Guo, W. Zoetelief, P. Steeman, Elongational rheology of glass fiber-filled polymer composites, Rheologica Acta 55 (2016) 833–845. https://doi.org/10.1007/s00397-016-0960-5
# Identification of the thermal conductivity of polymer materials during their crystallization

MOUSSALLEM Rita¹,ᵃ*, EL RASSY Elissa¹, FARAJ Jalal², LEFEVRE Nicolas¹ and BAILLEUL Jean-Luc¹

¹Nantes Université, UMR CNRS 6607, LTEN, Rue Christian Pauc, 44300 Nantes, France

²Lebanese International University, Mouseitbeh, Beirut, Lebanon

ªrita.moussallem@univ-nantes.fr

**Keywords:** Thermal Conductivity, Thermoplastics, Crystallization, Inverse Method

**Abstract.** Controlling the quality of industrial products requires an accurate comprehension of the material's behavior during the several transformation phases. An accurate estimation of the heat transfers taking place throughout the production phases necessitates the exact knowledge of the thermophysical properties. These properties are well known in the solid state, however they are less mastered in the liquid state and during transformation. The main objective of this research project is to estimate the evolution of the thermal conductivity during transformation by solving an inverse heat conduction problem. The calculation outputs ought to describe the evolution of the thermal conductivity function of two coupled fields: the temperature and the transformation degree. The inverse method relies on a finite difference numerical model and a hybrid optimization algorithm, combining a stochastic method with a deterministic method. The temperature evolution within a thermoplastic undergoing transformation is measured with the help of an instrumented mold. The thermal conductivity values are identified by minimizing the discrepancy between the experimentally measured temperature profile and the one numerically simulated. The acquired results are compared with the mixing law, classically used to take into account the phase change of a material. It is observed that the values acquired by the established inverse method reproduce the measured temperature profiles more accurately than the mixing law.

**Introduction**

Polymeric materials are widely used in the production industry and the sheer number of their utilizations is as vast as they are diverse. Their versatility and their extensive characteristics range make them the essence of a broad number of productions. The main polymer processing operations are extrusion and injection molding, during which thermoplastics undergo several phase changes [1]. The control of the quality product relies chiefly on the accurate estimations of the heat transfer taking place during the transformation phases. Indeed, a correct prediction of the material's thermal behavior avoids the generation of defects within the manufactured products such as shrink voids, delamination, frozen in stresses [2]. A precise simulation of the heat transfers requires the exact knowledge of the material's transformation kinetics as well as its thermophysical properties which are the thermal conductivity, specific heat and density. As a matter of fact, these properties are very well measured in the solid phase, yet their measurements in the liquid phase and during transformations, are less mastered.

In this context, the thermal characterization of polymeric materials has essentially focused on determining the temperature dependence of the thermophysical properties. The measurement or the identification techniques have only been restricted to a material in its fixed state and not during its transition from a state to another [3]. Until nowadays, no study has addressed the complex evolution of the thermophysical properties function of two coupled fields which are the temperature and the transformation degree. Indeed, inverse heat conduction problems have served

<figure><img src="image_2511.png" /></figure>
# Identification of the thermal conductivity of polymer materials during their crystallization

MOUSSALLEM Rita¹,ᵃ*, EL RASSY Elissa¹, FARAJ Jalal², LEFEVRE Nicolas¹ and BAILLEUL Jean-Luc¹

¹Nantes Université, UMR CNRS 6607, LTEN, Rue Christian Pauc, 44300 Nantes, France

²Lebanese International University, Mouseitbeh, Beirut, Lebanon

ªrita.moussallem@univ-nantes.fr

**Keywords:** Thermal Conductivity, Thermoplastics, Crystallization, Inverse Method

**Abstract.** Controlling the quality of industrial products requires an accurate comprehension of the material's behavior during the several transformation phases. An accurate estimation of the heat transfers taking place throughout the production phases necessitates the exact knowledge of the thermophysical properties. These properties are well known in the solid state, however they are less mastered in the liquid state and during transformation. The main objective of this research project is to estimate the evolution of the thermal conductivity during transformation by solving an inverse heat conduction problem. The calculation outputs ought to describe the evolution of the thermal conductivity function of two coupled fields: the temperature and the transformation degree. The inverse method relies on a finite difference numerical model and a hybrid optimization algorithm, combining a stochastic method with a deterministic method. The temperature evolution within a thermoplastic undergoing transformation is measured with the help of an instrumented mold. The thermal conductivity values are identified by minimizing the discrepancy between the experimentally measured temperature profile and the one numerically simulated. The acquired results are compared with the mixing law, classically used to take into account the phase change of a material. It is observed that the values acquired by the established inverse method reproduce the measured temperature profiles more accurately than the mixing law.

**Introduction**

Polymeric materials are widely used in the production industry and the sheer number of their utilizations is as vast as they are diverse. Their versatility and their extensive characteristics range make them the essence of a broad number of productions. The main polymer processing operations are extrusion and injection molding, during which thermoplastics undergo several phase changes [1]. The control of the quality product relies chiefly on the accurate estimations of the heat transfer taking place during the transformation phases. Indeed, a correct prediction of the material's thermal behavior avoids the generation of defects within the manufactured products such as shrink voids, delamination, frozen in stresses [2]. A precise simulation of the heat transfers requires the exact knowledge of the material's transformation kinetics as well as its thermophysical properties which are the thermal conductivity, specific heat and density. As a matter of fact, these properties are very well measured in the solid phase, yet their measurements in the liquid phase and during transformations, are less mastered.

In this context, the thermal characterization of polymeric materials has essentially focused on determining the temperature dependence of the thermophysical properties. The measurement or the identification techniques have only been restricted to a material in its fixed state and not during its transition from a state to another [3]. Until nowadays, no study has addressed the complex evolution of the thermophysical properties function of two coupled fields which are the temperature and the transformation degree. Indeed, inverse heat conduction problems have served

<figure><img src="image_2504.png" /></figure>
in estimating the unknown thermophysical properties of different types of materials. The resolution of the inverse problem is achieved by minimizing the discrepancy between experimental measurements and synthetic signals generated by a numerical or an analytical model. In this manner, the thermophysical properties of anisotropic materials were estimated by solving inverse heat conduction problems [4], [5], [6], [7]. Some studies ought to identify the linear evolution of the properties by solving a steady state problem [8], [9] while others investigated the temperature dependence on the thermal conductivity in a transient state [10], [11]. As a matter of fact, the thermal conductivity of a thermoplastic was identified in the liquid and solid state during cooling without taking into account the crystallization.

Furthermore, some authors relied on the traditional mixing law to model the thermophysical properties evolution function of temperature and relative crystallinity [12]. It is theoretically correct to model the heat capacity and the density by the mixing law however it is inconsistent for the thermal conductivity since it is not an extensive property.

Therefore, the main focus of this study is to establish an inverse method dedicated for the estimation of the thermal conductivity evolution function of temperature and relative crystallinity, without imposing an evolutionary profile. For this manner, a numerical model is developed to simulate the thermal response of a polymer during its transformation. A hybrid optimization algorithm combining a stochastic method with a deterministic one is adopted to solve the inverse heat conduction problem. The experimental temperature measurement is achieved with the help of an instrumented mold mounted on a pneumatic press equipped with a cooling and a heating system. The inverse method is applied on a polypropylene sample, whose crystallization kinetic as well as the temperature dependence of its specific heat capacity and density are characterized. The thermal conductivity values obtained for several combinations of temperature and relative crystallinity are compared with the mixing law in order to assess its reliability.

## Inverse method

**Numerical model.** The developed inverse method consists in estimating the unknown parameters that minimize the difference between the measured temperature profile and the profile numerically computed. For this manner, the thermal response of the polymer, during its transformation, is simulated using a finite difference model. The one directional heat transfer problem is discretized using the Crank-Nicholson scheme. The one dimensional heat equation modelling the thermal response of the polymer is coupled with the exothermal heat generated during the crystallization phase. The heat conduction problem is described by Eq. (1) and (2):

$$ \rho(\alpha, T)C_p(\alpha, T) \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( \lambda(\alpha, T) \frac{\partial T}{\partial x} \right) + \rho(\alpha, T) \Delta H \frac{\partial \alpha}{\partial t} \quad \forall x \in ]0; e[ \quad \forall t > 0. \quad (1) $$

$$ \frac{\partial \alpha}{\partial t} = K_{Nak}(T) \times n(1 - \alpha)[-\ln(1 - \alpha)]^{1 - \frac{1}{n}} \quad \forall x \in ]0; e[ \quad \forall t > 0. \quad (2) $$

With $\Delta H$ being the crystallization enthalpy, $K_{Nak}(T)$ the Nakamura coefficient function of temperature and $n$ the exponent of Avrami. The traditional differential form of Nakamura [13,14] was implemented and numerically solved using a simplified equation. Levy [13] proved the robustness and the accuracy of writing the crystallization kinetic in the following form:

$$ \frac{\partial \alpha}{\partial t} = K_{Nak}(T) \cdot G(\alpha). \quad (3) $$

With $G(\alpha)$ a function computed over the interval $[0,1]$.
in estimating the unknown thermophysical properties of different types of materials. The resolution of the inverse problem is achieved by minimizing the discrepancy between experimental measurements and synthetic signals generated by a numerical or an analytical model. In this manner, the thermophysical properties of anisotropic materials were estimated by solving inverse heat conduction problems [4], [5], [6], [7]. Some studies ought to identify the linear evolution of the properties by solving a steady state problem [8], [9] while others investigated the temperature dependence on the thermal conductivity in a transient state [10], [11]. As a matter of fact, the thermal conductivity of a thermoplastic was identified in the liquid and solid state during cooling without taking into account the crystallization.

Furthermore, some authors relied on the traditional mixing law to model the thermophysical properties evolution function of temperature and relative crystallinity [12]. It is theoretically correct to model the heat capacity and the density by the mixing law however it is inconsistent for the thermal conductivity since it is not an extensive property.

Therefore, the main focus of this study is to establish an inverse method dedicated for the estimation of the thermal conductivity evolution function of temperature and relative crystallinity, without imposing an evolutionary profile. For this manner, a numerical model is developed to simulate the thermal response of a polymer during its transformation. A hybrid optimization algorithm combining a stochastic method with a deterministic one is adopted to solve the inverse heat conduction problem. The experimental temperature measurement is achieved with the help of an instrumented mold mounted on a pneumatic press equipped with a cooling and a heating system. The inverse method is applied on a polypropylene sample, whose crystallization kinetic as well as the temperature dependence of its specific heat capacity and density are characterized. The thermal conductivity values obtained for several combinations of temperature and relative crystallinity are compared with the mixing law in order to assess its reliability.

## Inverse method

**Numerical model.** The developed inverse method consists in estimating the unknown parameters that minimize the difference between the measured temperature profile and the profile numerically computed. For this manner, the thermal response of the polymer, during its transformation, is simulated using a finite difference model. The one directional heat transfer problem is discretized using the Crank-Nicholson scheme. The one dimensional heat equation modelling the thermal response of the polymer is coupled with the exothermal heat generated during the crystallization phase. The heat conduction problem is described by Eq. (1) and (2):

$$ \rho(\alpha, T)C_p(\alpha, T) \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( \lambda(\alpha, T) \frac{\partial T}{\partial x} \right) + \rho(\alpha, T) \Delta H \frac{\partial \alpha}{\partial t} \quad \forall x \in ]0; e[ \quad \forall t > 0. \quad (1) $$

$$ \frac{\partial \alpha}{\partial t} = K_{Nak}(T) \times n(1-\alpha)[-\ln(1-\alpha)]^{1-\frac{1}{n}} \quad \forall x \in ]0; e[ \quad \forall t > 0. \quad (2) $$

With $\Delta H$ being the crystallization enthalpy, $K_{Nak}(T)$ the Nakamura coefficient function of temperature and $n$ the exponent of Avrami. The traditional differential form of Nakamura [13,14] was implemented and numerically solved using a simplified equation. Levy [13] proved the robustness and the accuracy of writing the crystallization kinetic in the following form:

$$ \frac{\partial \alpha}{\partial t} = K_{Nak}(T) \cdot G(\alpha). \quad (3) $$

With $G(\alpha)$ a function computed over the interval $[0,1]$.
The boundary conditions considering the imposed cooling rate at the upper and lower surfaces written as:

$$T(x = 0, t) = T_1(t) \quad \forall t > 0. \qquad (4)$$

$$T(x = e, t) = T_2(t) \quad \forall t > 0. \qquad (5)$$

The initial conditions of the thermal problem are:

$$T(x, t = 0) = T_{\text{Initial}} \quad \forall x \in [0; e]. \qquad (6)$$

$$\alpha(x, t = 0) = 0 \quad \forall x \in [0; e]. \qquad (7)$$

**Unknowns of the problem.** The resolution of the inverse heat conduction problem ought to identify the thermal conductivity function of two coupled fields which are the temperature and the relative crystallinity. For this manner, the thermal conductivity values, corresponding to the possible combinations of temperature and relative crystallinity, are stocked in a matrix of the following form:

$$\alpha_1 \quad T_1 \quad T_2 \quad \dots \quad \dots \quad \dots \quad \dots \quad T_{n-1} \quad T_n \\
\alpha_2 \quad \begin{pmatrix} \lambda_{11} & \lambda_{12} & \dots & \dots & \dots & \dots & \dots & \lambda_{1n} \\ \lambda_{21} & \lambda_{22} & \dots & \dots & \dots & \dots & \dots & \lambda_{2n-1} \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\ \alpha_{m-1} \quad \lambda_{m1} & \lambda_{m2} & \dots & \dots & \dots & \dots & \dots & \lambda_{mn-1} \\ \alpha_m \quad \lambda_{m1} & \lambda_{m2} & \dots & \dots & \dots & \dots & \dots & \lambda_{mn} \end{pmatrix} \qquad (8)$$

The matrix is defined by *m* levels of temperature and *n* levels of relative crystallinity and will assist in computing the thermal conductivity of the polymer during its crystallization. At each time step and at each position of the thickness, the thermal conductivity is calculated by performing a double linear interpolation function of temperature and relative crystallinity.

On the other hand, the polymer in the molten and solid states has a fixed relative crystallinity: $\alpha = 0$ and $\alpha = 1$ respectively. Therefore, the thermal conductivity of the molten and solid polymer is only dependent on the temperature. The thermal conductivity values are, therefore, calculated by a linear interpolation function of temperature.

One should note that the thermal problem may be over-parameterized since the thermal conductivity matrix can not be entirely estimated, based on a single cooling rate experiment. Indeed, the relative crystallinities $\alpha$, ranging between 0 and 1, are associated with temperature levels according to the crystallization kinetic [14] [15]. The thermal conductivities that can be accurately identified are the ones that are involved in the polymer's thermal response calculations.

**Cost function.** As previously mentioned, the resolution of the inverse heat conduction problem relies on the minimization of an objective function representing the discrepancy between the
experimental temperature measurements and the numerical results. The cost function is described by the following formula:

$$J = \frac{1}{n \times t_f} \sqrt{\sum_{i=1}^{n} \int_{0}^{t_f} (T_{i,Experimental}(\lambda) - T_{i,Numerical}(\lambda))^2 dt.} \quad (9)$$

With n being the number of points where the temperature variation is measured and computed, $t_f$ the experiment time length and $\lambda$ the set of thermal conductivities to identify.

**Optimization algorithm.** The optimization algorithm keeps on adjusting the unknown set of parameters until the cost function satisfies a predefined criterion. The identification of the thermal conductivity values is achieved by combining a stochastic algorithm with deterministic one. The genetic algorithm, mainly inspired from Darwin's evolution theory [16], is capable of handling the great number of unknowns of the complex and non-linear problem. It will contribute in converging towards the region of the global optimum and its stochastic aspect avoids getting trapped in local minima. The values found by the genetic algorithm are implemented as initial value to the interior point algorithm [17]. This deterministic method applies the Newton method on the Lagrangian of the problem while it switches to the gradient conjugate method when the problem is non-convex. The robustness, feasibility and accuracy of the estimation method has been verified using signals, generated by the numerical model and corrupted by a synthetic noise. Based on the experimental measurements registered by a K type thermocouple, a random Gaussian distribution with a standard deviation of 0.025 °C is representative of the measurement noise. In a previous study, the hybrid optimization algorithm was tested and proved to be adequate for the resolution of the inverse heat conduction problem [18]. Furthermore, the robustness of the established inverse method has been evaluated by taking into account the uncertainties on apriori known thermal parameters [19].

## Experimental measurements

**Material.** The material considered in the present study is an impact polypropylene copolymer, Sabic PP 48M10. According to the supplier, this polymer is characterized by its advanced rheological properties, its high rigidity and its elevated resistance to impacts. It is mainly used in the manufacturing of products having complex shapes, tough packages as well as automobile and electronic components. An experimental campaign aiming to characterize the thermophysical properties of the polymer and its crystallization kinetic is achieved. Indeed, the accurate knowledge of these properties is crucial for an exact identification of the thermal conductivities.

The specific heat $C_p$ is determined by differential scanning calorimetry by heating a polypropylene sample from 20 °C to 230 °C at a heating rate of 5 K/min. $C_p$ is then evaluated as a linear function of temperature for both the solid and the amorphous phases. The specific volume $v$ is measured with the help of a home-made PVT device [20] at different pressures of 25, 40 and 50 MPa and at a cooling rate of 2 K/min. Tait model is then utilized to estimate the temperature dependence of the specific volume at atmospheric pressure (or any desired pressure) [21]. The measured data are fitted following a linear regression of temperature for the solid and the amorphous states.

The crystallization of a thermoplastic consists in the formation of a nuclei in the melt and its growth into semi crystalline structures called spherulites. The progress of the crystallization process is perceived through the relative crystallinity $\alpha$, ranging between 0 and 1. During the molding operation, the crystallization occurs when cooling from the melt state to the ambient temperature. Therefore, the transformation taking place is strongly anisothermal and is best
experimental temperature measurements and the numerical results. The cost function is described by the following formula:

$$J = \frac{1}{n \times t_f} \sqrt{\sum_{i=1}^{n} \int_{0}^{t_f} (T_{i,Experimental}(\lambda) - T_{i,Numerical}(\lambda))^2 dt.} \quad (9)$$

With n being the number of points where the temperature variation is measured and computed, $t_f$ the experiment time length and $\lambda$ the set of thermal conductivities to identify.

**Optimization algorithm.** The optimization algorithm keeps on adjusting the unknown set of parameters until the cost function satisfies a predefined criterion. The identification of the thermal conductivity values is achieved by combining a stochastic algorithm with deterministic one. The genetic algorithm, mainly inspired from Darwin's evolution theory [16], is capable of handling the great number of unknowns of the complex and non-linear problem. It will contribute in converging towards the region of the global optimum and its stochastic aspect avoids getting trapped in local minima. The values found by the genetic algorithm are implemented as initial value to the interior point algorithm [17]. This deterministic method applies the Newton method on the Lagrangian of the problem while it switches to the gradient conjugate method when the problem is non-convex. The robustness, feasibility and accuracy of the estimation method has been verified using signals, generated by the numerical model and corrupted by a synthetic noise. Based on the experimental measurements registered by a K type thermocouple, a random Gaussian distribution with a standard deviation of 0.025 °C is representative of the measurement noise. In a previous study, the hybrid optimization algorithm was tested and proved to be adequate for the resolution of the inverse heat conduction problem [18]. Furthermore, the robustness of the established inverse method has been evaluated by taking into account the uncertainties on apriori known thermal parameters [19].

## Experimental measurements

**Material.** The material considered in the present study is an impact polypropylene copolymer, Sabic PP 48M10. According to the supplier, this polymer is characterized by its advanced rheological properties, its high rigidity and its elevated resistance to impacts. It is mainly used in the manufacturing of products having complex shapes, tough packages as well as automobile and electronic components. An experimental campaign aiming to characterize the thermophysical properties of the polymer and its crystallization kinetic is achieved. Indeed, the accurate knowledge of these properties is crucial for an exact identification of the thermal conductivities.

The specific heat $C_p$ is determined by differential scanning calorimetry by heating a polypropylene sample from 20 °C to 230 °C at a heating rate of 5 K/min. $C_p$ is then evaluated as a linear function of temperature for both the solid and the amorphous phases. The specific volume $v$ is measured with the help of a home-made PVT device [20] at different pressures of 25, 40 and 50 MPa and at a cooling rate of 2 K/min. Tait model is then utilized to estimate the temperature dependence of the specific volume at atmospheric pressure (or any desired pressure) [21]. The measured data are fitted following a linear regression of temperature for the solid and the amorphous states.

The crystallization of a thermoplastic consists in the formation of a nuclei in the melt and its growth into semi crystalline structures called spherulites. The progress of the crystallization process is perceived through the relative crystallinity $\alpha$, ranging between 0 and 1. During the molding operation, the crystallization occurs when cooling from the melt state to the ambient temperature. Therefore, the transformation taking place is strongly anisothermal and is best
depicted by the Nakamura model [14], [15]. The differential form of the crystallization kinetic (Eq. 2), developed by Patel *et al.* [22], requires the Avrami exponent *n* and the Nakamura coefficient $K_{Nak}$. It is reminded that the Avrami kinetic function, dedicated for modeling isothermal crystallization [23], [24], is linked to the Nakamura kinetic function by $K_{Nak} = K_{Nak}^{\frac{1}{n}}$. In this manner, the crystallization kinetic is investigated through the heat fluxes recorded during the isothermal plateau at temperatures ranging between 135 and 145 °C. In order to study isothermal crystallization at lower temperature values, differential nanocalorimetry is used. As a matter of fact, the DSC Flash allows to quench the polymer at a cooling rate that can reach 10000 K/s. The material is then completely amorphous at the beginning of the crystallization plateau since its anisothermal crystallization has been completely hindered by the high cooling rate. The isothermal crystallization is, therefore, inspected at temperatures ranging between 70 and 118 °C.

**Description of the instrumented mold.** The identification method is based on experimental measurements reflecting the thermal behavior of a polymer during its transformation. Therefore, an experimental bench has been developed for this purpose and is composed of an instrumented mold mounted on a pneumatic press. The mold, represented in Fig. 1, is composed of two main parts: the fixed part, with the molding cavity, and the mobile part. The molding cavity has a square shape with a length of 70 mm and allows the stretching of three thermocouples at distinct positions of the thickness, as shown in Fig. 2. The thermocouples have a diameter of 80 µm and are fully embedded in the molded material undergoing cooling and heating cycles. The mobile part allows the cooling of the material by circulating water or air on the top of the molding cavity. The piece, of thickness 5 to 6 mm, is molded under a constant pressure. The mold is placed between the two plates of a pneumatic press (Fig. 2), exerting pressure on the material, and equipped with a cooling and a heating system.

In order to reproduce accurate industrial conditions, the overall heating system is designed to reach a temperature of 400 °C. An additional cooling cycle can be applied on the molded piece by circulating water at 15 °C or air within the plates of the press. The purpose of this design is to apply asymmetric cooling at different rates which allows the crystallization occurrence at different temperature ranges. In fact, varying the cooling rate is convenient to inspect the thermal conductivity values corresponding to a broader crystallization domain.

**Experimental protocol and measurements.** Prior to placing the polypropylene granulates in the molding cavity, the thermocouples are stretched and the mold is mounted on the press. A mass of 25 g is required to achieve a thickness between 5 and 6 mm. The granulates are firstly melted at atmospheric pressure and at a temperature of 190 °C. After the complete fusion of the material, the mold is closed and the temperature acquisition is started. A constant pressure of 0.8 MPa is applied to maintain the contact between the upper part of the mold and the polymer during the heating and the cooling cycles. The thermocouple responses are recorded using a multichannel acquisition system. This system allows obtaining on the same support the measurement registered by all the thermocouples at an acquisition frequency of 10 Hz.
depicted by the Nakamura model [14], [15]. The differential form of the crystallization kinetic (Eq. 2), developed by Patel *et al.* [22], requires the Avrami exponent *n* and the Nakamura coefficient $K_{Nak}$. It is reminded that the Avrami kinetic function, dedicated for modeling isothermal crystallization [23], [24], is linked to the Nakamura kinetic function by $K_{Nak} = K_{Nak}^{\frac{1}{n}}$. In this manner, the crystallization kinetic is investigated through the heat fluxes recorded during the isothermal plateau at temperatures ranging between 135 and 145 °C. In order to study isothermal crystallization at lower temperature values, differential nanocalorimetry is used. As a matter of fact, the DSC Flash allows to quench the polymer at a cooling rate that can reach 10000 K/s. The material is then completely amorphous at the beginning of the crystallization plateau since its anisothermal crystallization has been completely hindered by the high cooling rate. The isothermal crystallization is, therefore, inspected at temperatures ranging between 70 and 118 °C.

**Description of the instrumented mold.** The identification method is based on experimental measurements reflecting the thermal behavior of a polymer during its transformation. Therefore, an experimental bench has been developed for this purpose and is composed of an instrumented mold mounted on a pneumatic press. The mold, represented in Fig. 1, is composed of two main parts: the fixed part, with the molding cavity, and the mobile part. The molding cavity has a square shape with a length of 70 mm and allows the stretching of three thermocouples at distinct positions of the thickness, as shown in Fig. 2. The thermocouples have a diameter of 80 µm and are fully embedded in the molded material undergoing cooling and heating cycles. The mobile part allows the cooling of the material by circulating water or air on the top of the molding cavity. The piece, of thickness 5 to 6 mm, is molded under a constant pressure. The mold is placed between the two plates of a pneumatic press (Fig. 2), exerting pressure on the material, and equipped with a cooling and a heating system.

In order to reproduce accurate industrial conditions, the overall heating system is designed to reach a temperature of 400 °C. An additional cooling cycle can be applied on the molded piece by circulating water at 15 °C or air within the plates of the press. The purpose of this design is to apply asymmetric cooling at different rates which allows the crystallization occurrence at different temperature ranges. In fact, varying the cooling rate is convenient to inspect the thermal conductivity values corresponding to a broader crystallization domain.

**Experimental protocol and measurements.** Prior to placing the polypropylene granulates in the molding cavity, the thermocouples are stretched and the mold is mounted on the press. A mass of 25 g is required to achieve a thickness between 5 and 6 mm. The granulates are firstly melted at atmospheric pressure and at a temperature of 190 °C. After the complete fusion of the material, the mold is closed and the temperature acquisition is started. A constant pressure of 0.8 MPa is applied to maintain the contact between the upper part of the mold and the polymer during the heating and the cooling cycles. The thermocouple responses are recorded using a multichannel acquisition system. This system allows obtaining on the same support the measurement registered by all the thermocouples at an acquisition frequency of 10 Hz.
<figure><img src="image_2512.png" /><figcaption>Fig. 1 Three dimensional view of the open and closed mold</figcaption></figure>

<figure><img src="image_2513.png" /><figcaption>Fig. 2 Mold mounted on the pneumatic press</figcaption></figure>

The precision of the overall system acquisition and experimental bench has to be verified. For this purpose, the repeatability and the reproducibility of the measurements are evaluated. The repeatability has been examined by repeating the measurements on the same molded piece using the exact instruments and without modifying any experimental condition. On the other hand, the reproducibility is tested by applying the same experimental protocols on different molded pieces of polypropylene. The obtained measurements have then been compared and the recorded temperature profiles are repeatable and reproducible (not shown here for reasons of space). This study emphasizes the fidelity and the reliability of the measurements that reflects the thermal behavior of the polymer during its transformation.

Furthermore, the first step in the mold development was to ensure a unidirectional heat transfer through the thickness of the polymer. For this manner, two configurations of the mold have been compared with the help of the commercial finite element software Comsol Multiphysics. The three dimensional configurations are identical and differ only in the boundary conditions. The first model is unidirectional as a Dirichlet boundary condition is imposed to its upper and lower surfaces while its lateral surfaces are considered to be adiabatic. The second model is three directional since a Dirichlet boundary condition is applied on all its surfaces. The temperature profiles at different points of the thickness are simulated and a comparison is done between the outputs of both models.
<figure><img src="image_2505.png" /><figcaption>Fig. 1 Three dimensional view of the open and closed mold</figcaption></figure>

<figure><img src="image_2506.png" /><figcaption>Fig. 2 Mold mounted on the pneumatic press</figcaption></figure>

The precision of the overall system acquisition and experimental bench has to be verified. For this purpose, the repeatability and the reproducibility of the measurements are evaluated. The repeatability has been examined by repeating the measurements on the same molded piece using the exact instruments and without modifying any experimental condition. On the other hand, the reproducibility is tested by applying the same experimental protocols on different molded pieces of polypropylene. The obtained measurements have then been compared and the recorded temperature profiles are repeatable and reproducible (not shown here for reasons of space). This study emphasizes the fidelity and the reliability of the measurements that reflects the thermal behavior of the polymer during its transformation.

Furthermore, the first step in the mold development was to ensure a unidirectional heat transfer through the thickness of the polymer. For this manner, two configurations of the mold have been compared with the help of the commercial finite element software Comsol Multiphysics. The three dimensional configurations are identical and differ only in the boundary conditions. The first model is unidirectional as a Dirichlet boundary condition is imposed to its upper and lower surfaces while its lateral surfaces are considered to be adiabatic. The second model is three directional since a Dirichlet boundary condition is applied on all its surfaces. The temperature profiles at different points of the thickness are simulated and a comparison is done between the outputs of both models.
The maximum temperature difference was found to be 3.5 K at the corners and does not exceed 0.03 K along the axis of the component where the thermocouples are positioned. As a result, the heat transfer is regarded as unidirectional as considered in the direct model.

Once the measurements are terminated, the molded piece is retrieved from the mold and cut perpendicularly to the thermocouples direction. The positions of the thermocouples are then localized by optical microscopy.

## Results and discussion

The overall temperature measurements as well as the characterized thermophysical properties and the crystallization kinetic are implemented in the inverse method to estimate the unknown parameters. The melted polymer is cooled by circulating water within the plates of the press. The mobile part of the mold is not subjected to a cooling cycle in order to accomplish crystallization at a slow cooling rate. The temperature evolutions measured by the upper and lower thermocouple are considered to be the boundary conditions while the middle thermocouple is used for the cost function computation. The outputs of the inverse calculations depict the thermal conductivity evolution in the solid state, amorphous state and during crystallization as represented in Fig.3. In order to evaluate the values estimated in the liquid and solid states, the obtained results are compared with thermal conductivities issued from the laser flash analysis [25]. It is reminded that this non-intrusive characterization method assists in determining the thermal diffusivity $a$ that is linked to the other thermophysical properties by the following relation: $a = \frac{\lambda}{\rho c_p}$. The identified thermal conductivities of the amorphous polymer are in good agreements with the ones obtained by the laser flash analysis. However, the thermal conductivities of the solid state are overestimated due to the low temperature gradient, indicating the low sensitivity of the temperature to the unknown parameters. It is noted that the average temperature gradient is around 2 K/mm in the solid state, whereas it reaches 6 K/mm in the amorphous state.

The variation obtained during crystallization is compared with the classical mixing law. It is observed that the identified thermal conductivity does not follow a linear variation function of temperature and relative crystallinity. The assessment of these results is achieved by computing the temperature residuals corresponding to three possible cases as depicted in Fig. 4. The thermal conductivities identified by the inverse method reproduce with high precision the recorded temperature evolution since the temperature residual is well-centered and have a standard deviation of $\sigma = 0.05$ °C. It is noted that the standard deviation of the experimental temperature noise is $\sigma_{Noise} = 0.025$ °C. The thermal conductivities used in the second and the third cases are computed by applying the mixing law based on the values identified in the solid and amorphous states and the values measured by laser flash analysis, respectively. The temperature profiles generated are not as adequate as the first case considering the temperature residuals that have drastically increased. The purpose behind using the same law with different values is to evaluate its reliability without being constrained by the potential inexact estimation of the inverse method. As observed, the results of the solid state are misleading. Nevertheless, it is concluded that the mixing law is not representative of the actual thermal conductivity evolution during the polymer crystallization. This conclusion emphasizes the fact that the thermal conductivity is not an extensive property and is not linearly dependent of the transformation degree.
The maximum temperature difference was found to be 3.5 K at the corners and does not exceed 0.03 K along the axis of the component where the thermocouples are positioned. As a result, the heat transfer is regarded as unidirectional as considered in the direct model.

Once the measurements are terminated, the molded piece is retrieved from the mold and cut perpendicularly to the thermocouples direction. The positions of the thermocouples are then localized by optical microscopy.

## Results and discussion

The overall temperature measurements as well as the characterized thermophysical properties and the crystallization kinetic are implemented in the inverse method to estimate the unknown parameters. The melted polymer is cooled by circulating water within the plates of the press. The mobile part of the mold is not subjected to a cooling cycle in order to accomplish crystallization at a slow cooling rate. The temperature evolutions measured by the upper and lower thermocouple are considered to be the boundary conditions while the middle thermocouple is used for the cost function computation. The outputs of the inverse calculations depict the thermal conductivity evolution in the solid state, amorphous state and during crystallization as represented in Fig.3. In order to evaluate the values estimated in the liquid and solid states, the obtained results are compared with thermal conductivities issued from the laser flash analysis [25]. It is reminded that this non-intrusive characterization method assists in determining the thermal diffusivity $a$ that is linked to the other thermophysical properties by the following relation: $a = \frac{\lambda}{\rho c_p}$. The identified thermal conductivities of the amorphous polymer are in good agreements with the ones obtained by the laser flash analysis. However, the thermal conductivities of the solid state are overestimated due to the low temperature gradient, indicating the low sensitivity of the temperature to the unknown parameters. It is noted that the average temperature gradient is around 2 K/mm in the solid state, whereas it reaches 6 K/mm in the amorphous state.

The variation obtained during crystallization is compared with the classical mixing law. It is observed that the identified thermal conductivity does not follow a linear variation function of temperature and relative crystallinity. The assessment of these results is achieved by computing the temperature residuals corresponding to three possible cases as depicted in Fig. 4. The thermal conductivities identified by the inverse method reproduce with high precision the recorded temperature evolution since the temperature residual is well-centered and have a standard deviation of $\sigma = 0.05$ °C. It is noted that the standard deviation of the experimental temperature noise is $\sigma_{Noise} = 0.025$ °C. The thermal conductivities used in the second and the third cases are computed by applying the mixing law based on the values identified in the solid and amorphous states and the values measured by laser flash analysis, respectively. The temperature profiles generated are not as adequate as the first case considering the temperature residuals that have drastically increased. The purpose behind using the same law with different values is to evaluate its reliability without being constrained by the potential inexact estimation of the inverse method. As observed, the results of the solid state are misleading. Nevertheless, it is concluded that the mixing law is not representative of the actual thermal conductivity evolution during the polymer crystallization. This conclusion emphasizes the fact that the thermal conductivity is not an extensive property and is not linearly dependent of the transformation degree.
<figure><img src="image_2514.png" /><figcaption>Fig. 3 Comparison between the identified thermal conductivity values, the values computed from the mixing law and the values found by laser flash analysis</figcaption></figure>

<figure><img src="image_2515.png" /><figcaption>Fig. 4 Comparison of the measured temperature profile with each of the temperatures profiles computed using the identified thermal conductivities, the mixing law based on the values identified in the solid and amorphous states and the mixing law based on the values measured by laser flash analysis</figcaption></figure>
<figure><img src="image_2507.png" /><figcaption>Fig. 3 Comparison between the identified thermal conductivity values, the values computed from the mixing law and the values found by laser flash analysis</figcaption></figure>

<figure><img src="image_2508.png" /><figcaption>Fig. 4 Comparison of the measured temperature profile with each of the temperatures profiles computed using the identified thermal conductivities, the mixing law based on the values identified in the solid and amorphous states and the mixing law based on the values measured by laser flash analysis</figcaption></figure>
## Summary

An estimation of the thermal conductivity evolution during the polymer crystallization is presented in this paper. The unknown parameters are identified by minimizing the discrepancy between the temperature evolution experimentally measured and the profile numerically computed. The inverse heat conduction problem is solved by adopting a hybrid optimization algorithm combining the genetic algorithm with the interior-point method. The temperature evolutions within a polymer undergoing crystallization are recorded with the help of an instrumented mold. The mold is mounted on a pneumatic press equipped with a cooling and a heating system allowing the fusion of the polymer and its crystallization at different cooling rates. Prior to applying the inverse method, an experimental campaign is achieved in order to characterize the crystallization kinetic of the studied polymer as well as the temperature dependence of its specific heat and density. The results obtained by the inverse calculations represent the thermal conductivity evolution in the solid state, liquid state and during crystallization. The values found in the amorphous and solid phases are compared with the values experimentally measured by laser flash analysis. The thermal conductivity of the amorphous polymer is accurately estimated contrary to the thermal conductivity of the solid polymer. The evolutionary profile estimated function of temperature and relative crystallinity is compared with the classical mixing law. It is observed that the estimated thermal conductivities do not obey a linear rule and reproduces the measured temperature with a greater accuracy than the mixing law. The next step will consist in applying the inverse method with several cooling rates in order to cover a broader crystallization domain. In fact, varying the cooling rate contributes in identifying the thermal conductivities corresponding to a multitude of temperature and relative crystallinity combinations.

## References

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## Summary

An estimation of the thermal conductivity evolution during the polymer crystallization is presented in this paper. The unknown parameters are identified by minimizing the discrepancy between the temperature evolution experimentally measured and the profile numerically computed. The inverse heat conduction problem is solved by adopting a hybrid optimization algorithm combining the genetic algorithm with the interior-point method. The temperature evolutions within a polymer undergoing crystallization are recorded with the help of an instrumented mold. The mold is mounted on a pneumatic press equipped with a cooling and a heating system allowing the fusion of the polymer and its crystallization at different cooling rates. Prior to applying the inverse method, an experimental campaign is achieved in order to characterize the crystallization kinetic of the studied polymer as well as the temperature dependence of its specific heat and density. The results obtained by the inverse calculations represent the thermal conductivity evolution in the solid state, liquid state and during crystallization. The values found in the amorphous and solid phases are compared with the values experimentally measured by laser flash analysis. The thermal conductivity of the amorphous polymer is accurately estimated contrary to the thermal conductivity of the solid polymer. The evolutionary profile estimated function of temperature and relative crystallinity is compared with the classical mixing law. It is observed that the estimated thermal conductivities do not obey a linear rule and reproduces the measured temperature with a greater accuracy than the mixing law. The next step will consist in applying the inverse method with several cooling rates in order to cover a broader crystallization domain. In fact, varying the cooling rate contributes in identifying the thermal conductivities corresponding to a multitude of temperature and relative crystallinity combinations.

## References

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[10] R. Le Goff, D. Delaunay, N. Boyard, Y. Jarny, T. Jurkowski, et R. Deterre, « On-line temperature measurements for polymer thermal conductivity estimation under injection molding conditions ». International Journal of Heat and Mass Transfer 52 (2009) 1443-1450, 2009.

[11] X. Tardif, A. Agazzi, V. Sobotka, N. Boyard, Y. Jarny, et D. Delaunay, « A multifunctional device to determine specific volume, thermal conductivity and crystallization kinetics of semi-crystalline polymers ». Polymer Testing 31 (2012) 819-827.

[12] R. Le Goff, G. Poutot, D. Delaunay, R. Fulchiron, et E. Koscher, « Study and modeling of heat transfer during the solidification of semi-crystalline polymers », *Int. J. Heat Mass Transf.*, vol. 48, n° 25, p. 5417-5430, déc. 2005.
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[13] A. Levy, « Robust Numerical Resolution of Nakamura Crystallization Kinetics », *Int. J. Theor. Appl. Math.*, vol. 3, n° 4, p. 143, 2017. https://doi.org/10.11648/j.ijtam.20170304.13

[14] « Some aspects of nonisothermal crystallization of polymers. I. Relationship between crystallization temperature, crystallinity, and cooling conditions - Nakamura - 1972 - Journal of Applied Polymer Science - Wiley Online Library ».
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[15] « Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition - Nakamura - 1973 - Journal of Applied Polymer Science - Wiley Online Library ».
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[16] J. H. Holland, « Genetic Algorithms », *Sci. Am.*, vol. 267, n° 1, p. 66-73, 1992.

[17] R. H. Byrd, J. C. Gilbert, et J. Nocedal, « A trust region method based on interior point techniques for nonlinear programming », *Math. Program.*, vol. 89, n° 1, p. 149-185, nov. 2000.
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[18] R. Moussalem, E. El Rassy, J. Faraj, et J.-L. Bailleul, « Identification of the thermophysical properties of polymer and composite materials during their transformation », *Proceedings of the 17th international heat transfer conference*, Cape Town, South Africa, août 2023.

[19] R. Moussalem, E. El Rassy, J. Faraj, et J.-L. Bailleul, « A New Method for Identifying the Thermal Conductivity of Semi-Crystalline Thermoplastics During Their Crystallization ». Rochester, NY, 22 décembre 2023. https://doi.org/10.2139/ssrn.4673128

[20] B. Pignon, X. Tardif, N. Lefèvre, V. Sobotka, et N. Boyard, « A new PVT device for high performance thermoplastics: Heat transfer analysis and crystallization kinetics identification ». Polymer Testing 45 (2015) 152-160.

[21] J. H. Dymond et R. Malhotra, « The Tait equation: 100 years on », *Int. J. Thermophys.*, vol. 9, n° 6, p. 941-951, nov. 1988. https://doi.org/10.1007/BF01133262

[22] « Crystallization kinetics during polymer processing—Analysis of available approaches for process modeling - Patel - 1991 - Polymer Engineering & Science - Wiley Online Library ».
https://4spepublications.onlinelibrary.wiley.com/doi/abs/10.1002/pen.760311008

[23] M. Avrami, « Kinetics of Phase Change. I General Theory », *J. Chem. Phys.*, vol. 7, n° 12, p. 1103-1112, déc. 1939. https://doi.org/10.1063/1.1750380

[24] M. Avrami, « Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei », *J. Chem. Phys.*, vol. 8, n° 2, p. 212-224, févr. 1940.
https://doi.org/10.1063/1.1750631

[25] J. A. Cape et G. W. Lehman, « Temperature and Finite Pulse-Time Effects in the Flash Method for Measuring Thermal Diffusivity », *J. Appl. Phys.*, vol. 34, n° 7, p. 1909-1913, juill. 1963. https://doi.org/10.1063/1.1729711
[10] R. Le Goff, D. Delaunay, N. Boyard, Y. Jarny, T. Jurkowski, et R. Deterre, « On-line temperature measurements for polymer thermal conductivity estimation under injection molding conditions ». International Journal of Heat and Mass Transfer 52 (2009) 1443-1450, 2009.

[11] X. Tardif, A. Agazzi, V. Sobotka, N. Boyard, Y. Jarny, et D. Delaunay, « A multifunctional device to determine specific volume, thermal conductivity and crystallization kinetics of semi-crystalline polymers ». Polymer Testing 31 (2012) 819-827.

[12] R. Le Goff, G. Poutot, D. Delaunay, R. Fulchiron, et E. Koscher, « Study and modeling of heat transfer during the solidification of semi-crystalline polymers », *Int. J. Heat Mass Transf.*, vol. 48, n° 25, p. 5417-5430, déc. 2005.
https://doi.org/10.1016/j.ijheatmasstransfer.2005.06.015

[13] A. Levy, « Robust Numerical Resolution of Nakamura Crystallization Kinetics », *Int. J. Theor. Appl. Math.*, vol. 3, n° 4, p. 143, 2017. https://doi.org/10.11648/j.ijtam.20170304.13

[14] « Some aspects of nonisothermal crystallization of polymers. I. Relationship between crystallization temperature, crystallinity, and cooling conditions - Nakamura - 1972 - Journal of Applied Polymer Science - Wiley Online Library ». https://onlinelibrary.wiley.com/doi/abs/10.1002/app.1972.070160503

[15] « Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition - Nakamura - 1973 - Journal of Applied Polymer Science - Wiley Online Library ». https://onlinelibrary.wiley.com/doi/abs/10.1002/app.1973.070170404

[16] J. H. Holland, « Genetic Algorithms », *Sci. Am.*, vol. 267, n° 1, p. 66-73, 1992.

[17] R. H. Byrd, J. C. Gilbert, et J. Nocedal, « A trust region method based on interior point techniques for nonlinear programming », *Math. Program.*, vol. 89, n° 1, p. 149-185, nov. 2000. https://doi.org/10.1007/PL00011391

[18] R. Moussalem, E. El Rassy, J. Faraj, et J.-L. Bailleul, « Identification of the thermophysical properties of polymer and composite materials during their transformation », *Proceedings of the 17th international heat transfer conference*, Cape Town, South Africa, août 2023.

[19] R. Moussalem, E. El Rassy, J. Faraj, et J.-L. Bailleul, « A New Method for Identifying the Thermal Conductivity of Semi-Crystalline Thermoplastics During Their Crystallization ». Rochester, NY, 22 décembre 2023. https://doi.org/10.2139/ssrn.4673128

[20] B. Pignon, X. Tardif, N. Lefèvre, V. Sobotka, et N. Boyard, « A new PVT device for high performance thermoplastics: Heat transfer analysis and crystallization kinetics identification ». Polymer Testing 45 (2015) 152-160.

[21] J. H. Dymond et R. Malhotra, « The Tait equation: 100 years on », *Int. J. Thermophys.*, vol. 9, n° 6, p. 941-951, nov. 1988. https://doi.org/10.1007/BF01133262

[22] « Crystallization kinetics during polymer processing—Analysis of available approaches for process modeling - Patel - 1991 - Polymer Engineering & Science - Wiley Online Library ». https://4spepublications.onlinelibrary.wiley.com/doi/abs/10.1002/pen.760311008

[23] M. Avrami, « Kinetics of Phase Change. I General Theory », *J. Chem. Phys.*, vol. 7, n° 12, p. 1103-1112, déc. 1939. https://doi.org/10.1063/1.1750380

[24] M. Avrami, « Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei », *J. Chem. Phys.*, vol. 8, n° 2, p. 212-224, févr. 1940. https://doi.org/10.1063/1.1750631

[25] J. A. Cape et G. W. Lehman, « Temperature and Finite Pulse-Time Effects in the Flash Method for Measuring Thermal Diffusivity », *J. Appl. Phys.*, vol. 34, n° 7, p. 1909-1913, juill. 1963. https://doi.org/10.1063/1.1729711
# Monitoring the temperature during thermoplastic composites assembling with fibre Bragg gratings: Validation using a rheometer

KORYCKI Adrian<sup>1,2,a</sup>, CARASSUS Fabrice<sup>1,2,b</sup>, GARNIER Christan<sup>1,c</sup>,
CHABERT France<sup>1,d</sup>, CASARI Pascal<sup>3,e</sup> and DJILALI Toufik<sup>2,f</sup>

<sup>1</sup>LGP-ENIT-INPT, University of Toulouse, 47 Avenue d'Azereix, 65016 Tarbes, France

<sup>2</sup>LAUAK FRANCE, 8 Rue Louis Caddau, 65000 Tarbes, France

<sup>3</sup>Nantes Université, Ecole Centrale Nantes, CNRS, GeM, UMR 6183, F-44600 Saint-Nazaire, France

<sup>a</sup>akorycki@uttop.fr, <sup>b</sup>fcarassus@uttop.fr, <sup>c</sup>cgarnier@uttop.fr, <sup>d</sup>fchabert@uttop.fr, <sup>e</sup>pascal.casari@univ-nantes.fr, <sup>f</sup>toufik.djilali@groupe-lauak.com

**Keywords:** Fibre Optic Sensor, Bragg Grating, Rheometer, Temperature, Thermoplastic Composite

**Abstract.** For many years, thermoplastic composites have been conquering the technological market in commercial applications in civil and military structures, with particular emphasis on aircraft. One of their most attractive advantages is the potential to be repaired and welded in a short time. However, due to the lack of knowledge on the impact of process parameters (time, pressure, temperature) bonding thermoplastic composites remains a challenge. The combined action of force and temperature leads to intimate contact between the substrates, which is the prerequisite for macromolecular interdiffusion and welding. A polymer film named Energy Director (ED) can be set up at the interface between substrates to enable the process and to ensure the strength of the joint. This leads to the need for a temperature measurement technique to better understand the physics responsible for the best bonding parameters. The use of Fibre Bragg Grating (FBG) seems to be suitable for obtaining real-time temperature data during the joining. The present work is challenging this technique by means of a rheometer as a device for results validation. The considered bonded materials are carbon fibre-reinforced polyetheretherketone (CF/PEEK) and polyetherimide (PEI). The integration of PEI film on top of the CF/PEEK composite parts is studied. The FBG sensors respond to both temperature and longitudinal strain. Then two kinds of measurements are examined under the rheometer: the first response of the fibre as a function of temperature in static mode during processing and the second one as a function of torque loading. Wavelength shifts and spectral form changes induced by the contraction of the composite during cooling were observed. The use of a rheometer is suitable for the simulation of CF/PEEK composites joining processes such as welding. FBG method has a higher potential for temperature measurement than incorporated thermocouples (TC) as studied during ultrasonic (US) welding [1]. Its advantage is the possibility to allow several measurement points along the optical fibre. The ultimate goal is to provide temperature mapping in the welding zone. The results from both techniques: optical fibre sensors and thermocouples were compared.

**Introduction**

Temperature monitoring remains a challenge, especially for high-frequency phenomena like US welding, however, optical fibre sensors may propose many important advantages for industrial uses. They are small with a diameter below 0.25 mm, highly sensitive to temperature and strain, multiplexable, immune to electromagnetic perturbation, and resistant to corrosion and fatigue. The fibres are flexible, and coated with a polymer-like polyimide that can readily be installed in industry without significantly disturbing the measurement environment [2]. The optical fibre

<figure><img src="image_2516.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.
# Monitoring the temperature during thermoplastic composites assembling with fibre Bragg gratings: Validation using a rheometer

KORYCKI Adrian<sup>1,2,a</sup>, CARASSUS Fabrice<sup>1,2,b</sup>, GARNIER Christan<sup>1,c</sup>,
CHABERT France<sup>1,d</sup>, CASARI Pascal<sup>3,e</sup> and DJILALI Toufik<sup>2,f</sup>

<sup>1</sup>LGP-ENIT-INPT, University of Toulouse, 47 Avenue d'Azereix, 65016 Tarbes, France

<sup>2</sup>LAUAK FRANCE, 8 Rue Louis Caddau, 65000 Tarbes, France

<sup>3</sup>Nantes Université, Ecole Centrale Nantes, CNRS, GeM, UMR 6183, F-44600 Saint-Nazaire, France

<sup>a</sup>akorycki@uttop.fr, <sup>b</sup>fcarassus@uttop.fr, <sup>c</sup>cgarnier@uttop.fr, <sup>d</sup>fchabert@uttop.fr,

<sup>e</sup>pascal.casari@univ-nantes.fr, <sup>f</sup>toufik.djilali@groupe-lauak.com

**Keywords:** Fibre Optic Sensor, Bragg Grating, Rheometer, Temperature, Thermoplastic Composite

**Abstract.** For many years, thermoplastic composites have been conquering the technological market in commercial applications in civil and military structures, with particular emphasis on aircraft. One of their most attractive advantages is the potential to be repaired and welded in a short time. However, due to the lack of knowledge on the impact of process parameters (time, pressure, temperature) bonding thermoplastic composites remains a challenge. The combined action of force and temperature leads to intimate contact between the substrates, which is the prerequisite for macromolecular interdiffusion and welding. A polymer film named Energy Director (ED) can be set up at the interface between substrates to enable the process and to ensure the strength of the joint. This leads to the need for a temperature measurement technique to better understand the physics responsible for the best bonding parameters. The use of Fibre Bragg Grating (FBG) seems to be suitable for obtaining real-time temperature data during the joining. The present work is challenging this technique by means of a rheometer as a device for results validation. The considered bonded materials are carbon fibre-reinforced polyetheretherketone (CF/PEEK) and polyetherimide (PEI). The integration of PEI film on top of the CF/PEEK composite parts is studied. The FBG sensors respond to both temperature and longitudinal strain. Then two kinds of measurements are examined under the rheometer: the first response of the fibre as a function of temperature in static mode during processing and the second one as a function of torque loading. Wavelength shifts and spectral form changes induced by the contraction of the composite during cooling were observed. The use of a rheometer is suitable for the simulation of CF/PEEK composites joining processes such as welding. FBG method has a higher potential for temperature measurement than incorporated thermocouples (TC) as studied during ultrasonic (US) welding [1]. Its advantage is the possibility to allow several measurement points along the optical fibre. The ultimate goal is to provide temperature mapping in the welding zone. The results from both techniques: optical fibre sensors and thermocouples were compared.

**Introduction**

Temperature monitoring remains a challenge, especially for high-frequency phenomena like US welding, however, optical fibre sensors may propose many important advantages for industrial uses. They are small with a diameter below 0.25 mm, highly sensitive to temperature and strain, multiplexable, immune to electromagnetic perturbation, and resistant to corrosion and fatigue. The fibres are flexible, and coated with a polymer-like polyimide that can readily be installed in industry without significantly disturbing the measurement environment [2]. The optical fibre

<figure><img src="image_2509.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.
Bragg gratings have been developed since the 90s to offer new sensing systems. The measurement for pressure, strain and temperature by the FBG system is extensive since the propagation of light within an optical fibre reflects particular wavelengths of light and transmits all others.

Three common principles of fibre optic temperature measurement were studied and compared by Hoffmann et al. [3] considering fibre Bragg gratings, Raman scattering and interferometric point sensors. They resumed that FBG is the most suitable where many temperature measurement points are required or where strain measurements are carried out.

Progress in applications of FBG sensors to large composites and concrete structures was investigated by Rogers [4] and Rao [2]. Systems based on fibre Bragg gratings, with particular reference to the measurements of pressure, strain and temperature in industrial environments have already been installed and become commercially available in the electrical power industry, medicine and chemical sensing. Since then, multimode FBG using correlation signal processing methods has been developed [5]. Strain testing has been done from 0 με to 10000 με and temperature testing from -40 °C to 80 °C for various applications. For use in aerospace extreme environments, the oxygen-chemical composition grating exhibited a response similar to the original FBG sensors at temperatures up to 1000 °C. The sensors would allow temperature measurement to be made within 3 % of the reference S-type thermocouple. Also, long-term survivability over 400 h of thermal cycling to 750 °C and 7 h of thermal cycling to 1000 °C has been demonstrated [6]. Then, Habisreuther et al. [7] by using sapphire FBG sensors showed the temperature sensing up to 1900 °C.

The method based on the measurements of the fibre Bragg grating phase obtained by combining optical low coherence interferometry and inverse scattering algorithm was proposed by Chapeleau et al. [8]. The authors performed non-uniform strain distribution and temperature gradient measurements using uniform or chirped FBG sensors. Recently, Pereira et al. [9] proposed a method to obtain independent strain and temperature measurements using embedded FBG in polymeric tensile test specimens, which is also promising for polymer fatigue test specimens. Generally, FBG sensors have a strain and temperature cross-sensitivity, making them inaccurate for tests where both change at the same time. An additional strain is created by temperature variation in the specimen, caused by thermal expansion. A method to decouple this cross-sensitivity, enabling independent and accurate measurement of strain and temperature, was developed. This technique can be accomplished by using two single mode FBG sensors embedded in the material.

In this work, the thermal analysis conducted on CF/PEEK composites using the PEI layer on the top is displayed. The fibre Bragg grating sensors were chosen to monitor temperature during assembly. The experiments present measurements where temperature profiles are analyzed through optical fibre sensors. FBG responded to changes in the material state. Finally, the Bragg wavelengths registered during assemblies of CF/PEEK with 250 μm PEI layer are correlated to the thermal profiles of thermocouples.

## Materials and Methods

Substrates are laminates from Carbon fibre-reinforced polyetheretherketone composite fabrics, named PEEK from Porcher Industries and the energy director is a polyetherimide, named Ultem 1000 from Sabic. The CF/PEEK composite glass transition temperature ($T_g$) and melting point ($T_m$) are 143 °C and 343 °C, respectively. Prepreg fibre areal weight is 456 g·m⁻² and the resin weight content is 38 wt.%. The $T_g$ of PEI is 220 °C.

The composite plates were produced under the thermo-compression device from Pinette Emidecau Industries with frames of appropriate thickness. Two types of plates were manufactured: (1) 2 mm thick CF/PEEK plates and (2) the same plates with an additional 250 μm PEI layer integrated on top. 7 plies of CF/PEEK fabric were stacked to create a mirror symmetry lay-up [0/90]. Plates were first consolidated at 390 °C under an equivalent force of 192 kN on the laminate
Bragg gratings have been developed since the 90s to offer new sensing systems. The measurement for pressure, strain and temperature by the FBG system is extensive since the propagation of light within an optical fibre reflects particular wavelengths of light and transmits all others.

Three common principles of fibre optic temperature measurement were studied and compared by Hoffmann et al. [3] considering fibre Bragg gratings, Raman scattering and interferometric point sensors. They resumed that FBG is the most suitable where many temperature measurement points are required or where strain measurements are carried out.

Progress in applications of FBG sensors to large composites and concrete structures was investigated by Rogers [4] and Rao [2]. Systems based on fibre Bragg gratings, with particular reference to the measurements of pressure, strain and temperature in industrial environments have already been installed and become commercially available in the electrical power industry, medicine and chemical sensing. Since then, multimode FBG using correlation signal processing methods has been developed [5]. Strain testing has been done from 0 με to 10000 με and temperature testing from -40 °C to 80 °C for various applications. For use in aerospace extreme environments, the oxygen-chemical composition grating exhibited a response similar to the original FBG sensors at temperatures up to 1000 °C. The sensors would allow temperature measurement to be made within 3 % of the reference S-type thermocouple. Also, long-term survivability over 400 h of thermal cycling to 750 °C and 7 h of thermal cycling to 1000 °C has been demonstrated [6]. Then, Habisreuther et al. [7] by using sapphire FBG sensors showed the temperature sensing up to 1900 °C.

The method based on the measurements of the fibre Bragg grating phase obtained by combining optical low coherence interferometry and inverse scattering algorithm was proposed by Chapeleau et al. [8]. The authors performed non-uniform strain distribution and temperature gradient measurements using uniform or chirped FBG sensors. Recently, Pereira et al. [9] proposed a method to obtain independent strain and temperature measurements using embedded FBG in polymeric tensile test specimens, which is also promising for polymer fatigue test specimens. Generally, FBG sensors have a strain and temperature cross-sensitivity, making them inaccurate for tests where both change at the same time. An additional strain is created by temperature variation in the specimen, caused by thermal expansion. A method to decouple this cross-sensitivity, enabling independent and accurate measurement of strain and temperature, was developed. This technique can be accomplished by using two single mode FBG sensors embedded in the material.

In this work, the thermal analysis conducted on CF/PEEK composites using the PEI layer on the top is displayed. The fibre Bragg grating sensors were chosen to monitor temperature during assembly. The experiments present measurements where temperature profiles are analyzed through optical fibre sensors. FBG responded to changes in the material state. Finally, the Bragg wavelengths registered during assemblies of CF/PEEK with 250 μm PEI layer are correlated to the thermal profiles of thermocouples.

## Materials and Methods

Substrates are laminates from Carbon fibre-reinforced polyetheretherketone composite fabrics, named PEEK from Porcher Industries and the energy director is a polyetherimide, named Ultem 1000 from Sabic. The CF/PEEK composite glass transition temperature ($T_g$) and melting point ($T_m$) are 143 °C and 343 °C, respectively. Prepreg fibre areal weight is 456 g·m⁻² and the resin weight content is 38 wt.%. The $T_g$ of PEI is 220 °C.

The composite plates were produced under the thermo-compression device from Pinette Emidecau Industries with frames of appropriate thickness. Two types of plates were manufactured: (1) 2 mm thick CF/PEEK plates and (2) the same plates with an additional 250 μm PEI layer integrated on top. 7 plies of CF/PEEK fabric were stacked to create a mirror symmetry lay-up [0/90]. Plates were first consolidated at 390 °C under an equivalent force of 192 kN on the laminate
for 10 min. A second thermo-compression cycle at 350 °C under the force of 117 kN for 10 min was applied for PEI integration. The plates were removed at 250 °C to avoid shrinkage and deformation. 25 mm diameter disc samples were then cut. Before experiments, materials were dried in the oven for at least 24 h at 130 °C.

The FBG are 10 mm long and placed in the middle of the Ø25 mm specimen. Their orientation is perpendicular to the carbon fibres. In the case of CF/PEEK with integrated PEI on top, the FBG without coating were previously inserted inside the PEI layer of the bottom specimen. The insertion procedure consisted of depositing the FBG on the PEI layer of the composite and covering it with treated Polyimide film and a 5 kg metal mass. The assembly was then placed in an oven at 290 °C for 40 min. Next, the FBG was extended to connect to a SmartScan interrogator.

Temperature measurements were performed using the oven of ARES rheometer from Rheometrics and thermocouple K-type from RS connected to the midi data recorder from Graphtec Corporation. The samples were clamped between 2 aluminium discs of 25 mm diameter in parallel plate configuration.

The experimental set-up shown in **Figure 1** has been provided to create a carefully controlled temperature gradient during composite assemblies. Two rheometer procedures were successively applied during temperature and wavelength measurements: holding plates (1) in static mode position and (2) in dynamic mode, meaning subjected to mechanical torque for 15 min with deformation of 0.1% and frequency of 1 Hz.

<figure><img src="image_2517.png" /><figcaption>Figure 1. Experimental set-up of rheometer procedure in (a) static mode (b) dynamic mode (c) zoom of assembly</figcaption></figure>

Temperature measurement and calibration

The fibre Bragg grating is made of a core with alternating refractive indices and a constant periodicity. The central wavelength of back-reflected light from a uniform Bragg wavelength, $\lambda_{Bragg}$, is given by the following equation:

$$ \lambda_{Bragg} = 2\Lambda n_{eff} \qquad (1) $$

where $\Lambda$ is the period of the grating and $n_{eff}$ is the effective index of the fundamental mode of the fibre. Both $\Lambda$ and $n_{eff}$ are affected by the strain and temperature of the grating through elongation and thermal expansion effects of the material. This formula can be extended to include the effect of strain and temperature on the effective refractive index of refraction and periodic spacing between the grating planes, so the Bragg wavelength is shifted.

$$ \Delta\lambda_{Bragg} = \lambda_0[(1 - P_e)\varepsilon + (\alpha + \xi)\Delta T] \qquad (2) $$
for 10 min. A second thermo-compression cycle at 350 °C under the force of 117 kN for 10 min was applied for PEI integration. The plates were removed at 250 °C to avoid shrinkage and deformation. 25 mm diameter disc samples were then cut. Before experiments, materials were dried in the oven for at least 24 h at 130 °C.

The FBG are 10 mm long and placed in the middle of the Ø25 mm specimen. Their orientation is perpendicular to the carbon fibres. In the case of CF/PEEK with integrated PEI on top, the FBG without coating were previously inserted inside the PEI layer of the bottom specimen. The insertion procedure consisted of depositing the FBG on the PEI layer of the composite and covering it with treated Polyimide film and a 5 kg metal mass. The assembly was then placed in an oven at 290 °C for 40 min. Next, the FBG was extended to connect to a SmartScan interrogator.

Temperature measurements were performed using the oven of ARES rheometer from Rheometrics and thermocouple K-type from RS connected to the midi data recorder from Graphtec Corporation. The samples were clamped between 2 aluminium discs of 25 mm diameter in parallel plate configuration.

The experimental set-up shown in **Figure 1** has been provided to create a carefully controlled temperature gradient during composite assemblies. Two rheometer procedures were successively applied during temperature and wavelength measurements: holding plates (1) in static mode position and (2) in dynamic mode, meaning subjected to mechanical torque for 15 min with deformation of 0.1% and frequency of 1 Hz.

<figure><img src="image_2510.png" /><figcaption>Figure 1. Experimental set-up of rheometer procedure in (a) static mode (b) dynamic mode (c) zoom of assembly</figcaption></figure>

Temperature measurement and calibration

The fibre Bragg grating is made of a core with alternating refractive indices and a constant periodicity. The central wavelength of back-reflected light from a uniform Bragg wavelength, $\lambda_{Bragg}$, is given by the following equation:

$$ \lambda_{Bragg} = 2\Lambda n_{eff} \quad (1) $$

where $\Lambda$ is the period of the grating and $n_{eff}$ is the effective index of the fundamental mode of the fibre. Both $\Lambda$ and $n_{eff}$ are affected by the strain and temperature of the grating through elongation and thermal expansion effects of the material. This formula can be extended to include the effect of strain and temperature on the effective refractive index of refraction and periodic spacing between the grating planes, so the Bragg wavelength is shifted.

$$ \Delta\lambda_{Bragg} = \lambda_0[(1 - P_{\epsilon})\epsilon + (\alpha + \xi)\Delta T] \quad (2) $$
where $\lambda_0$ is the initial value of Bragg wavelength, $P_\epsilon$ is the effective photo-elastic constant, $\epsilon$ is the strain applied to the gratings, $\alpha$ and $\xi$ stand for the coefficient of thermal expansion and the fibre thermo-optic coefficient of the grating material, respectively, and $\Delta T$ is the temperature variation. If no stress is applied to the FBG during the experiments, strain measurements of the FBG can be neglected. The corresponding Bragg wavelength shift is given by:

$$ \Delta\lambda_{Bragg} = \lambda_0[1 + (\alpha + \xi)\Delta T] \quad (3) $$

**Figure 2** shows the amplitude reflection coefficient of the FBG before the measurement. A temperature change causes a shift in the Bragg wavelength. The peak position strongly depends on temperature, and the reflected intensity from the FBG is sufficient for further signal processing. Only the peak wavelength is recorded by the software as a function of time.

<figure><img src="image_2518.png" /><figcaption>Figure 2. Amplitude reflection coefficient of FBG</figcaption></figure>

The thermal profile characterization was performed with temperatures ranging from room temperature to 350 °C. A short cycle of 2 min at 100 °C and 5 min at 350 °C in static mode was first tested to display the interrogator's response with an assembly of CF/PEEK with loose PEI layers. This thermal cycle was insufficient to observe temperature holding levels, but adequate to form a cohesive welding interphase incorporating the FBG with no risk of degradation. A unified interphase, which is created assembly joint, is also a way to limit the strain induced by the set-up for further calibration tests.

The calibration cycle was then performed in static mode: three isothermal temperatures (100, 200 and 300 °C) were applied for 15 min each to obtain a constant temperature, and the last one at 350 °C was kept until stabilization to avoid too long degradation of the material, **Figure 3.a**. The Bragg wavelength was centred at 1540.69 nm at room temperature. This calibration aims to determine the trend curve correlated between the Bragg wavelength shift and thermocouple temperature. Thermocouple measurements on the set-up are not reliable for accurately indicating the interphase temperature, but stabilizing the oven temperature guarantees a usable value. The oven's dimensions are small enough to ensure a uniform temperature around the grating and the reference thermocouple. The first observation is that stabilization time in a rheometer needs at least 5 min at the requested isotherm.
where $\lambda_0$ is the initial value of Bragg wavelength, $P_\epsilon$ is the effective photo-elastic constant, $\epsilon$ is the strain applied to the gratings, $\alpha$ and $\xi$ stand for the coefficient of thermal expansion and the fibre thermo-optic coefficient of the grating material, respectively, and $\Delta T$ is the temperature variation. If no stress is applied to the FBG during the experiments, strain measurements of the FBG can be neglected. The corresponding Bragg wavelength shift is given by:

$$ \Delta\lambda_{Bragg} = \lambda_0[1 + (\alpha + \xi)\Delta T] \quad (3) $$

**Figure 2** shows the amplitude reflection coefficient of the FBG before the measurement. A temperature change causes a shift in the Bragg wavelength. The peak position strongly depends on temperature, and the reflected intensity from the FBG is sufficient for further signal processing. Only the peak wavelength is recorded by the software as a function of time.

<figure><img src="image_2511.png" /><figcaption>Figure 2. Amplitude reflection coefficient of FBG</figcaption></figure>

The thermal profile characterization was performed with temperatures ranging from room temperature to 350 °C. A short cycle of 2 min at 100 °C and 5 min at 350 °C in static mode was first tested to display the interrogator's response with an assembly of CF/PEEK with loose PEI layers. This thermal cycle was insufficient to observe temperature holding levels, but adequate to form a cohesive welding interphase incorporating the FBG with no risk of degradation. A unified interphase, which is created assembly joint, is also a way to limit the strain induced by the set-up for further calibration tests.

The calibration cycle was then performed in static mode: three isothermal temperatures (100, 200 and 300 °C) were applied for 15 min each to obtain a constant temperature, and the last one at 350 °C was kept until stabilization to avoid too long degradation of the material, **Figure 3.a**. The Bragg wavelength was centred at 1540.69 nm at room temperature. This calibration aims to determine the trend curve correlated between the Bragg wavelength shift and thermocouple temperature. Thermocouple measurements on the set-up are not reliable for accurately indicating the interphase temperature, but stabilizing the oven temperature guarantees a usable value. The oven's dimensions are small enough to ensure a uniform temperature around the grating and the reference thermocouple. The first observation is that stabilization time in a rheometer needs at least 5 min at the requested isotherm.