**Preparation Nano-Structure Polytetrafluoroethylene (PTFE) Functional Film on the Cellulose Insulation Polymer and Its Effect on the Breakdown Voltage and Hydrophobicity Properties**

#### **Jian Hao 1,2,\*, Cong Liu 1, Yanqing Li 1, Ruijin Liao 1, Qiang Liao <sup>3</sup> and Chao Tang <sup>4</sup>**


Received: 21 April 2018; Accepted: 16 May 2018; Published: 21 May 2018

**Abstract:** Cellulose insulation polymer is an important component of oil-paper insulation, which is widely used in power transformer. The weight of the cellulose insulation polymer materials is as high as tens of tons in the larger converter transformer. Excellent performance of oil-paper insulation is very important for ensuring the safe operation of larger converter transformer. An effective way to improve the insulation and the physicochemical property of the oil impregnated insulation pressboard/paper is currently a popular research topic. In this paper, the polytetrafluoroethylene (PTFE) functional film was coated on the cellulose insulation pressboard by radio frequency (RF) magnetron sputtering to improve its breakdown voltage and the hydrophobicity properties. X-ray photoelectron spectroscopy (XPS) results show that the nano-structure PTFE functional film was successfully fabricated on the cellulose insulation pressboard surface. The scanning electron microscopy (SEM) and X-ray diffraction (XRD) present that the nanoscale size PTFE particles were attached to the pressboard surface and it exists in the amorphous form. Atomic force microscopy (AFM) shows that the sputtered pressboard surface is still rough. The rough PTFE functional film and the reduction of the hydrophilic hydroxyl of the surface due to the shielding effect of PTFE improve the breakdown and the hydrophobicity properties of the cellulose insulation pressboard obviously. This paper provides an innovative way to improve the performance of the cellulose insulation polymer.

**Keywords:** cellulose insulation pressboard; magnetron sputtering; polytetrafluoroethylene; nano structure; breakdown; hydrophobicity

#### **1. Introduction**

Converter transformer is one of the key equipment in HVDC (High Voltage Direct Current) transmission network. The main insulation of the valve side for converter transformer usually has a high failure rate because of the complicated electric field in the operating condition, including alternating current (AC), direct current (DC), AC, and DC compound electric field [1,2]. Oil-paper insulation is the main insulation form of the valve side in converter transformer. Its insulation reliability is closely related to the safe operation of a converter transformer. The insulation performance of the

insulation paper/pressboard under DC condition is an important factor to decide the operation reliability of the converter transformer.

It has been reported that polymer nanocomposites with metal oxide nanoparticle fillers can exhibit enhanced electrical breakdown strength [3,4]. In order to improve the breakdown and the mechanical properties of insulation paper, Liao Ruijin et al. developed the nano-Al2O3 doped cellulose insulation paper [5–7]. Results show that the nano-Al2O3 doped insulation paper possesses the better dielectric properties and AC breakdown strength. Chi Minghe et al. also studied the breakdown behavior of the Al2O3 modified pressboard [8]. Results show the breakdown strength of modified pressboard firstly increases and then decreases with the increase of nano-doping content, and reaches the peak value at 2.5% concentration. Liao Ruijin and Chi Minghe et al. also investigated the dielectric characteristics of nano-montmorillonite (MMT) modification insulation pressboard [9,10]. It is found that the breakdown strength of modified pressboard firstly increases and it then decreases with the growth of nano-doping content [5–10]. However, nanoparticle fillers research indicated that the difficulty of nano-doping is the agglomeration of nanoparticles [4–10]. In addition to adding nano-fillers to the material, it is worth investigating the fabrication of a special functional nano-structure film on the surface of the insulating material, which could provide an effective function for enhancing the electrical or the physicochemical properties of the oil impregnated insulation pressboard/paper that is used in the power transformer.

Moreover, moisture plays a detrimental role in the oil-paper insulation lifetime by reducing the thermal resistance and electrical breakdown strength and is regarded as "the first enemy" after temperature [11–13]. The production of moisture is inevitable in the service of a transformer. Field experience shows that the moisture content of a transformer is usually <0.5% in the initial stage of its operation, and it may increase to 2~4% at the last stage of its life [12]. The more moisture the insulation contains and the higher the temperature of the insulation system, the faster the oil-paper insulation material degrades [14,15]. Therefore, improving the hydrophobicity of insulating paper is very important for ensuring the performance of insulation paper.

Effective ways to improve the breakdown and hydrophobicity property of the oil impregnated insulation pressboard/paper used in power transformer are currently a popular research topic. PTFE has excellent insulation and hydrophobicity performance [16,17]. In this paper, the PTFE functional film on the cellulose insulation polymer was prepared by RF magnetron sputtering. Firstly, the structure and the existence form of the PTFE functional film were characterized. Then, the effect of the PTFE functional film on the breakdown and the hydrophobicity properties of the cellulose polymer were analyzed.

#### **2. Materials and Methods**

#### *2.1. Materials and Sample Preparation*

The cellulose insulation pressboard with a thickness 0.45 mm was used at here. The JPGF-480 reactive RF magnetron sputtering device at 13.56 MHz (Beijing Instrument Factory, Beijing, China) was used for pressboard coating. For PTFE film deposition, the insulation pressboard substrates were cut into 15 cm × 10 cm pieces, and a PTFE target (diameter 61.5 mm, thickness 5 mm) was sputtered. The distance between the target and the substrate sample was 10 cm. The vacuum chamber was pumped down to a base pressure of 4.0 × <sup>10</sup>−<sup>3</sup> Pa before sputtering. Deposition was conducted by using forward power 100 W. Argon was used as the working gas with a constant pressure of 1.5 Pa. The deposition mode was static, double-sided coating, and the deposition time was 10 min and 20 min at 28 ◦C. The sketch map for the RF magnetron sputtering PTFE functional film on the cellulose pressboard surface is shown in Figure 1. The sample composition is shown in Table 1.

**Figure 1.** RF magnetron sputtering polytetrafluoroethylene (PTFE) functional film on the cellulose pressboard surface.

#### *2.2. Characterization Methods and Sample Treatment*

X-ray photoelectron spectroscopy (XPS) with Al Kα X-ray source (XPS, Thermo escalab 250Xi, Waltham, MA, USA) was used to characterize the chemical binding state of the deposition film. The XPS spectra without argon etching were recorded in the fixed analyzer transmission mode with pass energy of 20 eV and a resolution of 0.1 eV. The deviation that is caused by the charging effect was calibrated using adventitious carbon referencing (C 1s, 284.6 eV). The scanning electron microscopy (SEM) (JSM-7800F, JEOL, Tokyo, Japan) and atomic force microscopy (AFM, Bruker Daltonics Inc., Billerica, MA, USA) were used to investigate the surface morphology of the coated surface. The X-ray diffractometer using Cu Ka (λ = 0.154 nm) radiation at a fixed incident angle of 2◦ was used to obtain the X-ray diffraction (XRD) (PANalytical Empyrea, Almelo, The Netherlands) patterns of the samples.

Before the DC (direct current) breakdown experiment, firstly, all of the samples were dried at 90 ◦C for 24 h in a vacuum box (1000 Pa). Then, new mineral oil was infused into the vacuum box and the temperature of the vacuum box was adjusted to 40 ◦C. The pressboard was impregnated at 40 ◦C for 48 h. The parameter of the oil used for impregnation is shown in Table 2. The measured moisture content of the oil-impregnated pressboard using Karl Fischer titration method was 0.95% after impregnation, and being cooled to room temperature. The DC breakdown voltage was measured according to Figure 2a. The pre-pressure DC voltage (15 kV/mm) was applied for 5 min. Then, the voltage was increased at 1 kV/s until sample breakdown. Five breakdown voltages were recorded for each sample. The breakdown test electrode setup is shown in Figure 2b. The test temperature is 28 ◦C.

**Figure 2.** Direct current (DC) breakdown test process and the DC breakdown test electrode setup. (**a**) DC breakdown test process; (**b**) DC breakdown test electrode setup.


**Table 2.** The parameter of the oil used for impregnation.

At last, the contact angle was measured with a Kyowa contact angle meter. Three measurements on different sample spots were made for each specimen. An average of the measurements was used for analysis. For XPS, SEM, AFM, XRD and contact angle test, non-impregnated pressboard samples were used. For the DC breakdown voltage test, the oil impregnated insulation pressboard was used.

#### **3. Results and Discussions**

#### *3.1. XPS Analysis*

Figure 3 shows the XPS survey spectra of the new pressboard, new pressboard surface as-prepared PTFE film for 10 min and 20 min. Cellulose insulation pressboard consists of linear, polymeric chains of cyclic, β-D-glucopyranose units, which are composed of C, H, and O element [18]. Therefore, there is only C 1s and O 1s peak, and extremely weak O 2s peak shown in Figure 3a. The molecular formula of PTFE is (C2F4)n. As shown in Figure 3b,c, it is obvious that the F 1s peak appears on the pressboard surface as-prepared PTFE film for 10 min and 20 min. With the increase of the coating time, the F 1s peak is obviously enhanced [19]. While the O 1s peak becomes weaker and weaker because of the coverage of the PTFE film on the surface of the cellulose pressboard. The O 1s peak almost disappeared for the pressboard surface deposited PTFE 20 min.

**Figure 3.** The X-ray photoelectron spectroscopy (XPS) spectra of the new pressboard (**a**), new pressboard surface as-prepared. PTFE film for 10 min (**b**) and 20 min (**c**).

Figures 4–6 show the C 1s, O 1s, and F 1s peak fitting in the XPS narrow scan spectra, respectively. The peak fitting can be used to make identify the chemical components. The identified chemical components with different binding energies and its concentration by C 1s, O 1s, and F 1s peak fitting are shown in Tables 3–5, respectively. The C1, C6, and C7 peaks that are presented in Figure 4a are attributed to C–C/C=C, C–O, and O–C=O, respectively [19,20]. It is particularly noteworthy from Figure 4b,c that new C2, C3, C4, C5 peaks appear for the sample NP-PTFE10 and NP-PTFE20. The C2, C3, C4, C5 peaks are attributed to O–C–CF3/CF2, CF, CF2, and CF3, respectively [19,20]. From the O 1s high resolution spectra shown in Figure 5b,c, it can be seen that new O3 peak appears for the coated samples. The O1 and O2 are attributed to O=C–O and O–C. The O3 is attributed to

O–C–CF3/CF2 [19,20]. Figure 6b,c show that there are also new F1 peak attributed to F–C appears for the pressboard surface deposited PTFE for 10 min and 20 min. With the coating time increase, due to the covering PTFE film, Figure 4b,c show that the intensity of the new C3, C4, C5 peaks becomes stronger, while the intensity of C1, C6, and C7 peaks becomes weaker. The intensity of new F 1 peaks for the pressboard surface as-prepared PTFE film for 20 min is significantly stronger than that of the sample as-prepared PTFE film for 10 min. From Figures 5 and 6, Tables 3–5, it could be deduced that the PTFE has been successfully fabricated on the cellulose insulation pressboard surface.

**Figure 4.** C 1s peak fitting for the new pressboard (**a**), new pressboard coated PTFE film for 10 min (**b**), and 20 min (**c**).

**Figure 5.** *Cont*.

**Figure 5.** O 1s peak of the new pressboard, pressboard surface coated PTFE film for 10 min and 20 min.

**Figure 6.** F 1s peak of the new pressboard, pressboard surface coated PTFE film for 10 min and 20 min.


**Table 3.** C 1s peak fitting result for NP, NP-PTFE10, and NP-PTFE20.


**Table 3.** *Cont*.

**Table 4.** O 1s peak fitting result for NP, NP-PTFE10, and NP-PTFE20.


**Table 5.** F 1s peak fitting result for NP, NP-PTFE10, and NP-PTFE20.


#### *3.2. Surface Topography Analysis*

The SEM micrographs of the untreated pressboard and the coated pressboard are shown in Figure 7. We can observe that the cellulose fibers of untreated pressboard (Figure 7a) intersect each other and its surface is relatively rough. There are some cracks where the fibers intersect. The pressboard surface with magnetron sputtering treatment for 10 min (Figure 7b) is more smooth and dense. There are many very small PTFE particles with nanometer covered on the surface. The PTFE particles filled the cracks between the fibers and were distributed uniformly on the surface. However, for the pressboard surface sputtered for 20 min, as shown in Figure 6c, the cracks also are be filled. Besides, PTFE is present in larger particles due to the agglomeration of particles. The PTFE particles are about a few dozen nanometers in size.

**Figure 7.** The scanning electron microscopy (SEM) of the new pressboard, pressboard surface coated PTFE film for 10 min and 20 min.

The microscopic appearance of insulating pressboard specimen before and after magnetron sputtering was measured by AFM (Figure 8). The AFM image shows a greater longitudinal undulating and some sharp protrusions, in good agreement with the SEM micrograph revealing a relatively rough surface. After specimen treatment, there are some obvious changes that have taken place. By comparing the fresh pressboard, we can find that the pressboard surface coated PTFE for 10 min (Figure 8b) is smoother than that of new pressboard, as well as the raised part is granular and relatively flat. Figure 8c shows the surface topography of sample that is modified by magnetron sputtering for 20 min, and as the sputtering time increases, the sample surface becomes slightly rougher again.

**Figure 8.** *Cont*.

**Figure 8.** The atomic force microscopy (AFM) of the new pressboard, pressboard surface coated PTFE film for 10 min and 20 min.

#### *3.3. XRD Analysis*

Figure 9 shows the XRD spectrum of new pressboard and the PTFE coated pressboard. Diffraction pattern for the pressboard has three broad peaks at 2θ = 15◦, 2θ = 22◦, and 2θ = 34◦, corresponding to (101), (002), and (040) diffraction peaks of cellulose, respectively [21]. In the diffraction pattern of the new pressboard, there is a sharp peak and some dispersive diffraction peaks, which means that the cellulose has a mixed structure of crystallization and amorphous phase. The diffraction peak of PTFE is at 17◦, 30◦, and 35◦ [22]. We can notice that there is no peak at 2θ = 17◦, 2θ = 30◦, and 2θ = 35◦ in the XRD results of coated pressboard, which proves that the PTFE film exists on the surface of insulation pressboard surface in the amorphous form.

**Figure 9.** X-ray diffraction (XRD) of the the new pressboard, pressboard surface coated PTFE film for 10 min and 20 min.

#### *3.4. DC Breakdown Analysis*

The DC pre-pressure breakdown strength of the new pressboard (NP), new pressboard deposited PTFE for 10 min and 20 min (NP-PTFE10, NP-PTFE20) is shown in Figure 10. The "pre-pressure breakdown strength" means the breakdown voltage obtained through the test process shown in the Figure 2. The average DC pre-pressure breakdown voltage for the NP, NP-PTFE10 and NP-PTFE20 is 136.37 kV/mm, 142.53 kV/mm, and 151.77 kV/mm, respectively. When compared with the new pressboard, the DC pre-pressure breakdown enhancement is 5% and 11% for NP-PTFE10 and NP-PTFE20, respectively. The PTFE functional film improves the breakdown property of the coated insulation pressboard, especially for the sample NP-PTFE20. This mainly because the nano PTFE particles filled the surface defects (Figure 7) and improved the breakdown performance.

**Figure 10.** DC pre-pressure breakdown strength of the new pressboard, new pressboard deposited. PTFE for 10 min and 20 min.

#### *3.5. Hydrophobicity and Hygroscopicity Analysis*

The insulation paper was developed from natural fiber. The structural characteristics of the fiber determines that it absorbs water very easily. However, the hygroscopicity of the insulation paper is a very bad feature when it is being used for insulation in the transformer. Therefore, if the insulation paper has better hydrophobicity, its performance is not easily destroyed by moisture. Figure 11 shows the detailed dynamic process of liquid droplets that are dripping on the surface of each sample. The contact angle is about 0◦ that it is impossible to measure, indicating that water droplet penetrated through the surface of pressboard due to the hydrophilicity of cellulose. However, the pressboard surface coated by PTFE shows hydrophobicity. Water droplets can last a long time on the PTFE surface. As reported in [23–25], the surface hydrophobicity should increase in the order –CH2 < –CH3 < –CF2 < –CF2H < –CF3. The pressboard surface coated PTFE has much C–F groups which improve its hydrophobicity. At the beginning, the contact angle of pressboard deposited PTFE for 10 min and 20 min is 118.2◦ and 116.6◦, respectively. As time increases, the contact angle decreases gradually. Before 45 min, both of the samples have the same change, and both are greater than 90◦. Then, the sample contact angle of pressboard surface as-prepared PTFE film for 10 min decreased faster than the PTFE film coated for 20 min.

**Figure 11.** The contact angle of the new pressboard, new pressboard deposited PTFE for 10 min and 20 min.

PTFE is a non-polar polymer with symmetrical structure, and it is one of the lowest surface energy materials [19,20]. In order to explain the change of surface hydrophobicity from the chemical mechanism, the Fourier transform infrared spectroscopy (FT-IR) spectroscopy (Nicolet iS5 FT-IR) was used to confirm the reason for the change of the contact angle. FT-IR analysis was further carried out. As shown in Figure 12, the peak at 3345 cm−<sup>1</sup> is assigned to the stretching vibration of O–H [26,27]. The peak at 2901 cm−1, 1426 cm−1, 1368 cm−1, and 1315 cm−<sup>1</sup> is assigned to the stretching vibration and the flexural vibration of C–H [26,27]. It is obvious that the shielding of nano-structure PTFE film leads to the reduction of hydroxyl, which is beneficial to reduce the interaction between hydroxyl and water. In addition, PTFE has the excellent hydrophobic and oleophylic properties [19,20]. The above two aspects increase the contact angle of the sputtered insulation pressboard surface.

**Figure 12.** FT-IR of the new pressboard, new pressboard deposited PTFE for 20 min.

The hygroscopicity of the dried new pressboard and the pressboard coated for PTFE was also compared at here. According to the moisture equilibrium experiment that was done by our team [28], the dried pressboard samples were placed into a humidity chamber. The temperature of the humidity chamber was set to 60 ◦C and the relative humidity was set to 60%. The absorption time was set as 0 min, 20 min, 40 min, 60 min, and 90 min. The moisture content of the dried new pressboard (NP) and the pressboard coated for PTFE (NP-PTFE20) is shown in Figure 13. It can be seen from Figure 13 that the moisture absorption rate for NP-PTFE20 sample is slower than that of the NP sample.

**Figure 13.** Moisture content of the NP and NP-PTFE20 samples under the absorption moisture condition.

For the moisture balance between paper and oil, the pressboard samples absorbed moisture for different times (0 min, 20 min, 40 min, 60 min, and 90 min) were placed into grinding bottles that were filled with new insulating oil. The grinding bottles were then sealed and placed in a constant temperature oven under controlled temperature 70 ◦C. The moisture concentration in oil and paper was constantly measured until the equilibrium state was considered to be achieved, when the measured moisture concentration remained constant. In this paper, the time that is required for reaching moisture equilibrium state was 13 days at 70 ◦C. The result for the moisture balance between paper and oil is shown in Figure 14. It can be seen that for the NP-PTFE20 sample, the moisture tends to stay in the oil.

**Figure 14.** Moisture balance between paper and oil at 70 ◦C.

#### *3.6. Oil Absorption and Impregnation*

In order to investigate the PTFE functional film influence on the oil impregnation, we measured the contact angle between oil and paperboard, and compared the process of oil drop that is entering into the pressboard with and without PTFE functional film. As shown in Figure 15, the NP-PTFE20 sample has higher contact angle between oil and paperboard. The oil drop entering into the NP is very quickly, while the oil drop entering into the NP-PTFE20 sample is very slow. It takes about 3 h to fully enter the interior of the NP-PTFE20 sample. Therefore, the oil impregnation process is slow for the pressboard PTFE functional film.

**Figure 15.** Contact angle between oil and paperboard.

In order to obtain the difference in the amount of oil that is impregnated into the NP and NP-PTFE 20 sample, the thermogravimetry (TG) and the derivative thermogravimetry (DTG) curves of the NP and NP-PTFE 20 sample impregnated with oil was measured, as shown in Figure 16. The heating rate is 7 ◦C/min. Each sample is 5.0 mg. The tested temperature is from 33 ◦C to 500 ◦C under a nitrogen flow of 50 mL/min. There are two peaks that can be seen for both NP and NP-PTFE20. This is because there is oil in the oil impregnated pressboard, and the thermal properties of oil and the pressboard are different. The first stage of weight loss in TG curve and the first peak in DTG curve is belonging to oil decomposition [29]. Subtracting the 0.95% moisture content, it can be deduced in Figure 16 that the NP sample contain 23.86% oil in the oil impregnated pressboard (mass ratio). The NP-PTFE20 sample contain 21.28% oil in the oil impregnated pressboard (mass ratio). The PTFE film fills many gaps on the surface, resulting in oil absorption being reduced.

**Figure 16.** TG for NP and NP-PTFE20.

For the oil impregnation experiment, the impregnation test model is shown in Figure 17. The size of the pressboard is 100 mm × 30 mm × 0.5 mm. The impregnation experiment was conducted at 30 ◦C, 1 atm. The impregnation length versus the impregnation time is shown in Figure 17. The samples that were used was new pressboard (NP) and new pressboard coated PTFE for 20 min (NP-PTFE20). Because the PTFE was coated on the two side surface of the pressboard, the oil impregnated the inner part from the bottom and other side surface of the samples where there is no PTFE. Thus, the oil impregnation rate of NP-PTFE20 is slower than that of NP sample.

**Figure 17.** Oil impregnation experiment and result.

#### **4. Conclusions**

The present study confirmed the finding about improving the DC pre-pressure breakdown and the hydrophobicity properties of the cellulose insulation polymer by sputtering nano-structure PTFE functional film on the surface. The conclusions are as follows:

The nano-structure PTFE functional film was successfully fabricated on the cellulose insulation pressboard surface by RF magnetron sputtering. When compared with the fresh cellulose insulation pressboard, for the pressboard sputtered PTFE for 10 min and 20 min, the new peaks attributed to O–C–CF3/CF2, CF, CF2, and CF3 appear in their C 1s XPS spectroscopy, the new peak that is attributed to O–C–CF3/CF2 appears in the O 1s XPS spectroscopy, and for F 1s XPS spectroscopy, the new peaks that are attributed to F–C, F2–C appear.

The SEM and XRD present that the nanoscale size PTFE particles were attached on the pressboard surface and exists in the amorphous form. The PTFE particles are about a few dozen nanometers in size for the surface sputtering 20 min. There are only three broad XRD peaks at 2θ = 15◦, 2θ = 22◦ and 2θ = 34◦, which belongs to cellulose. AFM result shows that the sputtered pressboard surface is still rough.

The DC pre-pressure breakdown enhancement is 5% and 11% for NP-PTFE10 and NP-PTFE20, respectively. The contact angle of the new pressboard is 0◦. However, the cellulose pressboard surface deposited PTFE for 10 min and 20 min is 118.2◦and 116.6◦, respectively. FTIR spectroscopy shows that the transmissivity of the peak at 3345 cm−<sup>1</sup> for O–H and the peaks at 2901 cm−1, 1426 cm−1, 1368 cm−1, and 1315 cm−<sup>1</sup> for C–H decreases for the sputtered sample. The rough PTFE functional film and the reduction of the hydrophilic hydroxyl of the surface due to the shielding effect of PTFE improve the DC pre-pressure breakdown and hydrophobicity properties of the cellulose insulation pressboard obviously.

The moisture absorption rate for NP-PTFE20 sample is slower than that of the NP sample. According to the result of the moisture balance between paper and oil, it shows that the moisture tends to stay in the oil. The NP sample contains 23.86% oil in the oil impregnated pressboard (mass ratio), and the NP-PTFE20 sample contains 21.28%. The oil impregnation rate of NP-PTFE20 is slower than that of the NP sample.

**Author Contributions:** J.H. designed the experiments, performed the breakdown, contact angle, XPS, SEM and FITR measurement and writing; C.L. and Y.L. performed the RF magnetron sputtering experiment, AFM and XRD analysis; J.H. and R.L. analyzed the data; C.T. contributed literature search; Q.L. contributed discussion and paper modification.

**Funding:** This research was funded by National Natural Science Foundation of China (51707022), China Postdoctoral Science Foundation (2017M612910), Chongqing Special Funding Project for Post-Doctoral (Xm2017040) and Funds for Innovative Research Groups of China (51321063).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Silk as a Natural Reinforcement: Processing and Properties of Silk/Epoxy Composite Laminates**

**Youssef K. Hamidi 1,\*, M. Akif Yalcinkaya 2, Gorkem E. Guloglu 2, Maya Pishvar 2, Mehrad Amirkhosravi <sup>2</sup> and M. Cengiz Altan <sup>2</sup>**


Received: 3 October 2018; Accepted: 26 October 2018; Published: 30 October 2018

**Abstract:** With growing environmental awareness, natural fibers have recently received significant interest as reinforcement in polymer composites. Among natural fibers, silk can potentially be a natural alternative to glass fibers, as it possesses comparable specific mechanical properties. In order to investigate the processability and properties of silk reinforced composites, vacuum assisted resin transfer molding (VARTM) was used to manufacture composite laminates reinforced with woven silk preforms. Specific mechanical properties of silk/epoxy laminates were found to be anisotropic and comparable to those of glass/epoxy. Silk composites even exhibited a 23% improvement of specific flexural strength along the principal weave direction over the glass/epoxy laminate. Applying 300 kPa external pressure after resin infusion was found to improve the silk/epoxy interface, leading to a discernible increase in breaking energy and interlaminar shear strength. Moreover, the effect of fabric moisture on the laminate properties was investigated. Unlike glass mats, silk fabric was found to be prone to moisture absorption from the environment. Moisture presence in silk fabric prior to laminate fabrication yielded slower fill times and reduced mechanical properties. On average, 10% fabric moisture induced a 25% and 20% reduction in specific flexural strength and modulus, respectively.

**Keywords:** epoxy; natural fiber composites; silk fibers

#### **1. Introduction**

During the last several decades, fiber-reinforced polymer composites have experienced remarkable growth in various sectors, ranging from packaging and sporting goods to automotive and aerospace industries. This increased usage is essentially due to their lightweight, higher mechanical properties, and superior corrosion resistance compared to conventional materials [1,2].

Recently, growing environmental awareness has led to stricter policies regarding sustainability and encouraged industry to pursue ecofriendly products [3–5]. In this context, natural fibers have attracted increased attention over the past several years as alternatives to traditional reinforcements, namely glass, carbon, and aramid fibers. Currently, glass fibers are the most commonly used reinforcement in composites [3], since they offer a stable supply chain and relatively low-cost products with high mechanical performance. However, these inorganic fibers introduce several drawbacks, including non-biodegradability, high abrasion of processing equipment, and potential dermal and respiratory irritations [6]. In contrast, natural fibers offer a lower density, less abrasiveness, as well as promising biodegradability and sustainability [4,5,7]. For instance, plant-based natural fibers such as sisal, flax, jute, and hemp have been widely investigated in the literature as potential low-cost, ecofriendly alternatives to synthetic fibers [5–7]. Nonetheless, composites reinforced with plant fibers

exhibit lower mechanical performance compared to those reinforced with glass fibers, which limits their use in structural applications [4,8,9]. Furthermore, plant fibers tend to exhibit thermal instability at elevated temperatures, lower impact strength, and mechanical degradation during processing. Despite these drawbacks, the commercial use of plant fiber composites in non-load-bearing applications has significantly increased, predominantly in the automotive industry [3,10].

In contrast to fibers extracted from plants, silk is an animal-based fiber that offers attractive features such as low density, flame resistance, and high elongation even at low temperatures [4,8,11]. More importantly, silk exhibits higher mechanical performance than plant fibers, and, in some cases, comparable specific mechanical properties to glass fibers [4,8,9]. Silk denotes a group of protein-based fibers, called fibroin, produced by several arthropods like silkworms, spiders, and scorpions [3,12]. Fibroin generally has an irregular, almost-triangular cross-section, with a width in the range of 8 to 13 μm [13]. Owing to its biocompatibility and bioresorbable properties as well as high strength and toughness, silk fibers are used in a variety of clinical applications, such as braided suture threads for surgical procedures and scaffolds for cartilage and bone repair [13,14]. Aside from biomedical applications, silk from the cocoons of the domesticated mulberry silkworm, *Bombyx mori*, is of particular interest in textile industry due to its availability [9,14,15]. Silk cocoons are generally degummed, spun into rovings and yarns, then woven into textile fabrics [14,15]. These woven silk fabrics may be used as a woven reinforcement in composites for structural applications [14–16]. In addition, some researchers have explored using abundant silk waste from textile industry to reinforce polymer composites [17–19].

Despite these promising features, silk fibers have received only limited interest as a reinforcement for polymer composite products, and practically no commercial use exists beyond biomedical applications [4,9,11,13,15]. One plausible explanation for this limited use is the higher cost of silk compared to plant fibers in a very cost-competitive environment, especially for nonstructural composite parts. While silk might be more expensive than conventional reinforcements, waste silk fabric can be processed and utilized in composite laminates in a cost-effective manner [17–19]. Another possible limiting factor of silk fibers seems to be the incompatibility between the hydrophilic natural fibers and the hydrophobic polymer matrix that requires some form of surface treatment to improve the interfacial bonding [3,6]. In addition, silk is known to be prone to environmental factors, such as moisture and UV radiation, that significantly alter the mechanical performance of the fibers [20,21]. Therefore, silk fibers and fabrics might require special storage and transportation conditions for best performance. Nevertheless, the high specific properties of silk fibers make it a suitable replacement for glass fibers in composite applications where lightweight and energy-absorbance are important, such as automotive, aerospace, and wind turbine structures [15,16].

The limited available literature on silk-reinforced composites mainly investigated either discontinuous silk fiber reinforced thermoplastics, or continuous silk fiber reinforced thermosetting composites. Due to their recyclability, discontinuous natural fibers, also referred to as short fibers, were traditionally used to reinforce injection-molded thermoplastics, particularly polypropylene [22]. More recently, short fiber silk composites were used to reinforce biodegradable thermoplastics, such as polylactic acid (PLA) [22], poly vinyl alcohol (PVA) [23], and polybutylene succinate [24]. For instance, Ho et al. [22] manufactured PLA composite reinforced with 5 wt.% short silk fibers by injection molding, and reported a 27% and 2% improvement over PLA in tensile and flexural moduli, respectively. Considerably higher improvements were reported in several mechanical properties for silk reinforced gelatin composites over neat gelatin [25], including a 260% increase in tensile strength, a 4-fold rise in tensile modulus, a 320% improvement in bending strength, a 450% increase in bending modulus, and a 260% improvement in impact strength. Although these improvements achieved using silk fibers are significant for certain ecofriendly applications, the obtained mechanical performance remains inferior to glass reinforced composites.

On the other hand, structural composite laminates, intended for energy-absorbing structures, are often fabricated using woven textile fabrics and stiffer thermosetting polymers [3,8,9,15,26,27]. Epoxy resins are frequently used owing to their lower cost, higher processability, higher mechanical properties, good adhesive performance, and chemical resistance [11,15]. For instance, Oshkovr and coworkers attempted to use woven silk/epoxy composite square tubes as energy-absorbers and evaluated their crashworthiness [8,26]. However, catastrophic failures were reported under compression tests in both studies. Although impressive single fiber properties might be reported in the literature [3,8,21], the actual improvement over unreinforced epoxy may be limited by defects in the silk fabric, such as fiber misalignment and waviness inadvertently introduced during weaving. Furthermore, Yang et al. [15] investigated the tensile, flexural, interlaminar shear, impact, dynamic, and thermal properties of the silk/epoxy composites at 30%, 40%, 50%, 60%, and 70% fiber contents. A linear increase of most properties was observed with increasing fiber content between 30% and 70%. Optimal tensile properties were observed at 70% fiber content, with 145%, 130%, and 70% improvement over neat epoxy in tensile stiffness, ultimate stress, and ultimate strain, respectively. In addition, impact strength was observed to increase significantly only for fiber contents above 60%. The same research group studied silk/epoxy laminates for two natural silk varieties: *Bombyx mori* and *Antheraea pernyi* silk [27]. The authors reported that at 60% fiber content, both silk types showed a 2-fold increase in both specific tensile modulus and strength compared to the unreinforced epoxy resin. For the 60% *Antheraea pernyi* silk/epoxy laminates, the breaking energy was found to be 11.7 MJ/m3, an order of magnitude higher than the 1.1 MJ/m3 measured for neat epoxy. Moreover, a 3-fold increase in specific flexural strength was also reported, reaching 316 MPa/g·cm<sup>−</sup>3.

More recently, Shah et al. [3,7,10] attempted to make a case for silk as a reinforcing agent in composite laminates by comparing their mechanical performance to flax- and glass-reinforced composites. The authors fabricated silk/epoxy laminates with nonwoven silk preform at 36% fiber content and woven silk fabric at 45% fiber content. The authors reported tensile and flexural specific strengths of ~90 MPa/g·cm−<sup>3</sup> and ~170 MPa/g·cm<sup>−</sup>3, respectively [3]. These values were comparable, although not necessarily superior, to those of glass/epoxy laminates. Other researchers incorporated silk into glass reinforced composites in the pursuit of hybrid composites with improved impact properties [16,17,28–30]. For example, Zhao et al. [16] investigated silk fabric/glass mat/polyester hybrid laminates at 14.5% and 2.4% fiber content of glass and silk, respectively. However, the authors reported practically no effect of the limited silk fabric presence on impact and flexural properties.

Surprisingly, two important aspects were not addressed in the available literature on silk reinforced composites. First, silk fabric is mostly used as received and surface treatment is seldom attempted to improve the silk/epoxy interface [31–33]. Generally, fiber sizing can be used to tune the bulk properties of composite laminates [34,35]. Surface treatment of natural fibers has been shown to significantly improve the properties of composite laminates [36–39]. Second, no attempt was made to investigate the effect of manufacturing processes and relevant process parameters on the produced silk composites. In fact, most of the reported investigations employed a rather simple, hand lay-up method to manufacture silk/epoxy laminates [16,17,30,40]. While simple fabrication methods such as hand lay-up can be attractive for their relative ease and low cost, they are operator-dependent, prone to process-induced defects, and often result in low-quality composite parts with higher void occurrence [40]. Presence of these defects, in turn, is known to significantly degrade the mechanical performance of composites [41]. A few other studies [9,15,27] used hand lay-up followed by hot pressing in order to increase the fiber content of the laminates, and thus improve the composite performance.

As described in the previous paragraph, remarkable improvements over neat epoxy were only achieved for silk/epoxy composites with fiber contents of 60% and higher [15,27]. Studies conducted at low or moderate fiber contents did not yield considerable improvement in mechanical performances. Consequently, investigating more appropriate manufacturing processes for silk/epoxy composite applications, such as variants of liquid composite molding (LCM), might be of interest. Only a couple of articles used vacuum-assisted resin transfer molding (VARTM) to manufacture silk/epoxy laminates [3,40]. In fact, Shah et al. [3] were able to achieve comparable mechanical performance to glass/epoxy laminates at a fiber content of only 45%. A lower occurrence of process-induced

defects within the silk composites is believed to play a significant role in reaching this performance. More recently, our research group investigated fabrication challenges for silk/epoxy laminates [40], which showed that compared to hand lay-up, VARTM was more appropriate for silk/epoxy laminate fabrication as it allows uniform impregnation of the silk preform by the liquid resin, yielding higher part quality and reduced void formation.

In order to investigate the suitability of silk as an alternative reinforcement to glass fibers in polymer composites, the processability of silk reinforced composites was verified by fabricating silk/epoxy laminates using VARTM. In addition, the effects of manufacturing process and microstructural parameters such as post-fill external pressure and silk fabric anisotropy on the process-induced microstructure of silk epoxy laminates were studied. The mechanical performance of the fabricated laminates was also compared with those of neat epoxy and glass/epoxy laminates. Finally, the effect of storage conditions of silk fibers and moisture absorbed by silk on the manufacturing and performance of silk/epoxy composites was investigated.

#### **2. Materials and Methods**

#### *2.1. Materials*

INF 114 epoxy (PRO-SET) was used as the resin and polyamine INF 211 (PRO-SET) was chosen as the hardener. Before laminate fabrication, the resin and curing agent were mixed for 5 min at 350 rpm at a ratio of 100:27.4 by weight and degassed for 10 min under vacuum.

A woven silk fabric (Satin Ahimsa, Aurora Silk, Inc., Portland, OR, USA) was used in this study. The silk was produced from degummed cultivated *Bombyx mori* mulberry silk and had an areal density of 81.4 g/m2. For each laminate, twelve layers of 152 mm-wide × 203 mm-long (6" × 8") silk fabric were prepared, stacked, and placed on the mold before infusion. Preparation of silk layers involved cutting the fabric to the desired size, ironing to remove wrinkles, and then drying in a vacuum oven at 50 ◦C. Since silk fabric exhibited an unbalanced weave pattern, laminates were fabricated with layers cut along both planar directions to investigate the effect of fabric anisotropy on the fill time and mechanical performance. Hence, two separate sets of laminates were investigated for each case: one set with fabric layers cut such that its length is parallel to the roll direction (longitudinal), and another set cut such that its length is perpendicular to the roll direction (transverse).

#### *2.2. Manufacturing Procedure*

An improved variant of vacuum-assisted resin transfer molding (VARTM) was used to fabricate silk/epoxy laminates. Figure 1 illustrates the experimental molding setup which can facilitate external air pressure on a typical VARTM mold to increase the limited compaction pressure in conventional VARTM (i.e., higher than 1 atm) [42]. Depending on the applied pressure, the fiber volume fraction in fabricated laminates can be significantly increased, which yields high-quality laminates with improved mechanical properties.

As seen in Figure 1, 12 layers of woven silk fabric (i.e., preform) were sealed with a vacuum bag and the epoxy/hardener mixture was infused into the mold from the inlet resin reservoir towards the vacuum source (i.e., exit). In order to reduce the effect of ambient temperature fluctuations, the mold temperature was kept constant at 30 ◦C. At this temperature, the viscosity of the resin was in the range of 180 to 200 mPa s. After the preform was completely wetted, infusion was continued for an additional 5 min (i.e., resin flushing) to mobilize and remove the process-induced voids with resin outflow from the exit gate [42]. Once the resin flushing was completed, the inlet port was closed to remove the excess resin from the exit of the mold (i.e., resin bleeding). In certain fabrication scenarios an external chamber pressure of 300 kPa (~44 psi) was applied during the post-filling stage to further compact the preform and improve the mechanical properties. All fabricated laminates were cured at 60◦C for 8 hours after resin gelation occurred in 5 h at 30 ◦C.

**Figure 1.** Experimental vacuum-assisted resin transfer molding (VARTM) setup with external pressure chamber to fabricate woven silk/epoxy composite laminates.

Table 1 presents the various fabrication scenarios used in this study and lists the laminate designations, reinforcement types, and fabric/lay-up details as well as the thicknesses of the fabricated laminates. For comparison purposes, neat epoxy samples (E) were manufactured by gravity casting and cured following the same cure schedule. In addition, glass/epoxy laminates (G), fabricated using the same resin in a recent study by our research group [43], were considered. Five different fabrication scenarios for silk composites (S) were performed. These scenarios were designed to assess the effects of fabric anisotropy, external pressure, and fabric moisture on the properties of the fabricated laminates. Furthermore, fabric anisotropy effects on wetting characteristics such as fill time, critical in defining the manufacturing cycle, were also investigated.


**Table 1.** Laminate designations, reinforcement types, and fabric/lay-up details. The external pressure is given in gauge pressure.

Figure 2a shows a representative image of the fabric and the disposition of longitudinal (*y*) and transverse (*x*) directions with respect to the fabric roll. Additionally, Figure 2b shows that the silk fabric was tightly woven with low porosity between the fibers with several silk threads in orthogonal directions. Abbreviations "L" and "T" were used to indicate whether the infusion was performed along the longitudinal or transverse directions of the fabric roll, respectively. In contrast, symbols *x* and *y*, depicted in Figure 2, were exclusively used in the designation to indicate testing directions of the composite samples. In addition, "P" indicates that external pressure was applied during the post-filling stage. "M" designates that the silk fabric was exposed to moisture prior to molding. For each fabrication scenario, two identical, 152 mm × 203 mm laminates were fabricated to ensure the repeatability of fabrication procedure.

**Figure 2.** Representative images of the fabric, showing (**a**) longitudinal (abbreviated L for filling and *y* for testing) and transverse (abbreviated T for filling and *x* for testing) directions with respect to fabric roll and (**b**) a macroscopic image of the weave pattern.

#### *2.3. Sample Preparation*

Each molded laminate was sectioned using a diamond saw into several rectangular specimens. According to ASTM standards (D792, E1131, D790, D7028, and D2344), five samples for density measurement, five for thermogravimetric analysis, twelve for flexural testing (six samples along the flow direction (*y*), and six along (*x*) perpendicular to the flow), ten for SEM imaging (five along and five perpendicular to the flow direction) were cut in particular dimensions. When the sample thickness allowed, ten rectangular samples were cut for short beam tests (five along and five perpendicular to the flow direction).

#### *2.4. Density Measurement and Volume Fraction Determinations*

The density of five samples from each laminate was measured according to ASTM D792. Similarly, the density of the neat epoxy (i.e., the matrix) was measured as *<sup>ρ</sup>Epoxy* = 1.140 ± 0.001 g/cm3. The density of silk fibers, on the other hand, was measured using a gas pycnometer (AccuPyc II 1340) as *<sup>ρ</sup>Silk* = 1.361 ± 0.002 g/cm3. Using both densities of silk and epoxy, as well as the measured density of each fabricated composite laminate, *ρLaminate*, both fiber volume fraction, *Vf*, and resin volume fraction, *Vr* can be calculated as

$$V\_f = \frac{\rho\_{Laminate} \,\,\mathcal{M}\_{Silk}}{\rho\_{Silk} \,\,\mathcal{M}\_{Laminate}}\tag{1}$$

$$V\_r = \frac{\rho\_{Laminate}}{\rho\_{Epoxy}} \times \frac{M\_{Laminate} - M\_{Silk}}{M\_{Laminate}},\tag{2}$$

where *MLaminate* is the measured mass of the laminate and *MSilk* is the measured mass of the twelve silk fabric layers. Using both fiber and resin volume fractions, void volume fraction, *Vν*, can be calculated for each laminate as

$$V\_{\upsilon} = 1 - (V\_f + V\_r) \tag{3}$$

#### *2.5. Thermogravimetric Analysis*

Thermogravimetric analysis (TGA) was used to verify the thermal stability and identify the maximum temperature at which the silk/epoxy composite laminates can be used. TGA thermograms were obtained by using a Thermogravimetry-Differential Scanning Calorimetry (TG-DSC) instrument (TA Instruments Q50, New Castle, DE, USA) at 10 ◦C/min heating rate in a nitrogen atmosphere.

#### *2.6. Mechanical Testing*

Flexural tests were performed according to the ASTM D790 standard to measure the flexural properties of each laminate. As mentioned earlier, specimens from each laminate were used to characterize the flexural properties along the longitudinal (*y*) and transverse (*x*) directions. Short beam tests were also executed on rectangular samples along the *y*- and *x*-directions cut from each silk/epoxy laminates. Interlaminar shear strength (ILSS) values were obtained in accordance with ASTM D2344. The mechanical testing was carried out at a rate of 2 mm/min.

#### *2.7. Dynamic Mechanical Analysis*

A dynamic mechanical analyzer (DMA) (TA Instruments DMA-Q800, New Castle, DE, USA) was used to measure the glass transition temperature, *Tg*, of selected configurations of the composites, namely neat epoxy (E), glass/epoxy (G), silk/epoxy impregnated along the transverse direction (S/T), and moist silk/epoxy impregnated along the transverse direction (S/T/M). For these particular measurements, 51 mm × 12.7 mm (2" × 0.5") specimens were prepared. The storage modulus, loss modulus, tanδ, and glass transition temperatures were determined for each sample.

#### *2.8. Scanning Electron Microscopy (SEM) Imaging*

SEM imaging was performed for the analysis of the microstructure of composite laminates. Specimen cut from the laminates were mounted in an acrylic resin to expose the through-the-thickness cross-section. Once polished, the specimens were sputter coated with 5 nm of gold/palladium to avoid charge build-up during SEM imaging. SEM images at different magnifications were obtained using a Zeiss Neon 40 EsB microscope (Carl Zeiss AG, Oberkochen, Germany). Additionally, fracture surfaces of the flexural test samples, as well as the silk preforms, were examined by SEM.

#### **3. Results and Discussion**

#### *3.1. Morphology and Microstructure of Silk Fabric*

Specialty material suppliers for composite reinforcement usually provide fabrics with balanced weave patterns, thus practically ensuring that the longitudinal and transverse properties would be similar. Having a fabric with a balanced planar weave fabric also ensures similar impregnation dynamics along both principal fabric directions. On the other hand, commercial fabrics for textile applications generally exhibit unbalanced weave patterns. For instance, the SEM micrograph of the silk fabric used by Yang et al. [15] showed a clearly unbalanced weave. Therefore, the morphology and microstructure of the silk fabrics that are often used for textile applications need to be investigated in detail to reveal possible anisotropy in their weave patterns.

SEM images presented in Figure 3 depict the microstructure of the silk fabric used in this study. Figure 3a shows the disposition of silk yarns along the longitudinal (*y*) and transverse (*x*) directions with respect to the fabric roll. The weave pattern was observed to be anisotropic, as clearly shown in Figure 3a,b. In fact, yarns along the transverse (*x*) direction have an average width of ~290 μm, which is approximately 60% higher than its counterpart along the longitudinal (*y*) direction (~180 μm). This unbalance in the weave pattern will likely induce disparate filling patterns and anisotropy in mechanical performance along these orthogonal directions.

**Figure 3.** Sample SEM images of the microstructure of silk fabric, showing (**a**) an SEM image of multiple yarns (50×) and (**b**) higher magnification SEM image of two orthogonal yarns (200×).

#### *3.2. Morphology and Microstructure of Silk/Epoxy Composite Laminates*

Figure 4 depicts representative SEM images of the through-the-thickness microstructure of the fabricated silk/epoxy laminates. Figure 4a is a representative image along the longitudinal direction (*y*), obtained at 30×. Figure 4b, on the other hand, shows a representative image along the transverse direction (*x*) obtained at the same magnification. On these micrographs, fiber tows can be seen in both parallel and perpendicular directions to the cross-section. While a good wetting of the silk fabric was observed for all considered cases, voids are occasionally observed within the resin. Void occurrence was observed to be lower for laminates fabricated with external pressure. Interestingly, tows along the *x* and *y* directions showed contrasting undulation through-the-thickness of the composite. Figure 4a shows a pronounced sinusoidal waviness of silk tows continuously along the longitudinal direction, while tows along the transverse direction were less wavy (Figure 4b). Fiber waviness is known to have a substantial influence on the mechanical performance of the composites [41], thus mechanical properties were expected to be significantly lower along the longitudinal direction compared to the transverse direction.

**Figure 4.** Representative SEM images of the through-the-thickness microstructure of fabricated silk/epoxy composite laminates: (**a**) along the longitudinal (*y*) direction and (**b**) along the transverse (*x*) direction. Both images are at 30×.

#### *3.3. Thermal Stability of Silk/Epoxy Composite Laminates*

Figure 5 shows TGA thermograms of neat epoxy, silk and glass fibers, in addition to the different composite laminates. The weight of neat epoxy was practically constant below 350 ◦C. Thermal decomposition of epoxy occurred mostly between 350 ◦C and 500 ◦C, after which no significant change in weight was observed. For silk fibers, no discernable change was observed at the processing temperature of 30 ◦C, indicating that the properties of silk fibers would not be altered during manufacturing. Furthermore, an initial weight loss of ~5%–10% was observed below 100 ◦C, which is believed to correspond to desorption of moisture absorbed by the silk fabric from the environment. Thermal decomposition of the silk started at ~300 ◦C and continued at a decreasing rate until ~800 ◦C. In contrast, glass fibers showed a minor thermal decomposition between ~350 and ~450 ◦C, after which glass fiber weight did not change up to ~800 ◦C. This slight weight loss is possibly due to the removal of the organic sizing on the glass fibers. The divergence in thermal degradation behaviors of the three composite constituents would originate from the dissimilarities in their chemical compositions as well as their surface treatments.

Figure 5 also presents TGA spectra of both glass/epoxy and silk/epoxy laminates. For both composite types, the thermal degradation pattern showed three main stages. The first stage took place before thermal degradation occurred, where the weight was fairly stable. The second stage started with the decomposition of organic constituents of the composite. For G laminates, this stage started at ~350 ◦C, initiated by the degradation of the neat epoxy. Similarly, S laminates decomposition started at ~300 ◦C concurrently with the degradation of silk fibers. For both G and S composites, the thermal decomposition continued until ~450 to 500 ◦C due to the combined decomposition of the epoxy matrix and either the silk fibers or the sizing of glass fibers. In the final stage up to ~800 ◦C, the weight loss was observed to be minimal. These results showed that no thermal degradation was observed for silk/epoxy laminates up to ~300 ◦C, which was almost comparable to that of glass/epoxy laminates.

**Figure 5.** TGA thermographs of neat epoxy, glass mats, silk fabric, as well as glass/epoxy and silk/epoxy laminates, under a nitrogen atmosphere at a heating rate of 10 ◦C/min.

#### *3.4. Fabric Anisotropy Effects on Fiber Wetting*

The anisotropy of the silk fabric significantly influenced the impregnation characteristics during fabrication by VARTM. As presented in Table 2, impregnation along the transverse (*x*) direction was found to be much faster with an average filling time of 20 min. In contrast, when the impregnation was along the longitudinal (*y*) direction of the fabric roll, an average fill time of 68 min was observed. This ~140% increase in fill time was attributed to the anisotropic permeability of the silk fabric. As shown in Figure 3, fiber tows were ~60% thicker along the transverse direction than the longitudinal direction. This difference in yarn distribution would induce contrasting preform fabric permeabilities along the transverse and longitudinal directions, yielding this substantial increase in fill time.

The fabric anisotropy not only affected the mold filling time but also the final void content in the fabricated laminates as the impregnation velocity significantly affect the void formation [44]. As Table 2 documents, slow impregnation while fabricating the S/L and S/L/P laminates yielded lower void contents than those impregnated more rapidly (i.e., S/T and S/T/P, respectively). For instance, silk/epoxy laminates impregnated along the longitudinal direction (S/L) filled in 68 min and yielded a void content of 0.7%. In contrast, the laminates impregnated under identical conditions along the

transverse direction (S/T) filled in 20 min, with a void content of 1.1%. A similar trend was observed for laminates manufactured with external pressure, as void contents of 0.5% and 1.2% observed for S/L/P and S/T/P, respectively. In LCM processes, voids are known to form mainly when air is trapped due to the unbalance between the velocities of the viscous macroflow occurring between fiber tows and the capillary flow inside fiber tows [44]. According to the modified capillary number analysis, any change in the equilibrium between these competing flows would affect the air entrapment void formation mechanism, thus affecting void presence in the final composite part [1]. The highest void content was observed for the fastest filling of 3 min corresponding to the glass/epoxy laminate case. Nonetheless, the comparison does not hold as the sized glass fibers possess an entirely different epoxy affinity and the glass fabric is in the form of a random mat.

**Table 2.** Density, fiber content, void content, and fill time of the manufactured composite laminates (n = 10, 95% confidence interval).


Furthermore, slower filling slightly increased the amount of resin intake during mold filling, resulting in a slight drop in fiber content (from 44% to 43% for S/T and S/L, respectively). Applying a post fill external pressure helped improve the fiber content in silk laminates from ~43% to ~47%. It is worth noting that the increase in fiber volume fraction induced a slight increase in the density of the composite laminate. Applying external pressure after the impregnation is completed, i.e., after formation of voids, can have opposing effect on the final void content of the part. On one hand, it helps in suppressing voids due to increased pressure and, on the other hand, it may cause void entrapment and prevent removal of mobile voids during flushing or bleeding of the resin. As a result, when impregnation was performed along the longitudinal direction, applying 300 kPa pressure reduced void content from 0.66% to 0.53%. However, in the case that impregnation was along the transverse direction, void content increased from 1.12% to 1.24%.

#### *3.5. Fabric Anisotropy Effects on Mechanical Properties of Silk/Epoxy Laminates*

Figure 6a shows both flexural strength and modulus of neat epoxy, random mat glass/epoxy laminates, and silk/epoxy laminates infused along both the longitudinal and transverse directions, each tested along orthogonal directions *x* and *y*. Moreover, Figure 6b depicts strain to failure and the breaking energy calculated as the area below flexural stress-strain curves of the tested specimen.

A strong anisotropy was observed in the flexural performance of silk/epoxy laminates. In fact, flexural strength, modulus, and breaking energy were observed to show disparate properties when tested along the longitudinal and transverse directions. As depicted in Figure 6a, flexural strength dropped by 46% from 229 MPa along the *x* direction to 123 MPa along the *y* direction for the silk/epoxy laminate infused along the longitudinal direction. A similar drop of 46% from 222 to 121 MPa was observed when infusing along the transverse direction. Flexural modulus showed an analogous tendency with 31 and 30% reductions between the *x* and *y* directions when infused along the longitudinal and transverse directions, respectively. Furthermore, Figure 6b depicts a similar trend for the breaking energy. For the silk epoxy laminate infused along the transverse direction (S/T), breaking energies of 13.8 and 3.6 MJ/m<sup>3</sup> were calculated respectively along the *x* and *y* directions, representing an almost 74% difference. Similarly, a 70% difference (11.8 to 3.6 MJ/m3) was observed in the breaking energy for S/L along the longitudinal direction. Strain to failure is the flexural property least affected by the fabric microstructure with only 14% difference along the *x* and *y* directions in both S/T and S/L.

**Figure 6.** Flexural properties of silk/epoxy composite laminates in comparison with neat epoxy and glass/epoxy laminates [43]: (**a**) Flexural strength and modulus and (**b**) strain to failure and breaking energy.

As shown in Figure 3, yarns along the transverse (*x*) direction are ~60% thicker than yarns along the longitudinal (*y*) direction, which implies a larger number of silk fibers would be under loading along the *x* direction compared to those along the *y* direction. Furthermore and as shown in Figure 4a, higher waviness of the silk tows throughout the laminate was observed in the longitudinal (*y*) direction. Localized wrinkles are known to dramatically reduce the composite mechanical properties depending on the wrinkle severity, defined as the ratio of the amplitude to the wavelength of the undulation [41]. The wrinkles of the silk fabric along the *y* direction shown in Figure 4a exhibited a wrinkle severity in the range of 0.25 to 0.30. Single wrinkles with a severity in that range are reported to induce as much as 80% reduction in mechanical properties [41]. Continuous undulations are known to cause even further deterioration of composite performance [41]. In a sense, the undulated silk fabric along the longitudinal direction may be acting more as a defect rather than a reinforcement.

The results given in Figure 6 indicate that the mechanical performance of silk/epoxy laminates did not seem to depend on the infusion direction. In fact, regardless of the infusion direction, the laminates tend to exhibit statistically similar mechanical properties. The slight differences in void and fiber contents did not seem to affect the resulting flexural and breaking energy performance. For instance, the S/T laminate exhibited a ~44% fiber content, similar to the ~43% fiber content of S/L. A small difference in the void contents was observed in these laminates, with 1.1 and 0.7% void contents for S/T and S/L, respectively. Hence, the efficiency of manufacturing silk composites can be eventually improved in an industrial setting by an appropriate selection of infusion direction that reduces filling times and manufacturing cycles.

#### *3.6. Silk/Epoxy Laminate Performance Compared to Neat Epoxy and Glass/Epoxy Laminates*

In addition to silk/epoxy laminates, Figure 6 depicts the flexural performance of glass/epoxy laminates from a past paper [43] and neat epoxy. Silk was found to improve the flexural strength and modulus, as well as the breaking energy of epoxy along *x* direction. For instance, more than 78% and 121% improvements were obtained in flexural strength and modulus, respectively, compared to pure epoxy along *x* direction. In contrast, change in flexural strength was negligible along the *y* direction. Conversely, flexural modulus showed more than 53% increase over the neat epoxy along the *y* direction.

An expected drop in strain to failure was observed for silk/epoxy laminates compared to neat epoxy, as the addition of fibers limits the ability of the epoxy resin to elongate. However, the measured values of 0.041 to 0.049 were definitely higher than the strain to failure of 0.036 exhibited by glass/epoxy laminates. This result was also predictable as silk fibers enjoy a remarkably high failure strain of ~20% compared to the ~2.5% of glass fibers [3,8,9]. Lai and Goh reported an even higher strain to failure of ~34% [21]. These large failure strains would allow the silk reinforced laminates to experience higher failure strains compared to glass/epoxy composites, yielding improved breaking energy.

Aside from strain to failure, the glass/epoxy laminates performed slightly better than silk/epoxy at comparable fiber contents (~45%) in terms of flexural properties. Along the *x* direction, silk composites enjoyed flexural strengths merely 12 to 15% lower than glass laminates, as shown in Figure 6a. Similarly, silk flexural moduli were ~36% lower than glass/epoxy laminates. In contrast, and owing to the superior elongation of silk, the breaking energy of silk/epoxy were 35% higher than that of glass/epoxy laminates.

In high-end applications where both lightweight and high performance are pursued, specific properties are often used to assess the composite parts [3,15]. Figure 7 illustrates the specific flexural strength vs. specific flexural modulus for the silk/epoxy and glass/epoxy composites investigated in this study. For comparison purposes, results reported in the literature for silk/epoxy laminates [3,15] and flax/epoxy laminates [3] with comparable fiber contents are also included.

**Figure 7.** Specific flexural properties of silk/epoxy laminates compared to glass/epoxy laminates and neat epoxy samples, as well as reported properties for silk/epoxy and flax/epoxy from the literature.

First, as shown in Figure 7, the measured specific flexural strength and modulus compared well with the values reported in the literature for silk/epoxy laminates [3,15], and performed better than flax/epoxy laminates [3]. It is worth noting that both references reported only the mechanical properties of silk/epoxy laminates along strongest direction, although the unbalanced weave patterns were observed in the silk fabric used in this study.

The lowest value of specific flexural strength of silk/epoxy in this study was measured at ~100 MPa/g·cm−<sup>3</sup> along the *<sup>y</sup>* direction, which is slightly lower than unreinforced epoxy. In contrast, the specific flexural strength along the *x* direction exhibited more than 66% improvement over epoxy. Moreover, silk reinforcement induced ~41 and ~104% increases in specific flexural modulus along the *x* and *y* directions, respectively.

Compared to glass/epoxy, silk/epoxy laminates showed a 19 to 23% higher specific flexural strength along the *x* direction, and a concurrent ~10% lower specific modulus. This improvement in specific properties is significant, given the large difference between the properties of individual silk and glass fibers [4,8,9,15,16,21]. Along the *y* direction, the specific flexural strength and modulus were ~35 to 37% lower than glass/epoxy laminates. This was expected as the silk was not observed to effectively reinforce the epoxy along the *y* direction. Applying a post-fill external pressure did not seem to affect the specific flexural properties of the silk/epoxy laminates. The slight improvement in absolute flexural strength and modulus was offset by the concurrent increase in laminate density. These results showed that silk/epoxy may provide comparable, if not better, specific properties to glass/epoxy at least along the transverse direction. Once balanced weave patterns are produced without yarn undulations, silk fabrics can deliver the same reinforcement along both principal directions.

#### *3.7. Silk/Epoxy Interface*

A possible explanation of the lower absolute flexural properties of silk/epoxy laminates compared to glass/epoxy laminates may be an inferior bonding between silk fibers and the epoxy matrix. In fact, unlike glass fibers that have a commercial sizing suitable for epoxy matrix bonding, the silk fabric was used as received and did not undergo any surface treatment. Thus, a weak fiber/matrix adhesion is expected due to the incompatibility between the hydrophilicity of untreated silk fibers and the hydrophobicity of the epoxy [3,6]. The silk/epoxy interface was investigated by the careful review of the SEM images of silk/epoxy laminate cross-sections, as depicted in Figure 8.

**Figure 8.** Sample SEM images at 200× of the microstructure of silk/epoxy laminate cross-sections (**a**) along the *y* direction and (**b**) along the *x* direction.

Inspection of the silk/epoxy interface under SEM showed extensive fiber/matrix debonding in all fabricated laminates, indicating an overall weak fiber/matrix adhesion. In addition, fiber/matrix debonding was observed to have a higher occurrence along the *y* direction, as depicted in Figure 8a,b. A weak fiber/matrix adhesion is expected due to the incompatibility between the hydrophilicity of untreated silk fibers and the hydrophobicity of the epoxy [3,6]. In addition, the pronounced undulations of silk yarns along the longitudinal (*y*) direction might increase the fiber/matrix debonding as the curvatures create a more tortuous path for the impregnating epoxy resin. Furthermore, fiber/matrix debonding was visually observed to be much less frequent in laminates manufactured with post-fill external pressure, as the application of external pressure might have increased the resin pressure, thus causing a reduction on the porosity as well as slightly improving the fiber/matrix interface [42,45].

Another method to investigate the fiber/matrix adhesion is to analyze fracture surfaces of the silk/epoxy laminates. As illustrated in Figure 9a,b, fiber pullouts were observed in SEM images of fracture surfaces of tested silk/epoxy specimens, even in the laminates fabricated with external pressure. These findings corroborate the weak fiber/matrix adhesion and highlight the potential benefit of an appropriate surface treatment for silk fibers.

**Figure 9.** Sample SEM images at 400× of the fractured surfaces of silk/epoxy laminates fabricated (**a**) without external pressure and (**b**) with external pressure.

#### *3.8. Effect of Post-Fill External Pressure on Silk/Epoxy Performance*

The results presented earlier indicate that the external pressure did not affect the flexural properties of silk/epoxy laminates. Statistically indistinguishable values of strength, modulus, and strain to failure were measured with and without applying pressure for all considered cases. Specific flexural strength and modulus also showed no sensitivity to external pressure as the data points are observed to overlap in Figure 7. This insensitivity could be due to minor increases in fiber volume fraction at the external pressure level applied in this study, which could only yield a modest increase of ~4 to 5% in fiber content.

Breaking energy and interlaminar shear strength (ILSS), on the other hand, showed discernible improvement with the application of post-fill external pressure. Figure 10 presents the percent property improvement of both the breaking energy and ILSS due to the application of external pressure. For example, the energy required to break silk/epoxy laminates along the *x* direction increased by ~17% from ~12 MJ/m<sup>3</sup> to ~14 MJ/m<sup>3</sup> after applying the external pressure for the slow-filled silk/epoxy laminates infused along the longitudinal direction. Lower improvements (3%–8%) in breaking energy were observed for the remaining cases. In addition, Figure 10 shows a consistent improvement in ILSS (3%–9%) after the application of external pressure. Again, the highest improvement in ILSS (i.e., 9% to 44 MPa) was observed in the slow-filled silk/epoxy laminates along the *x* direction. These improvements in breaking energy and ILSS can be attributed to a lower occurrence of silk/epoxy debonding at higher pressures observed during SEM analysis.

**Figure 10.** Effect of applying a 300 kPa post-fill external pressure to silk/epoxy laminates on the breaking energy and interlaminar shear strength (ILSS).

#### *3.9. Dynamic Mechanical Analysis of Silk/Epoxy*

Dynamic mechanical analysis (DMA) is usually used to investigate the mechanical properties and viscoelastic behavior of polymer-based materials as a function of temperature, frequency, and time [15]. In this study, DMA experiments were performed for two purposes: (a) to characterize the thermomechanical properties of the silk/epoxy composite laminates and (b) to compare glass transition temperature of silk/epoxy and glass/epoxy composites.

Figure 11 shows representative changes of the storage modulus E , loss modulus E", and tanδ (the ratio of loss modulus E" to storage modulus E ) over a temperature range of 30 to 150 ◦C for the epoxy, glass/epoxy, and silk/epoxy laminates. Glass/epoxy showed a higher storage modulus compared to silk/epoxy and neat epoxy for all considered temperatures, which is expected since glass fibers are much stiffer than silk. Glass transition temperature was calculated using the storage modulus, loss modulus, and tanδ for all tested samples, and the obtained average values are presented in Table 3.

**Figure 11.** Representative changes of the (**a**) storage modulus E , (**b**) loss modulus E", and (**c**) tanδ for epoxy, glass/epoxy, and silk/epoxy laminates over a temperature range of 30 to 150 ◦C.


**Table 3.** Glass transition temperature, Tg, of silk/epoxy compared to glass/epoxy and neat epoxy.

Silk/epoxy laminates were found to exhibit a glass transition temperature comparable, if not higher, than glass/epoxy. When measured using tanδ for instance, silk/epoxy exhibited a Tg of 79.5 ◦C compared to 78.2 ◦C for glass/epoxy. Comparable Tg values are also obtained when using both the storage and loss moduli. In addition, using silk as reinforcement was observed to increase the glass transition temperature of the epoxy resin. These findings showed that silk/epoxy laminates offer comparable glass transition temperatures to glass/epoxy, which could make silk a useful alternative to glass fibers in Tg sensitive applications.

#### *3.10. Silk Moisture Effects on Silk/Epoxy Laminate Performance*

Unlike glass and other inorganic fibers that do not absorb moisture [46], organic fibers readily absorb ambient moisture, which would alter the mechanical performance of the produced composites. In order to investigate the effect of storage conditions of the silk fabrics on the mechanical performance, silk/epoxy laminates were manufactured with silk fabric containing ~10% moisture by weight. As revealed in Figure 5, this moisture content approximately corresponds to the initial weight drop observed in silk fabrics during TGA tests. Therefore, after the usual drying cycle in a vacuum oven at 50 ◦C, the silk fabric layers were exposed to a humid environment at 35 ◦C, and their weight gains were monitored. Figure 12 presents a representative moisture absorption curve of silk fabric. A moisture content of about 10% is usually reached within 48 h.

**Figure 12.** Moisture absorption curve of silk fabric exposed to a humid environment at 35 ◦C.

Immediately after the moisture content reached 10%, a vacuum bag lay-up was prepared and the moist fabric was infused following the same VARTM procedure used in this study. Since the fabric is exposed to vacuum within the mold for about 5 min prior to impregnation, a mock molding was performed. During this mock molding, a similar lay-up was prepared, thus exposing the moist silk fabrics to vacuum for 5 min. The fabrics were taken out of the lay-up and weighed after the 5 min vacuum period. The difference in the fabric weights was negligible, thus indicating no appreciable moisture loss during this period. The faster infusion case (S/T) was chosen as a baseline for investigating the silk moisture effects. Hence, two laminates were fabricated by infusing resin along the transverse (*x*) direction of the moist silk fabric.

Interestingly, presence of moisture in the silk fabric was observed to affect the impregnation dynamics. As presented in Table 2, the average fill time increased from 20 to 32 min due to the presence of 10% moisture in the silk fibers. Conceivable causes of this ~60% increase in fill time include accelerated cross-linking and viscosity change of the epoxy resin due to moisture. Decreased preform permeability due to slight swelling of the fabric can also slow the impregnation. Moisture-induced preform swelling combined with a slower filling also resulted in a slight increase in part thickness from 2.43 to 2.51 mm, as shown in Table 1. Moisture contact with the advancing epoxy front during impregnation and evaporation of the water during curing might also have caused the slight increase in void content from 1.1% to 1.3% (Table 2).

As presented earlier in Figure 5, the TGA behavior of laminates fabricated with dry and moist silk fabric overlap, indicating a similar thermal degradation behavior. Furthermore, dynamic mechanical analysis was performed on dry and moist silk reinforced composites. As presented in Figure 11, moisture presence in silk fabric is found to decrease the thermomechanical properties of the silk/epoxy, including storage modulus, loss modulus, and glass transition temperature. For instance, the peak loss modulus decreased from ~561 MPa for dry silk/epoxy to ~485 MPa for moist silk/epoxy. A concurrent drop from ~6500 MPa to ~5500 MPa was observed in storage modulus at 30 ◦C. Glass transition temperature was also lower for moist silk/epoxy regardless of the calculation method as shown in Table 3. For instance, when calculated using the loss modulus, moisture presence in the silk fabric caused the glass transition to drop from ~74 to ~72 ◦C. A similar drop from ~61 to ~57 ◦C was observed using the storage modulus.

Additionally, silk fabric moisture was found to detrimentally affect the mechanical performance of silk/epoxy laminates, as depicted in Figure 13. The presence of 10% moisture in the silk fabric prior to fabrication was found to induce 23 and 20% reductions in specific flexural strength and modulus of the laminates along the transverse (*x*) direction, respectively. Similarly, in absolute values, moisture presence caused the flexural strength and modulus to drop respectively by 23 and 20% along the *x* direction, as depicted in Figure 13a. As depicted in Figure 13b, silk moisture also caused approximately 29 and 33% reductions in the breaking energy along both *x* and *y* directions, while the strain to failure dropped by 2 to 8%. Silk moisture also critically affected the interlaminar shear strength as shown in Figure 13c. A 20% reduction in ILSS was registered between dry and moist silk/epoxy laminates along the *x* direction. Hence, the storage conditions of the silk fabrics that are to be used in composite laminates should be carefully monitored. Drying silk fabrics to remove the absorbed moisture can significantly alleviate these adverse effects on the composite performance.

**Figure 13.** *Cont*.

**Figure 13.** Effect of the presence of 10% moisture in the silk fabric on the mechanical performance of silk/epoxy laminates: (**a**) Flexural strength and modulus; (**b**) strain to failure and breaking energy; and (**c**) ILSS.

#### **4. Conclusions**

The processing and properties of silk/epoxy composite laminates were investigated to assess the viability of silk as a natural alternative to glass as a reinforcement in polymer composites. Vacuum-assisted resin transfer molding (VARTM) was used to manufacture composite laminates reinforced with plain weave silk.

Silk/epoxy laminates exhibited similar thermal stability, glass transition temperature, and thermomechanical properties to glass/epoxy composites. In addition, specific mechanical properties of silk/epoxy laminates were comparable to those of glass/epoxy. Silk composites even exhibited a 23% improvement over glass in specific flexural strength. In addition, applying a 300 kPa post-fill external pressure did not show a considerable effect on mechanical properties, except the breaking energy and interlaminar shear strength (ILSS). However, silk/epoxy laminates showed anisotropic mechanical properties due to the unbalanced weave pattern of the silk fabric. Therefore, developing silk fabrics with a balanced planar weave may prove beneficial when used as an ecofriendly alternative to glass reinforcement in structural composites. SEM analysis of the silk/epoxy composites revealed extensive fiber/matrix debonding. Treating the silk surface seems to be necessary for higher silk/epoxy interfacial adhesion, and for further improvement of mechanical properties.

Finally, silk fabric was found to be prone to moisture absorption from the environment, which considerably degraded the mechanical properties of the fabricated laminates. The moisture presence in silk fabric prior to laminate fabrication yielded slower fill times and caused an overall reduction in thermomechanical properties. A 10% fabric moisture content induced 23 and 20% reductions in specific flexural strength and modulus, respectively. These results stress the elevated sensitivity of silk composites to the storage conditions of the silk preforms.

**Author Contributions:** Conceptualization, Y.K.H., M.A.Y., G.E.G., M.P., M.A., and M.C.A.; Methodology, Y.K.H., M.A.Y., G.E.G., M.P., M.A., and M.C.A.; Validation, Y.K.H., M.A.Y., G.E.G., M.P., M.A., and M.C.A.; Formal Analysis, Y.K.H., M.A.Y., G.E.G., M.P., M.A., and M.C.A.; Investigation, M.A.Y., G.E.G., M.P., and M.A.; Resources, M.C.A.; Writing—Original Draft Preparation, Y.K.H.; Writing—Review & Editing, Y.K.H., M.A.Y.,G.E.G., M.P., M.A., and M.C.A.; Visualization, Y.K.H., M.A.Y., G.E.G., M.P., and M.A.; Supervision, Y.K.H. and M.C.A.; Project Administration, Y.K.H. and M.C.A.; Funding Acquisition, M.C.A.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **"Skin-Core-Skin" Structure of Polymer Crystallization Investigated by Multiscale Simulation**

#### **Chunlei Ruan**

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China; ruanchunlei@haust.edu.cn

Received: 16 March 2018; Accepted: 13 April 2018; Published: 16 April 2018

**Abstract:** "Skin-core-skin" structure is a typical crystal morphology in injection products. Previous numerical works have rarely focused on crystal evolution; rather, they have mostly been based on the prediction of temperature distribution or crystallization kinetics. The aim of this work was to achieve the "skin-core-skin" structure and investigate the role of external flow and temperature fields on crystal morphology. Therefore, the multiscale algorithm was extended to the simulation of polymer crystallization in a pipe flow. The multiscale algorithm contains two parts: a collocated finite volume method at the macroscopic level and a morphological Monte Carlo method at the microscopic level. The SIMPLE (semi-implicit method for pressure linked equations) algorithm was used to calculate the polymeric model at the macroscopic level, while the Monte Carlo method with stochastic birth-growth process of spherulites and shish-kebabs was used at the microscopic level. Results show that our algorithm is valid to predict "skin-core-skin" structure, and the initial melt temperature and the maximum velocity of melt at the inlet mainly affects the morphology of shish-kebabs.

**Keywords:** "skin-core-skin" structure; flow-induced crystallization; multiscale simulation; crystal morphology

#### **1. Introduction**

Currently, semicrystalline polymers are widely used in industry [1]. Usually, such polymers should be processed to become useful products. Common processing techniques include injection molding, extrusion molding, blow molding, and so others. Among these, injection molding is the most widely used. It involves a high-speed flow field and complex temperature field. These processing conditions are key factors in determining the microstructure of the products (crystal types, crystal orientation, etc.). On the other hand, the mechanical properties of the products (strength, modulus, etc.) are strongly dependent on these microstructures. Therefore, it is of great significance to control the microstructures by precisely applying external flow and temperature fields to improve the performance of the products.

Experimental results show that the crystalline structure in the final injection product takes on a typical "skin-core-skin" structure: the shish-kebab structure with high orientation appears in the skin layer, and the spherulitical structure with essentially no preferred orientation appears in the core layer [2]. Figure 1 shows the cross-section of the shish-kebab structure and spherulitical structure of an injection product [2]. It has been reported that in the skin layer, because of the high shear stress and shear strain, the extended polymer chains lead to extended chain crystals and, ultimately, shish-kebab structures. In the core layer, because of the absence of shear, the random polymer chains lead to lamellar, chain-folded crystals and, finally, spherulites. Hence, the shish-kebab structure is related to flow-induced crystallization, and the spherulitical structure is related to quiescent crystallization [2–4]. Compared with the spherulitical structure, the shish-kebab structure improves the performance of

products in tensile strength, tensile elastic modulus in stress direction, but reduces the performance of products in impact strength in the direction perpendicular to the stress [5]. Therefore, it is important to predict the spherulitical structure and shish-kebab structure precisely.

**Figure 1.** "Skin-core-skin" structure in an injection polymer product [2].

To date, several numerical works have reported capturing the evolution of the spherulitical structure in quiescent crystallization. For example, Raabe [6] and Spina et al. [7] used the cell automaton method to simulate spherulite growth in polymer crystallization; Ketdee [8] presented Monte Carlo simulations to predict the kinetics and morphology of isothermal polymer crystallization; Ruan et al. [9,10] applied the pixel coloring method to capture the spherulite evolution in isothermal and non-isothermal polymer crystallization; and Liu et al. [11,12] constructed a level set method to capture the spherulite development during the polymer cooling stage.

Compared with the spherulitical structure in quiescent crystallization, models and methods for the determination of shish-kebab structure in flow-induced crystallization are rare. Eder [13] considered shish-kebabs as growing cylinders and obtained a series of differential equations by using the Schneider rate equation [14]. Zuidema et al. [15] thought that recoverable strain was the driving force for the nucleation of shish-kebabs and modified the Eder model. Zinet et al. [4,16] and Mu et al. [17] used a modified Schneider rate equation to describe the growth of thermally and flow-induced nuclei. Guo et al. [18,19] introduced a molecular deformation factor, which distinguished spherulites and shish-kebabs by comparing the molecular deformation factor with the critical one. Wang et al. [20] presented a phase field method to simulate the shish-kebab structure in simple shear and temperature fields. Although the above works are based on crystal morphology, crystallization kinetics models are also needed. Crystallization kinetics models, such as the Avrami model, are often reported with lower accuracy at the later stage of polymer crystallization. Furthermore, these works did not construct a method to reveal the details of shish-kebabs. Recently, Ruan et al. [21–23] presented a Monte Carlo method to simulate spherulites and shish-kebabs in a parametrical study, with simple shear flow and Couette flow. They obtained detailed crystal morphology and reliable crystallization kinetics without using a kinetics model.

In this study, we extended the multiscale method to simulate the "skin-core-skin" structure of the polymer crystallization in a pipe flow, which is treated as a simplification of the injection processing. Unlike our previous work of Couette flow [22], the conservation at the macroscopic level in pipe flow is more complicated. Therefore, the SIMPLE (semi-implicit method for pressure linked equations) algorithm on collocated coarse grid was used to calculate the flow and temperature fields at the macroscopic level. Rhie–Chow-type interpolation was introduced to overcome the pressure-velocity decoupling. The morphological Monte Carlo method on fine grid was used to capture the crystal growth fronts and compute the relative crystallinity. Effects of external flow and temperature fields, (e.g., temperature cooling rate of the mold, initial melt temperature, maximum velocity of the melt in inlet) on the crystal morphology were investigated and are herein discussed.

#### **2. Mathematical Model**

In injection molding, polymer melts are injected into a mold to form different products. A changing flow domain is more suitable. Some software, such as C-mold and Moldflow, can address

all stages of injection. In this work, we assumed the mold is a pipe, which is shown in Figure 2. Actually, the mold is supposed to have a thin-wall thickness in the *y* direction, which means the length in the *x* direction is substantially larger than the length in the *y* direction (*L* >> *W*). Our aim was to simulate the crystallization during and after shear treatment, which refer to the injection and cooling stages, respectively. We assumed the melt experiences shear effects with a parabolic velocity in the inlet that lasts for shear time *ts* (injection stage). We also assumed that after the shearing flow, the mold has experienced a large temperature change (cooling stage). Therefore, the mathematical model at the macroscopic level should be divided into two cases.

**Figure 2.** The pipe model for simulation.

#### *2.1. Conservation Equations at the Macroscopic Level*

We assumed the polymer melt is a non-isothermal, non-compressible, and non-Newtonian flow. Therefore, three conservation equations were needed. Furthermore, the melt is non-Newtonian, and a constitutive equation was needed.

(1) Conservation equations at the macroscopic level during shearing flow (injection stage)

The mass conservation equation is

$$
\nabla \cdot \mathbf{u} = 0,\tag{1}
$$

the momentum conservation equation is

$$\frac{\partial}{\partial t}(\rho \mathbf{u}) + \nabla \cdot (\rho \mathbf{u} \mathbf{u}) = -\nabla p + \nabla \cdot \mathbf{\tau}\_{\mathbf{c}\prime} \tag{2}$$

and the energy conservation equation is

$$\frac{\partial}{\partial t}(\rho c\_p T) + \nabla \cdot (\rho c\_p \mathbf{u} T) = \nabla \cdot (k\_p \nabla T) + \rho \Delta H \frac{\partial \mathbf{a}}{\partial t} + (-p\mathbf{I} + \pi\_c) : \nabla \mathbf{u} \tag{3}$$

where *ρ* is the density; **u** is the velocity; *p* is the pressure; *cp* is the heat capacity; *kp* is the thermal conductivity; *T* is the temperature; *α* is the relative crystallinity; Δ*H* is the crystallization enthalpy; **I** is the identity tensor; and τ*<sup>c</sup>* = τ*<sup>a</sup>* + τ*sc* is the composite tensor, with τ*<sup>a</sup>* being the stress of the amorphous phase and τ*sc* the stress of the semicrystalline phase.

We used the conception of Zheng et al. [24] to describe the non-Newtonian system. The amorphous phase is described by FENE-P (finite extensible nonlinear elastic model with a Peterlin closure approximation) dumbbells, while the semicrystalline phase is modeled as rigid dumbbells. The stress caused by FENE-P dumbbells is [24]

$$\mathbf{r}\_d = nkT\left(\frac{\mathbf{C}}{1 - tr\mathbf{C}/b} - \mathbf{I}\right),\tag{4}$$

and the evolution of the conformation tensor is [24]

$$
\lambda\_a(T)\overset{\nabla}{\mathbf{C}} + \left[\frac{1}{1 - tr\mathbf{C}/b}\mathbf{C} - \mathbf{I}\right] = 0,\tag{5}
$$

where *n* is the number density of the molecules, *k* is the Boltzmann constant, *b* is the dimensionless parameter of the nonlinear spring, *tr* is the trace of the matrix, **C** is the configuration tensor, and the upper-convected derivative of **C** is defined as ∇ **C** = *D***C**/*Dt* − (∇**u**) *<sup>T</sup>*·**<sup>C</sup>** <sup>−</sup> **<sup>C</sup>**·(∇**u**). *λα* is the relaxation time of the fluid, which obeys the Arrhenius equation, namely [24],

$$
\lambda\_a(T) = \exp\left[\frac{E\_a}{R\_\mathcal{\mathcal{S}}} \left(\frac{1}{T} - \frac{1}{T\_r}\right)\right] \lambda\_{a,r\prime} \tag{6}
$$

where *Tr* is a reference temperature, and *Ea*/*Rg* is a constant that can be determined from the experimental data. The stress caused by rigid dumbbells is [24]

$$\mathbf{r}\_{\text{sc}} = \frac{\eta\_{\text{sc}}}{\lambda\_{\text{sc}}} [\langle \mathbf{R} \mathbf{R} \rangle + \lambda\_{\text{sc}} \dot{\mathbf{y}} : \langle \mathbf{R} \mathbf{R} \mathbf{R} \mathbf{R} \rangle],\tag{7}$$

where *λsc* is the relaxation time of the rigid dumbbells, *ηsc* is the viscosity of the semicrystalline system, . γ is the deformation tensor, **RR** is the second-order orientation tensor, and **RRRR** is the fourth-order orientation tensor. The evolution of the orientation tensor **RR** is defined as [24]

$$
\langle \mathbf{R} \mathbf{R} \rangle = -\frac{1}{\lambda\_{sc}} (\langle \mathbf{R} \mathbf{R} \rangle - \frac{\mathbf{I}}{2} - \dot{\mathbf{y}} : \langle \mathbf{R} \mathbf{R} \mathbf{R} \mathbf{R} \rangle) \tag{8}
$$

The relationship between the viscosity of the semicrystalline system and the amorphous system is dependent on the following empirical equation [24]

$$\frac{\eta\_{sc}(\mathbf{x},T)}{\eta\_{a}(T)} = \frac{(a/A)^{\delta\_1}}{(1-a/A)^{\delta}} \qquad a < A\_{\prime} \tag{9}$$

and the relaxation times of the rigid dumbbells and FENE-P dumbbells are [24]

$$\frac{\lambda\_{\text{sc}}(\mathbf{x},T)}{\lambda\_{\text{a}}(T)} = \frac{\left(\alpha/A\right)^{\beta\_1}}{\left(1-\alpha/A\right)^{\beta}} \qquad \text{a} < A\_{\text{\textquotedblleft}}\tag{10}$$

where *β*1, *β*<sup>1</sup> and *A* are the empirical constants. Equation (9) clearly shows that when *α* → *A* (*A* being the "critical value" of the degree of crystallinity), the viscosity of the semicrystalline system approaches infinity.

To calculate the second-order orientation tensor **RR** from Equations (7) and (8), one shall use a closure approximation—such as the hybrid [25], EBOF (eigenvalue-based orthotropic fitting) [26,27], or IBOF (invariant-based orthotropic fitting) [28] method—to gain an expression of **RRRR** in terms of **RR**. Here, the hybrid expression was used, namely,

$$
\langle \mathbf{R} \mathbf{R} \mathbf{R} \mathbf{R} \rangle\_{ijkl} = \langle \mathbf{R} \mathbf{R} \rangle\_{ij} \langle \mathbf{R} \mathbf{R} \rangle\_{kl\prime} \tag{11}
$$

where **RR***ij* and **RR***kl* are the components of **RR**, and **RRRR***ijkl* is the component of **RRRR**.

(2) Conservation equations at the macroscopic level after shearing flow (cooling stage)

In the second case, we assumed there is no fluid flow and the melt is stationary. Therefore, the conservation equation was the energy equation, which can be written as follows,

$$
\rho c\_p \frac{\partial T}{\partial t} = \nabla \cdot (k\_p \nabla T) + \rho \Delta H \frac{\partial \alpha}{\partial t}.\tag{12}
$$

Actually, for high accuracy, the material parameters can be calculated with the mixture rule. For example, *ρ* = *αρsc* + (1 − *α*)*ρα*, with *ρsc* as the density of the semicrystalline phase and *ρα* as the density of the amorphous phase.

#### *2.2. Crystal Evolution Model at the Microscopic Level*

In injection processing, both the spherulitical structure and shish-kebab structure appear in polymer products. The former one is caused by temperature and is known as quiescent crystallization; the latter one is caused by shear or stress and is known as flow-induced crystallization.

In the morphological simulation, crystals follow the steps of nucleation-growth-impingement. Therefore, it is important to model the nucleation and growth of spherulites and shish-kebabs. In our previous study [21,23], we deduced the evolution equations of spherulites and shish-kebabs based on the Eder model [13] and Schneider rate model [14]. Here, we used the equations obtained in our previous work [23].

We assumed the relationship between the nucleation of spherulites (*Ns*) and temperature is [29]

$$N\_5(T) = N\_0 \exp[a\_n \Delta T + b\_n],\tag{13}$$

where *an* and *bn* are constants, and Δ*T* = *T*<sup>0</sup> *<sup>m</sup>* − *<sup>T</sup>* is the degree of supercooling, with *<sup>T</sup>*<sup>0</sup> *<sup>m</sup>* being the equilibrium melting temperature. We shall mention that different nucleation relations of *Ns* have been reported, and the reviews of Pantani et al. [5] are helpful. Usually, these relations may be quite restricting depending on the conditions or materials.

The growth rate of spherulites (*Gs*) is often adopted by the Hoffman–Lauritzen expression [30], which is

$$\mathcal{G}\_s(T) = \mathcal{G}\_0 \exp\left[ -\frac{\mathcal{U}^\*}{R\_\mathcal{\mathcal{S}}(T - T\_\infty)} \right] \exp\left[ -\frac{K\_\mathcal{\mathcal{S}}}{T\Delta T f} \right],\tag{14}$$

where *G*<sup>0</sup> and *Kg* are constants, *U*∗ is the activation energy of motion, *Rg* is the gas constant, *T*<sup>∞</sup> = *Tg* − 30 (where *Tg* is the glass transition temperature), and *f* = 2*T*/ *T*0 *<sup>m</sup>* + *T* .

We assumed the driving force of the nucleation of shish-kebabs (*Ns*−*k*) is the first normal stress difference, which can be written as [29] .

$$N\_{s-k} = \mathbf{CN}\_{1\prime} \tag{15}$$

where **C** is a constant, and *N*<sup>1</sup> is the first normal stress difference that can be calculated by Equations (4) and (7). Notice that the driving force for flow-induced nucleation is not well understood, and different approaches have been proposed. Examples of the driving forces include the shear rate [13], shear strain [31], recoverable strain [15], dumbbell free energy [24]. Equation (15) is the simplest but is also widely used in simulations [29,32].

Shish-kebabs are assumed to grow as a cylinder, which means they can grow in two directions, namely, along the length and radial directions. According to Eder [13], the length growth rate (*Gs*−*k*,*l*) obeys the following equation

$$\mathbf{G}\_{s-k,l} = \dot{\boldsymbol{\gamma}}^2 \cdot \mathbf{g}\_1 / \dot{\boldsymbol{\gamma}}\_{l,l}^2 \tag{16}$$

where *<sup>g</sup>*1/ . *γ*2 *<sup>l</sup>* is a constant, and . *γ* is the shear rate. The radial growth rate of the shish-kebabs (*Gs*−*k*,*r*) is always assumed to be equal to the growth rate of the spherulites, which is

$$G\_{\mathfrak{s}-k,r} = G\_{\mathfrak{s}}.\tag{17}$$

#### **3. Multiscale Method**

The conception of a multiscale method here is similar to the method we built up in the Couette flow case [22]. We used different methods at different scales and then coupled them together. The finite volume method at the macroscopic level is constructed to calculate the velocity, temperature, stress, etc. The finite volume method is a conservation method. It has advantages of small storage and cheap

computational cost, as well as easy handling of the couplings of velocity-pressure, velocity-stress, etc. [33]. Therefore, the finite volume method is widely used in CFD (computational fluid dynamics). The Monte Carlo method at the microscopic level is constructed to capture the development of crystals. The Monte Carlo method is also known as a stochastic simulation and can address the stochastic birth-growth process of spherulites and shish-kebabs. The advantages of the Monte Carlo method are that it can avoid the use of a crystallization kinetics model and it can also predict the detailed morphology evolution. The finite volume method and Monte Carlo method were implemented on different grids—namely, the finite volume method was used on a coarse grid to solve macroscopic Equations (1)–(3), (5), (8), and (12) to obtain the velocity, pressure, stress, and temperature, and the Monte Carlo method was used on a fine grid to capture the evolution of crystals by using Equations (13)–(17) to obtain the relative crystallinity. We refer to our previous work for the arrangement of the coarse grid and fine grid [22,34].

In the modeling part, we put fully coupled mass, momentum, and energy conservation equations together with the constitutive equations of amorphous and semicrystalline phases during the shear treatment (injection stage). However, in the algorithm of the finite volume method, we present a decoupled one. We solved the non-isothermal Newtonian flow to achieve the velocity and temperature. Then, with the results of velocity and temperature, we solved the constitutive equations of amorphous and semicrystalline phases. In other words, the velocity, pressure, and temperature were coupled, while the stress was decoupled. This is because the stresses caused by the amorphous and semicrystalline phases are seriously dependent on the relative crystallinity: a slight increase in relative crystallinity causes a dramatic increase in viscosity, which leads to a large increase in stress. If we put this stress into the momentum equation, we cannot obtain a convergent result because of the large stress source term. Therefore, in our simulation, Equations (1)–(3), (5), and (8) were not solved simultaneously. Actually, when we solve Equations (1)–(3), the SIMPLE method is used [35] . We assumed the flow is a non-isothermal Newtonian flow, which is incompressible. The collocated finite volume method was used. Compared with the finite volume method on a staggered grid, the collocated finite volume method has the advantage of easy implementation on the same grid to overcome the decoupling of velocity-pressure and velocity-stress [33]. It is also noted that in our previous work on the Couette flow model, a continuity equation could not be calculated that avoided the decoupling of velocity-pressure. Detailed implementation of the collocated finite volume method were as follows.

Equations (1)–(3), (5), and (8) can be written as a general transport equation

$$\frac{\partial(\delta\boldsymbol{\varrho})}{\partial t} + \nabla \cdot (m\mathbf{u}\boldsymbol{\varrho}) = \nabla \cdot (\Gamma \nabla \boldsymbol{\varrho}) + S\_{\boldsymbol{\varrho}\boldsymbol{\prime}} \tag{18}$$

where *δ*, *m*, and Γ are constant, and *ϕ* and *S<sup>ϕ</sup>* are the functions that are defined in Table 1. The terms in Equation (18) represent the transient, convective, diffusive and source contributions.

Equation (18) is integrated over the finite volume cell shown in Figure 3 in space, and the use of the divergence theorem yields

$$\begin{split} \int\_{V} \frac{\partial (\delta \boldsymbol{\varphi})}{\partial t} dV &+ \int\_{s}^{\boldsymbol{\eta}} [(m \mathbf{u} \boldsymbol{\varrho} - \Gamma \nabla \boldsymbol{\varphi})\_{\boldsymbol{\varepsilon}} - (m \mathbf{u} \boldsymbol{\varrho} - \Gamma \nabla \boldsymbol{\varphi})\_{\boldsymbol{w}}] d\boldsymbol{y} \\ &+ \int\_{w}^{\boldsymbol{\varepsilon}} [(m \mathbf{u} \boldsymbol{\varrho} - \Gamma \nabla \boldsymbol{\varphi})\_{\boldsymbol{n}} - (m \mathbf{u} \boldsymbol{\varrho} - \Gamma \nabla \boldsymbol{\varphi})\_{\boldsymbol{s}}] d\mathbf{x} = \int\_{s}^{\boldsymbol{\eta}} \int\_{\boldsymbol{w}} \mathcal{S}\_{\boldsymbol{\theta}} d\mathbf{x} d\boldsymbol{y}. \end{split} \tag{19}$$

The transient term in Equation (19) is integrated in time and then divided by Δ*t*. A linear approximation is used, which leads to

$$\frac{1}{\Delta t} \int\_{t} \delta \frac{\partial \rho}{\partial t} dV dt \approx \frac{\delta V \left(\rho\_P - \rho\_p^0\right)}{\Delta t},\tag{20}$$

where the superscript "0" indicates the value at the previous time step. The upwind scheme and central differences are used to approximate the convective and diffusive fluxes across each face, respectively. This gives rise to the following discretization

$$A\_P \phi\_P = A\_E \phi\_E + A\_W \phi\_W + A\_N \phi\_N + A\_S \phi\_S + Q\_P \tag{21}$$

where *AP*, *AE*, *AW*, *AN*, and *AS* are the coefficients of *φP*, *φE*, *φW*, *φN*, and *φS*, respectively, and *QP* is the source term. The Gauss–Seidel iteration method can be used to solve the above linear equations. Note that a Rhie–Chow-type [36] interpolation should be used to overcome the pressure-velocity decoupling. Details can be found in the work of Oliveira et al. [37] and Ruan et al. [38].

**Equation** *δ m φ* **Γ** *S<sup>φ</sup>* Continuity 0 1 1 0 0 Momentum *ρ ρ* **u** *η* −∇*p* Energy *ρcp ρcp T k ρ*Δ*H ∂α ∂t* FENE-P model 1 1 **<sup>C</sup>** <sup>0</sup> <sup>−</sup> <sup>1</sup> *λα*(*T*) **C** <sup>1</sup>− *tr***<sup>C</sup>** *b* − **I** + (∇**u**) *<sup>T</sup>*·**<sup>C</sup>** <sup>+</sup> **<sup>C</sup>**·∇**<sup>u</sup>** Rigid dumbbell model 1 1 **RR** <sup>0</sup> <sup>−</sup> <sup>1</sup> *λsc* (*T*) - **RR**<sup>−</sup> **<sup>I</sup>** 2 − . γ : **RRRR** + (∇**u**) *T* **RR** + **RR**·∇**u**

**Table 1.** Definition of constants and functions in the general equation.

**Figure 3.** A general control volume.

The Monte Carlo method was employed on the fine grid to track the development of spherulites and shish-kebabs. With the crystal evolution model of Equations (13)–(17), the detailed morphology can be obtained by the Monte Carlo method. This is the main advantage that the morphological simulation has. Furthermore, by using the Monte Carlo method, the relative crystallinity can also be obtained from the volume fraction of crystals under the assumption that the semicrystalline phase is spatially uniform. Thus, the relative crystallinity was calculated by the following equation

$$
\mu = \text{number of cells that are occupied by crystals/total number of cells.} \tag{22}
$$

Here, we shall not show the detailed implementation of the Monte Carlo method, but refer to our previous work [21,23] for more details.

Figure 4 shows the flowchart of the implementation of the multiscale method.

**Figure 4.** Flowchart for multiscale method in the simulation.

#### **4. Results and Discussion**

#### *4.1. Problem Definition*

Considering the injection mold shown in Figure 2, the length is *L* = 16 mm, and the thickness is *W* = 8 mm. We assumed the walls, with *y* = 0 mm and *y* = 8 mm, experience a constant cooling rate operation and set the boundary conditions as *T* = *T*<sup>0</sup> − *c* × *t*, with *T*<sup>0</sup> as the initial temperature and *c* as the cooling rate. The other boundary conditions were assumed as *∂T*/*∂***n** = 0, with **n** as the unit normal vector. Note that the mold is a thin wall with thickness in the *y* direction. Because of the complexity of the multiscale algorithm, here, we set the length in the *x* direction as twice the length as in the *y* direction. The adiabatic boundary conditions of *x* = 0 mm and *x* = 16 mm were used to obtain a condition similar to the thin-wall thickness of mold in industry. Moreover, here, we set a shear flow to account for the flow and flow history of the injection processing. We assumed the velocity at the inlet is *u* = *Uy*(*W* − *y*), where *U* is a constant, and last with the shear time *ts* s; once the time reaches

the "shear time" (*ts*), the flow field is vanished. We fixed the shear time to *ts* = 10 s and will not discuss this effect later.

The material here was the isotactic polypropylene homopolymer with tacticity 0.96. The parameters used were [5,15,24,29]: *an* = 0.156 K/m3, *bn* = 15.1 /m3, *<sup>G</sup>*<sup>0</sup> = 2.83 × 102 m/s, *<sup>U</sup>*∗/*Rg* = 755 K, *Kg* = 5.5 × 105 K2, *<sup>T</sup>*<sup>0</sup> *<sup>m</sup>* = 483 K, *Tg* <sup>=</sup> 269 K, *gl*/ . *γl* <sup>2</sup> = 2.69 <sup>×</sup> <sup>10</sup>−7, *<sup>C</sup>* = 106 /Pa/s2/m, *λα*,*<sup>r</sup>* = 4.00 × <sup>10</sup>−<sup>2</sup> s, *Tr* = 476.15 K, *<sup>E</sup>α*/*Rg* = 5.602 × 103 K, b = 5, n = 1.26 × <sup>10</sup><sup>26</sup> /m3, k = 1.38 × <sup>10</sup><sup>−</sup>23, β = 9.2, β<sup>1</sup> = 0.05, and A = 0.44. The other parameters we chose were *ρ* = 900 kg/m3, *cp* = 2.14 × <sup>10</sup><sup>3</sup> J/kg/K, *kp* = 0.193 W/m/K, <sup>Δ</sup>*<sup>H</sup>* = 107 × 103 J/kg, *<sup>T</sup>*<sup>0</sup> = 490 K, *<sup>c</sup>* = 2 K/min, and *<sup>U</sup>* = 625. In the implementation of the multiscale algorithm, the coarse grid was chosen as 16 × 18, and the fine grid was chosen as 500 × 500.

To show the validity of the model and the Monte Carlo method used at the microscopic level, isothermal crystallization was considered. Figure 5 shows the simulated data with the experimental data [29]. It can be seen that the numerical relationship between the shear rate and the half crystallization time is in good agreement with the experimental data. Therefore, our model and Monte Carlo method is valid.

**Figure 5.** Comparison of simulation result with the experimental result [29].

#### *4.2. Temperature, Relative Crystallinity Distribution, and "Skin-Core-Skin" Structure*

Figure 6 shows the temperature and relative crystallinity evolution at the profile of *x* = 8 mm. Results obtained for our algorithm are compared with the Avrami model. Here, the Avrami model is *<sup>α</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup> exp −*α<sup>f</sup>* , with *α<sup>f</sup>* = *Vsp* + *Vsh*, where *Vsp* is the undisturbed total volume of spherulites and *Vsh* is the undisturbed total volume of shish-kebabs. The Schneider rate equation [14,15] was used to compute *Vsp* and the Eder model [13,15] was used to calculate *Vsh*. The "Avrami model" in the temperature curves means that the temperature is calculated with the *α* obtained by the Avrami model. As can be seen in Figure 6, the simulation data show a good agreement with the Avrami model. In addition, as shown in the temperature curves, there is a "platform" in the core layer near 2800–3600 s. According to the evolution of relative crystallinity, the relative crystallinity value of the core layer in this period increases rapidly and finally reaches 1. Therefore, this period is the time that crystallization happens. Because of the latent heat released by crystallization, the temperature "platform" forms in the core layer. Furthermore, the crystallization rate in the skin layer is faster than that in the core layer. This result is consistent with our previous study on quiescent crystallization [39].

**Figure 6.** Evolution of temperature and relative crystallinity with time at the profile of *x* = 8 mm: (**a**) temperature, (**b**) relative crystallinity.

Figure 7 shows the evolution of temperature and relative crystallinity at different thicknesses in the profile at *x* = 8 mm. It is evident that crystallization occurs near 400–380 K. It is also clear that crystallization finishes earlier in the skin layer because of the lower temperature at the walls.

**Figure 7.** Distribution of temperature and relative crystallinity at different thicknesses: (**a**) temperature, (**b**) relative crystallinity.

Figure 8 shows the development of crystals in the control volume of the skin layer (8 mm, 0 mm) and in the control volume of the core layer (8 mm, 4 mm). It is clear that in the skin layer, the shish-kebab structure is dominant, while in the core layer, only the spherulitic structure appears. Crystals follow the steps of nucleation, growth, impingement, and, finally, fully filling the whole space. In fact, the shear rate near the skin layer is large, which is of benefit to the nucleation and growth of shish-kebabs. However, the shear rate is often absent or small in the core layer, which is not suitable to the development of shish-kebabs. However, a lower temperature is favorable for the nucleation and growth of spherulites. This development of crystal morphology is in agreement with the experimental finding of Koscher et al. [29].

**Figure 8.** Morphology evolution in the polymer control volume: (**a**) skin volume and (**b**) core volume.

Figure 9 shows the final crystal morphology in the computational domain. The structure takes on a typical "skin-core-skin" structure: in the skin layer, the crystal structure is mainly composed of the anisotropic shish-kebab; in the core layer, the crystal structure is the isotropic spherulite. This structure is consistent with experimental findings [5,40–42]. Our approach is valid in revealing the crystal microstructures. It should be mentioned that in our simulation, we do not consider a "frozen layer" [5,40–42]. Here, we consider a moderate temperature cooling boundary condition; therefore, a "frozen layer" cannot be captured in this case.

**Figure 9.** "Skin-core-skin" structure.

The Monte Carlo simulation also allowed us to show the details of spherulites and shish-kebabs. Figure 10 shows the number of spherulites and shish-kebabs at different thicknesses at the profile of *x* = 8 mm. It is evident that the number of shish-kebabs decreases from the skin to core, while the number of spherulites increases from the skin to core. The trend in number of shish-kebabs is caused

by the change in shear rate. It is worth noting that the trend in the number of spherulites is in contrast to the quiescent case [40]. In the quiescent case, because of the highest cooling rate being in the skin layer, the number of spherulites is largest, which leads to the smallest size of spherulites. Although in this case, the temperature performance is similar to the quiescent case, the shish-kebab structure appears, which restricts the number of spherulites.

**Figure 10.** Number of spherulites and shish-kebabs at the different thicknesses at the profile of *x* = 8 mm.

#### *4.3. Effects of Temperature Cooling Rate of the Mold Wall*

Three cases of temperature cooling rate of the mold wall were examined, namely, *c* = 1 K/min, *c* = 2 K/min, and *c* = 5 K/min. It is noted that the high cooling rate is related to the low wall temperature in real injection processing.

Figure 11 shows the temperature evolution and the rates of crystallization at the profile of *x* = 8 mm. To show the difference between the skin and core layers, we chose the skin point (8 mm, 0 mm) and core point (8 mm, 4 mm) as examples. As seen in Figure 11, the case with a high cooling rate leads to the fast decrease in temperature and high crystallization rate.

**Figure 11.** Effect of temperature cooling rate of the mold wall on the temperature and the rates of crystallization at the profile of *x* = 8 mm: (**a**) temperature, (**b**) half crystallization time.

Table 2 shows the parameters related to the microstructure. The average diameter of spherulites, number of shish-kebabs and the relative crystallinity caused by spherulites and shish-kebabs are displayed. It is evident that in the case of the higher cooling rate, the average size of spherulites decreases. However, the number of shish-kebabs does not change with the cooling rate. Therefore, it can be concluded that the temperature cooling rate of the wall mainly affects the nucleation and growth of spherulites. The predicted average diameter of spherulites also shows agreement with the experimental and numerical works of Pantanin et al. [5].

**Table 2.** Effect of the temperature cooling rate of the mold wall on the spherulites and shish-kebabs at the profile of *x* = 8 mm.


#### *4.4. Effects of Initial Melt Temperature*

Three cases of initial melt temperature were examined, namely, *T*<sup>0</sup> = 490 K, *T*<sup>0</sup> = 500 K, *T*<sup>0</sup> = 510 K. Figure 12 presents the evolution of the temperature and the rates of crystallization at the skin point (8 mm, 0 mm) and core point (8 mm, 4 mm) for different initial melt temperatures. It can be seen from Figure 12 that the higher the initial melt temperature, the later the occurrence of the temperature "platform" and crystallization. However, the curves only shift to the right when the initial melt temperature is increased.

**Figure 12.** Effect of the initial melt temperature on the temperature and the rates of crystallization at the profile *x* = 8 mm: (**a**) temperature, (**b**) half crystallization time.

Table 3 shows the effects of the initial melt temperature on the microstructures. These effects are reflected by the average diameter of spherulites, number of shish-kebabs, and the relative crystallinity contributed by the spherulites and shish-kebabs at the skin and core volume. It is clear that when the

initial melt temperature increases, both the contribution and the number of shish-kebabs are reduced. This is because the higher melt temperature reduces the first normal stress difference. According to Equation (15), the number of shish-kebabs reduces, which leads to a reduction in the contribution of shish-kebabs to the relative crystallinity. It is also evident that the initial melt temperature has minor effects on spherulites.


**Table 3.** Effect of initial melt temperature on spherulites and shish-kebabs at the profile *x* = 8 mm.

#### *4.5. Effects of the Maximum Velocity of Melt at the Inlet*

The effects of maximum velocity at the inlet were also investigated. We changed *U* from 125 to 1250 to obtain the velocity at the inlet. The velocity also affects the maximum shear rate. The shear rate was calculated with the velocity as . *γ* = |*∂u*/*∂y*|. Figure 13 shows the final crystal morphology of the control volume at *x* = 8 mm. When the maximum velocity is small (small shear rate), the shish-kebab structure in the skin layer is not apparent. With the increase in velocity (or shear rate), the shish-kebab structure becomes clear, and the thickness of the skin layer becomes wide. Hence, the velocity at the inlet has significant effects on the crystal morphology.

**Figure 13.** Final crystal morphology with different maximum velocities at the inlet. (**a**) . *γ*max =1s−1, (**b**) . *<sup>γ</sup>*max =3s<sup>−</sup>1, (**c**) . *<sup>γ</sup>*max =5s<sup>−</sup>1, (**d**) . *<sup>γ</sup>*max =7s<sup>−</sup>1, (**e**) . *γ*max = 10 s<sup>−</sup>1.

We now restrict our attention to the control volume of skin point (8 mm, 0 mm) and core point (8 mm, 4 mm) with different velocities (shear rate). Figures 14 and 15 show the morphologies of the skin and core volumes. As we can see in Figure 14, the morphology of the skin volume changes clearly when the velocity is increased. The number and anisotropy of shish-kebabs become higher in the larger shear rate case of the skin volume. The crystal morphology of the core volume in Figure 15 shows that shear rate has a minor effect on the number and size of spherulites.

**Figure 14.** Morphology of the polymer skin volume: (**a**) . *<sup>γ</sup>*max =1s<sup>−</sup>1, (**b**) . *<sup>γ</sup>*max =5s<sup>−</sup>1, (**c**) . *γ*max = 10 s<sup>−</sup>1.

**Figure 15.** Morphology at the polymer core volume: (**a**) . *<sup>γ</sup>*max =1s<sup>−</sup>1, (**b**) . *<sup>γ</sup>*max =5s<sup>−</sup>1, (**c**) . *γ*max = 10 s<sup>−</sup>1.

Table 4 shows the average diameter of spherulites, number of shish-kebabs, and the relative crystallinity caused by spherulites and shish-kebabs at the skin and core volume. The number of shish-kebabs and the contribution of shish-kebabs to relative crystallinity decrease from the skin to core. Furthermore, the number of shish-kebabs and the contribution of shish-kebabs to the relative crystallinity increase with the maximum velocity, and the impact is significant.


**Table 4.** Effect of the maximum velocity at the inlet on spherulites and shish-kebabs at the profile of *x* = 8 mm.

#### **5. Conclusions**

We have extended the multiscale simulation for polymer crystallization in a pipe flow related to simplified injection processing. The "skin-core-skin" crystal structure was obtained. Both the spherulitical structure and shish-kebab structure can be captured by our algorithm. We have also shown the effects of the mold temperature cooling rate, initial melt temperature, and the maximum velocity of the melt at the inlet on microstructures. The results indicate that the temperature cooling rate of the mold (or mold temperature) especially affects the morphology of spherulites, whereas the initial melt temperature and maximum velocity of the melt at the inlet mainly affect the morphology of the shish-kebabs. We hope the results presented here can provide more insight into the microstructural details of crystallization and thus be more helpful to industrial applications.

In this work, we did not consider the changing flow domain in the injection stage, and used the viscoelastic flow without a free surface as the flow field for simplicity. To model the crystallization more accurately, a melt with the free surface should be taken into account. Moreover, the temperature boundary condition used here reflects a moderate cooling rate. In real injection processing, a low mold temperature that generates a higher temperature gradient should be applied. Our future work will be concentrated on improving our multiscale method and combining it with other software for simulating real injection processing.

**Acknowledgments:** The financial supports provided by the Natural Sciences Foundation of China (Nos. 11402078, 51375148, U1304521) and the Scientific and Technological Research Project of Henan Province (No. 14B110020) are fully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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