Abstract
Two-dimensional models of die-melt and die-gas-melt were created using Polyflow software. The radial and axial directions flow rate, shear rate, pressure, and first normal stress of the specimen were numerically simulated under conventional extrusion and gas-assisted extrusion while taking into consideration the heat transfer on the free surface of the specimen. The crystallinity was determined by combining the simulation data with the crystallization kinetics equation. The computation results are then examined using Origin software. The findings demonstrate that the use of gas-assisted extrusion technology can cause the Vx to decrease or even turn negative by reducing the friction between the melting edge and the die wall. Additionally, it makes Vy , pressure, shear rate, temperature, first normal stress, and crystallinity increasingly steady and aids in reducing or avoiding the Barus effect. The crystallization phenomena can be measured by using the crystallization kinetics equation. The study of extruded parts at the microscopic level will benefit from this application.
1 Introduction
In recent years, the use of polymer extruded components in the industry has increased, as have the number of studies on these parts. The flow rate balance-based rubber material profile extrusion die design method was put forth by Liu et al. (1). According to the extrusion mechanism, Wang et al. constructed a mathematical model of flow analysis in the extrusion die, performed numerical simulation of the flow in the extrusion die, and projected the melt flow state in complicated die based on die structure (2). The simulation was utilized by Wang et al. to determine the pressure drop in the complicated die (3). Brzoskowski et al. was the first to use compressed air to provide a stable air cushion between the rubber melt and die wall, enhancing the rubber products’ quality and output (4). Liang aided the extrusion process by using slit air intake (5). Numerous specialists and academicians subsequently conducted experimental studies and numerical simulations on the gas-assisted extrusion process (6–11). Gas-assisted extrusion was suggested for use in micro-tubule extrusion by Ren et al. (12–14). Additionally, the associated forming research was completed. The correlation between mechanical qualities and the crystallization and orientation of poly(L-lactide glycolide) fibers was discovered by Li et al. in further in-depth research (15). The impact of carbon fiber length and orientation on the wear and friction characteristics of polyether ether ketone matrix composites was discovered by Qiu et al. (16). The impact of pericardial fiber orientation on compressive characteristics was discovered by Wu et al. (17). The impact of vibration extrusion on the melting and crystallization behavior of high pressure-low density polyethylene was discovered by Wang et al. (18). Yan and Duan explored the micro-deformation mechanism of semi-crystalline and non-crystalline polymers (19,20). Doufas et al. constructed the model of melt flow-induced crystallization and performed some associated simulations (21–24). Liang [25] and Xu [26] explored the crystallization behavior and flow properties of the polymers. The use of the coarse polymer model in polymer crystallization was described by Cosden and Lukes (27). According to the aforementioned studies, the study of polymers is becoming more focused on microscopic crystallization, fiber orientation, and their impact on mechanical properties.
In this research, the physical fields of shear field, pressure field, and velocity field were extended to include crystallization dynamics. The process of crystallization during extrusion was addressed and examined.
2 Modeling and theory
2.1 Geometric model and finite element model
Using Polyflow software, an axial symmetry two-dimensional geometric model was created to investigate the extrusion process and crystallization phenomenon. As the research object, a portion with 20 mm diameter and 80 mm length was chosen. 20 mm of the portion was melted inside the die, and 60 mm of the portion was an extruded sample outside the die.
Only half of the axial symmetry was used in the calculation to make it simpler. Figure 1 depicts its gridding and boundary setup. Based on earlier research, the die was added, and a finite element division was built to take the heat transfer between the melt and the die into account. The grid number of the traditional extrusion model is 1,300. The mesh number of the gas-assisted extrusion model is 1,360. The minimum length is 1 × 10−3 m.

Mesh of the axial symmetry model. (a) Conventional extrusion and (b) gas-assisted extrusion.
2.2 Basic assumptions and basic equations
We assume that the melt is incompressible. Laminar flow will be used to describe the entire flow process. The flow procedure will ignore the mass force and the inertial force. The melt is assumed to be fluid with viscosity.
Under these assumptions, the flow in the polymer extrusion process satisfies the following equations (28).
2.2.1 Governing equations of melt
Continuity equation:
Momentum equation:
Energy equation:
2.2.2 Constitutive equation
Phan-Thien-Tanner constitutive model was chosen for the differential viscoelastic constitutive model, the equation is given as follows:
where
Arrhenius law was chosen for the temperature-dependent viscosity model, the equation is given as follows:
The Arrhenius law is given as follows:
2.2.3 Heat transfer equation
The extruded product in contact with air heat conduction is taken into account, and the equation is given as follows (29):
In 1991, Patel et al. proposed the following formula (30):
where V is the velocity; and is the cross-sectional area of the sample.
Here the circular section area is A = 314 mm2,1V ref = 1 cm·s−1,
Substituting these values, we obtain
The data of the temperature field, shear rate, and stress field following the extrusion die of polymer melt can be acquired by simultaneously solving the aforementioned equations using Polyflow.
2.2.4 Crystallization kinetics equation
The calculated data are combined with the crystallization energy equation (31), the crystallization energy equation is given by
where
The crystallization rate is defined as follows:
The upper form ignores the dissipative terms and can be expressed as follows:
If the thermal conductivity k depends only on the temperature and is independent of the degree of transformation X, then
where
where
In Polyflow, it can be simplified to
Ignoring the effects of unstable states and secondary crystallization, the Ziabicki method (32) was chosen. The rate constant, which varies with temperature, was thus similar to the Gauss curve (33), and can be described as follows:
where K max is the maximum crystallization rate at T max; and W is the crystallization half-width.
The degree of crystallization at any time was represented by X(t), the empirical equation for crystallization (34) can be written as follows:
where X(t) is the crystallinity at different times; X
∞
is the final crystallinity; and T
max is the maximum rate temperature; T is the temperature; T
m is the melting temperature; K
max is the maximum crystallization rate at T
max; C is the stress-induced X(t) coefficient; ∆d
i is the amorphous intrinsic birefringence;
2.3 Boundary condition
Volume flow rate at melt inlet, Q = 1.13 × 10−4 m3·s−1, melt temperature, gas temperature, and mold temperature were set to 533 K. Using formula (6), the heat flow condition was applied as it is related to the heat exchange on the melt’s free surface.
In conventional extrusion, no-slip boundary conditions were adopted between the melt and die wall, i.e., V n = V s = 0.
When gas-assisted, the interface is used for melt and gas parts, and a no-slip boundary condition was used between the gas and die wall.
The upwind surface approach was employed to maintain the computation’s convergence while the free surface was set to the free surface and specified at both its entrance and exit. At the exit position, a traction velocity was applied to the melt end, V z = 5 m·s−1 and shear speed was set as V s = 0.
2.4 Physical parameter
The polymer material used was polyamide (Nylon 6 or PA6). The density is 1.15 × 103 kg·m−3. When numerical simulation, the gas layer is considered to be an incompressible Newton fluid during gas-assisted forming. Polymer melt data are shown in Table 1. The relaxation time is asymptotic function f(s) = s, from 0.02 to 1.
Material parameters
Material | PA6 |
---|---|
Melting point (℃) | 215–225 |
Melt flow index (g·10 min−1) | 2.8 |
|
750 |
ξ | 0 |
s | 0.25 |
ε | 0.2 |
K (W·m−1·K−1) | 0.2 |
ϕ ∞ | 0.45 |
K max (s−1) | 0.14 |
λ(s) | 0.02–1 |
W (K) | 46 |
T max (K) | 419 |
C | 225 |
Cop (m2·N−1) | 1.2 × 10−9 |
∆di | 8.25 × 10−2 |
|
1.88406 × 105 |
2.5 Numerical method
The EVSS Algorithm, Progressive Algorithm, Upwinding in the Kinetic Equation, Linear interpolation, and grid resetting were employed in the numerical calculation. UDF module was used to write the program and import it into Polyflow for numerical calculations.
Sections of UDF programs are as follows:
;-----------------------
; This is a polynomial function with 1 argument
(deffunction Heat_Transfer_Coefficient (?Vz)
(bind ?HTC(* 2.507 (** ?Vz 0.287))
;-----------------------
3 Result analysis and discussion
The model was created, and imported into the Polyflow software, and the necessary boundary conditions and numerical calculations were made. The axis L1(0,0) (0,0.08) and the free interface boundary L2 were extracted to investigate the extrusion velocity, pressure, temperature, first normal stress, and crystallization in the radial and axial directions during the extrusion process. At the same time, parallel to the radial axis, straight lines H1, H2, H3, H4, H5, H6, and H7 were created on the melt. Its relative axial coordinates are 0, 0.007, 0.014, 0.02, 0.04, 0.06, and 0.08, with units of m (Figure 2).

The distribution of the lines created. (a) Conventional extrusion and (b) gas-assisted extrusion.
3.1 Vx analysis
Figure 3(a) displays the straight lines H1–H7’s Vx . The Vx in the die is moving in a positive direction during traditional extrusion. The Vx is closest to zero when the die is closer to the die wall. Outside the die, the Vx is negative. The absolute velocity increases as the die moves farther from the center line. The larger the Vx when the conventional extrusion is at the sample’s end, the closer the radial coordinates are to the free surface.

Vx distributions on different lines. (a) radial coordination and (b) axial coordination.
During the extrusion process in gas-assisted extrusion, the velocity direction on each line segment is headed in the opposite direction. At the opening of the die and the end of the extrusion sample, the absolute value of Vx will gradually decrease. The absolute velocity in the die drops but does not reach zero when the melt coordinates are close to the die wall. The absolute velocity increases with the die’s distance from the center line.
The sample’s Vx curve on the free surface and the center line are displayed in Figure 3(b). The Vx along the center line does not significantly vary. The Vx at the die exit and the Vx at the end of the sample are both zero on the free surface’s boundary line. In the middle stretch length, the Vx is negative.
According to Figure 3, conventional extrusion results in a more abrupt change in axial direction velocity than gas-assisted extrusion.
In the actual extrusion process, the larger the Vx , the more obvious the phenomenon of die swell. The above figure further shows that gas-assisted extrusion can partly eliminate the phenomenon of die swell. The sample deforms less or more uniformly after leaving the die, which is beneficial to the extrusion molding.
3.2 Vy analysis
Figure 4(a) depicts the velocity along the line H1–H7 that is straight in the axial direction. At the end of the sample, the Vy n is 5 m·s−1. Gas-assisted extrusion has a higher Vy outside the die than traditional extrusion. The velocity is uniform on the same cross section during gas-assisted extrusion. Due to the impact of wall friction during traditional extrusion, Vy is slightly reduced.

Vy distributions on different lines. (a) radial coordination and (b) axial coordination.
The Vy on the free interface’s center line L1 and boundary line L2 for the extruded sample is depicted in Figure 4(b). First off, in the gas-assisted extrusion process, the Vy at the center line L1 is higher than it is in the conventional extrusion process. The Vy in the gas-assisted extrusion procedure increases after the sample is extruded from the die. The center line’s Vy lowers initially before increasing in the traditional extrusion procedure. The Vy at the tensile point at the end of the sample is the same at the free interface’s boundary line. In some places, gas-assisted extrusion has a faster Vy than regular extrusion.
According to the findings, gas-assisted extrusion has a more steady velocity variation in the axial direction than the conventional extrusion.
The simulation results also reveal that the Vy extrusion speed changes tend to be stable if the gas-assisted technology is used in the actual processing. In traditional extrusion, turbulence or rapid velocity change may occur in the die. Because of the turbulence of the melt flow rate or the rapid change in internal stress, the sample is easily distorted or deformed after the extrusion die. Therefore, gas-assisted extrusion is also beneficial for reducing sample distortion or deformation after extrusion.
3.3 Shear rate analysis
Figure 5(a) displays the shear rates along the lines H1–H7. The shear rates of traditional extrusion and gas-assisted extrusion are comparable at the sample’s extrusion end. In terms of numbers, gas-assisted extrusion has a lower shear rate than conventional extrusion.

Shear rate distributions on different lines. (a) radial coordination and (b) axial coordination.
Figure 5(b) displays the shear rate along the extruded sample’s center line L1, as well as the free interface boundary line L2. The shear rate of gas-assisted extrusion first rises and then falls at the center line L1. The shear rate of the gas-assisted extrusion on the center line L1 increases after the sample is extruded out of the die and then gradually drops. In typical extrusion, the shear rate first falls, then rises quickly, before falling once more. In comparison to gas-assisted extrusion, traditional extrusion has a higher maximum shear rate. Conventional extrusion has a larger shear rate at the sample’s end than gas-assisted extrusion.
When the sample is freshly extruded from the die, the shear rate of conventional extrusion is larger than that of gas-assisted extrusion on the boundary line of the free interface L2. The shear rate then abruptly drops to the same value before steadily rising again. In traditional extrusion, the shear rate value fluctuates more violently. The shear rate of conventional extrusion is larger than that of gas-assisted extrusion near the sample’s end.
The simulation results show that the shear rate of gas-assisted extrusion is more stable. The shear rate is the ratio of the velocity difference to the height difference between the two liquid surfaces. It also means that the melt flow between layers is more smooth during gas-assisted extrusion. Turbulence is less likely. The possibility of extrusion sample distortion or deformation is less.
3.4 Pressure analysis
In Figure 6(a), the pressure on lines H1–H7 is depicted. When using a typical extruder, the pressure inside the die is positive and drops as the die approaches the exit. Gas-assisted extrusion molding has low mold pressure. For both conventional and gas-assisted extrusion, the pressure values outside the die are negative. At the H5 line at the exit, the pressure will suddenly change in proximity to the free surface. The peak pressure occurs at the end of the sample. Conventional extrusion has a higher pressure absolute value than gas-assisted extrusion.

Pressure distributions on different lines. (a) radial coordination and (b) axial coordination.
Figure 6(b) displays the pressure change on the extruded sample’s center line L1 and free interface boundary line L2. The pressure drops on the L1 center line. In traditional extrusion, the pressure is positive to a maximum near the entrance. The pressure value is the highest negative value at the specimen’s end. The sample is under negative pressure during gas-assisted extrusion.
The pressure of conventional extrusion and gas-assisted extrusion are both negative on the boundary line of the free interface L2. The pressure is highest near the center line at the die exit. The center line and free surface’s pressures are similar and the change pattern is the same throughout the intermediate tension stage. The specimen’s end is around 10 mm from where the pressure abruptly shifts. The pressure of traditional extrusion is significantly higher than that of gas-assisted extrusion at the specimen’s end.
As shown in Figure 6, the extruded sample’s pressure changes in the Y direction with the help of gas in a relatively smooth manner.
The simulation results show that the pressure of gas-assisted extrusion is stable in the actual forming process. The whole process impact force is relatively small, conducive to noise reduction. It makes the processing environment more user-friendly.
3.5 First normal stress analysis
The first normal stress variation on the straight lines H1–H7 is shown in Figure 7(a). The first normal stress in traditional extrusion will abruptly alter when the melt is approximately 2 mm from the die wall and axial coordination is 7 mm into the die. The first normal stress of conventional extrusion is comparable to that of gas-assisted extrusion at the specimen’s end. Positive stress comes after a period of initial negative stress. The initial normal stress rises to the positive maximum after decreasing from the negative maximum to zero. The range of variation for conventional extrusion is wider.

First normal stress distributions on different lines. (a) radial coordination and (b) axial coordination.
In Figure 7(b), the initial normal stress fluctuation on the extruded sample’s center line L1 and free interface boundary line L2 is depicted. The first normal stress of the free surface of the conventional extrusion is higher than that of the gas-assisted extrusion when the sample has just been extruded from the die. The first normal stress of the free surface then gradually reduces, while the first normal stress of the free surface of the gas-assisted extrusion gradually increases. The two numbers are equal at the exit, which is around 5 mm. The first normal stress direction abruptly shifts at the exit at approximately 10 and 70 mm. All first normal stresses reach their maximum at the end of the specimen. In comparison to gas-assisted extrusion, the absolute value of the first normal stress in conventional extrusion is higher.
The first normal stress of the traditional extrusion steadily increases after the sample is extruded from the die, decreasing initially until it reaches the maximum negative value. The initial typical gas-assisted extrusion stress develops quickly at first, then gradually. The conventional extrusion’s first normal stress is higher than that of the gas-assisted extrusion at the sample’s conclusion. At this point, both are positive.
The first normal stress of gas-assisted extrusion is more stable. The magnitude of the first normal stress has a great influence on the extrusion swell and the stability of the extrusion surface. The results also show that gas-assisted extrusion is beneficial in reducing the die swell. And it is beneficial to improve the surface quality of the extruded sample.
3.6 Crystallization analysis
Figure 8(a) depicts the shift in crystallization along the lines H1–H7. The change in crystallization is smaller in the die when it is closer to the center line. The crystallinity increases as the die wall approaches. Near the die exit, such as H3, it is more evident. Conventional extrusion and gas-assisted extrusion exhibit similar crystallization changes at the sample’s conclusion. Compared to gas-assisted extrusion, conventional extrusion has a higher crystallinity.

Crystallization distributions on different lines. (a) radial coordination and (b) axial coordination.
Figure 8(a) depicts the extruded sample’s change in crystallization along the center line L1 and the free interface boundary line L2. When compared to gas-assisted extrusion, conventional extrusion’s crystallization value on the center line does not differ significantly. At the end of the sample, there are not many changes. The crystallinity value of conventional extrusion is somewhat higher than that of gas-assisted extrusion when axial coordination is 70mm and when the crystallinity value approached and then abruptly increased.
The crystallization of polymer has an obvious influence on its mechanical properties, density, optical properties, and thermal properties. The increase in crystallinity is beneficial to the increase in tensile strength, but the tensile ratio and impact strength tend to decrease. Generally, the crystallinity of crystalline polymers is low, and the transparency will increase. Through the simulation, we found that the crystallinity of the extruded sample can be predicted during the extrusion process. On this basis, we can predict the mechanical and optical properties of the extruded sample.
4 Conclusion
The conclusions are listed below. During the extrusion process, the gas-assisted extrusion technology has various effects on the radial and axial velocity, shear rate, pressure, temperature, first normal stress, and crystallization. Die swell can be successfully avoided in gas-assisted extrusion by reducing or even negative X direction velocity. In comparison to traditional extrusion, the velocity variation in the Y direction is also more steady. The die wall has a lesser impact on the melt flow velocity close to it. The die wall has a significant impact on the shear rate in the die. The die wall has a significant impact on the shear rate in the die. However, compared to gas-assisted extrusion, conventional extrusion has a substantially higher maximum shear rate. Gas-assisted extrusion has a narrow shear rate range. The transition is fairly seamless. Only at the input and the end does the pressure of gas-assisted extrusion vary significantly. There is a seamless transition in the middle segment. In traditional extrusion, the pressure difference is more noticeable. The sample’s temperature drops less during gas-assisted extrusion than during conventional extrusion. The temperature drop increases with distance from the die and center line. The first normal stress into and out of the die varies significantly between gas-assisted extrusion and traditional extrusion. The first normal stress in conventional extrusion diminishes increasing proximity to the die wall. Die walls have a negligible impact on gas-assisted extrusion. In gas-assisted extrusion, the first normal stress fluctuation range is more constrained and stable. The change in crystallization is smaller in the die when it is closer to the center line. During gas-assisted extrusion, the die’s crystallinity does not change significantly. At the die exits, only the crystallization close to the die wall will intensify. The crystallinity value of conventional extrusion is higher than that of gas-assisted extrusion at the sample’s conclusion.
In general, the Vx in gas-assisted extrusion tends to decrease, and the variation in Vy , pressure, and first normal stress tends to be stable. All these changes are beneficial to the extrusion process, the reduction in die swell, the reduction in distortion, and the surface quality of the sample after extrusion. It can partly predict the mechanical and optical properties of samples after extrusion. In the later stage, if the process parameters such as die, gas and melt temperature, gas pressure, and flow rate are changed, it may be clearer for the microanalysis of the crystallization of the extruded sample.
Acknowledgements
The authors would like to express their gratitude to EditSprings (https://www.editsprings.cn) for the expert linguistic services provided.
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Funding information: This study was financially supported by the Natural Science Foundation of China (Grant nos 21664002 and 51863014), the Industrial Field of Science and Technology Department of Jiangxi Province (Grant no. 20203BBE53065).
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Author contributions: Xuemei Huang: synthesis, methodology, data procuration, and writing – first draft, and manuscript handling; Hesheng Liu: formal analysis and project administration; Xingyuan Huang: formal analysis and project administration; Yibin Huang and Zhong Yu: methodology and formal analysis.
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Conflict of interest: The authors declare no conflicts of interest regarding this article.
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Data availability statement: All data generated or analyzed during this study are included in this published article and its supplementary files.
References
(1) Liu HS, Tu ZG, Xiong HH. Design of rubber and plastics profile extrusion dies according to the uniformity of flow rate. J Plast Eng. 2000;7(1):76–8.Search in Google Scholar
(2) Wang LX, Shen CY, Chen JB, Liu CT. Simulation of flow in profile extrusion die. China Plastics. 1996;7(10):56–62. 10.01.9278.1996.04.011.Search in Google Scholar
(3) Wang LX, Chen JB, Liu CT. Calculation of pressure drop in extrusion die for plastic profile. Mech Eng. 1998;4(20):17–9.Search in Google Scholar
(4) Brzoskowski R, White JL, Szydlowski W, Weissert FC, Nakajima N, Min K. Air-lubricated die for extrusion of rubber compound. Rubber Chem Tech. 1987;60(5):945–56.10.5254/1.3536166Search in Google Scholar
(5) Liang RF, Mackley MR. The gas-assisted extrusion of molten polyethylene. J Rheol. 2001;45(1):211–26.10.1122/1.1332786Search in Google Scholar
(6) Xu L, Liu HS, Huang XY, Huang YB. Inverse numerical simulation of T-shape dies for the extrusion of plastics profiles. China Plastics. 2010;24(1):103–6.Search in Google Scholar
(7) Liu HS, He JT, Huang XY, Deng XZ, Wan QF. Numerical simulation and experimental validation of die swell and deformation in L-shaped profile gas-assisted coextrusion. Ploym Mater Sci Eng. 2014;30(10):113–6.Search in Google Scholar
(8) He JT. Numerical simulation and experimental study on plastic profile gas-assisted coextrusion. Master’s thesis. Jiangxi, Nanchang: Nanchang University; 2014.Search in Google Scholar
(9) Huang XM, Liu HS, Huang XY, Huang YB, Yu Z, Jiang SY. Effects of opening arm length of U-shaped part and melt inlet flow rate on extrusion molding at its corner. Eng Plastics Appl. 2022;50(4):58–64.Search in Google Scholar
(10) Ren Z, Huang XY, Liu HS, Deng XZ, He JT. Numerical and experimental studies for gas assisted extrusion forming of molten polypropylene. J Appl Polym Sci. 2015;132(42):12365–77.10.1002/app.42682Search in Google Scholar
(11) Ren Z, Huang XY, Liu HS. Experiment and mechanism analysis of gas-assisted extrusion forming for plastic micro-tube. Materials Reports. 2020;34:20193–8.Search in Google Scholar
(12) Ren Z, Huang XY, Xiong ZH. Experimental and numerical studies for the gas-assisted extrusion forming of polypropylene micro-tube. Int J Mater Form. 2020;13:235–56.10.1007/s12289-019-01482-7Search in Google Scholar
(13) Luo C, Huang XY, Liu TK, Liu HS. Research on inner gas inflation improvements in double-layer gas-assisted extrusion of micro-tubes. Polymers. 2020;12(4):899.10.3390/polym12040899Search in Google Scholar PubMed PubMed Central
(14) Liu TK, Huang XY, Luo C, Wang DY. The formation mechanism of the double gas layer in gas-assisted extrusion and its influence on plastic micro-tube formation. Polymers. 2020;12(2):355.10.3390/polym12020355Search in Google Scholar PubMed PubMed Central
(15) Li J, Huang Q, Li X. Relationship between mechanical properties of PGLA fiber and crystallinity and orientation. Chem Fib Text Tech. 2010;39(1):1–4.Search in Google Scholar
(16) Qiu XT, Gao Y, Wang XL, Gu AQ, Yu ZL. Effects of carbon fiber length and orientation on the tribological properties of polyether ether ketone based composites. Tribology. 2020;40(2):240–51.Search in Google Scholar
(17) Wu ZB, Jin C, Wang LZ. Effects from fiber orientations of bovine pericardium on its compression performance. J Medi Biom. 2019;34(1):21–6.Search in Google Scholar
(18) Wang ZZ, Fan WC, Qu BJ. Combution characteristics of Mg(OH)2 flame retardant polyethylene using expandable graphite as synergist. China Synth Resin Plastucs. 2000;17(5):19–25.Search in Google Scholar
(19) Yan SD, Duan FL. Microscopic deformation mechanisms of semicrystalline and amorphous polymer. Ploy Mater Sci Eng. 2014;3(30):100–4.Search in Google Scholar
(20) Duan FL, Jin YK, Yan SD. Microstructure evolution during tension deformation of semi-crystalline polymer. Chin J Theo Appl Mech. 2016;48(3):60–377.Search in Google Scholar
(21) McHugh AJ, Doufas AK. Modeling flow-induced crystallization in fiber spinning. Composites. 2001;32:1059–106.10.1016/S1359-835X(00)00170-6Search in Google Scholar
(22) Doufas AK, McHuag AJ, Miller C. Simulation of melt spinning including flow-induced crystallization. Part Ⅰ. Model development and predictions. J Non-Newton Fluid Mech. 2000;92:27–66.10.1016/S0377-0257(00)00088-4Search in Google Scholar
(23) Schawe Jü, Rgen EK. Identification of three groups of polymers regarding their non-isothermal crystallization kinetics. Polymer. 2019;167:167–75. 10.1016/j.polymer.2019.02.011.Search in Google Scholar
(24) Doufas AK, McHuag AJ, Miller C, Immaneni A. Simulation of melt spinning including flow-induced crystallization. Part Ⅱ. Quantitative comparisons with industrial spinline data. J Non-Newton Fluid Mesh. 2000;92:81–103.10.1016/S0377-0257(00)00089-6Search in Google Scholar
(25) Liang JZ. A study of the flow properties and crystallization behaviour of HDPE melt during extrusion. China Synt Resin Plastucs. 1994;11(3):37–41.Search in Google Scholar
(26) Xu RJ. The polymer crystallization in extrusion-cast field and annealing process study. Ph.D.Thesis. Guangdong, Guangzhou: Guangdong University of Technology; 2015.Search in Google Scholar
(27) Cosden IA, Lukes JR. Coding coarse grained polymer model for LAMMPS and its application to polymer crystallization. Comput Phys Commun. 2013;184:1958–65.Search in Google Scholar
(28) Ferrás LL, Afonso AM, Alves MA, Nóbrega JM, Pinho FT. Annular flow of viscoelastic fluids: Analytical and numerical solutions. J Non-Newton Fluid Mech. 2014;212:80–91.10.1016/j.jnnfm.2014.07.004Search in Google Scholar
(29) Liang ZJ. Elongation rheology of polymer fluids. Guangzhou: East China University of Science and Technology Press: 2015.Search in Google Scholar
(30) Patel RM, Bheda JH, Spruiell JE. Dynamics and structure development during highspeed melt spinning of nylon 6. II. Mathematical modeling. J Appl Polym Sci. 1991;42:1671.10.1002/app.1991.070420622Search in Google Scholar
(31) Ozawa T. Kinetics of non-isothermal crystallization. Polymer. 1971;12(1):150–8.Search in Google Scholar
(32) Ziabicki A, Jarecki L. High-speed Fiber Spinning. In: Ziabicki A, Kawai H, (Eds.). New York: Wiley/Interscience; 1985.Search in Google Scholar
(33) Xue XF, Zhang HF. Non-isohtermal crystallization kinetics of polyvinyl alcohol/polyvinylpyrrolidone blends. Func Poly. 1993;2(6):150–6.Search in Google Scholar
(34) Ozawa T. Kinetics of non-isothermal crystallization. Polymer. 1971;12(1):150–8.10.1016/0032-3861(71)90041-3Search in Google Scholar
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- Preparation of itaconic acid-modified epoxy resins and comparative study on the properties of it and epoxy acrylates
- Synthesis and properties of novel degradable polyglycolide-based polyurethanes
- Fatigue life prediction method of carbon fiber-reinforced composites
- Thermal, morphological, and structural characterization of starch-based bio-polymers for melt spinnability
- Robust biaxially stretchable polylactic acid films based on the highly oriented chain network and “nano-walls” containing zinc phenylphosphonate and calcium sulfate whisker: Superior mechanical, barrier, and optical properties
- ARGET ATRP of styrene with low catalyst usage in bio-based solvent γ-valerolactone
- New PMMA-InP/ZnS nanohybrid coatings for improving the performance of c-Si photovoltaic cells
- Impacts of the calcinated clay on structure and gamma-ray shielding capacity of epoxy-based composites
- Preparation of cardanol-based curing agent for underwater drainage pipeline repairs
- Preparation of lightweight PBS foams with high ductility and impact toughness by foam injection molding
- Gamma-ray shielding investigation of nano- and microstructures of SnO on polyester resin composites: Experimental and theoretical study
- Experimental study on impact and flexural behaviors of CFRP/aluminum-honeycomb sandwich panel
- Normal-hexane treatment on PET-based waste fiber depolymerization process
- Effect of tannic acid chelating treatment on thermo-oxidative aging property of natural rubber
- Design, synthesis, and characterization of novel copolymer gel particles for water-plugging applications
- Influence of 1,1′-Azobis(cyclohexanezonitrile) on the thermo-oxidative aging performance of diolefin elastomers
- Characteristics of cellulose nanofibril films prepared by liquid- and gas-phase esterification processes
- Investigation on the biaxial stretching deformation mechanism of PA6 film based on finite element method
- Simultaneous effects of temperature and backbone length on static and dynamic properties of high-density polyethylene-1-butene copolymer melt: Equilibrium molecular dynamics approach
- Research on microscopic structure–activity relationship of AP particle–matrix interface in HTPB propellant
- Three-layered films enable efficient passive radiation cooling of buildings
- Electrospun nanofibers membranes of La(OH)3/PAN as a versatile adsorbent for fluoride remediation: Performance and mechanisms
- Preparation and characterization of biodegradable polyester fibers enhanced with antibacterial and antiviral organic composites
- Preparation of hydrophobic silicone rubber composite insulators and the research of anti-aging performance
- Surface modification of sepiolite and its application in one-component silicone potting adhesive
- Study on hydrophobicity and aging characteristics of epoxy resin modified with nano-MgO
- Optimization of baffle’s height in an asymmetric twin-screw extruder using the response surface model
- Effect of surface treatment of nickel-coated graphite on conductive rubber
- Experimental investigation on low-velocity impact and compression after impact behaviors of GFRP laminates with steel mesh reinforced
- Development and characterization of acetylated and acetylated surface-modified tapioca starches as a carrier material for linalool
- Investigation of the compaction density of electromagnetic moulding of poly(ether-ketone-ketone) polymer powder
- Experimental investigation on low-velocity-impact and post-impact-tension behaviors of GFRP T-joints after hydrothermal aging
- The repeated low-velocity impact response and damage accumulation of shape memory alloy hybrid composite laminates
- Exploring a new method for high-performance TPSiV preparation through innovative Si–H/Pt curing system in VSR/TPU blends
- Large-scale production of highly responsive, stretchable, and conductive wrapped yarns for wearable strain sensors
- Preparation of natural raw rubber and silica/NR composites with low generation heat through aqueous silane flocculation
- Molecular dynamics simulation of the interaction between polybutylene terephthalate and A3 during thermal-oxidative aging
- Crashworthiness of GFRP/aluminum hybrid square tubes under quasi-static compression and single/repeated impact
- Review Articles
- Recent advancements in multinuclear early transition metal catalysts for olefin polymerization through cooperative effects
- Impact of ionic liquids on the thermal properties of polymer composites
- Recent progress in properties and application of antibacterial food packaging materials based on polyvinyl alcohol
- Additive manufacturing (3D printing) technologies for fiber-reinforced polymer composite materials: A review on fabrication methods and process parameters
- Rapid Communication
- Design, synthesis, characterization, and adsorption capacities of novel superabsorbent polymers derived from poly (potato starch xanthate-graft-acrylamide)
- Special Issue: Biodegradable and bio-based polymers: Green approaches (Guest Editors: Kumaran Subramanian, A. Wilson Santhosh Kumar, and Venkatajothi Ramarao)
- Development of smart core–shell nanoparticles-based sensors for diagnostics of salivary alpha-amylase in biomedical and forensics
- Thermoplastic-polymer matrix composite of banana/betel nut husk fiber reinforcement: Physico-mechanical properties evaluation
- Special Issue: Electrospun Functional Materials
- Electrospun polyacrylonitrile/regenerated cellulose/citral nanofibers as active food packagings
Articles in the same Issue
- Research Articles
- Flame-retardant thermoelectric responsive coating based on poly(3,4-ethylenedioxythiphene) modified metal–organic frameworks
- Highly stretchable, durable, and reversibly thermochromic wrapped yarns induced by Joule heating: With an emphasis on parametric study of elastane drafts
- Molecular dynamics simulation and experimental study on the mechanical properties of PET nanocomposites filled with CaCO3, SiO2, and POE-g-GMA
- Multifunctional hydrogel based on silk fibroin/thermosensitive polymers supporting implant biomaterials in osteomyelitis
- Marine antifouling coating based on fluorescent-modified poly(ethylene-co-tetrafluoroethylene) resin
- Preparation and application of profiled luminescent polyester fiber with reversible photochromism materials
- Determination of pesticide residue in soil samples by molecularly imprinted solid-phase extraction method
- The die swell eliminating mechanism of hot air assisted 3D printing of GF/PP and its influence on the product performance
- Rheological behavior of particle-filled polymer suspensions and its influence on surface structure of the coated electrodes
- The effects of property variation on the dripping behaviour of polymers during UL94 test simulated by particle finite element method
- Experimental evaluation on compression-after-impact behavior of perforated sandwich panel comprised of foam core and glass fiber reinforced epoxy hybrid facesheets
- Synthesis, characterization and evaluation of a pH-responsive molecular imprinted polymer for Matrine as an intelligent drug delivery system
- Twist-related parametric optimization of Joule heating-triggered highly stretchable thermochromic wrapped yarns using technique for order preference by similarity to ideal solution
- Comparative analysis of flow factors and crystallinity in conventional extrusion and gas-assisted extrusion
- Simulation approach to study kinetic heterogeneity of gadolinium catalytic system in the 1,4-cis-polyisoprene production
- Properties of kenaf fiber-reinforced polyamide 6 composites
- Cellulose acetate filter rods tuned by surface engineering modification for typical smoke components adsorption
- A blue fluorescent waterborne polyurethane-based Zn(ii) complex with antibacterial activity
- Experimental investigation on damage mechanism of GFRP laminates embedded with/without steel wire mesh under low-velocity-impact and post-impact tensile loading
- Preparation and application research of composites with low vacuum outgassing and excellent electromagnetic sealing performance
- Assessing the recycling potential of thermosetting polymer waste in high-density polyethylene composites for safety helmet applications
- Mesoscale mechanics investigation of multi-component solid propellant systems
- Preparation of HTV silicone rubber with hydrophobic–uvioresistant composite coating and the aging research
- Experimental investigation on tensile behavior of CFRP bolted joints subjected to hydrothermal aging
- Structure and transition behavior of crosslinked poly(2-(2-methoxyethoxy) ethylmethacrylate-co-(ethyleneglycol) methacrylate) gel film on cellulosic-based flat substrate
- Mechanical properties and thermal stability of high-temperature (cooking temperature)-resistant PP/HDPE/POE composites
- Preparation of itaconic acid-modified epoxy resins and comparative study on the properties of it and epoxy acrylates
- Synthesis and properties of novel degradable polyglycolide-based polyurethanes
- Fatigue life prediction method of carbon fiber-reinforced composites
- Thermal, morphological, and structural characterization of starch-based bio-polymers for melt spinnability
- Robust biaxially stretchable polylactic acid films based on the highly oriented chain network and “nano-walls” containing zinc phenylphosphonate and calcium sulfate whisker: Superior mechanical, barrier, and optical properties
- ARGET ATRP of styrene with low catalyst usage in bio-based solvent γ-valerolactone
- New PMMA-InP/ZnS nanohybrid coatings for improving the performance of c-Si photovoltaic cells
- Impacts of the calcinated clay on structure and gamma-ray shielding capacity of epoxy-based composites
- Preparation of cardanol-based curing agent for underwater drainage pipeline repairs
- Preparation of lightweight PBS foams with high ductility and impact toughness by foam injection molding
- Gamma-ray shielding investigation of nano- and microstructures of SnO on polyester resin composites: Experimental and theoretical study
- Experimental study on impact and flexural behaviors of CFRP/aluminum-honeycomb sandwich panel
- Normal-hexane treatment on PET-based waste fiber depolymerization process
- Effect of tannic acid chelating treatment on thermo-oxidative aging property of natural rubber
- Design, synthesis, and characterization of novel copolymer gel particles for water-plugging applications
- Influence of 1,1′-Azobis(cyclohexanezonitrile) on the thermo-oxidative aging performance of diolefin elastomers
- Characteristics of cellulose nanofibril films prepared by liquid- and gas-phase esterification processes
- Investigation on the biaxial stretching deformation mechanism of PA6 film based on finite element method
- Simultaneous effects of temperature and backbone length on static and dynamic properties of high-density polyethylene-1-butene copolymer melt: Equilibrium molecular dynamics approach
- Research on microscopic structure–activity relationship of AP particle–matrix interface in HTPB propellant
- Three-layered films enable efficient passive radiation cooling of buildings
- Electrospun nanofibers membranes of La(OH)3/PAN as a versatile adsorbent for fluoride remediation: Performance and mechanisms
- Preparation and characterization of biodegradable polyester fibers enhanced with antibacterial and antiviral organic composites
- Preparation of hydrophobic silicone rubber composite insulators and the research of anti-aging performance
- Surface modification of sepiolite and its application in one-component silicone potting adhesive
- Study on hydrophobicity and aging characteristics of epoxy resin modified with nano-MgO
- Optimization of baffle’s height in an asymmetric twin-screw extruder using the response surface model
- Effect of surface treatment of nickel-coated graphite on conductive rubber
- Experimental investigation on low-velocity impact and compression after impact behaviors of GFRP laminates with steel mesh reinforced
- Development and characterization of acetylated and acetylated surface-modified tapioca starches as a carrier material for linalool
- Investigation of the compaction density of electromagnetic moulding of poly(ether-ketone-ketone) polymer powder
- Experimental investigation on low-velocity-impact and post-impact-tension behaviors of GFRP T-joints after hydrothermal aging
- The repeated low-velocity impact response and damage accumulation of shape memory alloy hybrid composite laminates
- Exploring a new method for high-performance TPSiV preparation through innovative Si–H/Pt curing system in VSR/TPU blends
- Large-scale production of highly responsive, stretchable, and conductive wrapped yarns for wearable strain sensors
- Preparation of natural raw rubber and silica/NR composites with low generation heat through aqueous silane flocculation
- Molecular dynamics simulation of the interaction between polybutylene terephthalate and A3 during thermal-oxidative aging
- Crashworthiness of GFRP/aluminum hybrid square tubes under quasi-static compression and single/repeated impact
- Review Articles
- Recent advancements in multinuclear early transition metal catalysts for olefin polymerization through cooperative effects
- Impact of ionic liquids on the thermal properties of polymer composites
- Recent progress in properties and application of antibacterial food packaging materials based on polyvinyl alcohol
- Additive manufacturing (3D printing) technologies for fiber-reinforced polymer composite materials: A review on fabrication methods and process parameters
- Rapid Communication
- Design, synthesis, characterization, and adsorption capacities of novel superabsorbent polymers derived from poly (potato starch xanthate-graft-acrylamide)
- Special Issue: Biodegradable and bio-based polymers: Green approaches (Guest Editors: Kumaran Subramanian, A. Wilson Santhosh Kumar, and Venkatajothi Ramarao)
- Development of smart core–shell nanoparticles-based sensors for diagnostics of salivary alpha-amylase in biomedical and forensics
- Thermoplastic-polymer matrix composite of banana/betel nut husk fiber reinforcement: Physico-mechanical properties evaluation
- Special Issue: Electrospun Functional Materials
- Electrospun polyacrylonitrile/regenerated cellulose/citral nanofibers as active food packagings