高分子材料动态成型过程中熔体非线性行为的研究

借助流变测量和连续介质理论,不依赖已有的本构关系,对平行叠加正弦振动条件下高分子熔体经毛细管的动态挤出过程进行了理论分析。以低密度聚乙烯(LDPE)为原材料,实验测量LDPE熔体在一定振动频率和振幅下毛细管入口压力、体积流量和挤出胀大的瞬态值,即可得到动态成型过程中高分子熔体剪切应力、剪切速率和表观粘度的变化规律:随振幅和频率的变化,LDPE熔体的表观粘度呈非线性变化趋势;在不同的振幅和频率下动态挤出LDPE熔体,跟稳态挤出时一样,壁面剪切应力与壁面剪切速率也成非线性比例关系。     

Mathematical model of shear rate of polymer melt dynamic extruding through capillary

With superimposing a sine vibration of displacement on the extruding direction of a polymer melt, the characterization formula of the shear rate of a polymer melt within a capillary was set up. By making use of the experimental equipment of a constant velocity type dynamic rheometer of capillary (CVDRC) designed by the authors, the calculating steps of the shear rate of the polymer melt at the wall of the capillary under a vibration force field were established. Through measuring and analyzing the instantaneous data of capillary entry pressure, capillary volume rate, and their phase‐difference under the superimposed vibration, the polymer melt's shear rate at the wall of the capillary can thus be calculated. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 95: 1056–1061, 2005     

Rheological equation for polymer melt under the action of vibration

Abstract

The entire extrusion process of a polymer melt within a capillary was analyzed thoroughly when a sinusoidal vibration of small amplitude was superimposed in parallel on the flow direction of the polymer melt. On the basis of rheological measurement, an equation for a polymer melt under parallel vibration, i.e. the apparent viscosity, was obtained. Calculation of the apparent viscosity was established by making use of novel experimental equipment. After collecting and analyzing the instantaneous data of capillary entry pressure, capillary volume flux and their phase difference in a superimposed vibration, the apparent viscosity of low-density polyethylene (LDPE) within a capillary was calculated. Meanwhile, the relationship of shear stress vs. shear rate for a LDPE melt with and without imposed vibration was presented.     

Correlation between entry pressure losses and elongation viscosity of polyethylene melts

The correlation between the entry pressure drop and elongation viscosity during entry converging flow of polymer melts was discussed in this article. The entry pressure drop during extrusion of a low density polyethylene (LDPE) melt and a linear low density polyethylene (LLDPE) melt was measured by means of a capillary rheometer under test conditions with temperature of 170 °C and shear rate varying from 10 to 300 s⁻¹. The results showed that the entry pressure drop increased nonlinearly with an increase of the shear stain rate, and the variation of entry pressure drop of the two melts was close to each other. The melt elongation viscosity of the two resins was estimated using Cogswell equation from the measured entry pressure drop data, and the predictions were compared with the melt extension viscosity measured by using a melt spinning technique published in literature. It was found that the melt extension viscosity from entry converging flow was slightly lower than that from melt spinning technique under the same temperature and extension strain rate.     

Effects of extrusion conditions on rheological behavior of acrylonitrile–butadiene–styrene terpolymer melt

The influence of temperatures and flow rates on the rheological behavior during extrusion of acrylonitrile–butadiene–styrene (ABS) terpolymer melt was investigated by using a Rosand capillary rheometer. It was found that the wall shear stress (τ_w) increased nonlinearly with increasing apparent shear rates and the slope of the curves changed suddenly at a shear rate of about 10³ s^?1, whereas the melt‐shear viscosity decreased quickly at a τ_w of about 200 kPa. When the temperature was fixed, the entry‐pressure drop and extensional stress increased nonlinearly with increasing τ_w, whereas it decreased with a rise of temperature at a constant level of τ_w. The relationship between the melt‐shear viscosity and temperature was consistent with an Arrhenius expression. The results showed that the effects of extrusion operation conditions on the rheological behavior of the ABS resin melt were significant and were attributable to the change of morphology of the rubber phase over a wide range of shear rates. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 606–611, 2002     

The effect of mixing on the modes of dispersion and rheological properties of two-phase polymer blends in extrusion

An experimental study was carried out to investigate the effect of mixing on the state of dispersion and rheological properties in the two-phase flow of polymer blends. For the study, blends of polystyrene and polypropylene were used, and two mixing devices were employed: a single-screw extruder combined with a “static mixer,” and a twin-screw compounding machine. Materials of various blending ratios were extruded at a constant temperature (200°C) through a capillary die having an L/D ratio of 20 (D = 0.125 in.). The state of dispersion in the two-phase system was investigated from pictures taken of the microstructure of the extrudate samples. It was found that different mixing devices have a profound influence on the state of dispersion of one polymer in another. Also determined were the rheological properties of the two-phase system investigated, from wall normal stress measurements. Our results show that, when shear stress is used as a parameter, the melt viscosity goes through a minimum, whereas the melt elasticity goes through a maximum. This is regardless of the type of mixing device employed, although the shapes of the curves are affected by the type employed. It is suggested that shear stress, instead of shear rate, be used in correlating the viscoelastic properties of two-phase polymer systems.     

Critcal stress and recoverable shear for polymer melt fracture

The phenomenon of extrudate distortion, which is called melt fracture, was studied for polystyrene samples of narrow and broad molecular weight distribution, and commerical samples of polypropylene and linear and branched polyethylene. It was experimentally found that the shear stress at the onset of melt fracture (τ_cr) is of the order of 10⁶ dynes/cm² and independent of the distribution of molecular weights. As the weight average molecular weight increases the shear stress τ_cr decreases. For polystyrene extruded at τ_cr the recoverable shear strain, which is defined to be half the ration (first normal stress difference/shear stress), was found proportional to the factor M _zM _z+1/M _w² which represents the distrubution of molecular weights. The proportionality is expected to hold for other polymer systems. The polymer behavior at the onset of melt fracture was explained in terms of Graessley's entanglement theory and his correlation between true and Rouse shear compliance.     

Melt flow behavior in capillary extrusion of nanosized calcium carbonate‐filled poly(L‐lactic acid) biocomposites

Nanosized calcium carbonate (nano‐CaCO₃)‐filled poly‐L ‐lactide (PLLA) biocomposites were compounded by using a twin‐screw extruder. The melt flow behavior of the composites, including their entry pressure drop, melt shear flow curves, and melt shear viscosity were measured through a capillary rheometer operated at a temperature range of 170–200°C and shear rates of 50–10³ s^?1. The entry pressure drop showed a nonlinear increase with increasing shear stress and reached a minimum for the filler weight fraction of 2% owing to the “bearing effect” of the nanometer particles in the polymer matrix melt. The melt shear flow roughly followed the power law, while the effect of temperature on the melt shear viscosity was estimated by using the Arrhenius equation. Hence, adding a small amount of nano‐CaCO₃ into the PLLA could improve the melt flow behavior of the composite. POLYM. ENG. SCI., 52:1839–1844, 2012. © 2012 Society of Plastics Engineers     

Rheological characterisation of hydroxyapatite filled polyethylene composites. Part 2 – Isothermal compressibility and wall slip

Abstract

Rheological characterisation of hydroxyapatite–high density polyethylene (HA–HDPE) composites has been performed in terms of isothermal compressibility and wall slip. Addition of HA to the polymer melt decreases the compressibility of the melt. The unfilled HDPE was found to exhibit wall slip at shear stresses as low as 0·10 MPa. The flow curves of the composites showed three distinct regions: a gradient at low shear rates; a plateau region; and a gradient at higher shear rate. An increase in rheometer pressure seems to suppress the slip in composites. The 40 vol.-% HA–HDPE composite exhibited two critical shear stresses, one corresponding to wall slip, which occurs in the lower shear rate region of the flow curve, and the other corresponding to a plateau, which is identified with the stick–slip behaviour of unfilled HDPE reported in the literature. The plateau shear stress increased with filler volume fraction and this effect is attributed to the decreased compressibility of the melt. A good correlation with a negative correlation coefficient was found to exist between compressibility and shear stress in the plateau region. The slip observed in unfilled HDPE and at low shear rates in the 40 vol.-% HA–HDPE systems has been explained in terms of a low molecular weight polymer layer formed at the melt/wall interface. The large interfacial slip observed in the plateau region is attributed to complete disentanglement of adsorbed chains from free chains at the melt/wall interface at and beyond the plateau region.     

Shear viscosity,extensional viscosity,and die swell of polypropylene in capillary flow with pressure dependency

The shear and extensional viscosities of a polypropylene resin were studied using a capillary rheometer and capillary dies of 1‐mm diameter and length of 10, 20, and 30 mm. Melt temperatures at 190, 205, and 220°C and shear rates between 100 and 5000 s^?1 were used. At the highest shear rate a visible melt fracture was observed. An equation relating the pressure drop and die length was derived with consideration of pressure effects on melt viscosities and the end effect. After the correction for pressure effects the true wall shear stress and end effect at zero pressure were calculated. The end effect showed a critical stress of melt fracture around 10⁵ Pa, and increased rapidly when shear stress increased above the critical stress. From shear stress the shear viscosity was calculated, and a power law behavior was observed. Extensional viscosity was calculated from the end effect and showed a decreasing trend when strain rate increased. After time–temperature superposition shift shear viscosity data correlated well, but an upward trend was observed in extensional viscosity when melt fracture occurred. Die swell ratio at different temperatures can be plotted as a function of wall shear stress and was higher for shorter dies. © 2002 Wiley Perioodicals, Inc. J Appl Polym Sci 84: 1269–1276, 2002; DOI 10.1002/app.10466     

聚合物振动挤出过程中熔体应力与应变关系的研究

在恒速型毛细管动态流变实验装置上对LDPE熔体进行动态挤出实验，在线测量了毛细管瞬时入口压力、柱塞杆振动位移、振动位移与毛细管入口压力波形的相位差；然后对上述动态流变数据进行时域分析和频域分析，分别得到振动力场下LDPE熔体的入口压力脉动量与体积流量脉动量之间的关系曲线、LDPE熔体在毛细管壁处剪切应力与剪切速率之间的关系曲线、以及入口压力脉动量与体积流量脉动量的比值随毛细管挤出流率Q的变化曲线。     

Unusual rheological behaviors of linear PE and PE/kaolin composite

The unusual flow behaviors of linear PE melts are caused by high molecular weight, tight entanglements of molecular chains, and strong adsorption of the melt at the capillary wall. Especially, the extreme change of interface adsorption is followed by an unusual flow, and at the molecular level, the dynamic variety of entanglement and disentanglement between the adsorption chain near the wall and the nonadsorption chain is the cause of the extrusion pressure vibration. Ultrahigh molecular weight polyethylene (UHMWPE)/kaolin composites prepared by polymerization filling could be smoothly extruded through the capillary. Also, with increase of the kaolin content, the apparent viscosity of the composite decreased and the processability was improved. Under slip boundary conditions, the real shear rate and shear stress of the melt near the capillary wall were reduced. The viscosity descent (desorption) and the deformation energy decrease of the melt near the wall were the important preconditions to gain a steady flow in a second glossy zone. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2154–2161, 2001     

Melt Flow Properties During Capillary Extrusion of Linear Low-Density Polyethylene

Abstract

The melt flow properties of a linear low-density polyethylene (LLDPE) were measured by means of a capillary rheometer under the experimental conditions of temperatures from 220° to 260°C and apparent shear rates varying from 12 to 120 s^?1. The end pressure drop (ΔP _end) was determined by employing the Bagley's plotting method. The results showed that ΔP _end increased nonlinearly with increasing shear stress. The end pressure fluctuation phenomenon was observed at lower shear stress level, and several plateau regions were generated in the end pressure drop-shear stress curves, suggesting onset of the wall-slip phenomenon during die extrusion of the resin melt. The critical shear stress with onset end pressure fluctuation phenomenon increased with a rise of temperature. Furthermore, the melt shear flow did not strictly obey the power law. The melt shear viscosity decreased nonlinearly with increasing shear stress and with a rise of temperature, whereas the dependence of the melt shear viscosity on the test temperature accorded with a formula similar to the Arrhenius expression.     

Wall slip and compressibility like effects in capillary rheometer tests on complex polymer systems

Abstract

Using an appropriate set of capillary dies, the applicability of the Mooney wall slip method has been investigated with several filled compounds. Inconsistent results were obtained, for example, ‘negative’ slip velocity. With respect to data measured in practical capillary rheometry, a model was developed for treating (barrel) pressure data versus die length/diameter ratio at fixed applied apparent shear rate, i.e. the so called Bagley plots. A very simple equation was obtained

P _meas = 2P _ends - 1/β ln [exp (P _ends β) - 4σ_w0 β L/D ]

which yields the wall shear stress at zero pressure σ_w0 , the ends pressure loss P _ends , and a factor β when fitted to experimental data by non-linear regression. Experimental results show that the factor β accounts for both wall slip and compressibility like effects. Negative β values indicate dominating wall slip effects, while positive values demonstrate compressibility like effects. Slip velocity is thus pressure dependent and consequently the combination of wall slip and a pressure dependent viscosity can mask the expected gap dependence in the analysis by Mooney.     

振动力场下聚合物熔体流变行为的响应与分析 Ⅰ.毛细管压力降和熔体表观粘度

在自行设计的恒速型毛细管动态流变装置上 ,对聚合物熔体进行动态挤出实验。借助已建立的振动力场下聚合物熔体流变行为的表征公式 ,分别计算振动力场下聚合物熔体在毛细管壁处的剪切应力、剪切速率和表观粘度。与稳态挤出时相比 ,引入振动力场后 ,发现毛细管压力降、表观粘度均显著降低 ,且随着振动频率和振幅的改变呈非线性变化趋势 ,作者对此进行了深入分析。     

The effect of shear on fusion and mechanical properties of rigid PVC pipes

The shear level was increased during twin screw extrusion of PVC at different melt temperatures by inserting a hole plate in front of the screw tips. The variation of shear level did not significantly affect the capillary pressure in capillary viscometry at 135°C. However, the falling weight impact strength was markedly influenced. In internal water pressure tests at 60°C premature failure was obtained for pipes extruded at 198°C at the highest shear level.     

Effect of process variables on melt velocity profiles in extrusion process using single screw plastics extruder

Abstract

Single screw extruders are used to generate a continuous flow of molten polymer in many industrial polymer processes. The melt velocity profile as extruded is important in determining the properties of the final product and influences process related phenomena such as die swell and the onset of sharkskin. The factors that influence the velocity profile would be expected to be the melt temperature (this affecting the viscosity of the melt), the screw and die geometry, and the output rate from the extruder. In the present work a thermocouple mesh sensor coupled with a cooled stainless tube has been used to determine velocity profiles in melts exiting from the screw of a single screw extruder. The results show that the technique can be used successfully to determine velocity profiles in the extrusion process.

It was found that the main influence on the magnitude of the melt velocity was the extruder screw speed. Melt temperature, and hence melt viscosity, were found to have little effect on the velocity profiles measured. The flow in the centre of the duct was retarded slightly owing to the flow across the screw tip and no rotational component of flow was observed. The velocity profiles measured seemed to be reasonably stable, only small changes being observed in the velocity profiles as the melt flowed along a duct of uniform cross-section, although these changes were limited in nature. Die diameter and length had a limited effect on the velocity profiles generated, although the die entry angle did have a significant effect on the shape of the velocity profile at higher screw speeds.     

Effects of convergent flow on in situ fibrillation of TLCP in PEN

A polymer melt entering a capillary die from a cylinder undergoes a convergent flow in which there is a complex combination of extensional and shear flows. The convergent flow plays an important role in controlling the in situ fibrillation of thermotropic liquid crystalline polymer (TLCP) in a thermoplastic matrix melt. This study examines effects of the convergent flow on development of TLCP fibrils in a TLCP/poly(ethylene naphthalate) (PEN) blend. A capillary rheometer was used and the extent of the convergent flow was varied by changing capillary dimension and shear rate. With a given capillary die, the TLCP fibrillation was found to increase with increasing shear rate because of the increased deformation of TLCP droplets. The establishment of a fully developed shear velocity profile by using a relatively long die is considered to be necessary to retain the TLCP fibrils initiated in the convergent flow region. At a given high shear rate, TLCP fibrillation improves with increasing capillary diameter (≤2 mm) because of the increased difference in velocity between the capillary and the cylinder. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1505–1513, 2004     

Superimposed effects in high‐shear‐rate capillary rheology of polystyrene melt

During micro‐injection molding, the polymer melt may undergo a shear rate up to 10⁶ s^?1, at which the rheological behaviors are obviously different from those in conventional molding process. Using both online and commercial rheometers, high‐shear‐rate capillary rheology of polystyrene (PS) melt is analyzed systematically in this work. The accurate end pressure drop and pressure coefficient of viscosity are determined via the enhanced exit pressure technique. Experimental and theoretical investigations are conducted on four significant effects, that is, the dissipative heating, end pressure loss, pressure dependence, and melt compressibility in capillary flow. For the PS melt, which exhibits distinct temperature and pressure dependence of viscosity, both dissipation and end effects become pronounced as the shear rate exceeds 2 × 10⁵ s^?1. From lower to higher shear rates (10³–10⁶ s^?1), the competition between dissipation and pressure effects results in the overestimation to underestimation of Bagley‐corrected pressure drop, and finally the comprehensively corrected viscosity becomes about half of the uncorrected one owing to the enhanced superimposed effects. Moreover, the compressibility shows a minor influence on the shear viscosity. Under the shear rate range investigated, the power‐law relationship is sufficient for describing the corrected viscosity curve of PS melt used. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

A study of bubble nucleation in a mixture of molten polymer and volatile liquid in a shear flow field

Bubble nucleation in a mixture of volatile liquid and polymer melt under shear flow conditions was investigated, using a light scattering technique. In the study, a mixture of polystyrene and trichlorofluoromethane was extruded through a slit die having glass windows and bubble nucleation in the flow channel was observed optically. A He-Ne laser was used to illuminate the nucleating and growing bubbles. The light flux scattered by the growing bubbles at a fixed angle was detected by a photomultiplier with the aid of a high-voltage power supply. The bubble nucleating site in the flow channel was located using a computer controlled tracking system, which was designed to move the entire optical system automatically in the three dimensional space, and also had the ability to follow the software control command and cooperate with the data acquisition system. When the site of bubble nucleation was located, the coordinates of this site in the flow channel and the experimental conditions were automatically recorded on a floppy diskette by entering a software command. The pressure profile along the flow channel was measured by pressure transducers, with the aid of a microprocessor-based pressure reading system. It has been found that the site of bubble nucleation varies with the position in the direction perpendicular to the flow direction, which is attributed to the nonuniform velocity and stress distributions in the slit flow channel. The present investigation suggests that bubble nucleation can be induced either by flow and/or shear stress; specifically, flow-induced bubble nucleation is the dominant mechanism at positions near the center of the die opening, and shear-induced bubble nucleation is the dominant mechanism at positions near the die wall. It should be mentioned that the bubble near the die wall may also be generated by cavitation brought about by the surface roughness of the wall and also by thermal fluctuations due to the heat transfer between the metal (die wall) and the mixture of polymer and volatile component. The present study indicates that bubble nucleation in a shear flow field can occur at an unsaturated condition. This is in contrast to bubble nucleation under static conditions, where supersaturation is necessary.