On Mooney viscosity and Mooney stress relaxation. I

Mooney relaxation is highly nonlinear, strongly differs from stress relaxation at small strains, and can be described by Wagner's nonlinear rheological model for polymer melts. In the practical evaluation, the Mooney Stress Relaxation slope is more accurate than quantities such as t₈₀. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1207–1219, 1999     

Investigation and prediction on the nonlinear viscoelastic behaviors of nylon1212 toughened with elastomer

Studies on the nonlinear viscoelastic behaviors of nylon1212 toughened with styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The linear relaxation curves at relatively low shear strains show good overlap, the relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model. The nonlinear relaxation curves of nylon1212 blends at different shear strains have been obtained and their damping functions were evaluated. Meanwhile, it is found that most blends in the experimental windows follow the strain‐time separation principle and Laun double exponential model can predict damping curves well. The successive start‐up of shear behavior was investigated. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data of nylon 1212 blend with 10 wt % SEEPS well, but there exists some deviation for experiment data of nylon1212 blends with high SEEPS concentrations. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

A comparison of Newtonian and viscoelastic constitutive models for dry spinning of polymer fibers

A comparison is made of the predictions of one‐dimensional mathematical model simulations of dry spinning based on Newtonian and viscoelastic constitutive equations for the spin dope. The viscoelastic model is based upon a modified Giesekus constitutive equation with a temperature and composition‐dependent relaxation time. The simulation algorithm includes the effects of the glass transition on the expected solution viscosity and relaxation time behavior along the spinline. Predictions of axial velocity, tensile stress, and composition profiles for the two cases suggest the role of viscoelasticity in the locking‐in behavior associated with fiber solidification along the spinline. The effects of model parameters and processing conditions are also discussed. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 2136–2145, 2003     

Effects of rheological properties and processing parameters on ABS thermoforming

Understanding effects of material and processing parameters on the thermoforming process is critical to the optimization of processing conditions and the development of better materials for high quality products. In this study we investigated the influence of both rheological properties and processing parameters on the part thickness distribution of a vacuum snap‐back forming process. Rheological properties included uniaxial and biaxial elongational viscosity and strain hardening and/or softening while processing parameters included friction coefficient, heat transfer coefficient, and sheet and mold temperatures. The Wagner two parameter nonlinear viscoelastic constitutive model was used to describe rheological behavior and was fit to shear and elongational experimental data. The linear viscoelastic properties along with the Wagner model were utilized for numerical simulation of the thermoforming operation. Simulations of pre‐stretched vacuum thermoforming with a relatively complex mold for a commercial refrigerator liner were conducted. The effects of nonlinear rheological behavior were determined by arbitrarily changing model parameters. This allows determination of which rheological features (i.e., elongational mode, viscosity, and strain hardening and/or softening) are most critical to the vacuum snap‐back thermoforming operation. We found that rheological and friction properties showed a predominant role over other processing parameters for uniform thickness distribution.     

Numerical simulations of annular extrudate swell of polymer melts

Numerical viscoelastic simulations were carried out using a K-BKZ type of separable integral constitutive equation. Both reversible and irreversible models were tried for several types of damping functions to calculate the annular extrudate behavior of high-density polyethylene (HDPE). There are two aims in this study; first, to clarify the properties of these dumping functions, and second, to investigate the influence of rheological characteristics on annular extrudate swell. In these numerical simulations, relaxation spectrum and shear viscosity were fixed, and the other characteristics were varied. The reversional response of the damping function mainly has an effect on the magnitude of the area swell even if the die is straight. The irreversible model expresses the experimental results of annular extrudate swell better than the reversible model. The accurate fitting of N1 by the damping model is important for predicting it. The magnitude of N1 predicted from the Wagner exponential model is lower than that of the PSM model, and the area swell shows the same tendency as N1. A modified PSM model that allows the N1 curve to shift can fit the magnitude of area swell. The relationship between the diameter and thickness of the extrudate depends on N2/N1, and it was estimated by simple linear elasticity of solids. The time dependent viscosity varies with the type of damping function, and it influences the time-dependent swell.     

不同门尼黏度NBR的制备及其对力学性能的影响

本文利用两种不同门尼含量的胶乳,利用掺混法成功制备了不同门尼黏度的NBR,研究了不同门尼黏度NBR对硫化性能及其对力学性能的影响,结果表明:随着门尼黏度的增大,NBR的最大扭矩值越大;随着门尼黏度的增加,NBR胶料的断裂伸长率逐渐降低;门尼黏度越大,NBR胶料的拉伸应力越高,同时恢复曲线的应力也越高,马林斯效应越明显.     

橡胶材料非线性高弹-粘弹性本构模型

本文提出的修正Zener模型,即以非线性弹簧与粘壶代替原来的线性弹簧与粘壶,得到一种适合橡胶材料在单轴作用下的非线性高弹-粘弹性本构模型。该模型可同时描述加载、卸载及应力松弛行为。模型将应力分解为弹性应力与粘性应力。弹性应力由Yeoh高弹性模型得到;粘性应力由加载及卸载过程的瞬时应力通过积分变换得到。此外考虑到应力松弛的作用,因此将粘性应力分解成两部分：一是在加载、卸载过程所用时间内由应变的改变所导致的粘性力;二是在该时间内由应力松弛所产生的反作用力。最后,将实验结果与该模型的计算结果进行对比,结果表明计算结果与实验结果具有良好的一致性,说明该本构模型可靠、合理。     

苯乙烯-丁二烯橡胶门尼黏度标准物质定值不确定度的评定

依照GB/T 1231.1-2000进行实验,利用JJF 1059-1999]对苯乙烯-丁二烯橡胶门尼黏度标准物质定值过程中的不确定度分量进行了分析和评定。该测定过程中所产生的不确定度主要由多家实验室测量重复性和定值样品均匀性、稳定性引入。定值样品苯乙烯-丁二烯橡胶SBR 1502的门尼黏度ML(1+4)100℃测量值49.1的不确定度为±0.8。     

Non-linear viscoelastic behavior and damping factor of polypropylene/clay nanocomposites

The non-linear viscoelastic properties of pure polypropylene and its clay nanocomposites are studied to establish structure–property relationship in conjunction with clay concentrations. First, flow birefringence is performed through a slit-die to obtain centerline principal stress difference during elongational flow for clay nanocomposites. The centerline stress profile of clay nanocomposite reveals additional viscoelastic nature even at low silicate concentrations, while similar short-time chain relaxation is observed. The effects of higher clay concentrations are further examined during the simple shearing flow to consider damping properties of the clay nanocomposites. The step strain, dynamic shear and steady shear are performed. All the samples show time-strain separable melt flow behavior adequately demonstrated through Wagner’s exponential damping function. The damping coefficient is found to be strongly dependent on clay percentage revealing viscoelastic differences therein. We have also used a time-strain separable Kaye-Bernstein Kearsley Zapas (K-BKZ) type constitutive equation to predict steady shear stress. The suggested constitutive model satisfies simple shear at lower fractions of clay while the damping function behaves similar to pure polymer thought to result from the absence of filler–filler interactions and chain length degradation. The unusual rheological behavior for maximum clay concentration studied is explained on experimental as well as theoretical basis. Thus, the results of this investigation would improve the theoretical understanding of possible molecular orientations at different clay concentrations during elongational and shearing flows.     

Constitutive modeling of visco-hyperelastic behavior of double-network hydrogels using long-term memory theory

Double-network hydrogels with viscoelastic behavior are appropriate materials for biomechanical applications. In this article, the standard linear solid (SLS) rheological model for the linear viscoelastic materials is generalized to the viscoelastic materials with large nonlinear deformations. Based on this viewpoint, the constitutive equation is proposed as sum of two parts including the strain-dependent elastic stress, and the viscous stress, which depends on the strain and strain rate. The elastic part of the stress is modeled via considering a hyperelastic strain energy function, while the main core of the viscous stress part requires a time-dependent weight function to satisfy the long-term memory fading principle. In addition, the weight function is proposed such that it can capture the mechanical behavior trend corresponding to the strain and strain rate for a double-network hydrogel in the relaxation test. Finally, to evaluate the performance of the proposed constitutive equation for the mechanical behavior modeling of double-network hydrogels, the tests on these materials have been used, and the material parameters are determined from fitting the experimental results to the theory. The agreement of test and theory results showed that the proposed model is capable to model the mechanical behavior of double-network hydrogels.     

丁二烯橡胶门尼粘度测试准确性的研究

门尼粘度分析结果与原料生产厂家提供的测试结果差距较大。对采样方法、分析步骤、分析过程及设备等引起误差的多方面进行了细化,减少了人为误差,提高了门尼粘度测试结果的准确性。     

有限变形下的橡胶材料非线性高弹-粘弹性本构模型

本文基于唯象学原理提出了一种适用于橡胶材料在有限应变条件下的非线性高弹-粘弹性本构模型,该模型将应力拆分为两部分：第一部分基于Yeoh模型计算得到的高弹性应力;第二部分由Boltzmann叠加原理计算得到的带有率依赖性的粘弹性应力。该本构模型中应变依赖性的高弹性应力通过修正Zener模型中的非线性弹簧表示,时间及应变依赖性的粘弹性应力通过修正Zener模型中的非线性Maxwell模型表示。利用提出的高弹-粘弹性本构模型模拟不同应变条件下的拉伸、回复、应力松弛及多步松弛在内的复杂加载过程,并与实验值对比,结果表现出良好的吻合性,说明该本构模型的合理、可靠。     

系列门尼粘度稀土异戊橡胶产品开发

采用Nd(vers)3-Al(i-Bu)2H-Al(i-Bu)2Cl均相稀土催化体系,以异戊二烯为单体和己烷为溶剂进行异戊二烯聚合反应,探讨稀土催化体系和聚合工艺条件对聚合物门尼粘度的影响规律,建立了不同条件下聚合物门尼粘度的关联曲线,提出稀土异戊橡胶门尼粘度优化控制方案。实验结果表明,稀土异戊橡胶门尼粘度随着催化剂中氢化二异丁基铝[Al(i-Bu)2H]与新癸酸钕[Nd(vers)3]配比、相对分子质量调节剂用量、催化剂用量和聚合温度的增加而降低;随着反应时间的增加而逐渐趋于稳定。开发出了门尼粘度为60±5、70±5、80±5、90±5的系列稀土异戊橡胶,满足不同橡胶制品对不同规格异戊橡胶产品的要求。     

Transient modeling of viscosity

Capillary and parallel plate rheological characterization was conducted for a low‐density polyethylene. In contrast with conventional rheological analysis, steady conditions were not assumed. Transient data, with time steps between 0.0001 and 0.2 s, were analyzed with a nonlinear, viscoelastic constitutive model in which the relaxation time was modeled as a function of the applied stress. The fit model explained more than 99% of the observed transient variation in the capillary and parallel plate rheometers. The model coefficients for the capillary and parallel plate were compared directly to conventional linear viscoelastic analysis of the same parallel plate data. The results indicate that the described constitutive model closely predicts the observed viscoelastic behavior of the polymer melt tested in the parallel plate rheometer. Furthermore, the results indicate that the relaxation spectrum modeled with the transient analysis of the capillary rheological data correlate closely to the results predicted by the same transient analysis of parallel plate rheological data. The conclusion is that described constitutive modeling describes the viscoelastic behavior in both capillary and parallel plate rheometers. Moreover, the analysis and results suggest that the viscoelastic behavior of the polymer melt is a significant factor during the rheological characterization and the modeling of the transient response should be taken into consideration during rheological analysis to provide high fidelity models. POLYM. ENG. SCI., 57:1110–1118, 2017. © 2017 Society of Plastics Engineers     

Effects of loading rate on viscoplastic properties of polymer geosynthetics and its constitutive modeling

On the basis of the special tensile test results under various loading histories, the rate‐dependent behaviors of three polymer geosynthetics due to their viscous properties have been investigated. All the investigated polymer geosynthetics show significant loading rate effects, creep deformation, and stress relaxation. Except for the polyester geogrid showing the combined viscosity, all the investigated polymer geosynthetics exhibit the isotach viscosity. An elasto‐viscoplastic constitutive model described in a nonlinear three‐component model framework is developed to simulate the rate‐dependent behaviors of polymer geosynthetics. The developed constitutive model is verified by comparing its simulated results with the experimental data of polymer geosynthetics presented in this study and those available from the literature. The comparison indicates that the developed model can reasonably interpret the rate‐dependent behaviors of polymer geosynthetics under arbitrary loading histories, including the step‐changed strain rate loading, creep, and stress relaxation applied during otherwise monotonic loading (ML). POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Viscoelastic behavior and constitutive modeling of PP/HNT composites prepared by water‐assisted extrusion

Poly(propylene) (PP) nanocomposites containing 5, 10, and 15 wt% unmodified halloysite nanotubes (HNTs) were prepared using extrusion with and without water injection. Scanning electron microscopy micrographs show that HNT aggregates prepared by water injection are smaller than those prepared by conventional melt extrusion (without water injection). The nanocomposites prepared by water injection exhibit higher storage modulus (G′) and complex viscosity (η*) values than those by conventional melt extrusion. Stress relaxation results indicate that the interaction between HNTs and PP matrix at low concentration (5 wt%) is stronger than its non‐water injection counterpart. Subsequently, for 5 wt% HNT sample, the transient viscosity is simulated numerically using the Kaye–Bernstein–Kearsley–Zapas (K‐BKZ) integral constitutive equation along with experimentally determined damping functions. It is found that the samples prepared by water injection exhibit a more obvious overshoot behavior than conventional samples and the Papanastasiou‐Scriven‐Macosko (PSM) model can predict the transient viscosity of the samples more accurately than Wagner model. Further, the relationship between the dispersion of HNTs and the damping factors in the constitutive models is discussed. The results of this investigation would improve the theoretical understanding of possible polymer–filler interaction during shear flow. POLYM. ENG. SCI., 59:1585–1592 2019. © 2019 Society of Plastics Engineers     

Relations between high‐temperature mastication and Mooney viscosity relaxation in natural rubber

Mastication of natural rubber (NR) is undertaken as a preliminary step towards the preparation of NR‐based vulcanizates, a process during which the elastomer is broken down to a homogeneous matrix of lower viscosity. Several tests and indicators are in use for characterizing the behavior of elastomers but these have mostly been adopted for the nonmasticated product. This study uses coefficients generated from modeled Mooney relaxation data, as indicators of elasticity, to examine the effect of high‐temperature mastication on the processability of the masticated rubber. Some derived coefficients such as the terminal relaxation time (τ) from Maxwell's triexponential model, the elastic component (a) from Wu‐Abbott model [Y = 1 + a* ln(t) ? bt/(c + t)], and the constant (b) from the Power law model (Y = at^?b), adequately characterized the effect of mastication on NR. Although the NR grades studied were quite different with respect to their initial molar mass distributions, they followed a similar response to the mechanical models before and after mastication, indicating therefore that mastication decomposes to a similar extent, the various components (long isoprene chains, densely crosslinked solvent‐insoluble gel, etc.) that account for the viscoelastic behavior of the raw elastomer. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

门尼粘度及支化程度对三元乙丙橡胶性能的影响

通过无转子硫化仪、橡胶加工分析仪、核磁交联密度仪等分析手段研究三元乙丙橡胶(EPDM)的门尼粘度、长链支化程度对过氧化物硫化EPDM的硫化特性及其硫化胶性能的影响。结果表明,门尼粘度的增加,有助于交联密度和硫化速率的提高,横向弛豫时间不断减小。高支化程度对EPDM胶料硫化速度不利。EPDM门尼粘度越高,初始储能模量G′0越大,储能模量迅速下降的临界应变值越小;不同长链支化度的EPDM硫化胶的储能模量大致相等,但长支化链的损耗因子值相对较高。门尼粘度对EPDM硫化胶拉伸强度变化影响较小;而长链支化程度的提高,使硫化胶拉伸强度和断裂伸长率略微降低。     

乙丙橡胶门尼粘度标准物质的研制与验证应用

经过三元乙丙橡胶(EPDM)的样品候选、均匀性检验、稳定性检验、定值、不确定度评估等系列工作,研制出了EPDM门尼粘度国家标准物质并得到了国家质量监督检验检疫总局的批准。EPDM门尼粘度标准物质定值结果在显著水平0.01时,数据间无异常值、呈现正态分布、各组数据间处于等精度,定值结果的总平均值为该门尼粘度标准物质的标称值。因此,EPDM标准物质在ML100℃(1+4)、ML100℃(1+8)不同测试条件下的标称值分别为42.4、40.4,不确定度分别为0.5、0.4,其不确定度小于国外标准样品,EPDM门尼粘度标准物质研制水平高于美国研制的标准物质。