聚合物注射成型流动残余应力的数值分析

建立了可压缩黏弹性聚合物熔体在薄壁型腔中充模/保压过程中非等温、非稳态流动 的数学模型,用数值方法实现了注射成型过程中流动应力和取向建立及松弛过程的模拟,研 究了熔体温度、模具温度和注射速率等工艺条件对分子冻结取向的影响,取得了与实验相符 的结果.     

Orientation and rheology of rodlike particles with strong Brownian diffusion in a second-order fluid under simple shear flow

An analysis of orientation in a dilute suspension of rodlike macromolecules in a second-order fluid is presented and the effect of the elasticity of the fluid on the orientation of the suspended particles is examined. Distributions of particle orientation under a simple shear flow have been obtained for small β where β is the ratio of the intrinsic relaxation time of the fluid to the rotational relaxation time of the particle, the latter being inversely proportional to the Brownian rotation diffusion coefficient D_r of the particle. The parameter β represents also the ratio of the Weissenberg number of the fluid to the non-dimensional shear rate, g/D_r. An expression of the stress tensor of the suspension is derived and used in conjuntion with the orientation distribution to obtain the rheological properties of the mixture subjected to a simple shear.     

Modeling flow induced crystallization in film casting of polypropylene

Data from iPP film casting experiments served as a basis to model the effect of flow on polymer crystallization kinetics. These data describe the temperature, width, velocity and crystallinity distributions along the drawing direction under conditions permitting crystallization along the draw length.In order to model the effect of flow on crystallization kinetics, a modification of a previously defined quiescent kinetic model was adopted. This modification consisted in using a higher melting temperature than in the original quiescent model. The reason for the modification was to account for an increase of crystallization temperature due to entropy decrease of the flowing melt. This entropy decrease was calculated from the molecular orientation on the basis of rubber elasticity theory applied to the entangled and elongated melt. The evolution of molecular orientation (elongation) during the film casting experiments was calculated using a non-linear dumbbell model which considers the relaxation time, obtained from normal stress difference and viscosity functions, to be a function of the deformation rate.The comparison between experimental distributions and model based crystallinity distributions was satisfactory.     

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.     

The interface migration in shear-banded micellar solutions

In this work, we study the diffusion of the interface between bands in wormlike micellar solutions that exhibit shear banding flow regimes, namely, systems undergoing coexistence of states of different shear rates along a constant stress plateau. The migration of the interface between bands possessing different birefringence levels is predicted by the BMP (Bautista-Manero-Puig) model in which a structural parameter (the fluidity) presents two states with differing order separated by an interface. The mechanical potential derived from the constitutive equations and a diffusion term for the structure evolution equation predict various time scales of interface migration at the inception of shear flow and under shear-rate changes along the plateau stress. It is shown that the extremes of the plateau (binodals) correspond to the minima in the mechanical potential as a function of fluidity or shear rate. We also predict the dependence of the diffusive length scale on the applied shear rate.     

A non-linear viscoelastic model with structure-dependent relaxation times: II. Comparison with l.d. polyethylene transient stress results

A model of non-linear viscoelasticity with relaxation times which depend on the structure is compared with experimental results reported in the literature for a L.D. polyethylene.The single parameter of the model is determined by comparison with steadystate shear results. The model is then used to interpret various transient data. These are: tangential and normal stress growth in shear, stress growth in elongation, normal stresses in shear creep.The comparison shows a good general agreement, thus supporting the suggestion of relating the change in time of the relaxation spectrum to structural variables.     

Transient rheological behaviour of poly-para-henylenetherephthalamide (PpPTA) in sulphuric acid

Nearly all the available information on the transient flow behaviour of liquid crystalline polymers has been obtained on model systems, especially on solutions of polybenzylglutamate (PBG) and hydroxypropylcellulose (HPC). The assessment of rheological models has been based almost entirely on these model systems. It is not clear how much of the available theoretical and experimental knowledge can be applied to systems of industrial relevance, which have quite different molecular structures. Here, an industrial lyotropic system, poly(p-phenylenetherephthalamide) (PpPTA) in sulphuric acid (TWARON from AKZO), is investigated. Various techniques to study transient behaviour are used, these include measurements of transient shear and normal stresses after sudden changes in shear rate, dynamic moduli and stress relaxation after cessation of flow and elastic recoil. At all shear rates studied the PpPTA solution is shear thinning, and the first normal stress difference remains positive. For the stress transients a strain scaling applies reasonably well as it did in model systems. The moduli increase with time upon cessation of flow, indicating that the molecules become less oriented in the previous flow direction. This particular behaviour is similar to that of HPC. Transients also resemble more closely those of HPC rather than those of PBG. This latter difference might be attributed to the higher flexibility of HPC and PpPTA chains as compared with PBG molecules.     

Stability analysis of soret-driven double-diffusive convection of Maxwell fluid in a porous medium

Stability analysis of double-diffusive convection for viscoelastic fluid with Soret effect in a porous medium is investigated using a modified-Maxwell-Darcy model. We use the linear stability analysis to investigate how the Soret parameter and the relaxation time of viscoelastic fluid effect the onset of convection and the selection of an unstable wavenumber. It is found that the Soret effect is to destabilize the system for oscillatory convection. The relaxation time also enhances the instability of the system. The effects of Soret coefficient and relaxation time on the heat transfer rate in a porous medium are studied using the nonlinear stability analysis, the variation of the Nusselt number with respect to the Rayleigh number is derived for stationary and oscillatory convection modes. Some previous results can be reduced as the special cases of the present paper.     

Numerical study of chain conformation on shear banding using diffusive Rolie-Poly model

Shear-banding phenomenon in the entangled polymer systems was investigated in a planar Couette cell with the diffusive Rolie-Poly (ROuse LInear Entangled POLYmers) model, a single-mode constitutive model derived from a tube-based molecular theory. The steady-state shear stress ?? _s was constant in the shear gradient direction while the local shear rate changed abruptly, i.e., split into the bands. We focused on the molecular conformation (also calculated from the Rolie-Poly model) around the band boundary. A band was found also for the conformation, but its boundary was much broader than that for the shear rate. Correspondingly, the first normal stress difference (N ₁) gradually changed in this diffuse boundary of the conformational bands (this change of N ₁ was compensated by a change of the local pressure). For both shear rate and conformation, the boundary widths were quite insensitive to the macroscopic shear rate but changed with various parameters such as the diffusion constant and the relaxation times (the reptation and the Rouse times). The broadness of the conformational banding, associated by the gradual change of N ₁, was attributed to competition between the molecular diffusion (in the shear gradient direction) and the conformational relaxation under a constraint of constant ?? _s.     

非等温黏弹性复杂流动的改进SPH方法模拟

非等温黏弹性流体广泛存在于自然界和工业生产中,准确预测黏弹性流体的非等温流动机理和复杂流变特性有着重要的应用价值.文章提出一种改进的光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法对非等温黏弹性复杂流动进行了数值模拟,其中流体的黏弹特性通过eXtended Pom-Pom本构模型来表征.为了提高模拟结果的精度,采用了一种核函数梯度的修正算法;为了灵活地施加边界条件,发展了边界粒子和虚拟粒子相联合的边界处理方法;为了消除流动过程中的拉伸不稳定性,施加了粒子迁移技术.运用改进SPH方法数值模拟了液滴撞击固壁和F型腔注塑成型问题,通过与Basilisk软件得到的结果进行比较验证了改进SPH方法求解非等温黏弹性流体的有效性.通过利用不同粒子初始间距进行计算,评价了改进SPH方法的数值收敛性.研究了非等温流动相较于等温流动的不同流动特征,深入分析了不同热流变参数对流动过程的影响.数值结果表明,文章提出的改进SPH方法可稳定、准确地描述非等温黏弹性复杂流动的传热机理、复杂流变特性和自由面变化特性.     

Viscoelastic plastic rheological model for particle filled polymer melts

A viscoelastic plastic model for suspension of small particles in polymer melts has been developed. In this model, the total stress is assumed to be the sum of stress in the polymer matrix and the filler network. A nonlinear viscoelastic model along with a yield criterion were used to represent the stresses in the polymer matrix and the filler network, respectively. The yield function is defined in terms of differential equations with an internal parameter. The internal parameter models the evolution of structure changes during floc rupture and restoration. The theoretical results were obtained for steady and oscillatory shear flow and compared with experimental data for particle filled thermoplastic melt. The experimental data included the steady state shear strress over a wide range of shear rates, the transient stress in a start up shear flow, stress relaxation after cessation of a steady state shear flow, the step shear and the oscillatory shear flow at various amplitudes.     

液滴在大振幅振荡剪切流动中的非线性行为研究

利用YB模型预测了黏性液滴在黏性基质中的形状和取向的非线性变化,并对比前人 的理论和实验工作,讨论了YB模型大振幅剪切流场中的适用性. 还着重 讨论了非线性行为的评估,提出了``峰高比加和法'和``峰面积 比加和法'两种新的评估方法.     

Time-dependent Viscoelastic Behavior of an LDPE Melt

Two differential constitutive equations, i.e. Giesekus model and Johnson–Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson– Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the melt at high shear rate.The project was supported by the National Natural Science Foundation of China (10402024, 50335010).The English text was polished by Yunming Chen.     

Mechanical behavior of amorphous polymers in shear

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “ viscous dissipation induced“ anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G‘ Sell et al. , thus the validity of the proposed model is verified.     

Rheology and flow-birefringence from viscoelastic polymer-clay solutions

 The shear orientation of viscoelastic clay-polymer solutions was investigated by means of rheology and flow birefringence (Δn). The polymer chains are in dynamic adsorption/desorption equilibrium with the clay particles to form a “network”. The elastic behavior of the network was characterized by constant stress, oscillatory shear, and stress relaxation experiments. Constant stress experiments indicated a yield stress upon which shear flow started and no strain recovery could be observed. Oscillatory shear experiments showed a broad elastic region followed by flow when a critical strain was reached. Stress relaxation experiments showed several relaxation times when the same critical strain was reached. Experiments under steady flow characterized the transient behavior of the network. With increasing steady shear rate a pronounced minimum in birefringence was observed at a critical shear rate. The shear rate dependent viscosity showed near power law behavior and no corresponding critical feature. While birefringence detects orientational effects on a microscopic length scale, rheology averages over macroscopic changes in the sample. The same degree of orientation could be achieved under constant shear rate or constant stress conditions. Received: 25 January 2001 Accepted: 22 May 2001     

A new thixotropic model for waxy crude

Waxy crude oil shows thixotropic behavior below the gelation temperature. The mostly used thixotropic model for waxy crude is the model proposed by Houska. One problem of Houska’s model is that after the stepwise change in shear rate, the predicted shear stress decreases to its equilibrium value more quickly than the measured data. To address this problem, a new viscoplastic thixotropic model is proposed. The evolution of structural parameter is described by a new kinetic equation. In the kinetic equation, a new pre-factor with shear strain as variable is introduced for the buildup and breakdown terms, and the breakdown term is assumed to be dependent on energy dissipation rate rather than on shear rate. The proposed model was validated by the stepwise shear rate test and hysteresis loop test. And the results showed that the new model’s fitting and predictive capability is satisfactory.     

Local fracture resistance based on microstructural efficiency concept and simulation of injection molding

Local fracture resistance (FR) of short (SGF) and discontinuous long glass fibre (LGF) reinforced polypropylene (PP) was predicted using the ‘microstructural efficiency concept’ together with a simulation program for fibre orientation in injection molding. The ‘microstructural efficiency concept’ describes the relation between microstructural parameters such as the fibre content, the fibre aspect ratio and the processing (injection molding) induced layer structure taking also into account the local fibre orientation. The local fibre orientation in injection molding was predicted with the MOLDFLOW^®-software. The predicted local FR was compared with the measured one, which was determined by using compact tension samples and linear elastic fracture mechanics (LEFM). The comparison showed, that for SGF-PP good consistence between the predicted and measured FR existed, for LGF-PP the discrepancy was higher. Yet for both materials, the ‘microstructural efficiency concept’ together with the results obtained from the simulation of the fibre orientation can be used for FR prediction of an injection molded workpiece.     

Fiber orientation kinetics of a concentrated short glass fiber suspension in startup of simple shear flow

The common approach for simulating the evolution of fiber orientation during flow in concentrated suspensions is to use an empirically modified form of Jeffery's equation referred to as the Folgar–Tucker (F-T) model. Direct measurements of fiber orientation were performed in the startup of shear flow for a 30 wt% short glass fiber-filled polybutylene terephthalate (PBT-30); a matrix that behaves similar to a Newtonian fluid. Comparison between predictions based on the F-T model and the experimental fiber orientation show that the model over predicts the rate of fiber reorientation. Rheological measurements of the stress growth functions show that the stress overshoot phenomenon approaches a steady state at a similar strain as the fiber microstructure, at roughly 50 units. However, fiber orientation measurements suggest that a steady state is not reached as the fiber orientation continues to slowly evolve, even up to 200 strain units. The addition of a “slip” parameter to the F-T model improved the model predictions of the fiber orientation and rheological stress growth functions.     

Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification

The rate-dependent behavior of filled natural rubber (NR) and high damping rubber (HDR) is investigated in compression and shear regimes. In order to describe the viscosity-induced rate-dependent effects, a constitutive model of finite strain viscoelasticity founded on the basis of the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts is proposed. The total stress is decomposed into an equilibrium stress and a viscosity-induced overstress by following the concept of the Zener model. To identify the constitutive equation for the viscosity from direct experimental observations, an analytical scheme that ascertains the fundamental relation between the inelastic strain rate and the overstress tensor of the Mandel type by evaluating simple relaxation test results is proposed. Evaluation of the experimental results using the proposed analytical scheme confirms the necessity of considering both the current overstress and the current deformation as variables to describe the evolution of the rate-dependent phenomena. Based on this experimentally based motivation, an evolution equation using power laws is proposed to represent the effects of internal variables on viscosity phenomena. The proposed evolution equation has been incorporated in the finite strain viscoelasticity model in a thermodynamically consistent way. Simulation results for simple relaxation tests, multi-step relaxation tests and monotonic tests at different strain rates using the developed model show an encouraging correlation with the experiments conducted on HDR and NR in both compression and shear regimes. Finally, an approach to extend the proposed evolution equation for rate-dependent cyclic processes is proposed. The simulation results are critically compared with the experiments.