Strain-coupling effects in start-up experiments

A strain-coupling integral constitutive equation is used to analyze a start-up shear flow experiment. The theory is used to examine the effect of strain-coupling on the strain at the maximum in the shear stress-time curve. The analysis shows that there is a significant dependence of this strain on the shear rate even when a factorable strain-coupling model is used.     

Strain-coupling effects in steady planar extension

This study is concerned with an evaluation of the capability of the strain-coupling model to predict steady shear and steady planar extensional flows. A comparison is made between the predictions of the K-BKZ and strain-coupling theories.     

Molecular theories of nonlinear viscoelasticity of polymers

It is emphasized that considerable advances have been made recently in the development of the molecular theories of nonlinear viscoelasticity of concentrated solutions and melts of linear polymers. The new ideas in this exceptionally important field of the rheology of polymers are analysed. The methods by which the constraints (entanglements) imposed on the motion of macromolecules by the polymer environment are taken into account are also considered in the paper. The most detailed discussion is devoted to the model of topological constraints in the form of a tube and to the self-consistent theory of anisotropic micro-viscoelasticity which takes into account the relaxation nature of the interaction of macromolecules with their surrounding medium as well as the anisotropy of their mobility.Invited paper, presented at the XII-th All-Union Symposium on Rheology held in Riga (USSR), December 7–9, 1982.     

Predicting the nonlinear hereditary viscoelasticity of polymers

A mathematical model for the nonlinear hereditary viscoelasticity of polymer materials is proposed to predict deformation processes of various complexity — from simple relaxation and simple creep to complex deformation-relaxation and reverse relaxation processes with alternative loading and unloading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 147–157, November–December, 2007.     

Torsion and normal force responses of glassy polymers in the sub-yield regime

While there is a major body of literature relating the non-linear response of both elastomers and polymer melts with the molecular structure and topology of the chains, the same cannot be said of the non-linear response, especially that below the yield point, for polymer glasses. Here we take an approach that uses ideas of finite deformation elasticity and apply them to the isochronal response of glassy polymers in torsional deformations. We find that, while the torsional (shear) responses are similar for different molecular structures, there seems to be a strong effect of side group relaxations on the normal forces. The results are discussed in terms of the strain energy density function and the opportunities for future research.     

On the damping function of shear relaxation modulus for entangled polymers

Published data of the damping function of the shear relaxation modulus, h(), are reviewed. This is the ratio of the relaxation modulus measured at a finite magnitude of shear, , to that at the limit of = 0. Majority of the data are in accord with the universal function of the Doi-Edwards tube model theory, in which the damping or the decrease of h() is attributed to the contraction along the tube of extended polymer chains. The weaker damping seems to be attributed to 1) comb-branching such as in LDPE; 2) lack of entanglement in too short chains; 3) bimodal molecular weight distribution. However, a star-branching does not cause a deviation from the tube model theory and a broadness of molecular weight distribution is not a major origin of a weaker damping. A star-branched polystyrene with 15 arms exhibits no strain dependence: h() = 1. For highly entangled systems with more than 50 entanglement points per molecule, the strain dependence is stronger than that of the Doi-Edwards theory. This could be due to a slip or an instability of deformation in the material.     

A molecular network model to describe the nonlinear viscoelastic behavior of polymers

A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed. The project supported by the National Natural Science Foundation of China and Doctorial Fund     

Primitive chain network simulations for branched polymers

We present simulations of branched polymer dynamics based on a sliplink network model, which also accounts for topological change around branch points, i.e., for branch-point diffusion. It is well-known that, with the exception of stars, branched polymers may show a peculiar rheological behavior due to the exceptionally slow relaxation of the backbone chains bridging branch points. Though Brownian simulations based on sliplinks are powerful tools to study the motion of polymers and to predict rheological properties, none of the existing methods can simulate the relaxation of the bridge chains. The reason for that is lack of a rule for network topology rearrangement around branch points, so that entanglements between bridge chains cannot be renewed. Therefore, we introduce in this paper one possible branch-point mobility rule into our primitive chain network model. For star polymers, diffusion coefficients were calculated and compared with experiments. For both star and H-shaped polymers, diffusion was simulated both with and without the new rule, and the effect on linear viscoelasticity was also determined in one case.     

Volume changes in glassy polymers

Summary Constitutive equations are derived for compressible glassy polymers at non-isothermal loading with finite strains. The model is based on the theory of temporary networks in its version of adaptive links concept. The stress–strain relations are applied to the analysis of uniaxial extension of a viscoelastic bar. Explicit formulas are developed for time-dependent Young's modulus and Poisson's ratio of the bar at small strains. Results of numerical simulation are compared with experimental data for polycarbonate, polyethylene, and poly(methyl methacrylate). It is demonstrated that (i) longitudinal stresses do not affect the specific free volume in the region of linear viscoelasticity at strains up to about 0.2%, and cause substantial changes in the free volume in the region of nonlinear viscoelasticity at strains about 1.0%; (ii) in the latter case, the increment of the free-volume fraction is proportional to the increase in the specific volume. Received 3 April 1998; accepted for publication 22 June 1998     

Thermodynamic admissibility of the pompon model for branched polymers

The pompon model for branched polymers is re-formulated within a general framework of nonequilibrium thermodynamics. While the original model of McLeish and Larson is found to be thermodynamically admissible, nonequilibrium thermodynamics strongly suggests several model modifications. As an immediate consequence, a nonzero second normal-stress coefficient in shear flow is predicted by the modified pompon model. Received: 12 April 2000 Accepted: 11 September 2000     

Geometric nonlinear formulation for curved beams with varying curvature

Based on exact Green strain of spatial curved beam, the nonlinear strain-displacement relation for plane curved beam with varying curvature is derived. Instead of using the previous straight beam elements, curved beam elements are used to approximate the curved beam with varying curvature. Based on virtual work principle, rigid-flexible coupling dynamic equations are obtained. Physical experiments were carried out to capture the large overall motion and the strain of curved beam to verify the present rigid-flexible coupling formulation for curved beam based on curved beam element. Numerical results obtained from simulations were compared with those results from the physical experiments. In order to illustrate the effectiveness of the curved beam element methodology, the simulation results of present curved beam elements are compared with those obtained by previous straight beam elements. The dynamic behavior of a slider-crank mechanism with an initially curved elastic connecting rod is investigated. The advantage of employing generalized-α method is pointed out and the special nonlinear dynamic characteristics of the curved beam are concluded.     

Viscoelasticity and diffusion in miscible blends of saturated hydrocarbon polymers

Linear viscoelasticity and tracer diffusion were investigated as functions of temperature, component molecular weight and blend composition for entangled, single-phase blends of nearly monodisperse poly(ethylene-alt-propylene) (PEP) and head-to-head polypropylene (HHPP). Both components are non-polar and, despite evidence for slight differences of component glass temperatures in their blends, the viscoelastic data obey time-temperature superposition rather well. The properties of the blends were compared at constant T-T _g (blend) with predictions of the tube-model theories. The composition dependence of viscosity agrees best with the double-reptation prediction, as had been found earlier for molecular weight blends. The variation in plateau modulus with composition is consistent with reptation, but the changes are too small to provide a definitive test. The tracer diffusion coefficients, D ^* _PEP and D ^* _HHPP are nearly independent of composition, consistent with the reptation prediction and in sharp contrast with tracer diffusion for blends with specific associations. Results for the recoverable compliance depart from this pattern, varying differently and much less strongly with composition than the predictions of either single or double reptation. It thus seems that microstructural blends may behave in significantly more complex ways than molecular weight blends even for components with only weak dispersive interactions and rather modest differences in glass temperature and plateau modulus.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

粘弹性阻尼器动力设计及其应用的实验研究

本文提出一种圆柱式剪切型粘弹性阻尼器，给出其具有结构阻尼特性的单自由度动力学系统模型，用正弦扫频实验技术实现了对阻尼器动力学特性的测量。通过实验，研究了粘弹性材料动态特性与阻尼器动力学特性的关系，并给出这种关系的数学表示，给出了这类阻尼器的设计方法和基本公式。实验结果表明，应用这种阻尼器可有效控制桁架结构的振动，实现对结构的阻尼控制。     

Evaluation of the Wagner irreversible constitutive equation

A constitutive equation based on the concept of the irreversibility of the rupture of a polymer network has been previously proposed as an improvement to the K-BKZ model. This Wagner irreversible constitutive equation is evaluated here using data from double-step shear strain experiments. It is shown that the Wagner irreversible model does not in general provide good predictions when a comprehensive set of deformation histories is considered.     

A predictive model for impact response of viscoelastic polymers in drop tests

We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum.     

Effect of ionic interaction on linear and nonlinear viscoelastic properties of ethylene based ionomer melts

The effect of ionic interaction on linear and nonlinear viscoelastic properties was investigated using poly(ethylene-co-methacrylic acid) (E/MAA) and its ionomers which were partially neutralized by zinc or sodium. Dynamic shear viscosity and step-shear stress relaxation studies were performed. Stress relaxation moduli G(t, y) of the E/MAA and its sodium or zinc ionomers were factorized into linear relaxation moduli G°(t) and damping functions h(y). The relaxation modulus at the smallest strain in each ionomer agreed with the linear relaxation modulus calculated from storage modulus G and loss modulus G. In the linear region, the ionic interaction shifted the relaxation time longer with keeping the same relaxation time distribution as E/MAA. In the nonlinear region, the ionic interaction had no influence on h(y) when the ion content was low. At higher ion content, however, the ion bonding enhanced the strain softening of h(y).     

Evaluation of rheological constitutive equations for branched polymers in step shear strain flows

The pom-pom rheological constitutive equation for branched polymers proposed by McLeish and Larson is evaluated in step shear strain flows. Semianalytic expressions for the shear-stress relaxation modulus are derived for both the integral and approximate differential versions of the pom-pom model. Predictions from the thermodynamically motivated differential pompon model of ?ttinger are also examined. Single-mode integral and differential pom-pom models are found to give qualitatively different predictions, the former displays time–strain factorability after the backbone stretch is relaxed, while the latter does not. We also find that the differential pompon model gives quantitatively similar predictions to the integral pom-pom model in step strain flows. Predictions from multimode integral and differential pom-pom models are compared with experimental data on a widely characterized, low-density polyethylene known as 1810H. The experiments strongly support time–strain factorability, while the multimode pom-pom model predictions show deviations from this behavior over the entire range of time that is experimentally accessible.     

Absorbing Balls for Equations Modeling Nonuniform Deformable Bodies with Heavy Rigid Attachments

We study degenerate nonlinear partial differential equations with dynamical boundary conditions describing the forced motions of nonuniform deformable bodies with heavy rigid attachments. We prove that the dynamical system generated by a discretization of these equations has an absorbing ball whose size is independent of the order of the discretization. This result implies the existence of an absorbing ball for the infinite-dimensional dynamical system corresponding to the original degenerate partial differential equation and thereby serves as a critical step for establishing the existence of global attractors for this system. Our results also address the interesting mechanical question of how nonuniformity complicates the longterm dynamics of the coupled systems we consider.     

New ill-posed problems in rheology

Many methods of material characterization by rheological methods lead to ill-posed problems. The nature of ill-posedness is discussed. In this light, some such new problems appearing in molecular weight characterization of homopolymers as well as in the characterization of size distribution of dispersed phases in polymer blends by rheological techniques are analyzed. The working capability of a nonlinear regularization method is demonstrated with examples of blend rheology. The role of Professor Meissner in motivating the research in the field of ill-posed problems as well as his important contribution to rheology of polymer blends is outlined.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland