Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006     

Nonlinear stress relaxation of a styrene–butadiene random copolymer

The isothermal uniaxial stress relaxation response in the vicinity of the glass-to-rubber transition has been measured for a lightly crosslinked poly(styrene–butadiene) random copolymer, 85% styrene by weight. The volume change during stress relaxation was determined by measuring the time-dependent lateral contraction of the specimen with a Hall-effect proximity detector. The specimen exhibited an instantaneous dilation upon application of the strain and a subsequent time-dependent volume decrease. The stress relaxation behavior and the associated volume relaxation were determined for a variety of strains and temperatures in both the linear and nonlinear viscoelastic regime. As the applied strain was increased the isothermal tensile modulus decreased and the shape of the log(modulus) vs. log(time) curve was altered. At equal levels of strain the tensile modulus exhibited increasing deviations from the linear viscoelastic response as the temperature was decreased. The maximum difference between the nonlinear tensile modulus and the linear viscoelastic response was observed at short times. Subsequently, the nonlinear tensile modulus began to approach the linear viscoelastic modulus with increasing time. Both the instantaneous dilation and the magnitude of the time-dependent part of the volume change increased as the level of applied strain was increased and/or as the temperature was decreased. The observed nonlinearity in the tensile stress relaxation response has been quantitively related to the experimentally measured volume relaxation with a free-volume model.     

Stress relaxation in hematite nanoparticles‐polystyrene composites

The viscoelastic behavior of a polystyrene matrix filled with hematite nanoparticles was investigated using the stress relaxation method. An increase in the elastic moduli of the composites, as well as in the magnitude of stress relaxation was found with increasing content of the inorganic phase. The obtained results are discussed in terms of a one‐process model.     

Strain and temperature accelerated relaxation in polycarbonate

The nonlinear viscoelastic behavior of glassy polymers and its relationship to ductile yielding is studied by single- and double-step stress relaxation experiments. In the latter case a small stress relaxation step is superimposed on a specimen at an elevated state of temperature or strain. The results show that the changes in the relaxation behaviors in the two cases closely parallel each other. The relaxation behavior at strains near yield closely approximates that at low strain but near Tg. The small strain relaxation response can be described well by a Kohlrausch-Williams-Watts (KWW) type function. The interpretation of these data in terms of a coupling model which includes the KWW form is discussed.     

Viscoelastic characterization of polymers using instrumented indentation. I. Quasi‐static testing*

The use of instrumented indentation to characterize the mechanical response of polymeric materials was studied. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for the creep compliance and stress relaxation modulus for two glassy polymeric materials, epoxy and poly(methyl methacrylate), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison with the indentation stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than the rheometry values. Additional study of the deformation remaining in epoxy after indentation creep testing as a function of the creep hold time revealed that a large portion of the creep displacement measured was due to postyield flow. Indentation creep measurements of the epoxy with a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the unfilled PDMS were mainly linear elastic, with the filled PDMS exhibiting some time‐dependent and slight nonlinear responses in both rheometry and indentation measurements. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1794–1811, 2005     

Long‐time relaxations in rubber‐modified polymer systems

Linear and nonlinear viscoelastic properties were measured in the molten state for several model ABS polymers with different rubber particle contents. Linear viscoelastic functions for ABS polymers can be separated in two parts. One is a relaxation associated with the entanglement of matrix SAN chains and the other comes from the particle‐particle interactions of rubber particles. This relaxation depends strongly on the degree of dispersion of rubber particles. The second‐plateau modulus appeared at low frequency with samples in which rubber particles agglomerate. While, the second‐plateau modulus was not observed with samples in which rubber particles are finely dispersed. Matching of AN content between grafted and matrix SAN and optimum graft density form a finely dispersed system. Large deformation relaxation measurements revealed that the damping of ABS polymers having a good dispersion of particles become stronger with an increase in rubber content. This strong damping can be explained by a layered structure. The very long relaxation was found for higher rubber content, when the neighboring grafted SAN chains contact with each other.     

Viscoelastic properties of decrosslinked irradiation‐crosslinked polyethylenes in supercritical methanol

The viscoelastic properties of decrosslinked irradiation‐crosslinked polyethylenes using a supercritical methanol were investigated via oscillatory dynamic shear measurements. Decrosslinked polymers at a low reaction temperature exhibited solid‐like rheological properties, as evidenced by a small slope at G′ and G″, a long relaxation time, slow stress relaxation behavior, and considerable yield stress. In contrast, decrosslinked polymers at a high temperature exhibited liquid‐like rheological properties that included a large slope in G′ and G″, a short relaxation time, fast stress relaxation behavior, and nonyield stress. The difference in the viscoelastic properties of the decrosslinked polyethylenes was attributed to the difference in the gel content with the reaction temperature. A higher gel content induced stronger solid‐like viscoelastic properties. Hence, the rheological measurements were useful for analyzing the molecular structure of decrosslinked polymers using a supercritical fluid. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1265–1270, 2010     

Rheo-optical properties of polyethylene films in the nonlinear viscoelastic region

A new apparatus was designed to investigate the dynamic viscoelastic properties of solid polymer materials in the nonlinear viscoelastic region. The apparatus was combined with a birefringence apparatus in such a way that birefringence could be measured simultaneously with stress under oscillatory deformation. The nonlinear viscoelastic behavior of bulk-crystallized high-density polyethylene films was examined. Nonlinearity of mechanical properties became evident around 30°C, while optical properties became markedly nonlinear around 50°C. The nonlinearity of viscoelastic properties changes very little when the films are swollen with tetrachloroethane. It is proposed that disruption of lamellae to crystallites in the drawing process is one of the most important causes of the nonlinear behavior of high-density polyethylene films.     

Investigating the Time Dependent Behavior of Thermoplastic Polymers under Tensile Load

The relationship between the results of the tensile and the stress relaxation tests of polypropylene specimens were analyzed and an attempt was made to find a way to estimate the former from the latter based on the measurements and the theory of linear viscoelasticity. The mechanical response of real polymers are basically of nonlinear character, therefore their behavior patterns do not meet the idealized (linear) ones. Experiments were performed on poly(propylene) (PP) as a test material and the stress relaxation behavior, as well as the linear elastic and linear viscoelastic approximation of the tensile load-time curve were analyzed. To demonstrate the applicability of our idea and to perform the numerical calculations we have chosen a flexible function with three parameters to realize the nonlinear behavior.     

单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

分数Maxwell模型应用于PTFE松弛模量的研究

用分数Maxwell模型对聚合物PTFE(Polytetrafluoethylene)的应力松弛过程进行了研究. 分数Maxwell模型的渐近行为是确定其参数的基本依据, 但根据实验数据确定的松弛时间与渐近解成立的条件并不自恰. 通过适当选定松弛时间, 利用起始时段的实验数据确定初始松弛指数和松弛模量, 并适当优化末端松弛指数, 分数Maxwell模型可以对粘弹性应力松弛过程给出非常好的描述.     

Predictive/fitting capabilities of differential constitutive models for polymer melts—reduction of nonlinear parameters in the eXtended Pom-Pom model

A phenomenological modification of the eXtended Pom-Pom (XPP) model is proposed with the aim to reduce the number of free nonlinear parameters. The modified XPP model includes three parameters per mode in total (two linear viscoelastic parameters—linear relaxation time λ and shear modulus G, and one nonlinear parameter). The original XPP model contains five parameters (two linear viscoelastic parameters and three nonlinear ones, one nonlinear parameter participates in the second normal stress difference prediction). The predictive/fitting capabilities of the modified model are compared with the Giesekus, eXtended Pom-Pom, and modified Leonov models using various low-density PE materials in steady and transient shear and uniaxial elongational flows. It has been found that the modified model is capable of predicting/fitting the rheological properties, with the exception of the second normal stress difference, for studied LDPE materials with sufficient accuracy, including strain hardening in uniaxial elongational flow.     

Nonlinear stress relaxation of an entangled linear polystyrene in single step‐strain flow: A quantitative theoretical investigation

The nonlinear stress relaxation of a nearly monodisperse, moderately entangled polystyrene solution (i.e., roughly seven entanglements per chain at equilibrium) in single step‐strain flow is investigated quantitatively by a detailed comparison of an existing set of experimental data with a simulation based on the tube model. The proposed simulation enables the effects of primary nonlinear relaxation mechanisms other than chain retraction to be identified more clearly and investigated individually. Two peculiar nonlinear relaxation behaviors are observed in this experiment. One is concerned with an apparent enhancement in the stress relaxation at short times, and the other is responsible for a seeming slowdown of the stress relaxation at long times. These findings are discussed within the tube model, in view of the effects of convective constraint release, partial strand extension, and nonaffine deformation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1281–1293, 2003     

The Nonlinear Viscoelastic Response of Glassy Polymers Subjected to Physical Aging

Constitutive equations are developed for the nonlinear viscoelastic behavior of amorphous glassy polymers in the sub‐yield region. A polymeric glass is treated as an ensemble of cooperatively rearranging regions bridged by links. Stress‐strain relations are derived and verified by comparison with experimental data in static mechanical tests on polycarbonate and poly(methyl methacrylate). We analyze the effects of the straining state (tension, compression and torsion), strain intensity, temperature and time of annealing on stress relaxation. Fair agreement is demonstrated between observations and results of numerical simulation.     

Sorbitan tristearate layers at the air/water interface studied by shear and dilatational interfacial rheology

The shear and dilatational rheology of condensed interfacial layers of the water-insoluble surfactant sorbitan tristearate at the air/water interface is investigated. A new interfacial shear rheometer allows measurements in both stress- and strain-controlled modes, providing comprehensive interfacial rheological information such as the interfacial dynamic shear moduli, the creep response to a stress pulse, the stress relaxation response to a strain step, or steady shear curves. Our experiments show that the interfacial films are both viscoelastic and brittle in nature and subject to fracture at small deformations, as was supported by in-situ Brewster angle microscopy performed during the rheological experiments. Although any large-deformation test is destructive to the sample, it is still possible to study the linear viscoelastic regime if the deformations involved are controlled carefully. Complementary results for the dilatational rheology in area step compression/expansion experiments are reported. The dilatational behavior is predominantly elastic throughout the frequency spectrum measured, whereas the layers exhibit generalized Maxwell behavior in shear mode within a deformation frequency regime as narrow as two decades, indicating the presence of additional relaxation mechanisms in shear as opposed to expansion/compression. If the transient rheological response from stress relaxation experiments is considered, then the data can be described well with a stretched exponential model both in the shear and dilatational deformations.     

Linear viscoelastic behavior of chitosan films as influenced by changes in the biopolymer structure

Films were prepared via solvent casting from different deacetylated and depolymerized chitosans obtained from β‐chitin. The linear viscoelastic behavior of the chitosan films was studied with uniaxial tensile stress–relaxation tests. All stress–relaxation profiles exhibited an asymptotically decaying trend, with a residual value different from zero, thus pointing out a solid‐like, viscoelastic behavior. The decay of the tensile modulus with time was phenomenologically described by a generalized Maxwell model consisting of three exponential functions and an equilibrium elastic modulus. Films prepared from chitosans with higher molecular weights showed higher residual elastic moduli and longer relaxation times. Within the range of the degrees of acetylation analyzed (0–27%), chitosans with the lowest and highest degrees of acetylation exhibited more pronounced solid‐like character. This behavior is explained on the basis of a complex balance between steric effects, types of intermolecular interactions, and aggregation of the chitosan samples. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1907–1915, 2007     

Mittag-Leffler函数及其在粘弹性应力松弛中的应用

Mittag-Leffler函数在分数阶粘弹理论中起着重要作用. 我们对该函数的计算及收敛性进行了分析; 利用遗传算法结合共轭梯度法, 提出了对广义函数进行非线性参数拟合的方法. 用分数Maxwell模型对强弱、硬柔具有显著差别的塑料、玻璃态合金及聚合物近熔体的应力松弛过程进行了研究.     

Flow,high-elastic (recoverable) deformation,and rupture of uncured high molecular weight linear polymers in uniaxial extension

The behavior of narrow molecular weight distribution polymers has been investigated under uniaxial extension at constant deformation rate and at constant stress. It has been established that up to rupture these polymers behave as linear viscoelastic bodies. A detailed investigation of the rupture phenomenon has shown that the rupture of fluid polymers is due to their transition to the rubbery state at critical deformation rates, with the result that they disintegrate like quasi-cured rubbers. The effect of the temperature and the molecular weight on the critical conditions of rupture has been described in terms of viscoelastic relaxation.