Loaded rubber-like materials subjected to small-amplitude vibrations

This paper proposes a constitutive law and a method for characterizing highly preloaded viscoelastic materials subjected to linear （small-amplitude） vibrations. A multiplicative non-separable variables law has been suggested to model the behavior that depends on both stretch and time/frequency. This approach allows splitting the intricate combined test performed simultaneously on both stretch and frequency, generally in a limited experimental domain up to 100 Hz, into two independent tests. Thus, on one hand, the dynamic complex modulus dependent on frequency alone is evaluated on the basis of vibration tests in a large experimental domain up to 100 kHz. On the other hand, energetic parameters are determined from a quasi-static hyperelastic tensile test. The complex modulus, dependent on both stretch and frequency, is then deduced from the results acquired from uncoupled investigations. This work shows that, in extension, the elastic modulus increases with increasing stretch, and the loss factor decreases with increasing stretch; while, in compression, around the material undeformed state, the modulus increases as the stretch increases till a certain value of compression stretch （upturn point depending on material characteristics）, and then the modulus decreases as the stretch increases. Globally, preload rigidifies materials but reduces their damping property. These results closely match a well-known observation in solid mechanics.     

Determination of non-linear dynamic properties of carbon-filled rubbers

A forced non-resonance test method is described for determining the dynamic mechanical properties of polymeric materials over wide ranges of strain and frequency. The use of this method for carrying out studies on carbon-filled rubbers is illustrated by results which demonstrate the variation of the dynamic shear modulus and damping factor of a tyre tread material with dynamic strain amplitude, frequency and temperature. Procedures are discussed for the analysis and presentation of such data.

Two methods are described for the determination of loss factor, and results from these are compared in order to assess the validity of phase angle measurements on non-linear materials.

Brief reference is made to dynamic testing under compressive and combined compression and shear modes of deformation. The prediction of performance under this combined loading situation from experimental data obtained in shear is demonstrated.     

Elastic and viscoelastic properties of sugarcane bagasse-filled poly(vinyl chloride) composites

Elastic and viscoelastic properties of sugarcane bagasse-filled poly(vinyl chloride) were determined by means of three-point bending flexural tests and dynamic mechanical and thermal analysis. The elastic modulus, storage modulus, loss modulus, and damping parameter of the composites at fibre contents of 10, 20, 30, and 40% in mass were determined, as well as those of the unfilled matrix. There was a correlation between the elastic modulus and storage modulus of the composites. Moreover, the elastic and viscoelastic properties of the composites were highly influenced by fibre content.     

High damping and mechanical properties of hydrogen-bonded polyethylene materials with variable contents of hydroxyls: Effect of hydrogen bonding density

Hydrogen bonding is considered to have significant effect on the interaction between polymeric chains and on the viscoelasticity of the polymeric materials. In this paper, we attempt to discuss the relationship between hydrogen bonding density and damping behavior and mechanical properties of polyethylene-based polymeric materials. For this reason, a series of pendant chain hydrogen bonding polymers(PCHBP) with different hydrogen bonding density(HBD) were prepared by quantitatively changing the content of pendent hydroxyl groups on the main chain of polyethylene. It was found that PCHBP with low HBD showed similar properties to polyethylene, indicating that the property of the materials was dependent mainly on the structure of the main chain. However, PCHBP with high HBD exhibited two tanδ peaks and a platform of loss modulus as well as a high storage modulus(about 400 MPa) at the second tanδ peak temperature, demonstrating that a polymeric material with high strength and damping properties was obtained. More importantly, the maximum of loss modulus showed a linear increase with the HBD, indicating that a higher HBD greatly improved the damping properties of the polymeric materials.     

Evidences of non-linear short-term stress relaxation in polymers

Back in 1986, investigating the Space Shuttle Challenger disaster, famous physicist Richard Feynman clearly showed how viscoelastic behavior of a polymeric material is of paramount importance in practical engineering. At present day a definitive universal rheological law is not yet available for polymers, as a consequence both theoretical models and experimental investigations of viscoelastic behavior must be necessarily focused independently on each single polymer or, at least, on well-defined classes of polymers. Accurate experimental evidences are needed in order to properly evaluate the mechanical properties of a polymeric material, as a function of its particular applications. In this paper measurements of the stress relaxation behavior of six polymeric materials under uniaxial tension and uniaxial unconfined compression tests, are performed and experimental results are modelled using a stretched exponential function, known as Kohlraush-Williams-Watts time-decay function. In particular the short-term stress relaxation is investigated, as a function of typical environmental temperature range, in order to assess viscoelastic behavior of tested polymeric materials for peculiar industrial and biomedical applications.     

Dynamic mechanical properties of aluminum nitride/cyanate ester composites for high performance electronic packaging

Viscoelastic ature is one of the key features of polymeric composites. A series of cyanate ester (CE)‐based composites with different aluminum nitride (AlN) contents for high performance electronic packaging, coded as AlN/CE, were developed; the viscoelastic nature of AlN/CE composites was intensively investigated by employing dynamic mechanical analysis (DMA). Results show that the AlN content has a great effect on dynamic mechanical properties of AlN/CE composites. The storage modulus in the glassy region increases linearly with the addition of AlN as well as the increase of AlN content. Meanwhile, all composites also exhibit notably higher loss modulus than cured CE resin due to the appearance of new energy dissipation forms. In addition, the incorporation of AlN has a significant effect on damping factor peak. All reasons leading to these phenomena are analyzed from the view of structure–property relationship. Copyright © 2009 John Wiley & Sons, Ltd.     

Interfacially induced additional damping peaks in dynamic mechanical spectra – micromechanical transitions in multipolymeric materials

The viscoelastic properties of several hypothetical multiphase polymeric materials were investigated in relation to their phase-property dependencies and microstructures. Theoretical mechanical considerations based on the self-consistent interlayer model were performed to point out that specific geometrical arrangements into phases of a set of properties of the pure constituents can lead to interfacially induced damping peaks in dynamic mechanical spectra (DMS). Such additional contributions in DMS were referred to micromechanical transitions to distinguish them from ordinary molecular transitions.     

国内外PVB材性研究

主要介绍了国内外研究PVB(聚乙烯醇缩丁醛)材性的现状。国内外研究表明,PVB是应变率及温度敏感材料。应变率增加,弹性模量变大;温度升高,弹性模量和剪切模量均下降。同时,国内外进行了少量的实验,研究PVB的本构模型。总结发现,PVB的本构模型可描述为线弹性、弹塑性、线性粘弹性和非线性粘弹性四种,但本质上PVB是非线性粘弹性材料,不同的环境条件与计算要求可选择不同的本构模型。目前,国内外学者比较认可的是用超弹性考虑其非线性,用Maxwell模型考虑其粘弹性。     

Nonlinear actuation of non-prismatic dielectric elastomeric membrane

ABSTRACT

Nowadays, the soft material, dielectric elastomers (DEs) are being used for many engineering applications due to their exceptional properties like high strain rate sensitivity, low power consumption, capable of static force measurement and capability of changing dimensions when subjected to voltage. They have the ability of converting mechanical energy to electrical energy and vice versa. In this article, nonlinear dynamic behavior of viscoelastic tapered DE under mechanical and electromechanical loading is studied. A dynamic model based on standard linear solid model is incorporated for viscoelasticity. Strain energy density of the system is derived from Gent model of hyperelasticity. The tapered DE is analyzed with different values of damping coefficients, ratio of shear moduli of springs, width and height tapers. The effects of tapers greatly put an impact on the dynamic responses of the system. The tapered DEs exhibits damped vibration and weak nonlinearity with an increase in damping force. The dynamic stability of tapered DEs is also studied using phase diagrams, and the results indicated that with an increase in damping force, the dynamic stability changes from a state of aperiodic vibration to quasi-periodic vibration. It is also found that the resonant frequency and peak amplitude reduce with an increase in the damping force.     

Experimental characterization and viscoelastic modeling of isotropic and anisotropic magnetorheological elastomers

The paper presents experimental research and numerical modeling of dynamic properties of magnetorheological elastomers (MREs). Isotropic and anisotropic MREs have been prepared based on silicone matrix filled by micro-sized carbonyl iron particles. Dynamic properties of the isotropic and anisotropic MREs were determined using double-lap shear test under harmonic loading in the displacement control mode. Effects of excitation frequency, strain amplitude, and magnetic field intensity on the dynamic properties of the MREs were examined. Dynamic moduli of the MREs decreased with increasing the strain amplitude of applied harmonic load. The dynamic moduli and damping properties of the MREs increased with increasing the frequency and magnetic flux density. The anisotropic MREs showed higher dynamic moduli and magnetorheological (MR) effect than those of the isotropic ones. The MR effect of the MREs increased with the rise of the magnetic flux density. The dependence of dynamic moduli and loss factor on the frequency and magnetic flux density was numerically studied using four-parameter fractional derivative viscoelastic model. The model was fitted well to experimental data for both isotropic and anisotropic MREs. The fitting of dynamic moduli and loss factor for the isotropic and anisotropic MREs is in good agreement with experimental results.     

Dynamic mechanical properties of an ultra high molecular weight polyethylene reference material SRM 8456

The dynamic mechanical analysis storage and loss modulus of a NIST SRM 8456 Ultra High Molecular Weight Polyethylene is determined in 3-point bending in an interlaboratory test. Mean values of (1.18?±?0.17)?GPa for storage modulus and (62.0?±?9.0)?MPa for loss modulus were determined at 21?°C. In addition, the temperature (molecular) spectrum for the material is observed between ?100 and +100?°C. These results permit the use of this material for calibration, conformance, and performance demonstration for dynamic mechanical analyzers.     

Comparison between 3-point bending and torsion methods for determining the viscoelastic properties of fiber-reinforced epoxy

Dynamic mechanical analysis is a technique used to determine the viscoelastic properties of polymers and their composites. The storage modulus, loss modulus and loss factor in correlation with the glass transition temperature can be detected by several means. In this study, these properties are determined using a dynamic mechanical analyzer in 3-point bending mode, as well as a rheometer in torsion mode. The materials under consideration are a unidirectional glass fiber-reinforced epoxy, a quasi-isotropic carbon fiber-reinforced epoxy and a quasi-isotropic glass fiber-reinforced epoxy. The results of each method and material are presented and the advantages and limitations of each method are discussed. 3-point bending proved to be more suitable to detect the effect of fiber orientation for unidirectional fiber-reinforced epoxy but requires careful control of sample dimensions for accuracy. Torsion, on the other hand, gave consistent measurements for samples of varying lengths, proving to be a suitable method if materials are scarce and limited.     

Effect of microstructure uncertainty and testing frequency on storage and loss moduli of injection molded MWCNT reinforced polyamide 66 nanocomposites

The viscoelastic behavior of multiwall carbon nanotube (MWCNT) reinforced polyamide 66 (PA 66) was evaluated to investigate the effect of CNT content and loading frequency on dynamic moduli (i.e. storage modulus E′ and loss modulus E″) and damping factor tan$\delta$. PA 66/CNT disk samples with five different CNT contents ranging from 3 wt % to 15 wt % were manufactured by injection molding. Testing was performed over the frequency range of 0.1–100 Hz at room temperature. Dynamic mechanical analysis results show that the mechanical properties are highly functions of tested frequency and the improvement on loss and storage modulus of nanocomposites with the addition of CNT is highly dependent on tested frequencies. The variability in loss modulus is significantly higher than the variability in the storage modulus indicating the correlation of loss modulus with uncertainties present in nanocomposite microstructure while storage modulus is essentially independent of microstructure for a given reinforcement content.     

非交联组份对端乙烯基聚环氧丙烷/聚苯乙烯网状共聚物粘弹性的影响

本文描述了端乙烯基聚环氧丙烷/聚苯乙烯网状共聚物的合成及表征。研究了非交联组份对共聚物的玻璃化转变温度T_g,贮能模量E'、耗能模量E'和阻尼系数tanδ等动态力学性能的影响,计算了试样的粘弹性参数。结果表明,非交联组份对交联网有明显塑化作用,使其T_g降低,自由体积分数和阻尼系数增大。     

A new high frequency dynamic mechanical analysis system: An approach to direct high frequency testing of tire tread rubber

Dynamic Mechanical Analysis (DMA) systems are measurement devices for obtaining master curves and complex modules of viscoelastic materials, such as rubbers. The conventional DMAs measurement systems in market have several limitations, which restrict their ability for operating at high frequencies. Thus, Williams, Landel and Ferry (WLF) relation is used to produce master curves and predict the material properties at high frequencies. In conventional DMAs, experiments are done in a range of temperatures, and then a master curve is made for a chosen reference temperature by shifting the measurements data to high frequencies. Therefore, the obtained results, which are not based on direct measurements, can be inaccurate. In order to overcome this problem a new simple shear high-frequency DMA (HFDMA) system is designed and built to directly measure the dynamic mechanical properties of viscoelastic material at high frequencies and the strain levels sufficient for tire manufacturers. The new HFDMA can be used to test any viscoelastic materials which have glass transmission temperature (Tg) lower than room temperature (about 23 °C) such as the Styrene-butadiene rubber (SBR). The SBR is the base material for tire tread. The designing process of this new HFDMA is presented in this paper. The rubber specimen shape is chosen by taking into account the shear elastic wave effect, bending, buckling effect and heat generation in the specimen. The repeatability test is accomplished to ensure that the results obtained from the new HFDMA are repeatable and the repeatability uncertainty is about 0.04%. The new HFDMA is validated by comparing to the direct test results of conventional DMA at 100 Hz. The direct high frequency (5 kHz) complex shear modulus and damping factor are compared with the master curve of the conventional DMA developed by the use of WLF relation for SBR. This comparison revealed that the complex shear modulus and damping factor of the SBR obtained from the HFDMA at 5 kHz and 0.05% strain amplitude are about 7% and 6.5% higher than those obtained from the conventional DMA, respectively.     

Determination of dynamic properties of flax fibres reinforced laminate using vibration measurements

Experimental and numerical methods to identify the linear viscoelastic properties of flax fibre reinforced polymer (FFRP) composite are presented in this study. The method relies on the evolution of storage modulus and loss factor as observed through the frequency response. Free-free symmetrically guided beams were excited in the dynamic range of 10 Hz to 4 kHz with a swept sine excitation focused around their first modes. A fractional derivative Zener model has been identified to predict the complex moduli. A modified ply constitutive law has been then implemented in a classical laminates theory calculation (CLT) routine. Overall, the Zener model fitted the experimental results well. The storage modulus was not frequency dependant, while the loss factor increased with frequency and reached a maximum value for a fibre orientation of 70°. The damping of FFRP was, respectively, 5 and 2 times higher than for equivalent carbon and glass fibres reinforced epoxy composites.     

Prestrained biaxial DMA investigation of viscoelastic nonlinearities in highly filled elastomers

Highly filled elastomers present strong nonlinear mechanical behavior. This study proposes a biaxial dynamic mechanical analysis (DMA) experiment to study the prestrain induced nonlinearity. This phenomenon has already been observed for uniaxial tests, revealing an increase of the amplitude of the dynamic modulus with prestrain. The novelty proposed here is to investigate the problem under biaxial conditions. For this purpose, a specific apparatus and an appropriate specimen have been designed. Strains and stresses have been measured using localization formulae and compared with measurements from digital image correlation and finite element computations. Biaxial DMA tests were performed on a propellant specimen, for different values of biaxial prestrain. The material is a highly filled elastomer with an important influence of the prestrain on the global viscoelastic behavior. The results exhibit increasing amplitude of the complex modulus with increasing prestrain, as in uniaxial experiments. Moreover, the dependence can be characterized using the second invariant of the prestrain, and the viscoelastic behavior is modeled using a closed-form spectrum of relaxation times.     

聚合物二元体系动态力学性能的估算

动态热机械分析是多相聚合物体系的一个重要研究手段.分析动态力学性能可以研究共混高聚物的相容性、复合材料的界面特性以及高分子运动机理等.本文综述了聚合物二元体系,即填充、纤维增强、共混体系动态力学性能的估算方法.在填充体系中,分别概述有无界面作用两种情况,当存在界面作用时,界面作用越强,模量越大,阻尼越小.对纤维增强体系,讨论了玻璃纤维有无取向的情况下模量和阻尼的估算.特别对于聚合物二元共混体系,分"海-岛"结构和双连续相两种情况,分别讨论了模量与阻尼的估算.     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.     

Fabrication and vibration characterization of electrically triggered shape memory polymer beams

Shape memory polymers (SMP) exhibit temperature, frequency and strain rate dependent properties which may be manipulated by various types of external stimuli to achieve desirable response characteristics. In recent years, the emphasis has been on designing SMPs which do not require external stimuli (such as a heat source) and have a rapid response time with large homogenous and reversible deformation characteristics. In this research, the fabrication process and dynamic vibration testing of an electrically activated SMP are presented. It is shown that conductive SMP beams can be fabricated to achieve tunable stiffness and damping with a reasonable thermal gradient generated by electrical triggering. This can allow the tuning of a range of frequency bandwidth and damping properties of SMPs for vibration control applications. The experimentation yielded modal properties (natural frequencies and damping) of the SMP beams. These parameters were validated against values obtained from the estimated performance of these beams based on the complex modulus parameters obtained using dynamic mechanical analysis (DMA). For a modest 20 °C temperature range in an epoxy based SMP, a resulting shift of approximately 7% in the natural frequency and 100% change in the damping ratio of a rectangular beam was successfully attained. These results recommend SMPs as being tunable materials that can enhance vibrational performance and expand the operational envelope of structures.