Linear Viscoelastic Behavior Research Articles

Effect of benzimidazolium salt on dispersion and properties of polyphenylene sulfide/organic clay nanocomposites via melt intercalation

Nanocomposites of polyphenylene sulfide (PPS) were prepared with a benzimidazolium surfactant used as organic modification for the montmorillonite (MMT) by melt blending. The benzimidazolium-modifided MMT (Bz-MMT) exhibited a large interlayer spacing of 3.26 nm and showed a high thermal stability compared to the commonly used clay modified by alkyl ammonium salts (DK-1N). The morphology of the polyphenylene sulfide (PPS)/Bz-MMT nanocomposites were evaluated by X-ray diffraction (XRD) and transmission electron microscope (TEM). The results showed good overall dispersion of the MMT in PPS matrix. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were used to evaluate the thermal properties of polymer/clay nanocomposites. The results of DSC showed the addition of MMT resulted in heterogeneous nucleation crystallization of PPS. The results of TGA showed the thermal stability of the polymer/clay nanocomposits was enhanced. The rheological properties of nanocomposites were also evaluated by a Anton Paar rheometer. The results indicated that the addition of Bz-MMT nanoplatelets affected the linear viscoelastic behavior of the PPS matrix by increasing the viscosity.

A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

This paper presents a unified procedure that can rapidly determine the discrete relaxation and retardation spectra of asphalt concrete. The new procedure involves three consecutive steps: (1) pre-smoothing the complex modulus data with the Havriliak–Negami (HN) model, (2) identifying the discrete relaxation spectrum from the smoothed data with a modified windowing method (MWM) and (3) converting the obtained spectrum into the corresponding discrete retardation spectrum. The HN model adopted furnishes reasonable analytical representations for all the complex modulus components and allows an asymmetrical inflection point for the dynamic modulus and storage modulus master curves on the log–log scale, effectively overcoming the drawbacks of the conventional sigmoidal function in characterizing the asphalt concrete linear viscoelastic (LVE) behavior. Also, the HN model can well predict the phase angle from the dynamic modulus data, substantially extending the application of the old data lacking the phase angle information in the LVE analysis. Additionally, the MWM offers a more appropriate estimation approach for the glassy modulus, successfully avoiding the undesirable spectrum oscillations and negative spectrum lines. A distribution of the time constants with 0.5 decade intervals was implemented in this procedure, completely excluding the waviness in the bell-shaped master curves of the generalized Maxwell (GM) and generalized Voigt (GV) models. Very few parameters are required for the initial inputs in the procedure and no empirical adjustments or selections are required for the GM or GV model constants during the whole computation process. The convergence of the iterations for determining the discrete spectra proved to be very fast.

Influence of the fiber/matrix strength on the mechanical properties of a glass fiber/thermoplastic-matrix plain weave fabric composite

In this work, we analyze the influence of different fiber surface treatments on the mechanical properties of plain weave composites. The reinforcement is a glass fibers fabric and the matrix is an acrylic polymer. Until very recently, this thermoplastic polymer family was not used in composite industry. It is therefore necessary to study if the existing fiber surface treatments are suitable for acrylic resins or if new ones have to be found. At the macroscale, composite materials corresponding to different fiber surface treatments were characterized with: (i) monotonic in-plane shear tests and (ii) heat-build up fatigue measurements on specimens with ±45° fiber orientations with respect to the tensile force. At the mesoscale (fabric scale), the development of damage was experimentally analyzed from (i) 3-D DIC (Digital Image Correlation) full-field strain measurements with spatial resolution smaller than the textile repeating unit and (ii) X-ray microtomography. We show that the analyzed composite materials exhibit linear viscoelastic behavior until a given stress threshold above which damage develops in the material. It was also found that the application on the fibers of a coupling agent specifically developed for promoting the bond between glass fibers and acrylic resins improves the composite mechanical properties, in particular the fatigue properties.

Revisiting the identification of generalized Maxwell models from experimental results

Linear viscoelastic material behavior is often modeled using a generalized Maxwell model. The material parameters, i.e. relaxation times and elastic moduli, of the Maxwell elements are determined from either a relaxation or a Dynamical Mechanical Analysis (DMA) experiments. The underlying mathematical problem is known to be ill-posed, which means that uniqueness of the identification is not assured and that small errors in the initial data will conduct to high discrepancies in the identified parameters. The standard technique to remove the ill-posedness is to chose a priori a series of relaxation times and to identify only the moduli. The aim of this paper is to propose two techniques to identify an optimal series of relaxation times. In the case of the relaxation experiment relaxation times will be optimized from the numerical integration of the measured relaxation spectrum. In the case of the DMA experiments we show that mathematical results obtained by Krein and Nudelmann can be used to determine the complete series of relaxation times. The methods are illustrated by identification examples using both artificial and experimental data. The results show that the methods provide a good match of the identified models in term of relaxation or complex moduli.

On the ageing of polymers and the time‐shifting procedure

The time‐shifting procedure, originally developed for time‐temperature equivalence in the modelling of polymers mechanical behaviour, has later on been extended to time‐age equivalence. The present paper discusses both situations in the context of linear viscoelastic behaviour, from the point of view of mathematical representation and the fitting of experimental data. The general equations in the cases of ageing and non‐ageing are introduced and the cases of hardening and softening types of ageing are precisely characterised. Situations in which time shifting can prove effective are delimited and alternative more general expressions are proposed.

Reclaimed asphalt pavement and additives’ influence on 3D linear behaviour of warm mix asphalts

This paper presents results of laboratory tests on nine types of specimens consisting of different hot and warm mix asphalts produced with a reclaimed asphalt pavement. Linear viscoelastic behaviour was investigated using tension–compression tests on cylindrical specimens on a wide range of temperatures (from −25°C to +45°C) and frequencies (from 0.03 to 10 Hz). Complex moduli, E*, and complex Poisson's ratios, ν*, were determined in two perpendicular material directions. Differences between measured ν* reveal a negligible anisotropy in the horizontal confection plane. The time–temperature superposition principle was verified with good approximation, with the same shift factor values, in one-dimensional and three-dimensional conditions. The same values of shift factor were also obtained for all specimens that contain bitumen with identical crude oil origin. Experimental results were modelled using the 2S2P1D model previously developed at the University of Lyon/ENTPE. In this paper, a new representation of results using normalised curves is proposed. These curves show identical properties for the different materials, which have the same origin of bitumen and aggregate. Finally, the performance of tested materials was compared.

Analysis and modeling of 3D complex modulus tests on hot and warm bituminous mixtures

This paper presents the results of laboratory testing of hot and warm bituminous mixtures containing Reclaimed Asphalt Pavement (RAP). Complex modulus measurements, using the tension–compression test on cylindrical specimens, were conducted to determine linear viscoelastic (LVE) behavior. Sinusoidal cyclic loadings, with strain amplitude of approximately 50⋅10−6, were applied at several temperatures (from −25 to +45 °C) and frequencies (from 0.03 Hz to 10 Hz). In addition to axial stresses and strains, radial strains were also measured. The complex modulus E∗ and complex Poisson’s ratios ν∗ were then obtained in two perpendicular directions. Measured values in these two directions do not indicate anisotropy on Poisson’s ratio. The time-temperature superposition principle (TTSP) was verified with good approximation in one-dimensional (1D) and three-dimensional (3D) conditions for the same values of shift factor. Experimental results were modeled using the 2S2P1D model previously developed at the University of Lyon/ENTPE. In addition, specific analysis showed that eventual damage created during complex modulus test is very small and is equivalent to the effect of an increase of temperature of about 0.25 °C.

Computational evaluation of effective stress relaxation behavior of polymer composites

This paper presents a micromechanics model to characterize the effective stress relaxation stiffness of polymer composites. The linear viscoelastic behavior of polymer material was modeled by hereditary integral. The proposed model was established based on the variational asymptotic method for unit cell homogenization (VAMUCH). All computations with this model were accomplished in the time domain, hence the Laplace transform and inversion commonly used for linear viscoelastic composites are not needed in this theory. The accuracy and efficiency of the proposed model were verified by comparing with the results and utilization of finite element models developed using ABAQUS.

Dynamic properties of air-jet yarns compared to rotor spinning

In yarn production, the mechanism of twist insertion is a major factor that affects the structure and ultimately the properties and characteristics of the produced yarn. Moreover, the differences within the same spinning technique may have a similar effect where, for instance, the properties of yarns produced using Murata Vortex Spinning (MVS) and Reiter air-jet spinning (J20) will differ, although both technologies are just varieties of the same twist insertion principle of using a stream of air. In this work, the structure and properties of Murata vortex, Reiter, and rotor-spun yarns are compared with more emphasis on their mechanical behavior under dynamic stresses. Unlike the dynamic mechanical analysis of materials that presumes linear viscoelastic behavior and is only valid under small strains, this work suggests a cyclic loading with larger strains as a means of the dynamic evaluation of the yarns. Results show no significant difference between the technologies in terms of their initial modulus and maximum elongation, while a significant difference between the technologies is observed in the maximum loading and, to some extent, the work of rupture. The dynamic sonic modulus is compared to the results of the standard mechanical and the suggested cyclic loading tests, and a high correlation between the values was observed.

Impact of maltene and asphaltene fraction on mechanical behavior and microstructure of bitumen

As a widely accepted concept, bitumen consists of four fractions that can be distinguished by their polarity. Highly polar asphaltene micelles are dispersed in a viscous phase of saturates, aromatics and resins (maltene phase). Different concentrations of asphaltenes in the bitumen result in a range of mechanical response properties. In an interdisciplinary study the impact of the maltene phase and asphaltenes on the linear viscoelastic behavior and the microstructure of bitumen were analyzed by creep recovery testing in a DSR and by atomic force microscopy (AFM). Therefore, bitumen was separated into the maltene and asphaltene fractions and artificial bitumen samples with different, pre-defined asphaltene concentrations were produced and investigated. It was found that the artificially produced, precipitated bitumen samples can be regarded as a representative, bitumen-like material in terms of mechanical behavior and microstructure. Asphaltenes play an important role in the typical viscoelastic behavior of bitumen being mainly responsible for stiffness and elasticity. Also, their concentration appears to be correlated to the occurrence and shape of the bee-like inclusions which can be typically observed by AFM.

Investigating linear and nonlinear viscoelastic behaviour and microstructures of gelatin-multiwalled carbon nanotube composites

The linear and nonlinear rheology of physically-crosslinked-gelatin gel-multiwalled carbon nanotube (MWNT), chemically-crosslinked-gelatin gel-MWNT, and chemically–physically-crosslinked-gelatin gel-MWNT composites, are investigated.

Choice of an Advanced Rheological Model for Modeling the Viscoelastic Behavior of Hot Mixtures Asphalt (HMA) from Sénégal (West Africa)

The main purpose of this article is to choose among advanced rheological models used in the French rational design, one that best represents the viscoelastic behavior of asphalt mixtures mixed with aggregates of Senegal. The model chosen will be the basis for the development of computational tools for stress and strain for Senegal. However, the calibration of these models needs complex modulus test results. In opposition to mechanical models the complex modulus can directly characterize the viscoelastic behavior of bituminous materials. Here determination is performed in the laboratory by using several types of tests divided into two groups: homogeneous tests and non-homogeneous tests. The choice of model will be carried out by statistical analysis through the least squares method. To this end, a study was carried out to “Laboratory of Pavement and Bituminous Materials” (LCMB) with asphalt concrete mixed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. In this study, the test used to measure the complex modulus is the Canadian test method LC 26-700 (Determination of the complex modulus by tension-compression). There mainly exist two viewing complex modulus planes for laboratory test results: the Cole and Cole plane and the Black space. The uniqueness of the data points in these two areas means that studied asphalt concretes are thermorheologically simple and that the principle of time-temperature superposition can be applied. This means that the master curve may be drawn and that the same modulus value can be obtained for different pairs (frequency-temperature). These master curves are fitted during the calibration process by the advanced rheological models. One of the most used software in the French rational design for the visualization of complex modulus test results and calibration of rheological models developed tools is named Visco-analysis. In this study, its use in interpreting the complex modulus test results and calibration models shows that, the studied asphalt concretes are thermorheologically simple, because they present good uniqueness of their Black and Cole and Cole and Black diagrams. They allow a good application of the principle of time temperature superposition. The statistical analysis of calibration models by the least squares method has shown that the three studied models are suitable for modeling the linear viscoelastic behavior of asphalt mixtures formulated with the basalt of Diack and the quartzite of Bakel. Indeed their calibration has very similar precision values of “Sum of Squared Deviation” (SSD) about 0.185. However, the lower precision value (0.169) is obtained with the 2S2P1D model.

Analysis of linear viscoelastic behaviour of alginate gels: effects of inner relaxation, water diffusion, and syneresis.

The mechanical behaviour of ionically cross-linked alginate gels is investigated here in detail. To determine the range of linear response of the materials, uniaxial, unconfined compression and torsional deformation experiments are performed, obtaining both the stress-strain and the viscoelastic behaviour of the gels. On-line measurements of the radii of the cylindrical gel samples in these experiments are also reported. The linearity range in the gel mechanical response is found to be rather limited, up to 6% strain, at most, contrary to more optimistic conclusions usually reported in the literature. We confirm the presence of a stress-diffusion coupling phenomenon in our alginates, i.e., the migration of water from/into the gels in response to the applied deformation. A phenomenon of inner (constitutive) relaxation of the network component of the gels is also clearly identified, and observed to occur, in parallel with solvent diffusion, upon compression. At sufficiently longer times after a deformation step, syneresis is always observed, with concomitant nonstandard viscoelastic effects, such as the growth of a normal force in torsion, and a size dependent decay of the longitudinal force in compression. We applied a two-fluid model, recently developed by two of the present authors [D. Larobina and F. Greco, J. Chem. Phys., 2012, 136(13), 134904], to simulate the relaxation tests upon torsional and compressive deformations, and to fit our own experiments. The model is found to well describe the coupling between constitutive relaxation and diffusion, and to reproduce the available force and radii data before the advent of syneresis.

架橋密度の異なるガラス状エポキシネットワークの大変形過程における過渡的粘弾性

The single relaxation time of glassy epoxy networks having different crosslink densities was evaluated during uniaxial compression processes by using a simple nonlinear single relaxation model to study the effect of crosslinked molecular structures on the transient nonlinear viscoelastic behavior of glassy epoxy networks. The model consisted of two elastic springs expressing linear viscoelastic behavior and a dashpot with variable viscosity as a single parameter representing strain-induced structural change. We calculated the strain-dependent relaxation time τSS during the compression by fitting the model to the experimental stress-strain curves obtained at various strain rates and at temperatures T 18℃ lower than the glass transition temperature Tg of the material being compressed. With increasing strain εn, τSS obtained for each epoxy network steeply decreased in the pre-yield region of strain and then reached to low steady values appearing in strain ranges larger than the yield strain, reproducing previously reported typical behavior observed for glassy polymers under large deformation. When compressed at an identical strain rate, τSS-εn relations for all epoxy networks almost coincided each other despite the difference in the crosslink density. This result indicates that, if the deformation is performed at the same condition i.e., strain rate and T-Tg, strain-induced variation of relaxation time in the epoxy glasses is almost not influenced by crosslinked molecular structures.

On Continuum Damage Modeling of Fiber Reinforced Viscoelastic Composites with Microcracks in terms of Invariants

A continuum damage model is developed for the linear viscoelastic behavior of composites with microcracks consisting of an isotropic matrix reinforced by two arbitrarily independent and inextensible fiber families. Despite the fact that the matrix material is isotropic, the model in consideration bears the characteristic of directed media included in the transverse isotropy symmetry group solely due to its fibers distributions and the existence of microcracks. Using the basic laws of continuum damage mechanics and equations belonging to kinematics and deformation geometries of fibers, the constitutive functions have been obtained. It has been detected as a result of the thermodynamic constraints that the stress potential function is dependent on two symmetric tensors and two vectors, whereas the dissipative stress function is dependent on four symmetric tensors and two vectors. To determine arguments of the constitutive functionals, findings relating to the theory of invariants have been used as a method because of the fact that isotropy constraint is imposed on the material. As a result the linear constitutive equations of elastic stress, dissipative stress, and strain energy density release rate have been written in terms of material coordinate description. Using these expressions, total stress has been found.

Melt rheology and properties of compatibilized recycled poly(ethylene terephthalate)/(styrene‐ethylene‐ethylene‐propylene‐styrene) block copolymer blends

Blends of recycled poly(ethylene terephthalate) (R‐PET) and (styrene‐ethylene‐ethylene‐propylene‐styrene) block copolymer (SEEPS) compatibilized with (maleic anhydride)‐grafted‐styrene‐ethylene‐butylene‐styrene (SEBS‐g‐MAH) were prepared by melt blending. The compatibilizing effects of SEBS‐g‐MAH were investigated systematically by study of the morphology, linear viscoelastic behavior, and thermal and mechanical properties of the blends. The results show that there is good agreement between the results obtained by rheological measurement and morphological analysis. The rheological test shows that the melt elasticity and melt strength of the blends increase with the addition of SEBS‐g‐MAH. The Cole‐Cole plots and van Gurp‐Palmen plots confirm the compatibilizing effect of SEBS‐g‐MAH. However, the Palierne model fails to predict the linear viscoelastic properties of the blends. The morphology observation shows that all blends exhibit a droplet‐matrix morphology. In addition, the SEEPS particle size in the (R‐PET)/SEEPS blends is significantly decreased and dispersed uniformly by the addition of SEBS‐g‐MAH. Differential scanning calorimeter analysis shows that the crystallization behavior of R‐PET is restricted by the incorporation of SEEPS, whereas the addition of SEBS‐g‐MAH improves the crystallization behavior of R‐PET compared with that of uncompatibilized (R‐PET)/SEEPS blends. The Charpy impact strength of the blends shows the highest value at SEBS‐g‐MAH content of 10%, which is about 210% higher than that of pure R‐PET. J. VINYL ADDIT. TECHNOL., 22:342–349, 2016. © 2014 Society of Plastics Engineers

Linear viscoelasticity of hot-pressed hybrid poplar relates to densification and to the in situ molecular parameters of cellulose

Hot pressing leads to changes in wood water sorption properties, linear viscoelastic behavior, and chemistry. In hot-pressed hybrid poplar, storage modulus linearly correlates with cellulose apparent crystallinity index and degree of polymerization, revealing the impact of cellulose hydrolysis on wood viscoelasticity during hot pressing. Heat treatment and densification during hot pressing are known to alter wood chemical, physical, and viscoelastic properties. Interrelationships between these properties and their changes during hot pressing are, however, unknown. They are expected to play a significant role on mat consolidation during the manufacture of wood-based composites. This study aims (1) to characterize the impact of hot pressing on the physical, viscoelastic, and chemical properties of hybrid-poplar wood and (2) to assess possible relationships between these properties. Dry and moist wood samples were hot-pressed under various conditions of temperature. Specific gravity, water sorption isotherms, and dynamic viscoelastic properties of hot-pressed wood were measured together with cellulose apparent crystallinity and molecular weight. Possible relationships between these properties were assessed with statistical analyses. Wood specific gravity, sorption isotherm, dynamic moduli, and cellulose crystallinity were all affected by the hot-pressing conditions. The viscoelastic response of hot-pressed wood was found to relate not only to the extent of densification but also to in situ molecular properties of cellulose. Cellulose apparent crystallinity index and degree of polymerization in hot-pressed wood linearly correlated with storage modulus, revealing the importance of cellulose hydrolysis during hot pressing on wood viscoelastic response. During hot pressing, wood cellulose hydrolysis appears to govern the viscoelastic response, in addition to wood densification.

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag–Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to show how predictions of nonlinear viscometric properties, such as shear-thinning in the viscosity and in the first normal stress coefficient, can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and suitably modify it for power-law materials exhibiting Mittag–Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox–Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel-Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule, which is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shear-thinning Cross-type or Carreau-type flow curves. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.

Graphene networks with low percolation threshold in ABS nanocomposites: selective localization and electrical and rheological properties.

Acrylonitrile-butadiene-styrene resin (ABS)/graphene nanocomposites were prepared through a facile coagulation method. Because the chemical reduction of graphene oxide was in situ conducted in the presence of ABS at the dispersion stage, the aggregation of the graphene nanosheets was avoided. It was shown by transmission electron microscopy that the graphene nanosheets were selectively located and homogeneously dispersed in the styrene-acrylonitrile (SAN) phase. The electrical conductivity and linear viscoelastic behavior of the nanocomposites were systematically studied. With increasing filler content, graphene networks were established in the SAN phase. Consequently, the nanocomposites underwent a transition from electrical insulator to conductor at a percolation threshold of 0.13 vol %, which is smaller than that of other ABS composites. Such a low percolation threshold results from extreme geometry, selective localization, and homogeneous dispersion of the graphene nanosheets in SAN phase. Similarly, the rheological response of the nanocomposites also showed a transition to solid-like behavior. Due to the thermal reduction of graphene nanosheets and structure improvement of graphene networks, enhanced electrical conductivity of the nanocomposites was obtained after annealing.

Effects of Core Microstructure on Structure and Dynamics of Star Polymer Melts: From Polymeric to Colloidal Response

The structure and linear viscoelastic behavior of four different model star polymer melts were investigated experimentally. The star polymers were prepared via different synthetic routes based on atom transfer radical polymerization (ATRP). Stars with small elongated (linear backbone) cores exhibited slight differences in the asymmetry of the core, which however did not affect the rheological properties significantly. The relaxation behavior of these stars with an asymmetric core was well-described by available tube models. On the other hand, stars with large cross-linked cores exhibited a core–shell morphology and their stress relaxation was dominated by a power-law decay over about 8 decades, akin to gel-like soft systems. This behavior reflected their liquid-like ordering and small intercore distances, and bares analogueies to that of interpenetrating soft colloids and microgels.