Complex Dynamic Modulus Research Articles

점탄성 제진 요소의 복소동강성계수 산출을 위한 상용유한요소 코드 이용시 복소탄성계수의 정하중 의존성 반영 방법

Little attention has been paid to static-strain-dependence of dynamic complex modulus of viscolelastic materials in computational analysisso far. Current commercial Finite Element Method (FEM) codes do not take such characteristics into consideration in constitutive equations of viscoelastic materials. Recent experimental observations that static-strain-dependence of dynamic complex modulus of viscolelastic materials, especially filled rubbers, are significant, however, require that solutions somehow are necessary. In this study, a simple technique of using a commercial FEM code, ABAQUS, is introduced, which seems to be far more cost/time saving than development of a new software with such capabilities. A static-strain-dependent correction factor is used to reflect the influence of static-strains in Merman model, which is currently the base of the ABAQUS. The proposed technique is applied to viscoelastic components of rather complicated shape to predict the dynamic stiffness under static-strain and the predictions are compared with experimental results.

Effects of commercial waxes on asphalt concrete mixtures performance at low and medium temperatures

Effects of adding two commercial waxes to three 160 / 220 penetration grade bitumens in asphalt concrete mixtures were studied using tensile stress restrained specimen test (TSRST), dynamic creep test and complex modulus test. Significant physical hardening of binders, observed in binder testing, could not be observed using TSRST. The reason could be that low temperature physical hardening does not have a large effect on fracture properties of the asphalt mix or that TSRST is a non-suitable test for showing these effects. In dynamic creep testing, the smallest strains were recorded for the asphalt mixture containing non-waxy bitumen and FT-paraffin, indicating better resistance to rutting . In complex modulus testing, adding of 6% commercial wax clearly increased the modulus and decreased the phase angle, an effect more pronounced for the mixture containing FT-paraffin compared to the one containing polyethylene wax.

Relationship between structural evolution and rheological measurements for polymer + organoclay nanocomposites

AbstractNanocomposites with synthetic biodegradable aliphatic polyesters (BAP) were synthesized by the solution intercalation method with addition of organically modified montmorillonite. The hybrid structural evolution, caused by nanoscopic interaction between matrix polymer and layered silicate, was analyzed using viscoelastic properties obtained from oscillatory rheological measurements. Changes of viscoelastic properties to more solid-like, especially in the terminal region, were explained by both formation of specific BAP chain mesostructures with organoclay incorporated and a rheological percolation threshold. This behaviour was analyzed via a modified Cole-Cole plot evaluating the structural changes with filler concentration as well as the frequency dependence of dynamic modulus, complex modulus, and phase angle. Furthermore, the stress relaxation behaviour successfully demonstrated structural changes and critical concentration of nanocomposites with a jump shift of the longest relaxation time towards longer time.

Characterization of chemically treated bacterial ( Acetobacter xylinum) biopolymer: Some thermo-mechanical properties

Bacterial cellulose prepared from pellicles of Acetobacter xylinum ( Gluconacetobacter xylinus) is a unique biopolymer in terms of its molecular structure, mechanical strength and chemical stability. The biochemical analysis revealed that various alkali treatment methods were effective in removing proteins and nucleic acids from native membrane resulting in pure cellulose membrane. The effect of various treatment regimens on thermo-mechanical properties of the material was investigated. The cellulose in the form of purified cellulose membranes was characterized by differential scanning calorimetry (DSC), thermo-gravimetric analysis (TGA) and dynamic mechanical thermal analysis (DMTA). The glass transition temperature ( T g) of the native cellulose (untreated, compressed and dried pellicle) was found to be 13.94 °C, in contrast, the chemically treated cellulose membranes has higher T g values, ranging from 41.41 °C to 48.82 °C. Investigations on isothermal crystallization were carried out to study the bulk crystallization kinetics. Thermal decomposition pattern of the native as well as alkali treated cellulose was determined by obtaining thermo-gravimetric curves. At higher temperatures (>300 °C), the biopolymer was found to degrade. Nevertheless, the alkaline treated cellulose membrane was more stable (between 343.27 °C and 370.05 °C) in comparison to the native cellulose (298.07 °C). Further, the percentage weight loss in case of native cellulose was found to be 26.57%, in comparison to 6.45% for the treated material, at 300 °C. The DMTA revealed complex dynamic modulus of the material, at different temperatures and fixed shear stress, applied at a frequency of 5 Hz. The study delineated the effect of alkali treatment regimens, on the thermo-mechanical properties of bacterial cellulose for its application over a wide range of temperatures.

Simulated Soft Tissue Nanoindentation: A Finite Element Study

To address the growing interest in nanoindentation for biomaterials, the following finite element study investigated the influence of indentation testing protocol and substrate geometry on quasi-static and dynamic load-displacement behavior of linear viscoelastic materials. For a standard linear solid, the conventional quasi-static indentation modulus, EQS, fell between the instantaneous and equilibrium modulus of the model. EQS approached the equilibrium modulus only for indentation unloading times 1000 times greater than the characteristic relaxation time of the model. It was nearly insensitive to other changes in the indentation testing protocol, such as tip radius and penetration depth, exhibiting variations of only 5–10%. Dynamic nanoindentation provided a quantitatively accurate assessment of the complex dynamic modulus (within ±12%) for a range material of parameters at physiologically relevant testing parameters. Both quasi-static and dynamic moduli calculated from the irregular surfaces varied with the size and shape of the irregularities but were still within 10% of the smooth surface values for penetration depths larger than the dimensions of the surface irregularities.

RHEOLOGICAL PROPERTIES OF ER-FLUIDS IN TERM OF MULTIPARTICLE PHYSICAL MODEL AND MONTE-CARLO COMPUTER SIMULATION

An electrorheological fluids (ERF) are the suspensions consisting of dielectric rigid particles in the viscous (or viscoelastic) media. Based on the three-dimensional well-ordered multi-particle model (the crystal model) we describe rheological properties of ERF. We use the model of cubic body-centered lattice. We also assume that the electric field is orthogonal to the velocity of shear of fluid's layers. The displacement gradients are assumed to be different (from small to finite values). For small deformations in the framework of the approach proposed and under assumptions made it was stated that the ERF can be treated as a viscoelastic body and it is consequently described on the basis of the linear theory of viscoelasticity. We obtain a complex dynamic shear modulus as a function of the electric field strength, volume fraction of filler, electric properties of components of ERF and viscosity of the fluid phase. For finite deformation the relation between stresses and shear rate gradients has also been made. The relation does not keeps whatever phenomenological or arbitrary parameters and takes into account contribution an electrostatic interaction painted by external field dipoles. From other side a bunch of computational experiments by Monte-Carlo approximation to model both the structure and the peculiarities of ERF were made. We use a procedure by Metropolis for canonic NVT ensemble and parallel computational technologies. The structural characteristics, density, energetic parameter and others for system under consideration have been estimated. In order to verify a theoretical predictions we compare both approaches and some experimental data.

The use of a novel PLGA fiber/collagen composite web as a scaffold for engineering of articular cartilage tissue with adjustable thickness.

It has been a great challenge to make the thickness of engineered cartilage adjustable to cover the range of both partial-thickness and full-thickness articular cartilage defects. We developed a novel kind of composite web scaffold that could be used for tissue enginnering of articular cartilage with the thickness adjustable between 200 microm and 8 mm. The composite web showed a unique structure having web-like collagen microsponges formed in the openings of a mechanically strong knitted mesh of poly(lactic-co-glycolic acid). The knitted mesh served as a skeleton reinforcing the composite web, while the web-like collagen microsponges facilitated cell seeding, cell distribution, and tissue formation. Bovine chondrocytes cultured in the composite web showed a spatially even distribution, maintained their natural morphology, and produced cartilaginous extracellular matrices such as type II collagen and aggrecan. The thickness of the implant can be simply adjusted by laminating or rolling the web sheets. Not only did the histological structure of the engineered cartilage patches match the bovine native articular cartilage, but also their dynamic complex modulus, structural stiffness, and phase lag reached 37.8, 57.0, and 86.3% of those of native bovine articular cartilage, respectively. The composite web could be an important scaffold for tissue engineering.

An experimental technique for complete dynamic characterization of a viscoelastic material

An experimental technique for completely characterizing a viscoelastic material, by determining the Poisson ratio and the complex dynamic Young's modulus of a small beam-like specimen subject to seismic excitation is presented in this paper, together with the theoretical background. The same experimental device is used basically for both kinds of tests: the specimen is instrumented, placed into a temperature controlled chamber and excited by means of an electrodynamic shaker. The longitudinal and the transversal deformations are measured by strain gauges to get the Poisson ratio, whereas the vertical displacement of the specimen and the acceleration of the support are measured to get Young's modulus of the tested material. The experimental curves of the Poisson ratio and of Young's modulus, obtained at different temperatures, are then gathered into a unique master curve by using the reduced variables method. The two master curves, respectively, represent the Poisson ratio and Young's modulus for the tested material in a very broad frequency range.

EFFECT OF METHOCEL AS A WATER BINDER ON THE LINEAR VISCOELASTIC PROPERTIES OF MOZZARELLA CHEESE DURING EARLY STAGES OF MATURATION

Changes in the dynamic and transient rheological character of highmoisture, skim milk (HMSM) Mozzarella cheese due to the addition of 0.2% Methocel (methyl cellulose) as a water binder at room (25C) and refrigeration (7C) temperatures during early stages of maturation (1, 5, 7, and 14 days after manufacture) were investigated. The HMSM Mozzarella with 0.2% Methocel was softer (lower dynamic storage and loss modulus, and higher creep and recovery compliance) compared to HMSM Mozzarella without Methocel, due to improved water holding capacity. The age‐dependent frequency dispersions of dynamic mechanical spectra (storage and loss modulus) were fitted to a power‐law model. A six‐element Voigt‐Kelvin mechanistic model described the age‐dependent retardation spectra (compliances, viscosities, and retardation times) obtained from creep experiments. Strong correlation was obtained between the viscoelastic

A “Wobble-Plate” Dynamic Test Device

Abstract A simple dynamic tester is proposed, in which a disk of rubber is subjected to a rotating tilting deformation. In one arrangement, the rubber disk rests on a horizontal base and a light steel plate rests on its upper surface. A circular groove in the upper surface of the plate is centered on the axis of the rubber disk. An off-center vertical load is then applied to the rubber disk via a steel ball running in the circular groove. As the ball rolls round the groove, driven by friction with a rotating countersurface, the rubber disk undergoes a rotating off-center compression - a tilting deflection - that rotates at the same rate as the ball. If the rubber is perfectly elastic, no torque is required to maintain this motion and the deflection of the rubber will be exactly in phase with the compressive force. The maximum deflection then occurs at the location of the ball. However, if the rubber exhibits delayed elasticity, then the maximum deflection occurs after the ball has passed, at an angular separation δ, where δ is the angle of mechanical loss. Thus, the phase angle δ can be observed and measured directly. Also, if required, the separate components E′ and E″ of the complex dynamic modulus can be calculated from the applied force and deflection, and the torque required to maintain the motion.

Fatigue Life Of Asphalt Concrete With Rubber Grains

This paper presents some results achieved in a wide research carried out in the road material laboratory of the Rome University La Sapienza to assess the suitability of a new hot mix asphalt (HMA), containing crumb rubber (particle size 2-5 mm), as sub-ballast in railways or base layer in road pavements. This material could be effective in the reduction of vehicular traffic vibrations; however, crumb rubber is responsible for reducing mechanical characteristics of the asphalt concrete. The aim of this step of the program here discussed is to evaluate the influence of kind and content of crumb rubber on bituminous mixes, regarding fatigue life. The experimental analysis was directed to detect .the initial modulus value, above which this bituminous material will remain structurally serviceable for a considerable period. The tests were conducted on cylindrical specimens, using a servo-hydraulic loading system and operating in a loaded-controlled fashion (tension-compression), at a frequency of 10 Hz and a temperature of 20 C. The adopted failure criterion, considering an assigned constant stress amplitude, was the number of load repetition that causes a decrease in modulus to half the initial value or, depending on the progress of the test, the fracture of the specimen due to macro-cracking. The tests were performed with various stress levels, related to the stiffness of the mix. This study documents the relationship between stiffness, as characterized by dynamic (complex) modulus, and fatigue life. Four mixes, different in kind and content of rubber, were checked and compared with a traditional WMA. The interpretation of experimental results demonstrates that mixes, containing a certain kind and a weight content up to 3% of crumb rubber, show a fatigue life comparable with traditional HMA. Transactions on Engineering Sciences vol 40, © 2003 WIT Press, www.witpress.com, ISSN 1743-3533

Model studies for wheat sourdough systems using gluten, lactate buffer and sodium chloride

Model studies were conducted in order to study the influence of acid and NaCl, as occurring in wheat sourdough bread, on fundamental rheological properties of wheat gluten. Gluten was divided into pieces and subjected to a swelling period in lactate buffer of pH 3.9, with or without added NaCl (3 g/100 ml). The respective controls were unbuffered NaCl solution and pure water. The microstructure of the gluten pieces was studied by laser-scanning confocal microscopy and the recombined pieces were examined using fundamental rheology. The combination of buffer (pH 3.9) and NaCl in comparison to unbuffered NaCl solution caused a denser, but partially dissolved fibrillar microstructure. Further to this, swelling of the gluten was reduced (62.0% versus 65.9% moisture) and an increase in firmness and elasticity was observed: in comparison with unbuffered NaCl solution, the absolute value of the complex dynamic modulus (|G*|) was higher, while the phase angle was lower in dynamic oscillatory measurements at 30 °C and dynamic temperature sweeps (30–95 °C), while in creep tests at 30 °C and 95 °C strain values were lower and relative recovery higher. In contrast, pH 3.9 buffer without added NaCl caused softer rheological behaviour than water and a film-like microstructure.

Relaxation mechanism in several kinds of polyethylene estimated by dynamic mechanical measurements, positron annihilation, X-ray and 13C solid-state NMR

Relaxation processes of several kinds of polyethylene films and fibers with different molecular orientational degrees and crystallinities were extensively investigated by the dynamic mechanical relaxation, positron annihilation and 13C nuclear magnetic relaxation ( 13C NMR). From complex dynamic tensile modulus, the activation energies of α 1 and α 2 relaxations were determined to be 97–118 and 141–176 kJ/mol, respectively. The activation energy of β relaxation was 114–115 kJ/mol. These values were similar to those of α 1 relaxation reported already. For γ relaxation mechanisms, there existed two mechanisms, γ 1 and γ 2, the activation energies being 9–11 and 23–25 kJ/mol, respectively. The values were independent of the molecular orientation and crystallinity. The two local motions indicate that non-crystalline phase composes of two regions of non-crystalline phase, rubber-like amorphous phase and interfacial-like amorphous phase. From 13C NMR measurements of 13C longitudinal relaxation time for the non-crystalline phase, the activation energy was 20.7 kJ/mol. This value is close to the activation energy (23–25 kJ/mol) of the γ 2 relaxation estimated by the dynamic mechanical measurement. The result by 13C NMR did not provide two kinds of activation energy, indicating combined influence of the two correlation times. Even so, the activation energies obtained by 13C NMR indicated that the γ 2 relaxation mainly is due to the motion of the C–C central bond of a short segment (e.g. three to four CH 2) within interfacial-like amorphous phase. The γ and β relaxation peaks by the dynamic mechanical measurements corresponded to the first and second lifetime transition of ortho-positronium indicating, in turn, a drastic change in free volume by local mode relaxation.

Acoustic measurement of the low-energy excitations in Nd 2− xCe xCuO 4+ δ

The complex dynamic Young's modulus of ceramic Nd 2− x Ce x CuO 4 with x=0, 0.05 and 0.20 has been measured from 1.5 to 100 K at frequencies of 1–10 kHz. In the undoped sample the modulus starts decreasing below ∼20 K, instead of approaching a constant value as in a normal solid. The modulus minimum has been interpreted in terms of paraelastic contribution from the relaxation of the Nd 3+ 4f electrons between the levels of the ground state doublet, which is split by the interaction with the antiferromagnetically ordered Cu sublattice. The value of the splitting is found to be 0.34 meV, in excellent agreement with inelastic neutron scattering, infrared and specific heat experiments. With doping, the anomaly shifts to lower temperature and decreases in amplitude, consistently with a reduction of the local field from the Cu sublattice.

Modelling corn starch swelling in batch systems: effect of sucrose and hydrocolloids

Hydrocolloids are used in starch-based products to improve stability and to obtain specific textural characteristics. In stirred batch systems with constant jacket temperature, xanthan gum, guar gum and sodium alginate (1% w/w) were added to corn starch (10% w/w) and sucrose (15% w/w) in aqueous systems to test their effects on granule swelling, starch gelatinization temperatures and viscoelastic behavior of the hot paste. As heating is not instantaneous, time–temperature relationships cannot be avoided. In this regard, heat penetration was faster in viscoelastic systems with lower complex dynamic modulus ( G *) values, while pastes containing gums showed lower heat transfer rates during gelatinization. Microscopy and image analysis were applied to describe the granule swelling process in starch gelatinization. Starch granule swelling was considerably reduced by the presence of gums due to the lower heating rates and the decreased mobility of water molecules. The presence of sucrose increased starch gelatinization temperatures, measured by differential scanning calorimetry; gum addition did not show a significant influence on these temperatures. The effect of time and temperature on the starch swelling process was modelled considering, as driving force, the difference between the instantaneous mean curvature of the granule (reciprocal of the diameter) and the asymptotic curvature. Gelatinization rate constants were calculated for the different pastes and the lowest values were observed for starch pastes added with gums. Activation energies ranged from 80 (±14) to 119 (±3) kJ mol −1, being comparable to values reported in the literature for starch gelatinization measured by different methods.

Effect of Single Strain and Traditional Mixed Strain Starter Cultures on Rheological Properties of Wheat Dough and on Bread Quality

ABSTRACTInvestigations were made to test the effect of two different sourdough starter culture types on wheat dough and bread quality. Two single‐strain starter cultures consisting of well‐defined strains of lactic acid bacteria (Lactobacillus plantarum, L. brevis) and a traditional mixed‐strain sourdough culture (containing L. crispatus, L. pontis, and Saccharomyces cerevisiae) were evaluated for their effects on the rheological characteristics of wheat dough using both fundamental rheological and standard baking tests. Two other doughs were also evaluated, one which was chemically acidified to a comparable pH value by the addition of lactic acid, and a control which was not acidified. Dynamic oscillation tests were performed using a controlled stress rheometer. The phase angle and the absolute value of the complex dynamic modulus were measured for all doughs at frequencies of 0.1–10 Hz. The addition of sourdough prepared using single‐strain or mixed‐strain cultures significantly increased the phase angle and reduced the complex modulus of the doughs at all frequencies (P < 0.05). Significant differences were found between the dough which was chemically acidified and those doughs which were biologically acidified. The addition of sourdough effected an increase in loaf specific volume relative to both the chemically acidified and the nonacidified doughs.

MAGNETOSTRICTIVE PHENOMENA IN MAGNETORHEOLOGICAL ELASTOMERS

A host of fascinating and useful magnetic phenomena are found in composites containing magnetizable particles in viscoelastic solids. Embedding magnetically soft iron particles in natural rubber produces a class of magnetostrictive composites sometimes termed magnetorheological (MR) elastomers. We have previously shown that these materials can exhibit viscoelastic moduli that increase substantially in an applied magnetic field. In this paper, we incorporate MR elastomers in a simple resonant structure called a tuned absorber to measure the complex dynamic shear moduli of these materials at high frequencies. We find that the fluid-induced modulus increase in MR elastomers is substantial even at kilohertz mechanical frequencies. As in previous measurements at low frequencies, the moduli are generally found to decrease with strain amplitude. We also report preliminary measurements of the relatively large elongation of these materials in applied magnetic fields.

Disentangling α from β mechanical relaxations in the rubber-to-glass transition of high-sugar–chitosan mixtures

The occurrence of molecular motions in addition to those of the glass-transition region (α mechanism) were investigated in chitosan and a branched derivative substituted with alkyl chains having eight carbon atoms. Once hydrophobic interactions of the alkyl groups in aqueous solution were demonstrated, polymers were mixed with glucose syrup at high levels of solids. The real ( G′) and imaginary ( G′′) components of the complex dynamic modulus in high-solid mixtures were measured between 0.1 and 100 rad s −1 in the temperature range from −55 to 50 °C. The method of reduced variables gave superposed curves of G′ and G′′, which unveiled an anomaly in the dispersion of the alkylated derivative both in terms of higher modulus values and dominant elastic component of the polymeric network, as compared with the glass-transition region of chitosan. It was proposed that the new mechanical feature was due to β mechanism, and master curves of viscoelastic functions and relaxation processes were constructed to rationalize it.

Frictionally excited thermoelastic instability in viscoelastic and poroelastic media

Friction materials commonly used in sliding applications, such as clutches and brakes, can be poroelastic and exhibit a viscoelastic behaviour. To the author's knowledge, there are no comprehensive analysis of the influence of poroelastic and viscoelastic material properties on the onset of the phenomenon of frictionally excited thermoelastic instability in sliding systems. This issue is here analysed in some details. Firstly, a linear standard model for the friction material is adopted, introducing an effective complex dynamic modulus E=|E| e jδ and individuating three independent parameters, E 1, E 2/ E 1 and c 2/ E 1, that fully describe its viscoelastic behaviour. Subsequently, a similarity between viscoelastic and poroelastic formulation is presented and the three independent parameters introduced are related to the viscosity of the fluid μ f , the permeability k p and elastic properties M, α B of the porous material. The linear elastic formulation proposed by Decuzzi et al. (ASME J. Tribiol. 2001;123:865) has been modified in order to take account of the new constitutive model and the variation of the critical sliding speed with the wave parameter, and viscoelastic/poroelastic properties of the material are examined. It has been found that the susceptibility towards thermoelastic instability increases by increasing both the elastic E 2/ E 1 and viscoelastic c 2/ E 1 parameters, or by increasing the Biot modulus M and effective stress coefficient α B , the viscosity μ f of the fluid, and by reducing the permeability k p of the porous skeleton. It has been shown that for porous friction materials employed in wet clutches which are weakly viscoelastic, the neglect of its poroelastic behaviour leads to an overestimation of the critical speed smaller than 10%. However, much larger variations are predicted for elastomeric and porous materials with more pronounced viscoelastic behaviour.

Use of Stiffness of Hot-Mix Asphalt as a Simple Performance Test

The objective was to determine whether the stiffness of a mix could be used as a simple performance test (SPT) parameter to complement the Superpave® volumetric mix design. This was investigated by a statistical analysis of the strength of the correlation between different mixture stiffness parameters and field performance (rutting, thermal, and fatigue cracking). A total of 30 mixtures were tested with laboratory-fabricated specimens. The studied stiffness parameters were compressive dynamic (complex) modulus | E*|, simple shear tester (SST) shear (complex) modulus | G*|, and dynamic elastic modulus Ed, obtained from ultrasonic wave propagation. Also, computed stiffness factors | E*|/sin ϕ and | G*|/sin ϕ for rutting and | E*|sin ϕ for cracking were studied as analogous to the Superpave binder specification. Research indicated that the correlation to rutting varied based on test temperature and frequency; it peaked at 54.4°C and 5 Hz. At peak conditions, | E*|/sin ϕ had better statistical correlation to rutting than | E*|, but correlations reversed at lower frequencies. Although | E*| and | G*| had similar correlation to rutting, analysis of test data indicated that the SST shear testing gave lower stiffness values and higher phase-angle values than the compressive dynamic modulus testing, even when Poisson’s ratio effects were considered. This was especially true at high temperatures. Because of these and other reasons, the dynamic modulus | E*| was recommended as the SPT parameter for rutting as well as for fatigue cracking. None of the studied parameters turned out to be adequate performance indicators for thermal cracking.