Complex Modulus Measurements Research Articles

Microstructure, AC conductivity and complex modulus analysis of Ca-ZnO nanoparticles for potential optoelectronic applications

In the present work, we investigate the conductivity characteristics and microstructure of Ca-doped ZnO (ZO_Ca) nanoparticles. ZO_Ca nanoparticles were created using a straightforward sol-gel manufacturing method and annealed at various temperatures. Powder X-ray diffraction analysis provided proof of the ZO_Ca nanoparticles' purity, crystalline nature, and hexagonal structure. Meanwhile, the transmission electron microscopy (TEM) was used to establish the morphology and shape of the ZO_Ca nanoparticles, and energy dispersive X-ray spectroscopy analysis was used to discover the components that make up the particles' makeup. Moreover, AC conductivity measurements have been used to examine the electrical characteristics of ZO_Ca nanoparticles. Reduced activation energy values demonstrate the material's appropriateness for photonics devices, and the small proportion of activation energy derived from AC conductivity and complex modulus measurements is an added benefit for the construction of optoelectronic devices.

Complex modulus of cement-bitumen treated materials produced with different reclaimed asphalt gradations

The increasing attention over cold recycling technologies as sustainable paving solutions requires a proper characterisation in terms of complex modulus for supporting the pavement design. Among cold recycled materials, cement bitumen treated materials (CBTM) benefit from the presence of both bituminous and cementitious binders. This research aims at characterising the complex modulus of CBTM mixtures produced with three different gradations, modified bitumen emulsion and two types of cement. The complex modulus measurements were modelled considering the usual viscous dissipation behaviour, linked to the bituminous component of the mixtures, along with a time- and temperature-independent dissipation component. The results showed that both the aggregate skeleton and the composition of the fine aggregate matrix affected the rheological behaviour. Furthermore, the role played by the aged binder contained in the reclaimed asphalt aggregate was highlighted by the parameters of the rheological model.

A new empirical model for predicting complex modulus of asphalt concrete materials

Asphalt concrete materials are often used in the construction of pavement layers. The complex modulus is one of the fundamental properties in mechanistic-empirical pavement design and analysis that can describe the mechanical response of this composite material. In the present study, a new complex modulus predictive model of asphalt concrete, called 9P50F has been established. The main objective of the paper is to develop a predictive empirical equation for the Moroccan pavement design guide based on several complex modulus tests and an existing database of asphalt concrete formulations. The proposed model equation depends on the results of classical tests that related to the most significant formulation parameters including, stiffening effect and proportion of mineral fillers, maximum aggregate size, ratio of coarse aggregates to sand, penetration point, ratio of fillers to asphalt binder, apparent density, softening point, and binder richness modulus. As a result, the developed model provides a higher correlation coefficient (R2 = 0.873). Furthermore, based on the complex modulus measurements of twenty-one asphalt concrete samples, by using a 2-point bending device, the goodness of fit measure for the E* predictions indicates a very good accuracy.

Measured power law attenuation of shear waves in swine liver

To characterize the attenuation and dispersion behavior of shear waves in excised swine liver samples, the complex shear modulus was measured with a Rheospectris C500 + from 10 Hz to 2000 Hz. The shear wave attenuation and shear wave speed were calculated from the complex modulus measurements. A power law fit was evaluated for the shear wave attenuation, and a power law fit with and without a constant offset was evaluated for the shear wave speed. The power law closely matches the measured shear wave attenuation over most of the frequency range evaluated, although some differences are observed in several of the samples below 400 Hz. The power law without the constant offset closely matches the measured shear wave speed above 200 Hz in all measurements, where the addition of the constant offset achieves a much closer fit in all measurements that contain discrepancies below 200 Hz. The results demonstrate that shear wave attenuation in swine liver follows a power law and that a power law with a constant offset is an effective model for the shear wave speed in swine liver. [Work supported in part by NIH Grants DK092255, EB023051, and EB012079.]

Degradation of asphalt mixtures with glass aggregates subjected to freeze-thaw cycles

Pavements in cold regions undergo extreme weather conditions such as prolonged exposure to water and repeated freeze-thaw cycles (FT). The objective of this paper was to evaluate the moisture susceptibility and degradation due to FT of asphalt mixture with glass aggregates. This was done using a new method based on complex modulus measurements. Samples were tested in dry condition and then saturated with water prior to various conditioning such as hot water soaking and multiple FT. The 2S2P1D rheological model was used to simulate the materials behaviour and evaluate the evolution of linear viscoelastic properties. Results showed that the presence of water in the mixture voids increased the mixture stiffness at temperature below freezing point. Also, repeated FT damaged the samples, glass asphalt mixture was damaged faster than the reference mixture. However, both mixtures reached equivalent damage after 10 FT cycles.

Asphalt and binder evaluation of asphalt mix with 70% reclaimed asphalt

With modern recycling technologies, reclaimed asphalt (RA) has been successfully used in new hot mix asphalt (HMA). However, even if the conventional technical specifications on binders and asphalt mixtures are met, HMA produced with high amount of RA, 50% and higher, may show poor performance behaviour. This is particularly true for cracking susceptibility due to the different chemical and physical properties of aged bituminous binder. The benefit of a purposely designed rejuvenating agent can help in using a high amount of RA in new HMA. This paper presents an evaluation of asphalt mixtures comparing a virgin asphalt mix with 0% RA and mix with 70% of RA with and without a bio-based rejuvenating agent. The different asphalt mixtures were characterised with complex modulus measurement at different temperatures and frequencies, and low-temperature cracking susceptibility through the thermal stress restrained specimen test. The binder was extracted and recovered from the different mixes to be also investigated through complex shear modulus and low-temperature behaviour using the bending beam rheometer. The outcomes of the tests showed positive effects of the bio-based rejuvenating agent especially at low temperature to restore flexibility. These effects were consistent on both the binder and the asphalt mix scale.

Comparison of complex modulus and elasticity modulus of bitumen bonded materials

The European standards for asphalt mixture testing are mainly focused on empirical parameters of asphalt mixtures. On the other hand, functional parameters (e.g. fatigue, stiffness) of asphalt mixtures describe real behavior of the material in-situ. These parameters are used for design of road construction according to the Slovak design method where the elasticity modulus is used instead of the complex modulus. The problem is that no standard for elasticity modulus measurement exists in the collection of the European standards. In this study complex modulus measurement was performed according to the European standard, and for comparison elasticity modulus measurement was also done according to the Australian standard.

GS0306 動的粘弾性試験による複素モジュラスと粘弾性ボアソン比の同時測定

GS0306 動的粘弾性試験による複素モジュラスと粘弾性ボアソン比の同時測定

Deformation Parameters and Fatigue of the Recycled Asphalt Mixtures

Abstract The deformational properties of asphalt mixtures measured by dynamic methods and fatigue allow a design the road to suit the expected traffic load. Quality of mixtures is also expressed by the resistance to permanent deformation. Complex modulus of stiffness and fatigue can reliably characterize the proposed mixture of asphalt pavement. The complex modulus (E*) measurement of asphalt mixtures are carried out in laboratory of Department of Construction Management at University of Žilina by two-point bending test method on trapezoid-shaped samples. Today, the fatigue is verified on trapezoid-shaped samples and is assessed by proportional strain at 1 million cycles (ε6). The test equipment and software is used to evaluate fatigue and deformation characteristics.

Quantification of biasing effects during fatigue tests on asphalt mixes: non-linearity, self-heating and thixotropy

Various phenomena other than fatigue (so-called “biasing effects”) occur during laboratory fatigue tests on asphalt mixes because of cyclic loading applications, thus altering experimental results and leading to misleading conclusions. The purpose of the study is to isolate and quantify biasing effects, therefore isolating real fatigue damage. In particular, non-linearity, self-heating and thixotropy (defined as a recoverable viscosity reduction after shear application) were evaluated. Six different mixes were produced using three distinct asphalt binders. Tests were performed in tension/compression mode on cylindrical samples. A particular test procedure was followed, consisting of two parts. In the first part, complex modulus measurements were performed at temperatures from 8°C to 14°C and strain amplitudes from 50 to 110 µm/m, at 10 Hz. Regression equations were fitted in order to evaluate variations of norm of complex modulus and phase angle caused by temperature and strain-level changes around common fatigue test conditions (10°C, 100 µm/m). In the second part of the test, five partial fatigue tests (each one consisting of 100,000 cycles at a 100 µm/m strain amplitude) were performed at 10°C, 10 Hz. After each fatigue lag, a 24 hour rest period was imposed. During rest periods, short complex modulus measurements were performed (10°C, 10 Hz) in order to monitor the recovery of mechanical properties. Surface and internal temperature of samples were constantly measured throughout the entire test, in order to monitor self-heating due to repeated loading. A significant temperature increase was observed during each fatigue lag, while, during rest periods, temperature rapidly decreased to the initial value. Self-heating was observed to be correlated to viscoelastic energy dissipation. The procedure used in the study allowed quantitatively estimating biasing effects. Therefore, unrecovered mechanical properties, due to damage accumulation, were obtained. Ninety per cent of total complex modulus and phase angle variations observed during each fatigue lag were found to be completely reversible. Non-linearity and thixotropy appear to influence mechanical properties variations more importantly than self-heating.

Micromechanical contribution for the prediction of the viscoelastic properties of high rate recycled asphalt and influence of the level blending

This research deals with an experimental and micromechanical study of high rate recycled asphalt with 70% of RAP. Rheological measurements of shear complex modulus of virgin, RAP and blended binders were performed at different temperatures and frequencies. Then, a micromechanical model based on the generalized self-consistent scheme (GSCS) was suggested for the prediction of the effective mechanical properties of the recycled asphalt. The GSCS-based approach aims to homogenize the heterogeneous material taking into account the intergranular porosity, on the one hand, and the possible interactions between its phases on the other one. The suggested method was compared to a step-by-step (successive) homogenization approach and literature data in elastic case were used for this purpose. The results have shown that the GSCS-based approach presents a good agreement with the data especially for higher volume fractions of aggregates. Furthermore, the significant influence of the blend homogeneity level on the estimation of the effective mechanical properties of the recycled asphalt was highlighted.

Observation of Fatigue of Bituminous Mixtures Using Wave Propagation

AbstractFatigue phenomenon is one of the main distresses observed in pavements. It is therefore quite complex to characterize in the laboratory using traditional fatigue tests. This paper presents the results of an experimental fatigue campaign led on a cement treated mixture containing reclaimed asphalt material, which gives it viscous properties. Classical cyclic fatigue tension/compression tests on cylindrical samples are considered. Damage is characterized all over the test duration using complex modulus measurements in the axial loading direction (quasistatic method) and analysis of compression wave propagation in the radial direction (dynamic method). The results show that fatigue phenomenon is clearly observable using compression wave propagation. Moreover, correlations can be found between measurements that are performed by the two methods and for various axial stress levels.

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.

Linear and nonlinear viscoelastic behaviour of bituminous mixtures

As it is the case for all materials, the behaviour of bituminous materials becomes nonlinear when the strain (stress) amplitude level increases. In this study, only “small” nonlinearities (where the applied strain amplitudes are lower than 100 µm/m) of a bituminous mixture are investigated. An improved complex modulus test campaign has been carried out on cylindrical samples. Sinusoidal cyclic loadings in tension and compression were applied at different temperatures (from −26 to 50 °C) and different frequencies (from 0.01 to 10 Hz). During sinusoidal loadings, for each temperature and frequency, three levels of strain amplitude (lower than 125 µm/m) were applied to characterize nonlinearity. Measurements of complex modulus E * and complex Poisson’s ratio ν * characterizing the viscoelastic properties of the material in 3 dimension case (3D) are introduced. From experimental results, nonlinearity of bituminous mixture is observed even at small strain amplitudes on both norm and phase angle of complex modulus. It is verified that the effect of nonlinearity is dependent on the considered equivalent temperature–frequency couple, which imply the respects the time temperature superposition principle. Moreover, the observed nonlinearity acts in the same direction in the E * Black’s diagram, and Cole–Cole diagram when increasing strain level. The viscoelastic linearity limits for tested material, which vary with equivalent temperature–frequency couple, are also presented. For the considered strain amplitude levels, no nonlinearity was observed on complex Poisson’s Ratio. A model with a continuum spectrum called 2S2P1D (two Springs, two Parabolic elements, one Dashpot), developed at the ENTPE (Ecole Nationale des Travaux Publics de l’Etat), is used to simulate the linear viscoelastic behaviour of tested bituminous mixtures. An improved version of this model is proposed to introduce nonlinear properties.

Behaviour of asphalt mixtures containing reclaimed asphalt pavement and asphalt shingle

This paper presents the results of laboratory research on asphalt mixtures containing reclaimed asphalt pavement (RAP) and asphalt shingle, including the study of their linear viscoelastic (LVE) behaviour and fatigue characteristics. Complex modulus measurements using the tension-compression test on cylindrical specimens were conducted to determine LVE behaviour. Sinusoidal cyclic loadings with a strain amplitude of approximately 50×10−6 were applied at several temperatures (from−30°C to+40°C) and frequencies (from 0.01 to 10 Hz). In addition to axial stresses and strains, radial strains were also measured. The complex modulus E* and complex Poisson's ratio ν* were then obtained and the three-dimensional (3D) LVE behaviour (with isotropy hypothesis) was then completely described. The time–temperature superposition principle was verified with good approximation in uni-dimensional and 3D conditions for the same values of shift factor. Experimental results were modelled using the 2 springs, 2 parabolic creep elements and 1 dashpot model developed at University of Lyon/ENTPE. Fatigue properties were evaluated by tension-compression tests on cylindrical specimens using the same testing device used for complex modulus. Sinusoidal loading at 10 Hz in controlled axial strain mode was applied at 10°C. The variation of complex modulus E* and complex Poisson's ratio ν* as a function of the number of cycles was obtained. The fatigue test results were analysed using six different fatigue life criteria. The analysis of the results provided a ranking of the tested materials. The influence of RAP and asphalt shingle contents was quantified.

Investigation of Cellular Contraction Forces in the Frequency Domain Using a PDMS Micropillar-Based Force Transducer

Polydimethylsiloxane (PDMS) micropillar-based biotransducers are extensively used in cellular force measurements. The accuracy of these devices relies on the appropriate material characterization of PDMS and modeling to convert the micropillar deformations into the corresponding forces. Cellular contraction is often accompanied by oscillatory motion, the frequency of which ranges in several hertz. In this paper, we developed a methodology to calculate the cellular contraction forces in the frequency domain with improved accuracy. The contraction data were first expressed as a Fourier series. Subsequently, we measured the complex modulus of PDMS using a dynamic nanoindentation technique. An improved method for the measurement of complex modulus was developed with the use of a flat punch indenter. The instrument dynamics was characterized, and the full contact region was identified. By incorporating both the Fourier series of contraction data and the complex modulus function, the cellular contraction force was calculated by finite-element analysis (FEA). The difference between the Euler beam formula and the viscoelastic FEA was discussed. The methodology presented in this work is anticipated to benefit the material characterization of other soft polymers and complex biological behavior in the frequency domain.

Dynamic properties of human round window membrane in auditory frequencies running head: Dynamic properties of round window membrane

Round window is one of the two openings into cochlea from the middle ear. Mechanical properties of round window membrane (RWM) affect cochlear fluid motion and play an important role in the transmission of sound into cochlea. However, no measurement of mechanical properties of RWM has been reported because of the complication of its location and small size. This paper reports the first investigation on dynamic properties of human RWM using acoustic stimulation and laser Doppler vibrometry measurement. The experiments on RWM specimens were subsequently simulated in finite element (FE) model and an inverse-problem solving method was used to determine the complex modulus in frequency-domain and the relaxation modulus in time-domain. The results show that the average storage modulus of human RWM changes from 2.32 to 3.83MPa and the average loss modulus from 0.085 to 0.925MPa over frequencies of 200–8000Hz. The effects of specimen geometry and experimental condition on complex modulus measurements were discussed through FE modeling analysis. Dynamic properties of RWM reported in this paper provide important data for the study of middle ear and cochlear mechanics.

Stress-Optical Relationship for Particle Dispersion Systems

Simultaneous measurements of complex modulus and complex strain-optical (birefringence) coefficient were performed for silica particle suspensions in order to clarify the stress-optical relationship. The dynamic modulus was found to be described with three Maxwell models. The strain-optical coefficient changed its sign form positive to negative with increasing frequency, suggesting the coefficient was composed of two relaxation modes. The relationship between stress and birefringence were found to be described with the modified stress-optical rule, composed of two relaxation modes. The fast mode having negative birefringence was assigned to the anisotropic distribution of particles due to deformation. The slow mode having positive birefringence was tentatively assigned to the aggregation of particles. Although the examined particle dispersion system was not ideal it was strongly suggested that the stress-optical rule would hold valid for the ideal hard particle dispersion systems.

Investigating self healing behaviour of pure bitumen using Dynamic Shear Rheometer

Self healing is known as a built-in property of bitumen, which can help bitumen and asphalt concrete to recover its strength after damage. Healing can also extend the service life of asphalt pavements. A two-piece healing (TPH) test was developed to investigate the self healing behaviour of pure bitumen using the Dynamic Shear Rheometer (DSR). During the TPH test, a healing process was directly simulated by pressing the two pieces of bitumen together under a parallel-plate system. Two phases can be distinguished from the TPH healing test, the initial healing phase due to gap closure, and the time dependent healing phase. The results are summarised as following. (1) Initial healing phase: The initial healing phase has a three-stage complex modulus increase with the closure of the gap thickness. A rapid increase of the complex modulus is observed in the second stage of the initial healing curve due to a 0.5mm gap reduction. (2) Time dependent healing phase: The time dependent healing results show a distinctive difference between the gap constant control mode and the normal force constant control mode. The normal force control healing can be decomposed into the time dependent healing during a gap constant mode and additional healing by compression. It was indicated that the compressive normal force strongly promotes healing development. (3) It was also demonstrated that many factors can influence the complex modulus measurement results by using the DSR parallel-plate geometry.

Study of the influence of experimental conditions applied to the indirect tensile test versus type of bituminous mixture

The reference modulus of bituminous mixes, used for road design in France, is determined by the complex modulus measurement, carried out in the frequency domain at 15°C, 10 Hz or by the secant modulus in direct tension at 15°C, 0.02 s. However, there is strong interest to access this modulus using the indirect tensile (IT) test carried out in the time domain. Actually, this test appears to be easier to implement due to the sample manufacturing and numerous laboratories are already equipped. The present study proposes to determine the experimental condition to be applied to the IT test in order to get the reference modulus. A theoretical approach, based on the Maxwell and Huet viscoelastic linear models, is used to find the testing conditions at which the IT test has to be performed to give as precisely as possible the reference modulus. This procedure is applied on a large database of materials for which the viscoelastic spectrum has been provided. The influence of the loading waveform, which cannot be systematically controlled, is studied. For a force increasing linearly with time, the temperature at which the IT test has to be performed is close to 10°C, whatever the bituminous mix type. Moreover, the error that would have been committed by applying the equivalent temperature Teq = 10°C during the indirect tensile test is evaluated. This error depends on the loading waveform but always remains, theoretically, under 1000 MPa. This study has been carried out in the framework of collaboration between LCPC and USIRF (Union des Syndicats de l’Industrie Routiere francaise).