Relaxation behavior of neat and particulate filled polypropylene in uniaxial and multiaxial compression

The recently developed confined compression test was used to measure the viscoelastic bulk and shear relaxation moduli of neat, glass bead and talc filled polypropylene. In this paper further modifications of the test are introduced and a criterion for the assessment of the quality of experimental data is suggested. As expected, shear as well as the bulk relaxation moduli were found to increase with the addition of particles. In order to determine the pressure sensitivity of the material, unconfined compression tests were also performed and compared with the confined tests through interconversion of the measured moduli. In agreement with earlier results on other polymers, it turned out that the relaxation response is significantly retarded at higher confinement levels. It is shown that the effect of filler particles on the long-term behavior depends on the specific uniaxial or multiaxial stress state. Poisson’s ratio was calculated by interconversion from the bulk and shear relaxation modulus; these results show that with a single test in the confined configuration, a complete viscoelastic characterization of the material can be obtained.     

The viscoelastic response of cement paste to three-dimensional loading

The majority of the viscoelastic constitutive data for cement paste or concrete found in the literature deal exclusively with uniaxial loading. To predict the isotropic response of concrete or cement paste under multiaxial loading or multiaxial prescribed deformation, it is necessary to have knowledge of at least two viscoelastic constitutive properties. In the past, the typical treatment of three-dimensional modeling of concrete viscoelasticity has involved the assumption of a time-independent viscoelastic Poisson ratio. However, the experimental evidence supporting this simplification is inconclusive. In this study, experiments were performed on hardened cement paste that allowed the simultaneous measurement of both the dilatational and shear compliances, allowing the full three-dimensional characterization of the constitutive response. It was found that the dilatational compliance leveled off after several days for three of four mixtures tested. In these three materials, the Poisson’s ratio was found to be an increasing function of time. Prediction of the measured uniaxial compliance using the measured bulk and shear compliances indicated that the confined compressive test used in this research may cause changes in the material which affect the measured dilatational compliance, and therefore the calculated viscoelastic Poisson ratio.     

Viscoelastic properties of architected foams based on the Schoen IWP triply periodic minimal surface

Abstract

In this article, we studied the viscoelastic properties of an architected foam based on the mathematically-known Schoen IWP triply periodic minimal surface (TPMS) under both time and frequency domains. IWP-based architectures possess unique multifunctional attributes when used as a three-dimensional (3D) reinforcement in composites. The 3?D representative volume elements (RVEs) of different relative densities (i.e., the ratio of the foam’s density to the density of its solid counterpart) were generated and studied using the finite element method in order to predict the effective uniaxial, shear, and bulk viscoelastic responses of IWP-foams as a function of relative density and/or frequency. The principle of time-temperature superposition principle was used to create the master curve of the observed relative-density dependent mechanical responses (loss tangent, storage and loss moduli) in frequency domains. Reduced uniaxial, bulk, and shear stiffness-loss map results suggested that the IWP-foam possesses strongest uniaxial viscoelastic response while highest damping can be achieved under shear responses. Relaxation behavior of IWP-foam was compared with other six different types of open-cell periodic foams. It was found that IWP-foam uniaxial response is similar to simple cubic foam, bulk relaxation response is similar to primitive-foam while shear response follows the behavior of body centered cubic foam. Among these foams, we found that IWP-foam is the best candidate to use as a damper under uniaxial and hydrostatic loading conditions.     

Fitting stress relaxation experiments with fractional Zener model to predict high frequency moduli of polymeric acoustic foams

This paper presents a time domain method to determine viscoelastic properties of open-cell foams on a wide frequency range. This method is based on the adjustment of the stress–time relationship, obtained from relaxation tests on polymeric foams’ samples under static compression, with the four fractional derivatives Zener model. The experimental relaxation function, well described by the Mittag–Leffler function, allows for straightforward prediction of the frequency-dependence of complex modulus of polyurethane foams. To show the feasibility of this approach, complex shear moduli of the same foams were measured in the frequency range between 0.1 and 16 Hz and at different temperatures between ?20 °C and 20 °C. A curve was reconstructed on the reduced frequency range (0.1 Hz–1 MHz) using the time–temperature superposition principle. Very good agreement was obtained between experimental complex moduli values and the fractional Zener model predictions. The proposed time domain method may constitute an improved alternative to resonant and non-resonant techniques often used for dynamic characterization of polymers for the determination of viscoelastic moduli on a broad frequency range.     

Creep rupture and viscoelastoplasticity of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformations with small strains. The stress-strain relations involve eight material constants that are found by fitting the experimental data. The model is applied to the numerical analysis of creep failure of polypropylene under various deformation modes (uniaxial tension, equi-biaxial tension, shear, multiple-step creep tests).     

Viscoelastic–plastic damage model for porous asphalt mixtures: Application to uniaxial compression and freeze–thaw damage

Porous asphalt mixture increasingly used in highway pavement applications is an open graded composite material which has fewer fines and more air voids compared with conventional dense graded asphalt mixtures. The freeze thaw resistance of the mixture is crucial for the performance of porous asphalt pavement especially when clogging is unavoidable. A simple viscoelastic–plastic damage model is developed to evaluate the effects of freeze–thaw of porous asphalt mixtures. Generalized Maxwell and Drucker–Prager model are used to determine the viscoelastic and plastic responses respectively. The damage and its evolution is characterized by Weibull distribution function. Experimental data from uniaxial compressive strength tests, conducted at different strain rates and temperatures, are used to calibrate the model. The sensitivity of model parameters to loading conditions is identified. Simulation results suggest that loss of cohesion is the dominant mechanism of failure in porous asphalt mixtures under freeze–thaw cycles. Freeze–thaw effects also lead to changes of plastic potential surface and induce large volumetric strains under loading.     

Validation of the time–temperature superposition principle for crack propagation in bituminous mixtures

The time–temperature superposition principle (TTSP) is known to be valid in the small strain domain where the behaviour of bituminous mixtures is linear viscoelastic (LVE). The behaviour is then called thermorheologically simple. In this work, an experimental campaign was performed at University of Lyon/ENTPE (France) to check the validity of the TTSP in the linear domain in the tridimensional case and also when cracks occur and propagate in bituminous mixture. A four-point bending test, which has been designed at University of Lyon/ENTPE, was used as crack propagation test. First, a complex modulus test is performed on cylindrical specimen in the LVE domain. Then, a series of crack propagation tests are carried out at different temperatures and different imposed displacement rates. The same shift factors obtained for master curve of complex modulus is also applied for the crack propagation tests analysis. The results allow obtaining a unique curve, for identical loadings when plotting as a function of reduced time. This result confirms that the TTSP is also valid for crack propagation in bituminous mixtures.     

Modelling dilation in an idealised asphalt mixture using discrete element modelling

This paper investigates the use of discrete element modelling (DEM) to simulate the behaviour of a highly idealised bituminous mixture under uniaxial and triaxial compressive creep tests. The idealised mixture comprises single-sized spherical (sand-sized) particles mixed with bitumen and was chosen so that the packing characteristics are known (dense random packing) and the behaviour of the mixture will be dominated by the bitumen and complex aggregate interlock effects will be minimised. In this type of approach the effect of the bitumen is represented as shear and normal contact stiffnesses. A numerical sample preparation procedure has been developed to ensure that the final specimen is isotropic and has the correct volumetrics. Elastic contact properties have been used to investigate the effect of the shear and normal contact stiffnesses on bulk material properties. The bulk modulus was found to be linearly dependent on the normal contact stiffness and independent of the shear contact stiffness. Poisson’s ratio was found to be dependent on only the ratio of the shear contact stiffness to the normal contact stiffness. An elastic contact has been assumed for the compressive normal contact stiffness and a viscoelastic contact for shear and tensile normal contact stiffness to represent the contact behaviour in idealised mixture. The idealised mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on the rate of dilation with shear strain for the sand asphalt. The numerical results have been validated with experimental data.     

Rheological characterisation of modified binders at mixing and compaction temperature

The mixing temperature for binders is normally chosen by the pavement engineer based on a specific ‘viscosity’ required during hot mix asphalt production. Majority of the unmodified binders exhibit Newtonian behaviour at the mixing temperature and hence the determination of the same is straight-forward. However, when modified binders are used, experiments using a rotational viscometer indicate that the binder exhibits viscoelastic non-Newtonian fluid characteristic even at very high temperature. Consequently, the ‘viscosity’ varies with time and the location where it is measured, and hence is not a unique property of the material. In this work, a thermodynamically consistent, frame-invariant viscoelastic non-Newtonian fluid model was developed to characterise the rheological properties of the binders tested in a rotational viscometer. In the investigation reported here, two types of modified binders, polymer and crumb rubber, and one unmodified binder were used. These binders were subjected to steady and variable shear rate experiments in a rotational viscometer. The viscoelastic non-Newtonian model developed was able to predict reasonably the response of binders subjected to various protocols. In addition, bituminous mixtures were fabricated at different mixing and compaction temperatures using these binders, and the evolution of volumetric properties was investigated. The experimental investigation on mixtures showed that for identical aggregate gradation, the apparent viscosity of the binders played a critical role on the final volumetric properties obtained.     

Analysis of viscoelastic laminated composite plates

A micromechanics analysis is performed for the determination of the five independent elastic moduli of unidirectional fiber composites. By considering viscoelastic phases and by using the correspondence principle and the inversion of the Laplace transform, the five time-dependent functions which characterize the effective behavior of viscoelastic composites are established. The predicted time-dependent behavior is applied for the analysis of viscoelastic laminated plates. The resulting viscoelastic effects are shown, and comparison between the results obtained within the classical laminated plate theory and the first-order shear deformation theory is discussed.     

Deformation analysis of tunnel excavation in gravelly formation using the anisotropic degradation model

This study adopts a shear-induced anisotropic degradation model to analyze the deformation of excavation in gravelly formations. The adopted model is a variable moduli model with the following characteristics: the stress–strain relationship originates from degradation of the bulk modulus and shear modulus subjected to different loadings. Under hydrostatic loading, gravelly soil may behave as an isotropic material. However, when gravelly soil is subjected to shear loading, the material becomes anisotropic and degrades before ultimate strength is attained. Therefore, this study introduces an anisotropic factor to reflect the tendency to shear-induced volumetric deformation. To analyze the deformation of the Pakuashan tunnel, which passes through a gravelly formation in Taiwan, the model was first validated by comparing the drained triaxial test results of gravelly materials sampled from the tunnel. The proposed model is implemented with a finite element code to predict the tunnel deformation under construction. A comparison between the monitoring data and numerical analysis shows that the proposed model can reasonably simulate the behavior of a gravelly formation under excavation. Numerical analysis shows that the main deformation of the tunnel is the result of significant degradation of the moduli around the whole section, especially at the crown and invert of the tunnel.     

Uniaxial tensile and shear deformation tests of gold-tin eutectic solder film

This paper describes a novel experimental technique for measuring mechanical properties of gold-tin (Au-Sn) eutectic solder film used for soldering package in microelectromechanical systems (MEMS). Dual-source DC magnetron sputtering was employed to deposit Au-20 weight % (wt%) Sn film. The tensile test with in situ X-ray diffraction (XRD) measurement evaluates the Young's modulus and Poisson's ratio at intermediate temperatures. The Young's modulus and Poisson's ratio at room temperature were found to be 51.3 GPa and 0.288, lower than bulk values. The Young's modulus decreased with increasing temperature, whereas the Poisson's ratio did not depend on temperature. The XRD tensile test also showed creep deformation behavior of Au-Sn film. We have developed a shear deformation test technique, which is performed by using Au-Sn film sandwiched by two single crystal silicon (Si) cantilever structures, to characterize the shear properties of the film. The shear moduli obtained from the shear deformation tests ranged from 11.5 to 13.3 GPa, about 38% lower than those from the XRD tensile tests. The measured shear strength from 12 to 17 MPa exhibited a temperature dependency. Information about the tensile and shear characteristics would likely to be of great use in designing Au-Sn soldering packages for MEMS.     

Three‐dimensional analysis of fatigue tests on bituminous mixtures

A tension–compression test on cylindrical specimens was used to study the three‐dimensional behaviour of bituminous mixtures during fatigue tests. The tests were carried out at 10 °C, 10 Hz at constant strain amplitude mode. The axial strain, radial strain and axial stress were measured using a prototype apparatus developed at the University of Lyon/“Ecole Nationale des TPE” (ENTPE). In addition to axial stress and strain analysis, the measurements of the radial strain made it possible to obtain the complex Poisson ratio and the volumetric strains during the tests. The results showed good correlations between the volumetric strains and global damage. The effects of the change of temperature due to viscous dissipation on the volumetric strain and on the complex modulus were also analysed.     

Unilateral interactions in granular packings: a model for the anisotropy modulus

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.     

Measurement of Bulk Mechanical Properties and Modeling the Load-Response of Rootzone Sands. Part 2: Effect of Moisture on Continuous Sand Mixtures

The compression and failure responses of four rootzone sand mixtures (with different types of particle shapes) were analyzed, compared, and modeled at two different moisture states (air dried and 30 cm tension). Differences in particle packing characteristics arising from particle shape and moisture were quantified. The air-dried and moist samples of the sand mixtures had initial bulk density (IBD) values ranging from 1.55 to 1.67g/cc and 1.23 to 1.48g/cc, respectively. The low IBD values observed for moist mixtures were attributed to the particle-particle agglomeration effects that take place in the presence of moisture. In addition, it was observed that the sand mixture's porosity increased with decreasing particle sphericity. During compression testing, moist samples underwent a greater volumetric deformation compared to the air-dried samples for the same pressure levels, e.g., at 69kPa, the volumetric strain of moist round sand mixtures was 8% higher than that of the air-dried round sand mixtures. Therefore, moisture acted as lubricant during volumetric compression of sand mixtures. Also, the bulk modulus values decreased with increasing moisture content and decreasing particle sphericity. During shear testing, the moist samples underwent a larger amount of strain deformation compared to the air-dried samples for the same stress difference values. This suggests that the presence of moisture makes the sand mixtures ductile during shear testing, unlike the usual brittle response in air-dried state. Shear modulus values linearly increased with the increase in mean pressure for the air-dried samples, whereas, for moist samples, the shear modulus values increased gradually or remained practically constant. The effect of pressure, moisture, and particle shape was also quantified for two elastoplastic parameters (consolidation and swelling indices). It was generally observed that the average consolidation index values decreased with pressure but increased with moisture and particle angularity. On the other hand, average swelling index values increased with pressure, moisture, and particle angularity. Overall, it was concluded that the moisture and particle shape had a decisive influence on the compression and shear profiles of continuous rootzone sand mixtures.     

Probabilistic parametric approach for rutting evaluation: application to hot and warm asphalt

This paper deals with a stochastic approach to evaluate the rut depth of hot and warm bituminous mixtures. First, the rutting performance of both mixtures using the French rutting tester device was evaluated. Given the random uncertainties derived from the numerous experimental measurements of the rut depth, statistical information was collected. Accordingly, the entropy maximum principle was used here to define adequate probability density function of the rut. Confidence regions with a high probability of 99% were determined for the estimation of the rut depth. In addition, comparison of mechanical and rheological results is performed with aged bitumen recovered from reclaimed asphalt and virgin bitumen to analyse the effect of ageing on bitumen viscoelastic properties. The experimental characterisation of the different binders based on rheological and conventional tests showed stiffening and hardening effects due to bitumen ageing.     

Fatigue and healing properties of nano-reinforced bituminous binders

The research work focused on fatigue and healing properties of bituminous binders containing carbon nanotubes (CNTs) and nanoclays (NCs) as reinforcing additives. Investigations were carried out by means of a dynamic shear rheometer and by employing specifically devised testing protocols. Experimental results were analysed with the specific goal of highlighting the role played by additive type and base bitumen. Although fatigue response of base bitumens was always improved by nano-modification, effectiveness of nano-particles was found to be highly dependent on the physico-chemical properties of blend components, which strongly influence the morphological configuration assumed by additives within bituminous media. Results obtained in healing tests were processed in order to discern between self-healing of cracks induced by fatigue damage and other artefact phenomena which are related to viscoelastic changes occurring in the bulk of the material. Outcomes of fatigue and healing tests were found to be coherent with interaction mechanisms which take place at the nano-scale.     

Measurement of Bulk Mechanical Properties and Modeling the Load-Response of Rootzone Sands. Part 1: Round and Angular Monosize and Binary Mixtures

The bulk mechanical properties of two different types of rootzone sands (round and angular) were measured using a cubical triaxial tester. Two monosize sands (d 50 = 0.375 mm and 0.675 mm) and their 50:50 binary mixtures (d 50 = 0.500 mm) were studied. The compression, shear, and failure responses of the above-mentioned six compositions were analyzed, compared, and modeled. Two elastic parameters (bulk and shear moduli) and two elastoplastic parameters (swelling and consolidation indices) of the six sand compositions were also calculated and compared. The angular sand was more compressible than round sand during isotropic compression. In addition, the angular sands tended to have lower initial bulk density and high porosity values. Among the three different size fractions, the 0.375 mm mixture was least compressible for both sand shapes. The failure strength and shear modulus of the angular sand were higher than the round sands. In addition, due to their simplicity, phenomenological models were developed to predict the compression and shear behavior of the sands. The prediction models were validated using subangular and subround sands. Average relative difference values were calculated to determine the effectiveness of the prediction models. The mean average relative difference values for compression profiles, i.e., volumetric stress vs. volumetric strain, were from 16 % to 39 %, except for the initial load-response portion (< 1 % volumetric strain). The predictive models were effective in reproducing the failure responses: at 17.2 kPa confining pressure, the mean of average relative difference was 23 %; at 34.5 kPa , the mean difference was 24 %.     

Viscoelastic linearity limits for bituminous materials

As bituminous materials are viscoelastic in nature, their performance must be characterised using test methods and analytical techniques that account for time (or rate) of loading and temperature. In addition, it is usually advisable to confine the characterisation of a bitumen to its linear viscoelastic response (small strains) to simplify the mathematical modelling of the material, as non-linear response, particularly for viscoelastic materials, is extremely difficult to characterise in the laboratory and model in practical engineering problems. This paper describes an investigation of the linearity limits of a range of unmodified and modified bituminous binders and mixtures using a dynamic shear rheometer and a purpose-built dynamic, direct tension-compression, servo-hydraulic testing apparatus. The results show that there are strain dependent linearity criteria for both binders and asphalt mixtures at high stiffness values (low temperatures for binders and low to intermediate temperatures for mixtures) as well as a high temperature strain dependent linearity criterion for elastomeric modified binders. The linearity strain criterion for the mixtures was found to be in the order of 100 microstrain with the criterion for the binders being at least 100 times greater at just over 10,000 microstrain and the polymer network strain criterion at 1,000,000 microstrain.