Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

This paper is aimed at exploring the interconversion path between the relaxation modulus E(t) and the corresponding complex modulus E ^?(ω) for linear viscoelastic solid materials. In contrast to other approximate methods, the fast Fourier transform (FFT) algorithm is directly applied on the time-dependent part of the viscoelastic response R(t). Firstly, the method foundations are presented. Then, a theoretical example is performed by means of a generalized Maxwell model, where the influence of sampling conditions and eventual experimental error and data dispersion is analyzed. Finally, an application example using experimental data is carried out to assess the method. As a result, the proposed procedure allows obtaining the complex modulus by means of relaxation tests, and vice versa.     

Scaling of conductivity and Young’s modulus in replicated microcellular materials

Scaling exponents for the conductivity and stiffness of replicated microcellular materials exceed commonly predicted values of 1 and 2. We show here that this is caused by the fact that, in replicated microcellular materials, the solid architecture varies with the relative density: a simple derivation based on the physics of powder consolidation returns and explains the observed scaling behaviour. The same derivation also gives an explanation for Archie’s law, known to describe the conductivity of wet soils.     

Low frequency dielectric relaxation from complex impedance and complex electric ‘modulus’

The low frequency dielectric characteristics of many materials are often difficult to obtain accurately because of the d.c. conductivity contribution, which is the major portion of the loss, and which has to be subtracted from the total dielectric loss. This is particularly true for small dielectric relaxation peaks which tend to be overwhelmed by the d.c. conduction loss. An equation was derived which enables one to calculate the dielectric characteristics at low frequency, for specimens with small dielectric relaxation peaks, without subtracting the d.c. conductivity, from the complex impedance plot and complex electric modulus plot.     

Young’s modulus evolution at high temperature of SiC refractory castables

The evolution of Young’s modulus versus temperature has been evaluated in SiC-based hydraulically bonded refractories used in waste-to-energy (WTE) plants. Two types of low cement castables (LCC) with 60 and 85 wt% of SiC aggregates have been considered. The study was conducted by the way of a high temperature ultrasonic pulse-echo technique which allowed in situ measurement of Young’s modulus during heat treatment starting from the as-cured state up to 1400 °C in air or in neutral atmosphere (Ar) and during thermal cycles at intermediate temperatures (1000 and 1200 °C). For comparison in order to facilitate interpretation, thermal expansion has also been followed by dilatometry performed in the same conditions. Results are discussed in correlation with phase transformations occurring in the oxide matrix (dehydration at low temperature, crystallization of phases in the CaO–Al₂O₃–SiO₂ system) above 800 °C and damage occurring when cooling. The influence of oxidation of SiC aggregates on elastic properties is also discussed.     

Successful ‘smart materials’ needs a different mindset

The laser was once defined as a solution in search of a problem. It is a definition that could equally apply to smart materials. Successful users have to be able to integrate an aspect of this wide versatility, back in the product design or redesign phase. A reason to suspect that smart materials are in fact spreading quietly into industry and consumer worlds comes not from success stories, but because those using materials successfully are selling a more effective product. This offers customers a genuinely cost effective approach to whatever application seek. The presence of smart materials themselves, is of no more significance to a user than knowing the precise types and grade of plastic making up a component. It's the real and perceived benefits that matter.     

Micro-mechanical modelling of Young’s modulus of semi-crystalline polyamide 6 (PA 6) and elastomer particle-modified-PA 6

In this study semi-crystalline polyamide 6 (PA 6) and its composites consisting of a semi-crystalline PA 6 matrix filled with up to 32.9 vol.% submicron elastomeric copolymer particles are investigated. The aim of this paper is to show how micro-mechanical modelling can predict the elastic behaviour of these composites from the experimentally observed morphology and determined parameters.Semi-crystalline PA 6 possesses a spherulitic morphology, consisting of a radial assembly of amorphous layers and nano-sized crystalline lamellae. In the continuum mechanical representation of semi-crystalline PA 6, nano-sized crystallite lamellae are considered as a phase which is additionally embedded into the amorphous matrix. The 2D self-consistent embedded cell model was chosen to predict the Young’s modulus of the semi-crystalline PA 6 material. In this model a rectangular lamella is surrounded by an amorphous matrix, which is again embedded in the semi-crystalline PA 6 material with the mechanical behaviour to be determined iteratively in a self-consistent manner. The Young’s modulus of PA 6 has been calculated by an appropriate integration of results of all orientations of the crystalline lamellae. The Young’s modulus of PA 6/elastomer composite is also predicted by a 3D self-consistent embedded cell model. In this model a circular inclusion is surrounded by the PA 6 polymer matrix, which is again embedded in the PA 6/elastomer composite. Good agreement is obtained between experiments and the prediction with the self-consistent embedded cell models.     

Measurement of Young’s modulus of oxides at high temperature related to the oxidation study

Abstract

α-Al₂O₃, Cr₂O₃, and α-Fe₂O₃ specimens were prepared by a sintering process. A 400 – 1000-Hz sine wave was applied to the specimen at 290 – 1273 K. The applied and respond waves were monitored by using force and acceleration sensors. The intensity ratio and phase shift between the applied and respond waves were analysed, and the anti-resonance frequency was obtained. Young’s moduli of α-Al₂O₃, Cr₂O₃, and α-Fe₂O₃ are estimated to be 386, 286, and 220 GPa at 298 K, respectively. The temperature dependence values of these oxides are estimated to be 54.3, 46.9, and 42.0 MPa K^-1, respectively. The temperature dependence of Young’s modulus can be classified on the basis of the crystal structure of solids. The estimation of Young’s modulus at 1273K is possible with an error range of 10 – 30 GPa for a crystalline solid if the crystal structure of the solid is known. It is found that the temperature dependence of Young’s modulus depends on the density of the oxides, and an experiment in which well-characterized crystalline solids are used must be conducted to minimize the error range.     

Young’s modulus and Poisson’s ratio of concrete at high temperatures: Experimental investigations

When exposed to fire, Young’s modulus of concrete degrades. Thus, exact knowledge of temperature-dependent reduction is important to determine the fire-resistance of concrete or composite members. Nevertheless, existing material properties for the Young’s and shear modulus of concrete are linked with some incertitudes.In addition, normative regulations lack information on the temperature-dependent Poisson’s ratio. In an attempt to overcome some of the existing uncertainties, experimental work was conducted to investigate elastic material properties of fire-exposed concrete. For this purpose, the Impulse Excitation Technique was used as an innovative testing technique. Based on experimental results, the authors propose new elastic material formulations for fire-exposed concrete.     

Molecular cloisonné: multicomponent organic alternating nanostructures at vicinal surfaces with tunable length scales

By careful management of the adsorption preference of organic molecules at faceted vicinal surfaces, organic alternating structures can be extended to multilayers and multicomponent with tunable size scales ranging from several to a few tens nanometers.     

On Young’s modulus of multi-walled carbon nanotubes

Carbon nanotubes (CNTs) were discovered by Iijima in 1991 as the fourth form of carbon. Carbon nanotubes are the ultimate carbon fibres because of their high Young’s modulus of ≈ 1 TPa which is very useful for load transfer in nanocomposites. In the present work, CNT/Al nanocomposites were fabricated by the powder metallurgy technique and after extrusion of the nanocomposites bright field transmission electron microscopic (TEM) studies were carried out. From the TEM images so obtained, a novel method of ascertaining the Young’s modulus of multi-walled carbon nanotubes is worked out in the present paper which turns out to be 0·9 TPa which is consistent with the experimental results.     

One-dimensional modelling of ‘verso’ laser cleaning

In this paper we present a one-dimensional model describing the verso laser cleaning technique, already experimentally tested, for particle removal from a substrate. The equation for displacement is treated for a one-dimensional case, and the temporal behaviour of the rear surface deformation is determined. Taking into account the van der Waals adhesion force and elastic deformation of a spherical particle (JKR model), the ejection condition has been obtained. Numerical values for an example are consistent with experimental observation.     

Measurement and prediction of Young’s modulus of a Pb-free solder

Accurate and reproducible measurements of the Youngs modulus of solders are complicated by the early onset of yielding, microporosity, and variations in cooling rate. In this study, we report measurements of Youngs modulus of an Sn–3.5 wt % Ag solder by two techniques: (a) loading–unloading measurements in tension, and (b) non-destructive resonant ultrasound spectroscopy. Both techniques yielded similar values of Youngs modulus. The modulus decreased with increasing microporosity, in accordance with predicted values. Cooling rate affected the Ag₃Sn intermetallic morphology, but not Youngs modulus since the distribution of the particles was relatively random. This result was confirmed by microstructure-based finite element modeling.     

Steel and nickel alloys at high temperatures: Part D of ‘The requirements for and limitations of materials at high temperatures’

The range of steels considered includes corrosion resistant ferritic and austenitic steels and low alloy, martensitic 12% Cr and austenitic steels for higher strength applications. Nickel superalloys are discussed under the gas turbine applications for which they were largely developed. Nickel alloys for corrosion resistant applications are discussed and a short section on the refractory materials Mo, Nb, Tn and W is included.     

Finite element modelling of rubber-like materials — a comparison between simulation and experiment

In this work finite element simulations are used based on the micro structure of polymers in order to transfer the information of the micro level to the macro level. The microscopic structure of polymers is characterized by a three-dimensional network consisting of randomly oriented chain-like macromolecules linked together at certain points. Different techniques are used to simulate the rubber-like material behaviour of such networks. These techniques range from molecular dynamics to the finite element method.The proposed approach is based on a so-called unit cell. This unit cell consists of one tetrahedral element and six truss elements. To each edge of the tetrahedron one truss element is attached which models the force-stretch behaviour of a bundle of polymer chains. The proposed method provides the possibility to observe how changes at the microscopic level influence the macroscopic material behaviour. Such observations were carried out in [1]. The main focus of this work is the validation of the proposed approach. Therefore the model is compared to different experimental data and other statistically-based network models describing rubber-like material behaviour.     

Metrological complex for transmission of length units in the range of 0.001–50 m

A metrological complex for reproduction and transmission of the length units in the range of 0.001 to 50 m (MKD-50) with a total error of 0.2+0.25L μm, where L is the measured length in meters, is described. The MKD-50 complex has been entered into the State Register of Measurement Standards of Ukraine as a working standard for length units of 1–50 m (VETU 01-03-05-98). Ukraine. Translated from Izmeritel’naya Tekhnika, No. 12, pp. 31–33, December, 1999.     

Predictions of Young’s modulus of short inorganic fiber reinforced polymer composites

An expression of Young’s modulus of short inorganic fiber reinforced polymer composites was derived based on the tensile strength equation proposed in the previous paper, and the factor affecting the Young’s modulus was analyzed. This equation was applied to estimate the Young’s modulus of short inorganic fiber reinforced polymer composites. The results showed that the relative Young’s modulus increased nonlinearly with increasing fiber volume fraction, while increased linearly with an increase of fiber length-diameter ratio. Finally, the equation was verified preliminarily by using the measured Young’s modulus of the short glass fiber (SGF) reinforced polycarbonate/acrylnitrile–butadiene–styrene copolymer composites and the polypropylene reinforced respectively with SGF and short carbon fiber reported from literature, good agreement was found between the predictions and the experimental data.     

Prediction models of mixtures’ dynamic modulus using gene expression programming

The dynamic modulus (E*) among asphalt mixtures’ mechanical property parameters not only is important for asphalt mixtures’ pavement design but also in determining asphalt mixtures’ pavement performance associated with pavement response. Based on the principle of gene expression programming (GEP) algorithm, this paper explored two different GEP approach models, namely: GEP-I and GEP-II to predict the E* of hot mix asphalt (HMA) and mixtures containing recycled asphalt shingles, respectively. In this paper, The GEP-I was developed from a large database containing 2750 test data points from 205 unaged laboratory-blended HMA mixtures including 34 modified binders, and the GEP-II model was developed using the E* database containing 1701 sets of experimental data from 4 different demonstration projects. Both the GEP-I model and GEP-II model were compared with other E* prediction models. A sensitivity analysis of each model parameter was conducted by correlating these parameters with dynamic modulus. Both the GEP-I model and GEP-II model showed significantly higher prediction accuracy compared with the existing regression models and could easily be established. It is expected that these two GEP models could lead to more accurate characterisation of the asphalt mixtures’ E*, resulting in better performance prediction.