Prediction of Young’s modulus and Poisson ratio for foamed metals using octahedron model

Abstract

The present paper deals with the mathematical–physical expression of Young’s modulus and Poisson ratio of foamed metals. As it is known that, Young’s modulus and Poisson ratio are two basic mechanical parameters of engineering materials. Foamed metal is a class of excellent engineering materials with dual attributes of structural and functional characteristics; therefore, these two parameters are investigated for these materials, and the relevant mathematical–physical expressions are derived from the ‘octahedron model’ of porous materials in the present paper. The results show that the apparent Young’s modulus displays a quite complicated mathematical relationship to porosity of the porous body, and the apparent Poisson ratio is just a characteristic of the material constant almost not relative to porosity of the foamed metal.     

Measurement of the dynamic Young’s modulus of porous titanium and Ti6Al4V

The dynamic Young’s modulus of porous titanium and Ti6Al4V with various porosities was measured using the electromagnetic acoustic resonance method. The dependence of Young’s modulus (E) on the porosity (P) has been analysed in detail based on Phani–Niyogi relation and Pabst–Gregorová relation . We find that both Phani–Niyogi relation and Pabst–Gregorová relation with fixed material constant n = 2 or a = 1 but varying P _C can correctly account for the dependence of Young’s modulus on the porosity for porous titanium and Ti6Al4V.     

Simple dynamic models of elastic–plastic structures under impact

The dynamic behaviour of elastic–plastic structures is much more difficult to predict in comparison with the corresponding quasi-static one because of complicated loading conditions and the effect of inertia. If the quasi-static structural and interface behaviour of a structure is specified, by assuming that its dynamic deformation mode is broadly similar to the quasi-static one and the material is strain-rate insensitive, two simple mechanical models, namely the stick model and non-stick model, are proposed in this paper to predict the dynamic response of the structure under a rigid-projectile impact. Each model contains two lumped masses and two inelastic springs. While spring

1. Download : Download full-size image

represents the highly non-linear and inelastic mechanical property of the interface between the target structure and the striker, spring

1. Download : Download full-size image

represents the elastic–plastic behaviour of the structure itself, with hardening, perfectly plastic or softening in the plastic range. With the complicated deformation history involving loading, unloading and reversed loading being taken into account, the dynamic response can be predicted by these models. A number of numerical examples are given to demonstrate the effects of the mass ratio, energy ratio, structural stiffness/local rigidity and the hardening/softening factor on the maximum and final deformations of the simple models. Finally, the validity of the models proposed for real structures is verified by the impact tests on simply supported beams.     

Prediction of driving ability: Are we building valid models?

The prediction of on-road driving ability using off-road measures is a key aim in driving research. The primary goal in most classification models is to determine a small number of off-road variables that predict driving ability with high accuracy. Unfortunately, classification models are often over-fitted to the study sample, leading to inflation of predictive accuracy, poor generalization to the relevant population and, thus, poor validity. Many driving studies do not report sufficient details to determine the risk of model over-fitting and few report any validation technique, which is critical to test the generalizability of a model. After reviewing the literature, we generated a model using a moderately large sample size (n = 279) employing best practice techniques in the context of regression modelling. By then randomly selecting progressively smaller sample sizes we show that a low ratio of participants to independent variables can result in over-fitted models and spurious conclusions regarding model accuracy. We conclude that more stable models can be constructed by following a few guidelines.     

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.     

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.     

Time programming of material’s properties via self-irradiation phenomena

We consider theoretically programming of ageing processes in materials over large time intervals via the introduction of small quantities of unstable nuclei in a material’s structure. Incorporation of minuscule amounts of radio-active species (e.g. carbon-14, tritium) in the structure of polymers, such as polytetrafluoroethylene, can be used for presetting self-decomposition of plastic products to a certain term. Radio-decay of unstable nuclei embedded in conductive polymers and dielectrics might enable the design of electrical resistors and capacitors with time-dependent characteristics. Relaxation of internal mechanical stresses, amorphization and swelling driven by self-irradiation can be used for programming configurations of mechanical systems over large terms (from years to thousands of years). Implementations of the time-programmed materials and their possible applications are discussed.     

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 intervals for the original response when using Manly’s exponential transformations

Motivated by A-10 single engine aircraft climb experiments, in this article we consider prediction interval estimation in the original units of observation after fitting a linear model using Manly’s exponential transformations. We assume that the residuals obtained from fitting the model in the transformed space are iid zero-mean normal random variables, at least approximately. We discuss the bias in the retransformed mean and derive a reduced bias estimator for the kth moment of the original response, given settings of the design variables. This is then used to compute reduced-bias estimates for the mean and variance of the untransformed response at various locations in design space. We then exploit Chebychev’s inequality, along with our proposed moment estimator, to construct an approximate 100(1 ? α)% prediction interval on the original response, given settings of the design factors. We used Monte Carlo simulation to evaluate the performance of our proposed prediction interval estimator relative to a more commonly used alternative in practice. Our results suggest the proposed method is often the better alternative when the sample size is small and/or when the underlying model is misspecified.     

Young’s modulus of ceramic particle reinforced aluminium: Measurement by the Impulse Excitation Technique and confrontation with analytical models

Young’s modulus of particulate metal matrix composites with volume fractions of reinforcement ranging from 40% to 60% is measured with the Impulse Excitation Technique. Results are compared with predictions of four common micromechanical mean-field models. Good agreement is obtained with the Torquato identical hard spheres (TIHS) and the generalized self-consistent (GSC) model.     

The influence of the applicants’ gender on the modeling of a peer review process by using latent Markov models

In the grant peer review process we can distinguish various evaluation stages in which assessors judge applications on a rating scale. Bornmann & al. [2008] show that latent Markov models offer a fundamentally good opportunity to model statistically peer review processes. The main objective of this short communication is to test the influence of the applicants’ gender on the modeling of a peer review process by using latent Markov models. We found differences in transition probabilities from one stage to the other for applications for a doctoral fellowship submitted by male and female applicants.     

RILEM Draft Recommendation ‘Determination of the modulus of elasticity of prestressing steel strands’

RILEM Draft Recommendations

RILEM Draft Recommendation ‘Determination of the modulus of elasticity of prestressing steel strands’     

Measuring Young’s modulus of biological objects in a liquid medium using an atomic force microscope with a special probe

A special probe with a 5-μm-diameter ball fixed at the end is developed for an atomic force microscope (AFM), with the use of which it is possible to obtain more correct values of the Young’s moduli of biological objects in liquid media and eliminate the risk of damaging the sample surface. In particular, the AFM measurements with this probe in situ revealed an increase in the Young’s modulus of rat blood vessel under the action of chlorhexidine.     

Micromechanical modelling of bituminous materials’ complex modulus at different length scales

The aim of this work is to establish a multi-scale modelling technique usable in the study of the complex viscoelastic properties of asphalt mixes. This technique is based on a biphasic approach. At each scale, the heterogeneous media is considered as a two-phase material composed of granular inclusions with linear elastic properties and a matrix of bituminous materials exhibiting linear viscoelastic behaviour at small strain values. In this approach, the homogeneous equivalent properties of biphasic composites are transferred from one scale of observation to the next, higher scale of observation. The viscoelastic properties of the matrix and the elastic properties of the aggregates serve as the input parameters for the numerical models. The generalised Maxwell rheological model is used to describe the viscoelastic behaviour of the matrix. Thanks to the rheological properties of bitumen and the elastic properties of the aggregates, the viscoelastic properties of mastic, mortar and hot mix asphalt (HMA) as bituminous composites can be, respectively, estimated using a micromechanical finite element model. Random inclusions of varying sizes and shapes are generated in order to construct the granular skeleton. A cyclic loading was imposed on the top layer of the digital model. The dynamic modulus of the pre-cited bituminous composites, obtained from the presented multi-scale modelling process while passing from the bitumen to the HMA scale, is validated by comparison with experimental measurements when possible. Concerning our results, we have found that at low temperature (?10 °C), the predicted dynamic modulus is satisfactorily comparable to the experimental measurements. On the other hand, an acceptable gap between predicted numerical results and experimental data takes place when the temperature increases.     

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.     

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.     

Prediction of ground multipath parameters from range-gain measurements using Prony?s technique

Prony's technique is used to estimate multipath parameters from range-gain patterns produced by ground multipath interference in line-of-sight radio links. The field distribution at the transmitting antenna side is obtained by digital reconstruction from the range-gain pattern that is recorded, at constant height, along ground surface. The technique is presented as a competitive alternative to the Fourier transform, where much shorter data windows are sufficient for the proposed technique. The technique is validated by calculated and measured range-gain patterns, and the predicted values are in good agreement with the actual ones. Prony's technique produced predictions with comparable errors to the Fourier technique from much smaller data windows.