Determination Of Elastic Modulus Research Articles

Quantitative characterization of porosity and determination of elastic modulus for sintered micro-silver joints

High resolution serial block-face scanning electron microscopy has been performed on sintered micro-silver pastes that are used as lead replacement joints for die bonding. The size and spatial distributions of the porosity before and after ageing were determined by quantification of the segmented 3D images. The elastic modulus was determined by an image-based finite element model and validated by results obtained from a dynamical resonance method. In agreement with contemporary analytical models on the elastic behaviour of porous materials, the elastic modulus was found to be a function of pore fraction only. Ageing the specimens does not alter the density or Young's modulus.

Effect of Interaction Parameters on the Hardness and Elastic Modulus of Crumb Rubber Modified Asphalt

Instrumented indentation presents an approach to measure the mechanical properties such as hardness and elastic modulus of materials on micro and nano scale. This gives an idea about the behavior of materials during their application when they are laid as layers of thickness of the nano or micro scale level. Two advantages can be achieved from the utilization of instrumented micro-indentation on crumb rubber modified asphalt; the first would be to measure the properties of asphalt layers of thicknesses on the micro scale to simulate the behavior of thin asphalt layer on aggregate. The second advantage would be to investigate the effect of interaction (blend processing) synthesis parameters (mixing speed, temperature and time) on the final product hardness and elastic modulus. Through the current work, it was found that the interaction parameters play a major role on the determination of the hardness and elastic modulus of crumb rubber modified asphalt (CRMA). The utilization of moderate (30 Hz) to high (50 Hz) interaction speeds at low interaction temperature (160℃) resulted in minimal enhancements in both the hardness and elastic modulus. On the other hand, the utilization of moderate (190℃) interaction temperature with high interaction speed (50 Hz) resulted in major property enhancements for both the hardness and elastic modulus. At 220℃ interaction temperature, deterioration in both the hardness and elastic modulus was observed after 4 hrs of interaction time regardless of the interaction speed utilized.

Vibrational modes of a thin bar

Although most traditional acoustics textbooks that treat vibration (e.g., Rayleigh, Lamb, Morse, Morse and Ingard, Kinsler and Frey) address the longitudinal, torsional, and flexural modes of a thin bar, they do not stress the importance of sound speed measurements for the experimental determination of elastic moduli. This presentation will demonstrate a simple and inexpensive apparatus that uses two coils of copper wire and permanent magnets, developed by Bob Leonard and Izzy Rudnick at UCLA, that can be used to excite and detect all three modes of a free-free bar, accurately measure their modal frequencies, and use those results to provide accurate and precise values for the elastic moduli of the bar material [JASA 88(1), 210 (1990)].

Effects of Span-to-depth Ratio and Poisson's Ratio on Elastic Constants from Bending and Plate Tests

The goal of this study is to evaluate the limitation of ASTM D 198 bending and ASTM D 3044 in determination of elastic modulus and shear modulus. Different material properties and span to depth ratios were used to analyze the effects of material property and testing conditions. The ratio of true elastic modulus to apparent elastic modulus evaluated from ASTM D 198 bending sharply decreased with increment of span to depth ratio. Shear modulus evaluated from ASTM D 198 bending decreased with increment of depth, whereas shear modulus evaluated from ASTM D 3044 was hardly influenced by increment of depth. Poisson's ratio influenced shear modulus from ASTM D 198 bending but did not influence shear modulus from ASTM D 3044. Different shearing factor was obtained for different depths of beams to correct shear modulus obtained from ASTM D 198 bending equivalent to shear modulus from theory of elasticity. Equivalent shear modulus of materials could be obtained by applying different shearing factors associated with beam depth for ASTM D 198 bending and correction factor for ASTM D 3044.

Determination of Hashin–Shtrikman bounds on the isotropic effective elastic moduli of polycrystals of any symmetry

Although methods to determine optimal Hashin–Shtrikman bounds for polycrystals of cubic to monoclinic symmetry have been described, the calculation of bounds for triclinic crystals has not previously been possible. The recent determination of elastic moduli of common minerals with low symmetry provides motivation to extend the Hashin–Shtrikman formulation to lower symmetry. Here, Hashin–Shtrikman moduli, valid for crystals of any symmetry, are calculated as a function of the properties of a reference isotropic material. Defining the difference between moduli of the crystal and the moduli of the reference isotropic material as the residual tensor, the optimal lower (and upper) bounding moduli are found by a search along the boundary of positive (or negative) definite regimes of the residual elasticity tensor. The new numerical approach reproduces earlier results for higher symmetry crystals and successfully provides optimal bounds for triclinic crystals that have previously not been subject to analysis. The algorithm is sufficiently compact that implementation is relatively easy within any modern computational environment. Hashin–Shtrikman bounds for triclinic minerals in the plagioclase solid solution series are reported. These bounds are significantly narrower than extremal Voigt–Reuss bounds. The Hill averages moduli lie within the Hashin–Shtrikman bounds.

Determination of Elastic Modulus of Gelatin Gels by Indentation Experiments

Mechanical characterization of hydrogels is a challenging task because they are much softer than metals, ceramics or polymers. The elastic modulus of hydrogels is within 100-102kPa range. Because they easily break and slump under their own weight, tensile and bending tests are not suitable configurations to assess elastic modulus. This work reports on the determination of elastic modulus of a gelatin gel by indentation experiments. Indentation is very simple configuration, it is of technological importance and it can be applied at different length scales with high accuracy. The gelatin hydrogel behavior is first calibrated by uniaxial compression and low strain rheological measurements. It behaves as a hyperelastic solid with strain hardening capability at large strains and shows no dependence with frequency in the linear viscoelastic range. It can be properly characterized by the First order Ogden material model. Indentation experiments are carried out at macro and nanoscales using spherical and flat-ended cylindrical punches. Elastic contact solutions and inverse analysis accounting for hyperelasticity are used to extract the elastic modulus from experimental force-depth curves. Adhesion between punch and hydrogel influences the indentation response and affects the accuracy of elastic modulus determination in a larger extent than the assumption of linear elasticity. Adhesion leads to overestimation of elastic modulus values. The influence of adhesive forces increases with decreasing the length scale. A markedly decay of elastic modulus with increasing maximum load is observed at nanoscale. A hybrid model based on Hertz elastic contact solution and Johnson-Kendal-Roberts model for adhesion is used to determine elastic modulus. This model yields an elastic modulus in good agreement with that obtained from uniaxial compression test.

New system for measuring impact vibration on floor decking sheets.

Currently, there is a narrow range of materials that are used as attenuators of impact noise and building vibrations. Materials used in construction, such as elastic materials, must meet the requirement of having very low elastic modulus values. For the determination of the material's elastic modulus and the acoustic insulation of the same, costly and difficult to execute testing is required. The present paper exposes an alternative system that is simpler and more economic, consisting of a predefined striking device and a sensor able to determine, once the strike is produced, the energy absorbed by the plate. After the impact is produced, the plate undergoes a deformation, which absorbs part of the energy, the remaining part being transmitted to the slab and, at the same time, causing induced airborne noise in the adjoining room. The plate absorbs the power through its own deformation, which is measured with the help of a capacitive sensor. This way, it would be possible to properly define the geometry of the plates, after the execution of the test, and we will try to establish a relationship between the values proposed in this research and the acoustic behavior demanded by the Spanish standards.

On the statistical mechanics of shape fluctuations of nearly spherical lipid vesicle

The mechanical properties of biological membranes play an important role in the structure and the functioning of living organisms. One of the most widely used methods for determination of the bending elasticity modulus of the model lipid membranes (simplified models of the biomembranes with similar mechanical properties) is analysis of the shape fluctuations of the nearly spherical lipid vesicles. A theoretical basis of such an analysis is developed by Milner and Safran. In the present studies we analyze their results using an approach based on the Bogoljubov inequalities and the approximating Hamiltonian method. This approach is in accordance with the principles of statistical mechanics and is free of contradictions. Our considerations validate the results of Milner and Safran if the stretching elasticity Ks of the membrane tends to zero.

The effect of specimen cross-sectional area on the strength and toughness of two-dimensional C/SiC composites

The current work investigates the effect of specimen cross-sectional area on the strength and toughness of two-dimensional carbon fiber-reinforced SiC matrix composites (C/SiC). Three types of C/SiC specimens with varying cross sections were fabricated by chemical vapor infiltration followed by heat treatments at 1500°C and 1900°C. Dogbone composite specimens were tested in tension for the determination of tensile strength, fracture toughness and elastic modulus. Results showed that, as specimen cross-sectional area decreased, fracture toughness and elastic modulus increased while tensile strength increased only marginally. Heat treatment was found to limit the effect of cross-sectional area on the tensile strength and elastic modulus of the C/SiC composites.

Determination of Elastic Modulus of Steel Wire Ropes for Computer Simulation

Modulus of elasticity of steel wire rope (elastic modulus) is a characteristic value, which is important not only for users of the steel rope, but also for designers of machines and machinery that are equipped with the steel wire rope. Values of the elastic modulus depends predominately on the elastic modulus of the material, which the rope is manufactured from as well as it depends on the various other factors. The most important influencing factors are as follows: rope construction, type of core, angle and way of wire stranding, angle and way of rope lay as well as kind of lubricant. The real value of the elastic modulus has also impact on prolongation of the steel wire rope and on intensity of its dynamical loading. The rope elastic modulus value can be determined by means of the various methods. There are analysed in this article such methods for determination of the rope elastic modulus, which can be applied for a computer simulation.

Comparison of Nondestructive Evaluation Findings, Constrained and Unconstrained Wave Speeds, Dynamic Moduli, and Poisson’s Ratio of Core Specimens from a Concrete Structure Damaged by Fire

This article discusses the use of nondestructive and subsequent laboratory materials testing techniques in evaluation of extent of fire damage to a precast prestressed parking structure. The nondestructive and laboratory testing findings were used in determination of extent of fire damage to concrete and potential effects on the prestressing tendons. The in-situ nondestructive testing phase consisted of scanning affected areas using ultrasonic pulse velocity through concrete members and use of impact echo on a confirmatory limited basis. Subsequently, cores were removed and tested for resonant frequency-based dynamic modulus in accordance with ASTM C 215. Upon determination of dynamic elastic modulus of the entire core per ASTM C 215, the cores were sawn into 25-mm (1-in.) disks. Young’s modulus of individual disks was determined by utilizing nondestructive measurement of resonant frequency. Determination of Young’s modulus at small depth increments permitted assessment of the heat-induced damage gradient into the concrete and more importantly at the level of the prestressing tendons. The data from multiple techniques provided a means of comparison between constrained in-situ ASTM C 597 pulse velocity to unconstrained compression wave velocity obtained from ASTM C 1383, and an estimated unconstrained compression wave velocity based on dynamic modulus based on disks. The results of these comparisons should be of value to practicing engineers utilizing these techniques in forensic evaluations.

Preparation and characterisation of ionic liquid confined hybrid porous silica derived from ultrasonic assisted non-hydrolytic sol–gel process

A series of porous silica matrices have been synthesized using ionic liquid (IL) 1-ethyl-3-methylimidazolium thiocyanate ([EMIM][SCN]) by nonhydrolytic sol–gel method with and without ultrasonic irradiation during gelation. The properties of IL confined silica gel matrices so prepared have been studied using N2-sorption measurement (BET characterisation for determining pore parameters), pulse echo technique (for sound velocity and hence elastic modulus determination), DSC, TGA, FTIR, TEM, SEM and fluorescence techniques. From the N2-sorption measurement, it has been found that BET surface area increased (due to creation of pits on the surface caused by ultrasonic irradiation) while pore volume, average pore size and porosity for ultrasonicated samples decreased. Elastic modulus of the samples containing IL in silica matrices have been found to change with IL content. Glass transition temperature and thermal stability of the IL have been found to increase upon confinement in silica gel matrices. FTIR spectra (experimental as well as computed) show changes in vibrational bands of IL on confinement in pores of silica matrices. Particularly, for ultrasonic assisted samples, the bands related to the imidazolium ring, aliphatic chain and anion SCN of the IL are found to shift upon confinement. Optimised geometry of the IL in porous matrix shows interaction of these groups with the oxygen present on silica pore wall. Fluorescence spectra of samples containing IL shows a shift compared to the bulk IL.

Flexural free vibration as a non-destructive test for evaluation of viscoelastic properties of polymeric composites in bending direction

In many applications, viscoelastic properties of reinforced composites need to be determined prior to their real service life. Such properties can be assured by destructive and non-destructive tests. In this paper, a novel non-destructive test (NDT) method based on flexural free vibration is introduced to investigate the viscoelastic properties of fiber-reinforced composites. Three different types of industrial fibers (carbon, glass, and hemp) and an unsaturated polyester resin were selected to produce bar-shaped composites via pultrusion technique. These composite bars were used in a simple NDT method which just required a wooden hammer, two elastic jaws, a microphone and a recorder software program to perform the experiment. The composite bars were mounted on elastic jaws and hit by a wooden hammer at one end of the specimen as a perpendicular impulse. The produced sound at the other side of the bars was recorded. By analyzing the recorded sounds by means of fast Fourier transform (FFT), viscoelastic properties such as flexural elastic modulus and the loss parameter (Tan {\delta}) were calculated for the fiber-reinforced composites. For determination of flexural elastic modulus, the first three modes of vibration in FFT graphs were analyzed using Temuschenco theory. Also, Tan {\delta} was determined by analyzing the drop in the intensity of vibrational energy as a function of time. Although there was a slight discrepancy between the calculated values from the NDT method and the actual data from dynamic mechanical thermal analysis (DMTA) approach, a good agreement was achieved between NDT and DMTA results.

Elastic properties of rocks containing oriented systems of ellipsoidal inclusions

Abstract In the present work the effective elastic moduli of a rock containing one or more systems of parallel inclusions of 3D-ellipsoidal shape were calculated. The calculations were performed for the conditions of constant strain and stress at infinity. The results were obtained for non-interacting inclusions (low concentration). The presence of movable fluid in the rock is described by the universal Gassmann relations for an anisotropic medium. The comparison of the results obtained with the experimental data has shown that it is possible to apply the proposed calculation technique for the determination of elastic moduli and acoustic waves' velocities in rocks, for example, for double-porosity carbonate formations.

ОПРЕДЕЛЕНИЕ МОДУЛЯ УПРУГОСТИ МЕЖФАЗНОЙ ЗОНЫ В СЛОИСТОМ ПОЛИМЕРНОМ КОМПОЗИЦИОННОМ МАТЕРИАЛЕ

ОПРЕДЕЛЕНИЕ МОДУЛЯ УПРУГОСТИ МЕЖФАЗНОЙ ЗОНЫ В СЛОИСТОМ ПОЛИМЕРНОМ КОМПОЗИЦИОННОМ МАТЕРИАЛЕ

Interpretation of Results of Penetration Tests Performed on Timber Structures in Bending

The paper concentrates on the determination of local elastic moduli of timber in the fiber direction. To that end a single commercially produced glued timber beam was subjected to 3600 penetration measurements. The beam was first covered by a regular grid of monitoring points at which the depth of indentation was measured. The pin was shot into the wood with a given energy (Pilodin 6J). At the same time the moisture content at 80 selected points was determined. A specific measurement order was assumed to exclude principal measurement errors on the one hand and to minimize systematic measurement errors on the other. We expect the measured elastic moduli to serve as an input for advanced finite element simulations on the bases of stochastic analysis. In such a case the local measured moduli represent in a given segment of each lamella an ensemble of data characterized by a selected probability distribution. These distributions are then employed in the LHS based stochastic simulation to provide probability distribution of the maximum deflection for a given load level. Apart from that it appears meaningful to compare independently the probability distributions of the elastic moduli for segments of the lamella (these may considerably differ owing to the specifics of the production of structures made from glued lamella timber) with statistical data from the whole beam. Based on the measured data the correlation matrix relating statistical dependence of individual segments can be estimated thus improving the quality of the stochastic model.

High-pressure (GPa) impedance measurements based on an indentation-induced local stress field

Electrical measurements of conducting and dielectric materials under high pressures (in the order of GPa) reveal important information regarding orbital overlaps, electronic states, changes in transition temperatures, and activation volumes (Delta V). In this study, we demonstrate a new method for high-pressure impedance measurements, up to 4 GPa, utilizing an indentation-induced local stress field. The current system does not require any pressure mediums or pressure calibrations. The Delta V for O2- ion conduction in 10 mol\% Y2O3-doped zirconia at 500 degrees C was estimated to be 3.0 cm(3) mol(-1). Delta V increased with increasing temperatures from 500 to 600 degrees C. The technique also allows the concurrent determination of the effective elastic modulus by fitting the experimental data obtained from the indentation load-depth profile curve with the Hertzian elastic model. The experimental values were consistent with the theoretical values. (C) 2013 Elsevier B.V. All rights reserved.

Vibration Tests for Determination of Longitudinal Elasticity Modulus and Shear Modulus of some Structures Welded with Tubular Wire

The purpose of this paper is to determine Young's modulus and the shear modulus of some welded joints made with usual tubular steel by flexural vibration tests. This is the case of the type carbon steel plates S235 JR according to EN 10025, with a thickness of 3 mm welded with MIG/MAG welding process with R713 tubular wire with a diameter of 1.2 mm, using SelcoNeoMig 3500 equipment. The technological part is detailed: welding parameters used, advantages and disadvantages of tubular wires use, problems regarding ambient protection, punctual applications of welding procedures with tubular wire. Processing the obtained signal based on vibration response the elasticity modulus is determined and its value is then compared with the value of elasticity modulus obtained through tensile stress and also with the value obtained by theoretical way.

An analysis of the elastic properties of a porous aluminium oxide film by means of indentation techniques

The elastic modulus of thin films can be directly determined by instrumented indentation when the indenter penetration does not exceed a fraction of the film thickness, depending on the mechanical properties of both film and substrate. When it is not possible, application of models for separating the contribution of the substrate is necessary. In this work, the robustness of several models is analyzed in the case of the elastic modulus determination of a porous aluminium oxide film produced by anodization of an aluminium alloy. Instrumented indentation tests employing a Berkovich indenter were performed at a nanometric scale, which allowed a direct determination of the film elastic modulus, whose value was found to be approximately 11GPa. However, at a micrometric scale the elastic modulus tends toward the value corresponding to the substrate, of approximately 73GPa. The objective of the present work is to apply different models for testing their consistency over the complete set of indentation data obtained from both classical tests in microindentation and the continuous stiffness measurement mode in nanoindentation. This approach shows the continuity between the two scales of measurement thus allowing a better representation of the elastic modulus variation between two limits corresponding to the substrate and film elastic moduli. Gao's function proved to be the best to represent the elastic modulus variation.

Determination of dynamic elastic moduli and shear moduli of aged wood by means of ultrasonic devices

Due to ecological and environmental factors, re-using aged wood is becoming more and more important, also in applications where mechanical strength plays a central role. The aim of this study was to examine specific mechanical parameters of naturally aged and dried wood and to better understand the influence of aging on the elastic behaviour of wood. To this aim, measurements on boards and on small, clear wood specimens were carried out. Ultrasound velocities of longitudinal and, in some cases, of transversal waves were measured to determine dynamic elastic moduli and shear moduli. The measurements were performed on structural timber of aged Norway spruce (aged wood) and compared with specimens of recently cut and kiln dried timber of the same species (recent wood) as a reference with comparable density properties and average annual ring width. The measurements revealed higher values of dynamic elastic modulus for aged wood in the longitudinal and radial directions, but no significant difference was found in the tangential direction or in the shear moduli. It is supposed that the difference is more likely a consequence of variability in densities and the structure parameters (annual ring structure, microfibril angle, growth conditions) rather than a consequence of the wood age. The relation between the dynamic elastic modulus in the longitudinal direction and wood density was nearly the same for aged and recent wood specimens, so with increased prudence, grading methods developed for recent wood can also be applied for aged wood.