Bending strength and effective modulus of atmospheric ice

Bending strength and the effective modulus of atmospheric ice accumulated in a closed loop wind tunnel at temperatures − 6 °C, − 10 °C and − 20 °C with a liquid water content of 2.5 g/m³ have been studied at different strain rates. More than 120 tests have been conducted. Ice samples, accumulated at each temperature, have been tested at the accumulation temperature. In addition, tests have been performed at temperatures of − 3 °C and − 20 °C, for the ice accumulated at − 10 °C. These tests showed a clear dependency of bending strength of atmospheric ice on test temperature at low strain rates. Strain rate effects are implied because the spread in bending strength for the different temperatures diminishes as strain rate increases. The results also reveal that, in most cases, the effective modulus of atmospheric ice increases with increasing strain rate. The bending strength of atmospheric ice accumulated at − 10 °C has been found to be greater than that of ice accumulated at − 6 °C and − 20 °C. The results show that the effective modulus of ice accumulated at − 20 °C at higher strain rates is less than that of the two other types.     

Determination of the hardness and elastic modulus from continuous vickers indentation testing

Continuous Vickers (H _v) indentation tests were performed on different materials (ion crystals, metals, ceramics, silica glass and plastic). Load-indentation depth curves were taken during the loading as well as during the unloading period by a computer controlled hydraulic mechanical testing machine (MTS 810). The indentation work measured both the loading and the unloading periods, and these were used for the evaluation of parameters characterizing the materials. It was found empirically that there were linear connections between the maximum load to the power 3/2 and the indentation work. These connections were used to relate the conventional hardness number, H _v, and Young's modulus, E, with the work performed during loading and unloading. This work can be determined with great accuracy from the measurements. The values of the Young's modulus and the Vickers hardness determined this way agree well with those obtained by conventional methods. On the basis of continuous indentation tests, materials can be easily classified into the isomechanical groups introduced by Ashby. For this classification the H _v/E ratio is generally used. As a substitute for H _v/E another parameter is recommended which can be determined easily from a single measurement.     

Determination of elastic modulus in a nickel alloy from ultrasonic measurements

Elastic constants relate technological, structural and safety aspects to various materials phenomena and to their fundamental interatomic forces. Hence, they are of fundamental importance in almost all engineering applications. Thus its determination is of utmost importance. The aim of the present investigation is to study the behaviour of elastic constants and the variation on heat treatment in a nickel base super alloy Nimonic 263 by ultrasonic velocity measurements. From the present study it is evident that the elastic moduli of the material are very sensitive to any minor compositional changes, resulting due to the formation of intermetallic phases on heat treatment and can be effectively monitored by ultrasonic.     

Determination of the shear modulus of orthotropic materials from off-axis tension tests

The paper is concerned with the study of the possibility to determine the shear modulus of orthotropic materials using testing under tension in the direction making some angle with the principal material axis. Conditions that should be imposed on the material properties providing the possibility of this test are derived and analyzed in application to composite materials.     

Determination of the young modulus from elastic section of the Berkovich indenter loading curve

A new procedure for the determination of a local elastic modulus is suggested, which is based on the comparison between the nanoindentation data and the results of a numerical modelling of the contact interaction in the indenter-sample system. An image of an indent of the Berkovich indenter in a material with a low elastic recovery have been obtained by atomic force microscopy and the geometry of an equivalent indenter in the form of a body of revolution required for the adequate setting of a model contact problem have been defined. A procedure for the determination of the Young modulus by solving the inverse problem of the theory of elasticity from the condition of the best correlation between the experimental and calculated loading curves has been suggested. The data reported in the paper show that the taking into account of the real tip shape of the Berkovich indenter allows more precision measurements of the elastic modulus in nanoindentation as compared with other methods.     

Designing concrete mixtures for strength,elastic modulus and fracture energy

There are many methods for determining a concrete mix proportion when the compressive strength is the design criterion; however, there is much less information available when other criteria, such as the fracture energy or the elastic modulus, are specified. For these cases, a new mix design nomogram has been developed from well-established concrete relationships. The application of this method is demonstrated by an experimental programme which shows the influence of cement content, water-to-cement ratio and aggregate-to-cement ratio on the compressive strength, modulus of elasticity, spliting tensile strength, fracture energy, and characteristic length of concrete. Six concrete mixtures with different water-to-cement ratios and workabilities were studied. The mix design nomogram, besides being a tool for the practitioner, can also help the researcher in selecting the most adequate mix parameters for experimental and scientific purposes. It is noted that when studying the effect of mix parameters on the properties of concrete certain constraints should be used: for instance when varying the water-to-cement ratio, the workability of fresh concrete should be kept constant and vice versa.

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Resume Il existe plusieurs méthodes de détermination du dosage d'un béton quand la résistance à la compression est prise comme critère de calcul; toutefois, on dispose de nettement moins de données quand il s'agit d'autres critères, tels l'énergie de rupture ou le module d'élasticité. Pour ces derniers cas, on a développé un nouveau nomogramme de formulation à partir des relations connues du béton. L'application de cette méthode est démontrée par un programme expérimental qui montre l'influence de la teneur en ciment, des rapports eau/ciment et granulat/ciment sur la résistance à la compression, le module d'élasticité et la résistance à la traction par fendage, l'énergie de rupture et la longueur caractéristique du béton. On a étudié six mélanges de béton présentant des rapports eau/ciment et une ouvrabilité différents. Outre qu'il est un outil pour le praticien, le nomogramme de formulation peut aussi aider le chercheur à sélectionner les paramètres de dosage les mieux appropriés à des buts expérimentaux et scientifiques. On remarque que certaines contraintes devraient être observées quand on étudie l'effect des paramètres de dosage sur les propriétés du béton.

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Effect of nonlinear response of concrete on its elastic modulus and strength

The purpose of this paper is to investigate the effect of nonlinear response of concrete on the relationship between modulus of elasticity at static and dynamic loading as well as on its strength. The obtained relationships are based on the thermofluctuation strength theory coupled with a nonlinear stress–strain material model. From the corresponding equations it was found that the ratio of the static to the dynamic modulus of elasticity depends on the strength of concrete, its temperature, rate of loading. Also it was confirmed that the dynamic modulus is greater than static modulus of elasticity. These equations explain the influence of the value of applied stress on the value of the static or dynamic modulus of elasticity. Comparative study shows substantial agreement with existing experimental results and the general equations given in standard BS 8110, Part 2:1985, and ACI documents. Based on the obtained relationships new methods for evaluating the static modulus of concrete and its strength from the results of dynamic tests are described subsequently.     

The porosity dependence of flexural modulus and strength for capsule-free hot isostatically pressed porous alumina

Structural properties such as flexural moduli and strength have been measured for a range of porous alumina specimens of different initial powder sizes and final porosities, sintered using the capsule-free hot isostatic pressing method. This processing method produces a porous body in which the closed porosity is negligible. The relationship of these structural properties to total porosity has been investigated. The results indicate that both a power and an exponential function could adequately describe the porosity dependence of flexural strength. The strength values obtained were test method dependent, and were significantly lower for specimens with sintering aids. A power law model based on a critical porosity, as proposed by Phani, gave the best fit for the modulus measurement data. No dependence of mechanical properties on particle size was observed. The strength measurement results did not appear to support suggestions that better strength could be obtained by the capsule-free hot isostatic pressing method than conventional sintering, as reported elsewhere.     

Young Arctic frazil sea ice: Field and laboratory strength tests

Methods of conducting and analysing uniaxial compressive strength and deformation measurements in the field and in the laboratory by means of conventional and closed-loop controlled test machines, respectively, are described, plus procedures for sampling, shipping, storing specimens and microstructural studies. Reliable measurements of the rate sensitivity of strength and deformation modulus of young congealed frazil sea ice can be obtained irrespective of location. Observations of Poisson's ratio, its variation during the tests, and its dependence on rate of loading are discussed.     

Calculating the elastic modulus from nanoindentation and microindentation reload curves

The Oliver–Pharr method was used to calculate the elastic modulus from the reloading curve and was compared to the traditional unloading curve method. Nanoindentation and microindentation testing instruments were used. This method was applied to load–unload–reload–unload, multistep, and cycle indentation testing procedures at various hold times and force rates. On unloading the reverse plasticity added to the elastic recovery which increased the apparent elastic modulus. During reloading there was mainly elastic deformation making it more reliable for the elastic modulus calculation. It was also found that the metals tested started yielding between 70% and 100% of the reload curve. The reload indentation elastic modulus for fused silica and several metals was equivalent to the tensile test elastic modulus from reference literature.     

Weibull modulus of nano-hardness and elastic modulus of hydroxyapatite coating

Here we report the microstructural dependence of nano-hardness (H) and elastic modulus (E) of microplasma sprayed (MIPS) 230 μm thick highly porous, heterogeneous hydroxyapatite (HAP) coating on SS316L. The nano-hardness and Young’s modulus data were measured on polished plan section (PS) of the coating by the nanoindentation technique with a Berkovich indenter. The characteristic values of nano-hardness and Young’s modulus were calculated through the application of Weibull statistics. Both nano-hardness and the Young’s modulus data showed an apparent indentation size effect. In addition, there was an increasing trend of Weibull moduli values for both the nano-hardness and the Young’s modulus data of the MIPS-HAP coating as the indentation load was enhanced from 10 to 1,000 mN. An attempt was made in the present work, to provide a qualitative model that can explain such behavior.     

Determination of the elastic modulus of adherent cells using spherical atomic force microscope probe

When the conventional Hertz formula is used to extract the elastic modulus, E, of cells based on the compression test using atomic force microscope spherical probe, the inconsistency between the actual situation and the assumption of the formula will lead to a large error. Using the ABAQUS for finite element modeling and analysis, here, a modified Hertz formula was developed to reduce the effects of cell radius, cell thickness, probe radius and compression depth on the extracted E of cells. Experimentally, the insensitivity of the extracted E to the compression region of cell and probe radius reflects the validity of the modified formula. Owing to the poor resolution of spherical probes, it's unlikely to know the actual thickness of cell at the measured point, which can lead to a huge error. Based on the modified formula, we further proposed an approach to control the effect of the uncertainty of cell thickness and ensured that a 10% difference in cell thickness does not incur over 10% variation in the obtained elastic modulus.

     

The elastic modulus of spruce wood cell wall material measured by an in situ bending technique

Using a novel in situ testing technique, the elastic modulus of wood cell wall material can be determined with great accuracy. The method relies on a focussed ion beam system (FIB) to prepare samples from individual structural components at a length scale which otherwise is hardly, if at all, accessible for testing. To determine the elastic modulus of cell wall material, cantilevers are cut with the FIB from wood cells for beam bending experiments inside the FIB or a scanning electron microscope (SEM). This type of sample preparation is site-specific and, at the same time, minimises the usual sample mounting problems. Once cut, the cantilever is tested by applying a known force with a piezoresistive AFM tip that is mounted on a micromanipulator. The resulting displacement is determined from SEM micrographs taken during the test. The cross-sectional area of the cantilever is determined for a number of positions along its length using the FIB as a cutting tool. Applying this method, we measured the elastic modulus of spruce wood cell wall material to be ∼28 GPa.     

Influence of thermal quench on fracture strength,elastic modulus and internal friction of glass plates

The fracture strength and residual stress in glass microscope slides for water, oil and air thermal quenching are compared with the authors' prior theoretical analysis. In addition, elastic modulus and internal friction measurements are used to evaluate the effects of the thermal quenching.     

On the elastic modulus of metallic nanowires

Previous atomistic simulations and experiments have attributed size effects in the elastic modulus of Ag nanowires to surface energy effects inherent to metallic surfaces. However, differences in experimental and computational trends analyzed here imply that other factors are controlling experimentally observed modulus changes. This study utilizes atomistic simulations to determine how strongly nanowire geometry and surface structure influence nanowire elastic modulus. The results demonstrate that although these factors do influence the elastic modulus of Ag nanowires to some extent, they alone are insufficient to explain current experimental trends in nanowire modulus with decreasing dimensional scale. Future work needs to be done to determine whether other factors, such as surface contaminants or oxide layers, contribute to the experimentally observed elastic modulus increase.     

Evolution of elastic modulus in roll forming

Roll forming is a continuous process in which a flat strip is incrementally bent to a desired profile. This process is increasingly used in automotive industry to form High Strength Steel (HSS) and Advanced High Strength Steel (AHSS) for structural components. Because of the large variety of applications of roll forming in the industry, Finite Element Analysis (FEA) is increasingly employed for roll forming process design. Formability and springback are two major concerns in the roll forming AHSS materials. Previous studies have shown that the elastic modulus (Young’s modulus) of AHSS materials can change when the material undergoes plastic deformation and the main goal of this study is to investigate the effect of a change in elastic modulus during forming on springback in roll forming. FEA has been applied for the roll forming simulation of a V-section using material data determined by experimental loading-unloading tests performed on mild, XF400, and DP780 steel. The results show that the reduction of the elastic modulus with pre-strain significantly influences springback in the roll forming of high strength steel while its effect is less when a softer steel is formed.     

Elasticity and yield strength of pentagonal silver nanowires: In situ bending tests

This paper reports in situ mechanical characterization of silver nanowires (Ag NWs) inside a scanning electron microscope using a cantilevered beam bending technique. Measurements consisted in controlled bending of a cantilevered NW by the tip of an atomic force microscope glued to the force sensor. Relatively high degree of elasticity followed by either plastic deformation or fracture was observed in bending experiments. Experimental data were numerically fitted into the model based on the elastic beam theory and values of Young modulus and yield strength were extracted. Measurements were performed on twenty Ag NWs with diameters from 76 nm to 211 nm. Average Young modulus and yield strength were found to be 90 GPa and 4.8 GPa respectively. In addition, fatigue tests with several millions of cycles were performed and high fatigue resistance of Ag NWs was demonstrated.     

Stochastic analysis of interphase effects on elastic modulus and yield strength of nylon 6/clay nanocomposites

The multifunctional properties of polymer clay nanocomposites (PCNs) can be related to the interaction of clays, polymer and interphase region. Several experimental, analytical and numerical studies have been conducted to characterize the mechanical behavior of PCNs. The elastic behavior of PCNs is well documented in the literature but their other material properties like yield strength are rather vague. On the other hand, the variation of material parameters and the stochastic nature of interphase region hinder the use of deterministic methods. In this study, a stochastic analysis along with a hierarchical multiscale method is used to analyze the effect of interphase properties on the macroscopic properties of PCNs. Since the interphase layer is expected to be weaker than the polymer matrix, a weakening coefficient is defined to describe the interphase properties based on the matrix properties. This weakening coefficient and the interphase thickness are considered as the stochastic inputs. The elastic modulus and yield strength of nylon 6/clay nanocomposites are calculated using the stochastic multiscale framework. The uncertainty propagation and sobol sensitivity analysis are performed to study the effect of random inputs on the elastic modulus and yield strength of PCNs. Despite the wide range of input variations, the accuracy of the proposed stochastic multiscale framework for the prediction of the PCNs properties is estimated by validating our results against the available experimental data in the literature.