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.     

Influence of free water content on the compressive mechanical behaviour of cement mortar under high strain rate

The effect of free water content upon the compressive mechanical behaviour of cement mortar under high loading rate was studied. The uniaxial rapid compressive loading testing of a total of 30 specimens, nominally 37 mm in diameter and 18.5 mm in height, with five different saturations (0%, 25%, 50%, 75% and 100%, respectively) were executed in this paper. The technique ‘Split Hopkinson pressure bar’ (SHPB) was used. The impact velocity was 10 m/s with the corresponding strain rate as 10²/s. Water-cement ratio of 0.5 was used. The compressive behaviour of the materials was measured in terms of the maximum stress, Young’s modulus, critical strain at maximum stress and ultimate strain at failure. The data obtained from test indicates that the similarity exists in the shape of strain–stress curves of cement mortars with different water content, the upward section of the stress–strain curve shows bilinear characteristics, while the descending stage (softening state) is almost linear. The dynamic compressive strength of cement mortar increased with the decreasing of water content, the dynamic compressive strength of the saturated specimens was 23% lower than that of the totally dry specimens. With an increase in water content, the Young’s modulus first increases and then decreases, the Young’s modulus of the saturated specimens was 23% lower than that of the totally dry specimens. No significant changes occurred in the critical and ultimate strain value as the water content is changed.     

Mechanical Properties of (Cu<Subscript>0.5</Subscript>Tl<Subscript>0.5</Subscript>)-1223 Substituted by Pr

Cu_0.5Tl_0.5Ba₂Ca_2−x Pr _x Cu₃O_10−δ superconducting samples, with 0≤x≤0.15, were prepared by a single-step solid state reaction on a form of rectangular bar. The prepared samples were characterized using X-ray powder diffraction (XRD) and scanning electron microscope (SEM). The room temperature Vickers microhardness was measured at different loads (0.25–3 N). The experimental results were analyzed using Meyer’s law, Hays–Kendall approach, elastic/plastic deformation model, proportional specimen resistance model, and the indentation-induced cracking (IIC) model. Surprising results were obtained and showed that all samples in the form of rectangular bars exhibited reverse indentation size effect in contrary with those in the form of discs. Vickers microhardness values were decreased as Pr-content increased that consisting with the porosity results. Furthermore, the Young’s modulus was determined using the dynamic resonance technique. A relation between Young’s modulus (E) and Vickers microhardness (H _V) was obtained.     

Analysis of the elastic buckling of a plywood column

Buckling tests were conducted on specimens of 5-ply lauan plywood for a range of slenderness ratios to measure its buckling stress. Three-dimensional finite element calculations of buckling stress were performed and their validity examined by comparison with experimental results. Both experimental and calculated results revealed that buckling stress is influenced by Young’s modulus values (a measure of stiffness) obtained not only under flexural loading but also under axial loading. When the axial Young’s modulus is larger than the flexural Young’s modulus, the buckling stress is measured as larger than that obtained using the flexural Young’s modulus alone. Inversely, when the axial Young’s modulus is smaller than the flexural Young’s modulus, the buckling stress is measured as smaller than that obtained using the flexural Young’s modulus alone. Therefore, both the Young’s modulus values should be taken into account for determining the buckling stress of a plywood column.     

Measurement of Young’s relaxation modulus using nanoindentation

In a previous paper (Lu et al., Mechanics of Time-Dependent Materials, 7, 2003, 189–207), we described methods to measure the creep compliance of polymers using Berkovich and spherical indenters by nanoindentation. However, the relaxation modulus is often needed in stress and deformation analysis. It has been well known that the interconversion between creep compliance and relaxation function presents an ill-posed problem, so that converting the creep compliance function to the relaxation function cannot always give accurate results, especially considering that the creep data at short times in nanoindentation are often not reliable, and the overall nanoindentation time is short, typically a few hundred seconds. In this paper, we present methods to measure Young’s relaxation functions directly using nanoindentation. A constant-rate displacement loading history is usually used in nanoindentations. Using viscoelastic contact mechanics, Young’s relaxation modulus is extracted using nanoindentation load-displacement data. Three bulk polymers, Polymethyl Methacrylate (PMMA), Polycarbonate (PC) and Polyurethane (PU), are used in this study. The Young’s relaxation functions measured from the nanoindentation are compared with data measured from conventional tensile and shear tests to evaluate the precision of the methods. A reasonably good agreement has been reached for all these materials for indentation depth higher than a certain value, providing reassurance for these methods for measuring relaxation functions.     

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.     

Gd–Ni–Al bulk glasses with great glass-forming ability and better mechanical properties

A series of Gd–Ni–Al ternary glassy alloys with the maximum diameter of 4 mm were obtained by common copper mold casting. The maximum values of the reduce glass transformation temperature (T _g/T _m) and the distance of supercooling region ΔT _x of these alloys in this study were 0.648 and 50 K, respectively. The compressive fracture strength (σ _f) and Young’s modulus (E) of Gd–Ni–Al glassy alloys were 1,240–1,330 MPa and 63–67 GPa, respectively. The magnetic properties of these BMGs were investigated. The Gd–Ni–Al bulk glassy alloys with great glass forming ability and good mechanical properties are promising for the future development as a new type of function materials.     

Elastic characteristics of iron-glass materials at low temperatures

We present the results of an investigation of the influence of low temperatures on the elastic characteristics of iron-glass materials with 3, 5, 12, or 20 wt.% of glass at 77–300 K and show that Young’s modulus exponentially decreases as the glass content of the material increases. We suggest a relation for the evaluation of the Young’s modulus of a composite at various temperatures according to its value at room temperature. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 42 – 46, January – February, 1998.     

Microtensile tests of mechanical properties of nanoporous Au thin films

The mechanical properties of nanoporous Au (NPG) thin films were investigated by uniaxial microtensile tests. Such mechanical parameters as Young’s modulus, tensile strength, and breaking strain were obtained from the recorded force–displacement curves. Through observations on the microstructure and fracture surface morphology of the samples after the tension tests by a scanning electronic microscope (SEM) and an optical microscope, we analyzed the physical mechanisms underlying the mechanical behavior of NPG thin films. It was found that the NPG films exhibit mechanical properties distinctly different from its bulk counterpart.     

Changes of wood properties treated with aqueous amine solution,bending tests and X-ray analysis of wood after amine treatment

Bending tests were conducted on oven-dried wood samples (Picea jezoensis Carr.) following treatment with various concentrations of aqueous ethylenediamine (EDA) to investigate the influence of amine treatment on the mechanical properties of wood. Under oven-drying conditions following EDA treatment and a methanol rinse, the densities of wood samples increased at concentrations above 50%, and the Young’s modulus decreased at concentrations above 60%. The specific Young’s modulus of wood samples decreased at concentrations above 60%, and stress- and strain-at-yield changed slightly at EDA concentrations in the range of 60–70%. X-ray analysis showed that the structures of cellulose changed at concentrations above 60% EDA and confirmed the transformation into cellulose III_I at 70% EDA. These results indicate the possibility that changes in the structure of the cell wall, accompanied by changes in the structures of cellulose microfibrils, contributed to changes in the specific Young’s modulus of the treated wood samples. In the same concentration range, changes in the Young’s modulus of wood samples increased with increasing relative humidity (RH). This also suggests that changes in the cell wall structure during the treatment contributed to changes in the Young’s modulus of wood at different RHs.     

圆弧型柔性球铰柔度设计计算

 通过研究圆弧型柔性球铰的柔度性能,使该柔性球铰可代替传统的双轴柔性铰链应用于空间多自由度柔顺机构.根据《材料力学》中的卡氏第二定理,圆弧型柔性球铰柔度的解析公式被推导出,然后利用ANSYS12.0软件对其进行有限元分析, 结果表明有限元分析与解析式的计算结果基本一致.通过改变圆弧型柔性球铰的各结构参数来分析其性能,得出各结构参数对其柔度的影响大小依次为：最小截面直径 t、圆弧的圆心角θ^_m、圆弧半径R、杨氏模量E. 此设计计算和特性分析为柔性球铰在柔顺机构的应用提供了依据.     

Young’s modulus of cast HMS 2112-C f composite—prediction and ultrasonic evaluation

Various models for the prediction of strengthening mechanism of metal matrix composites (MMCs) containing either fibres or particulates are analysed. Assuming that the matrix strengthening by dislocations could be treated as equivalent to the effect of different volume fraction of dispersoids, as well as by considering the effect of morphology of reinforcement on the Young’s modulus, an expression for Young’s modulus for MMCs has been derived. The Young’s modulus values thus predicted, using this model, have been validated by ultrasonically-derived values of Young’s modulus of an Al-alloy matrix composite containing 5, 8 and 12 wt% chopped carbon fibre (C _f) dispersoids, in as cast and extruded conditions. Further, the theoretically- and ultrasonically-derived Young’s modulus of cast Al-alloy-C _f composites with 5 and 8 wt%C _f have been found to be comparable with the reported values of Young’s modulus for these weight fractions.     

On Measuring of Overall Mechanical Properties of Small Animal Bones using Grid Method

Overall mechanical properties of bones strongly depend on their microstructure. They can be determined by developing adequate micromechanics modeling or by direct experimental measurements. Both approaches are important for a better understanding of the connection between the bone’s microstructure and resulting macro-properties. In this work, a simple experimental method is proposed for the determination of the longitudinal Young’s modulus and Poisson’s coefficient of small, and especially short, bones, based on a combination of compression and grid method. The developed experimental set-up allows measuring the displacement and strain distribution on the surface of the bone sample subjected to a compressive test, as well as the longitudinal Young’s modulus and Poisson’s coefficient. Some results for the determined macroproperties of small bones are presented and compared with the results obtained using a more sophisticated method – the Digital Image Correlation (DIC) one.     

Numerical simulation with finite element and artificial neural network of ball indentation for mechanical property estimation

A combined mechanical property evaluation methodology with ABI (Automated Ball Indentation) simulation and Artificial Neural Network (ANN) analysis is evolved to evaluate the mechanical properties for Carbon Manganese Steel (SA-333 Grade-6) and Stainless Steel (SS-304LN). The experimental load deflection data is converted into meaningful mechanical properties for these materials and their evaluated property is verified with experimental tensile specimen results. An ANN database is generated with the help of contact type finite element analysis by numerically simulating the ABI process for various magnitudes of yield strength (σ _yp ) (200 MPa–400 MPa) with a range of strain hardening exponent (n) (0.05–0.5) and strength coefficient (K) (600 MPa–1600 MPa). For the present problem, a ball indenter of 1.57 mm diameter having Young’s modulus higher than test piece is used to minimize the error due to indenter deformation. Test piece dimension is kept large enough in comparison to the indenter configuration in the simulation to minimize the deflection at the outer edge of the test piece. Further, this database after the neural network training; is used to analyse measured material properties of different test pieces. The ANN predictions are reconfirmed with contact type finite element analysis for an arbitrary selected test sample. The methodology evolved in this work can be extended to predict material properties for any irradiated nuclear material in the service. Extensions of the ABI tests and the associated database analysis could lead to evaluation of the indentation energy to fracture needed for the structural integrity assessment of aged components.     

Mechanical characterization of Ti–5Al–2.5Sn ELI alloy at cryogenic and room temperatures

An experimental campaign consisting of tensile and fracture tests at cryogenic and room temperatures has been conducted on a Ti–5Al–2.5Sn extra-low-interstitial (ELI) alloy. It has been assessed that, at decreasing testing temperature: Young’s modulus slightly increases; yield and failure strengths increase significantly; fracture toughness decreases. Since a ductile void growth to coalescence micromechanism always governs failure in the spanned temperature interval, crack growth is simulated by allowing for material nonlinearities in the process zone, where ductile tearing takes place. Numerical results have been obtained by modeling the response of the process zone through either a cohesive model or Gurson’s constitutive law for porous-ductile media. It is shown that the latter approach can accurately describe the failure mechanism at any test temperature and for any specimen geometry, whereas the former one is not able to account for stress triaxiality at the crack tip and therefore requires a new calibration anytime the specimen geometry is varied.     

Mechanical characterization of microwave sintered zinc oxide

The mechanical characterization of microwave sintered zinc oxide disks is reported. The microwave sintering was done with a specially designed applicator placed in a domestic microwave oven operating at a frequency of 2.45 GHz to a maximum power output of 800 Watt. These samples with a wide variation of density and hence, of open pore volume percentage, were characterized in terms of its elastic modulus determination by ultrasonic time of flight measurement using a 15 MHz transducer. In addition, the load dependence of the microhardness was examined for the range of loads 0.1–20 N. Finally, the fracture toughness data (K _IC) was obtained using the indentation technique.     

Ultrasonic evaluation of polyether ether ketone and carbon fiber-reinforced PEEK

Polyether ether ketone (PEEK) and carbon fiber-reinforced (CFR) PEEK are commonly used in medical implants. This study evaluated the mechanical moduli of PEEK and CFR PEEK using nondestructive, ultrasonic tests. The Young’s modulus of CFR PEEK was determined in all the spatial directions. Ultrasonic attenuation has not been studied extensively in PEEK, and not at all in CFR PEEK. The broadband ultrasound attenuations (BUAs) were determined for PEEK and CFR PEEK. The average Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio of PEEK were 4.21, 1.52, 6.25, and 0.388 GPa, respectively. The maximum and minimum Young’s moduli of CFR PEEK were 15.1 and 5.1 GPa measured parallel and perpendicular to the fiber axis respectively. The longitudinal and transverse BUAs of PEEK were 1.33 and 4.37 dB/cm MHz, respectively. The longitudinal BUAs of CFR PEEK parallel and perpendicular to the fiber axis were 2.43 and 1.45 dB/cm MHz, respectively. Characterization of Young’s modulus of CFR PEEK in all the spatial directions is useful for stiffness matching in implant design. The BUA values are useful in modeling the interaction of ultrasound and the PEEK materials and can also be used for developing non-destructive tests to find structural defects in implants made from these materials.     

Ab initio study on fracture toughness of Ti<Subscript>0.75</Subscript>X<Subscript>0.25</Subscript>C ceramics

Ab initio density functional theory calculations have been performed to evaluate the fracture toughness for selected Ti_0.75X_0.25C ceramics (X = Ta, W, Mo, Nb and V). The calculated Young’s modulus E, surface energy γ and fracture toughness K _IC of pure TiC are in a good agreement with experimental data and other theoretical calculations. The results for Ti_0.75X_0.25C system show that alloying additions increase Young’s modulus, and all but vanadium increase surface energy. It was observed that tungsten has the most significant effect on increasing Young’s modulus, while tantalum on increasing surface energy of the Ti_0.75X_0.25C system. Surface energy plays a dominated role in determining the trend of fracture toughness. Overall, tantalum and tungsten are the most effective alloying elements in increasing the fracture toughness of Ti_0.75X_0.25C ceramics.     

Elastic properties of B19’ structure of NiTi alloy under uniaxial and hydrostatic loading from first principles

The uniaxial and hydrostatic deformations of martensitic structure B19’ of NiTi shape memory alloy are studied using first-principles calculations. The bulk and Young’s moduli and the theoretical strength under uniaxial tension and hydrostatic loading are computed from crystal response to applied deformations. The behavior of angle β of the B19’ structure was investigated along the whole deformation path. The computed values of Young’s moduli are compared with available experimental results. The results obtained complement and extend the known characteristics of NiTi alloy. __________ Translated from Problemy Prochnosti, No. 1, pp. 20–23, January–February, 2008.