Interconnected microstructure and flexural behavior of Ti_(2)C-Ti composites with superior Young’s modulus

To enhance the Young’s modulus(E)and strength of titanium alloys,we designed titanium matrix composites with intercon-nected microstructure based on the Hashin-Shtrikman theory.According to the results,the in-situ reaction yielded an interconnected microstructure composed of Ti_(2)C particles when the Ti_(2)C content reached 50vol%.With widths of 10 and 230 nm,the intraparticle Ti lamellae in the prepared composite exhibited a bimodal size distribution due to precipitation and the unreacted Ti phase within the grown Ti_(2)C particles.The composites with interconnected microstructure attained superior properties,including E of 174.3 GPa and ultimate flexural strength of 1014 GPa.Compared with that of pure Ti,the E of the composite was increased by 55% due to the high Ti_(2)C content and interconnected microstructure.The outstanding strength resulted from the strong interfacial bonding,load-bearing capacity of interconnected Ti_(2)C particles,and bimodal intraparticle Ti lamellae,which minimized the average crack driving force.Interrupted flexural tests revealed preferential crack initiation along the{001}cleavage plane and grain boundary of Ti_(2)C in the region with the highest tensile stress.In addition,the propagation can be efficiently inhibited by interparticle Ti grains,which prevented the brittle fracture of the composites.

PSO algorithm for Young's modulus reconstruction

To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displacements of boundary tissues and the force distribution, the Young＇s modulus is calculated by constructing the unit system and the inverse finite element method （IFEM）. Then a tough range of the modulus for the whole tissue is estimated referring the value obtained before. The improved particle swarm optimizer （PSO） method is adopted to calculate the whole Yong＇s modulus distribution. The presented algorithm overcomes some limitations in other Young＇s modulus reconstruction methods and relaxes the displacements and force boundary condition requirements. The repetitious numerical simulation shows that errors in boundary displacement are not very sensitive to the estimation of next process; a final feasible solution is obtained by the improved PSO method which is close to the theoretical values obtained during searching in an extensive range.

A method to determine Young's modulus of soft gels for cell adhesion

A convenient technique is reported in this note for measuring elastic modulus of extremely soft material for cellular adhesion. Specimens of bending cylinder under gravity are used to avoid contact problem between testing device and sample, and a beam model is presented for evaluating the curvatures of gel beams with large elastic deformation. A self-adaptive algorithm is also proposed to search for the best estimation of gels＇ elastic moduli by comparing the experimental bending curvatures with those computed from the beam model with preestimated moduli. Application to the measurement of the property of polyacrylamide gels indi- cates that the material compliance varies with the concentrations of bis-acrylamide, and the gels become softer after being immersed in a culture medium for a period of time, no matter to what extent they are polymerized.

Measurement of Young's Modulus and Poisson's Ratio of Thermal Barrier Coatings

In gas turbines, thermal barrier coatings （TBCs） applied by air plasma spraying are widely used to lower the temperature of hot components. To analyze the characteristics of TBCs such as residual stress, bond strength, fracture toughness, and crack propagation ratio, the Young＇s modulus and Poisson＇s ratio are important parameters. For TBC is a brittle and thin film, it is desirable to evaluate those properties while the coatings are bonded to a substrate. An atmospheric plasma spray MCrAIY bond coat and Yttria stabilized zirconia （YSZ） top coat are deposited onto a nickel-base superalloy GH150 substrate. The Young＇s modulus and Poisson＇s ratio are measured by cantilever beam bending with NDI. The method will be developed to test the Young＇ s modulus and Poisson ratio of other multilayer systems.

Prediction and optimization of process variables to maximize the Young’s modulus of plasma sprayed alumina coatings on AZ31B magnesium alloy

Like other manufacturing techniques,plasma spraying has also a non-linear behavior because of the contribution of many coating variables.This characteristic results in finding optimal factor combination difficult.Subsequently,the issue can be solved through effective and strategic statistical procedures integrated with systematic experimental data.Plasma spray parameters such as power,stand-off distance and powder feed rate have significant influence on coating characteristics like Young’s modulus.This paper presents the use of statistical techniques in specifically response surface methodology(RSM),analysis of variance,and regression analysis to develop empirical relationship to predict Young’s modulus of plasma-sprayed alumina coatings.The developed empirical relationships can be effectively used to predict Young’s modulus of plasma-sprayed alumina coatings at 95%confidence level.Response graphs and contour plots were constructed to identify the optimum plasma spray parameters to attain maximum Young’s modulus in alumina coatings.A linear regression relationship was established between porosity and Young’s modulus of the alumina coatings.

CALCULATION OF THE YOUNG'S MODULUS OF AN ADSORBED POLYMER LAYER

Polymer layers adsorbed to a surface or in a confined environment often change their mechanical properties. There is even the possibility of solidification of the confined layer. To judge the stiffness of such a layer, we used the Hertz model to calculate the Young＇s modulus of the polymer layer in the confinement of AFM experiments with silicon nitride tip with a radius of curvature ofR ≈ 50 nm and a glass sphere attached to the cantilever R =5 μm. Since there is no visible indentation of the layer in the AFM experiments, the layer is either penetrated very easily, or the indentation is too small to be seen in a force curve. The latter would be the case for a polymer layer with a Young＇s modulus above 4 × 10^8 Pa in case of an experiment with a silicon nitride tip and 4×10^5 Pa in case of a glass sphere.

Determination of reduced Young s modulus of thin films using indentation test

The flat cylindrical indentation tests with different sizes of punch radius were investigated using finite element method （FEM） aimed to reveal the effect of punch size on the indentation behavior of the film/substrate system. Based on the FEM results analysis, two methods was proposed to separate film＇s reduced Young＇s modulus from a film/substrate system. The first method was based on a new weight function that quantifies film＇s and substrate＇s contributions to the overall mechanical properties of the film/substrate system in the flat cylindrical indentation test. The second method, a numerical approach, including fitting and extrapolation procedures was put forward. Both of the results from the two methods showed a reasonable agreement with the one input FE model. At last, the effect of maximum indentation depth and the surface micro-roughness of the thin film on the reduced Young＇s modulus of the film/substrate system were discussed. The methods proposed in the present study provide some new conceptions on evaluating other properties of thin films, e.g. creep, for which a flat-ended punch is also employed.

Analysis of the elastic-plastic indentation properties of materials with varying ratio of hardness to Young’s modulus

The elastic-plastic indentation properties of materials with varying ratio of hardness to Young’s modulus(H/E) were analyzed with the finite element method. And the indentation stress fields of materials with varying ratio H/E on the surface were studied by the experiment. The results show that the penetration depth, contact radius, plastic pile-up and the degree of elastic recovery depend strongly on the ratio H/E. Moreover, graphs were established to describe the relationship between the elastic-plastic indentation parameters and H/E. The established graphs can be used to predict the H/E of materials when compared with experimental data.

Probing the effect of Young's modulus on the plugging performance of micro-nano-scale dispersed particle gels

The effect of mechanical strength of the dispersed particle gel(DPG)on its macro plugging performance is significant,however,little study has been reported.In this paper,DPG particles with different mechanical strengths were obtained by mechanical shearing of bulk gels prepared with different formula.Young’s moduli of DPG particles on the micro and nano scales were measured by atomic force microscope for the first time.The mapping relationship among the formula of bulk gel,the Young’s moduli of the DPG particles and the final plugging performance were established.The results showed that when the Young’s moduli of the DPG particles increased from 82 to 328 Pa,the plugging rate increased significantly from 91.46%to 97.10%due to the distinctly enhanced stacking density and strength at this range.While when the Young’s moduli of the DPG particles surpassed 328 Pa,the further increase of plugging rate with the Young’s moduli of the DPG particles became insignificant.These results indicated that the improvement of plugging rate was more efficient by adjusting the Young’s moduli of the DPG particles within certain ranges,providing guidance for improving the macroscopic application properties of DPG systems in reservoir heterogeneity regulation.

The influence of defects on the effective Young's modulus of a defective solid

It is difficult to establish structure-property relationships in a defective solid because of its inhomogeneous-geometry microstructure caused by defects. In the present research, the effects of pores and cracks on the Young’s modulus of a defective solid are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate how the shape, size, and distribution of defects affect the effective Young’s modulus. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective Young’s modulus. Different from the results obtained from the traditional empirical analyses, mixture law or statistical method, for the first time, our results from the finite element method （FEM） and strict analytical calculation show that the influence of pore radius and crack length on the effective Young’s modulus can be quantified. It is found that the longest crack in a typical microstructure of ceramic coating dominates the contribution of the effective Young’s modulus in the vertical direction of the crack.

Influence of Temperature Conditions on Dynamic Young’s Modulus Testing

The Young’s modulus was measured at high temperatures by impulse excitation of vibration method,and the effects of heating rate,holding time and temperature cycle on the test results were analyzed.The results show that the heating rate has obvious effect on the high temperature Young’s modulus of the green body,but has no obvious effect on that of the sintered products;the holding time of the heating process has no regular effect on the Young’s modulus,and the effect varies with the different products at a certain temperature;the method can also be used to test the Young’s modulus during cooling process.

An improved model for predicting effective Young's modulus of the twisted structure under cyclic loading:taking into account the untwisting effect

Twist structures have diverse applications, ranging from dragline, electrical cable, and intelligent structure. Among these applications, tension deformation can＇t be avoided during the fabrication and working processes, which often leads to the twist structure rotation （called untwisting effect） and twist pitch increasing. As a consequence, this untwisting behavior has a large effect on the effective Young＇s modulus. In this paper, we present an improved model based on the classical Costello＇s theory to predict the effective Young＇s modulus of the basic structure, twisted by three same copper strands under cyclic loading. Series of experiments were carried out to verify the present model taking into account the untwisting effect. The experimental results have better agreements with the presented model than the common Costello＇s model.

Achieving highest Young’s modulus in Al-Li by tracing the size and bonding evolution of Li-rich precipitates

For decades,it has been well accepted that every 1 wt.%Li addition to Al will reduce Al alloy’s density by 3%and increase its Young’s modulus by 6%.However,the fundamental mechanism of modulus improve-ments stays controversial though all studies agreed that the contribution of such a substantial boosting comes from Li-rich clusters either in solid solution or precipitations.In this study,we experimentally produce nano-sized Li-rich clusters by non-equilibrium solidification using centrifugal casting and trace their evolutions as a function of subsequent heat treatments.High-resolution transmission electron mi-croscopy(HRTEM)reveals a further decrease in the lattice constants of Li-rich regions from the as-cast(0.406 nm),solid solution(0.405 nm)to the aged state(0.401 nm),while Young’s modulus of the Al-Li al-loy reaches 89.16 GPa.Small-angle neutron scattering(SANS)experiments and first-principle calculations based on density functional theory have shown both the bond strength around precipitates and the size of those Li-rich region dominate Young’s modulus.At the beginning,it is volumetric compression due to Li addition that increases modulus,tightening the Al-Al potential curves.In the end,it is the Al-Al and Al-Li valence bonds in Al 3 Li at large size and high-volume fraction which increase its second derivative of internal energy and thus Young’s modulus.

Probing the Young＇s modulus and Poisson＇s ratio in graphene/metal interfaces and graphite： A comparative study

By analyzing phonon dispersion, we have evaluated the average Young＇s modulus and Poisson＇s ratio in graphite and in graphene grown on Ru（0001）, Pt（111）, Ir（111）, Ni（111）, and BC3/NbB2（0001）. In both flat and corrugated graphene sheets and in graphite, we find a Poisson＇s ratio of 0.19 and a Young＇s modulus of 342 N/m. The unique exception is graphene/Ni（111）, for which we find different values because of the stretching of C-C bonds occurring in the commensurate overstructure （0.36 and 310 N/m for the Poisson＇s ratio and Young＇s modulus, respectively）. Such findings are in excellent agreement with calculations performed for a free-standing graphene membrane. The high crystalline quality of graphene grown on metal substrates leads to macroscopic samples with high tensile strength and bending flexibility for use in technological applications such as electromechanical devices and carbon-fiber reinforcements.

INFLUENCE OF YOUNG'S MODULUS ON DRAG-REDUCTION IN TURBULENT FLOW USING FLEXIBLE TUBES

In order to develop technologies of friction drag reduction with a flexible tube to be used for water transport, experimental studies were carried out on the influence of Young’s modulus on the turbulent drag reduction. The friction coefficients of flexible tubes with different Young’s modulus were examined by using a sleeve-tube structure. The fluctuating vibration of the outer wall and the fluctuating pressure on the inner wall of the tubes were measured with a laser displacement sensor and a pressure sensor. The results are as follows. The smaller the Young’s modulus of a flexible tube and the larger the Reynolds number, the larger the turbulent drag reduction rates become. The transition from laminar flow to turbulent flow can be delayed with an appropriate Young’s modulus. Non-dimensional amplitude of fluctuating vibration on the outer wall is smaller than that of a viscous sub-layer thickness, and is positively correlated with the friction drag reduction.

Determination of complex Young's modulus of viscoelastic bars using forced longitudinal vibration of slender rods

A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.

Young's modulus determination of low-k porous films by wide-band DCC/LD LSAW

Low-k interconnection is one of the key concepts in the development of high-speed ultra-large-scale integrated（ULSI） circuits.To determine the Young＇s modulus of ultra thin,low hardness and fragile low-k porous films more accurately,a wideband differential confocal configured laser detected and laser-generated surface acoustic wave（DCC/LD LSAW） detection system is developed.Based on the light deflection sensitivity detection principle, with a novel differential confocal configuration,this DCC/LD LSAW system extends the traditional laser generated surface acoustic wave（LSAW） detection system＇s working frequency band,making the detected SAW signals less affected by the hard substrate and providing more information about the thin porous low-k film under test.Thus it has the ability to obtain more accurate measurement results.Its detecting principle is explained and a sample of porous silica film on Si（100） is tested.A procedure of fitting an experimental SAW dispersion curve with theoretical dispersion curves was carried out in the high frequency band newly achieved by the DCC/LD LSAW system.A comparison of the measurement results of the DCC/LD LSAW with those from the traditional LSAW shows that this newly developed DCC/LD LSAW can dramatically improve the Young＇s modulus measuring accuracy of such porous low-k films.

Size-and temperature-dependent Young's modulus and size-dependent thermal expansion coefficient of nanowires

Nanowires(NWs) exhibit size-dependent mechanical properties due to the high surface/volume ratio, in which temperature also plays an important role. The surface eigenstress model is further developed here to quantitatively predict the size-dependent mechanical properties of NWs and results in analytic formulas. Molecular dynamics(MD) simulations are conducted to study the size-dependent mechanical of [100], [110] and [111] Ni and Si nanowires within the temperature range of 100–400 K and the MD results verify perfectly the newly developed surface eigenstress model.

Young＇s Modulus Enhancement and Measurement in CNT/Al Nanocomposites

Young＇s modulus is a critical parameter for designing lightweight structure, but Al and its alloys only demonstrate alimited value of 70-72 GPa. The introduction of carbon nanotubes （CNTs） is an effective way to make Al and its alloysstiffer. However, little research attention has been paid to Young＇s modulus of CNT/Al nanocomposites attributed to theuncertain measurement and unconvincing stiffening effect of CNTs. In this work, improved Young＇s modulus of 82.4 ± 0.4 GPa has been achieved in 1.5 wt% CNT/Al nanocomposite fabricated by flake powder metallurgy, which wasdetermined by resonance test and 13.5% higher than 72.6 ± 0.64 GPa of Al matrix. A comparative study and statisticalanalysis further revealed that Young＇s modulus determined by tensile test was relatively imprecise （83.1 ± 4.0 GPa） dueto the low-stress microplasficity or interface decohesion during tensile deformation of CNT/Al nanocomposite, while thevalue （98-100 GPa） was highly overestimated by nanoindentation due to the ＂pile-up＂ effect. This work shows an in-depthdiscussion on studying Young＇s modulus of CNT/Al nanocomposites.

Young's modulus characterization of low-k films of nanoporous Black Diamond^(TM) by surface acoustic waves

The laser-generated surface acoustic wave（SAW） technique is an accurate,fast and nondestructive solution to determine the mechanical properties of ultra thin films.SAWs are dispersive during the wave propagation on the layered structure.The Young＇s moduli of thin films can be obtained by matching the experimentally and theoretically calculated dispersive SAW curves.A short ultraviolet laser pulse is employed to generate the broad spectral range of the dispersive SAWs.The frequency range of dispersive SAWs in this study reaches 180 MHz,which is adequate for the SAW technique applied for the investigated samples.In this work,the Young＇s moduli of a series of nanoporous Black Diamond^（TM） low dielectric constant（low-k） films deposited on a Si（100） substrate are characterized successfully by the SAW technique.