Macroscopic Young’s Elastic Modulus Model of Particle Packing Rock Layers

Based on the Hertzian granular contact mechanics model, the paper built up a Macroscopic Young’s Elastic Modulus of particle/granular packing rock layers, and built up a ties to connecting Young’s Elastic Modulus of sand particle in Meso and the Macroscopic Young’s Modulus of granular packing rock layers. The Macroscopic Young’s Modulus of granular packing rock layers is far less than the Young’s Modulus of sand particle. The Macroscopic Young’s Modulus of granular packing rock layers is proportioned to the powers of 1/3 of the vertical contact force of sand particles. The Macroscopic Young’s Modulus is inversely proportional to particle diameter. The paper calculated the vertical contact force of five types aligning mode of the particles. When equal stress, the increased of the coordination number lead to the decrease of the contact force fn, this lead to the coordination number is an inverse proportion to Macroscopic Young’s Modulus. But the larger coordination number change only means very little Macroscopic Young’s Modulus change.

A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

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.

SIMULATION AND STUDY OF THE MODULUS OF ELASTICITY OF NANOCRYSTALLINE MATERIALS

In this paper, a molecular dynamics simulations are provided for atomic structure of nanocrystals(1～3nm)by which t he lattice parameter of X_ray diffraction, cohesive energy and modulus of elas ticity were computed. The results show that the structure of grain and grain bou ndaries in the same in both nanocrystal and coarse grain materials. The decrease of grain size and the increase volume fraction of grain boundaries lead to a se ries of different features, the modulus of elasticity of nanocrystalline materia ls have been found to be much reduced.

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.

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.

Experimental Study on Young′s Modulus of Concrete

Young′s Modulus of concrete is studied on the basis of triaxial compressive experiments. The authors proposed two empirical equations to calculate its static Young′s modulus and dynamic Young′s modulus when dynamic Poisson ratio μ d varies nearby 0.20.P wave velocity and elastic modulus have the same varying tendency as letter N. μ,μ d decrease with the increase of loading rate and μ d has a great effect on the parameters E d and E D.

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.

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.

Biodegradation of Polymethylmethacrylate Bone Cement May Not Be a Serious Issue in Total Hip Arthroplasty—Retrieval Study for Knoop Hardness and Young’s Modulus

Introduction: To investigate a long-term in vivo deterioration of polymethylmethacrylate (PMMA) bone cement over time, we evaluated retrieved PMMA cement in terms of chemical elements presenting in the cement using energy dispersive analysis of X-rays;Knoop hardness;and the Young’s modulus using scanning acoustic microscopy. Materials and Methods: For mechanical evaluation, we could neglect the influences of entrapped air bubbles or blood by the use of small specimens. The study was based on thirteen cement samples (six used in the acetabulum and seven in the femur) derived from eight patients (age at revision surgery: mean 72.5, range 68 to 79). All of these samples were Simplex-P?cement. They were functioning well at least ten years after the previous surgery. Duration until revision surgery was ranged 12 to 25 years (average, 17.4 years). The reason for revision was aseptic mechanical loosening. Twenty samples of Simplex-Preg;cement were served by manually mixing as a control. Results: The average of the hardness of the cement was 17.0 ± 1.2 (range, 13.4-20.6). In the control, the hardness was 17.8 ± 1.5 (range, 14.0-24.6). There was no significant difference between these values. The mean of Young’s modulus of the cement was 5.61 ± 0.19 GPa (range, 5.09-6.10). In the control, the modulus was 6.04 ± 0.13 GPa (range, 5.68-6.45). Although the modulus was significantly less than that of the control, there was only 7% decrease in average between twelve and twenty-five years in vivo. Conclusions: Our results suggest that long-term implantation and functional loading in vivo may not be the limiting factor in the mechanical integrity of the bone cement.

Vibration of Gold Nano-Beam with Variable Young’s Modulus Due to Thermal Shock

In this paper, we will study the most important effects in the nano-scale resonator: the coupling effect of temperature and strain rate, and the non-Fourier effect in heat conduction. A solution for the generalized thermoelastic vibration of nano-resonator induced by thermal loading has been developed. The Young’s modulus is taken as a linear function of the reference temperature. The effects of the thermal loading and the reference temperature in all the studied fields have been studied and represented in graphs with some comparisons. The Young’s modulus makes significant effects on all the studied fields where the values of the temperature, the vibration of the deflection, stress, displacement, strain, stress-strain energy increase when the Young’s modulus has taken to be variable.

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.

A methodology to determine the elastic properties of anisotropic rocks from a single uniaxial compression test

This paper introduces a new methodology to measure the elastic constants of transversely isotropic rocks from a single uniaxial compression test.We first give the mathematical proof that a uniaxial compression test provides only four independent strain equations.As a result,the exact determination of all five independent elastic constants from only one test is not possible.An approximate determination of the Young’s moduli and the Poisson’s ratios is however practical and efficient when adding the Saint-Venant relation as the fifth equation.Explicit formulae are then developed to calculate both secant and tangent definitions of the five elastic constants from a minimum of four strain measurements.The results of this new methodology applied on three granitic samples demonstrate a significant stress-induced nonlinear behavior,where the tangent moduli increase by a factor of three to four when the rock is loaded up to 20 MPa.The static elastic constants obtained from the uniaxial compression test are also found to be significantly smaller than the dynamic ones obtained from the ultrasonic measurements.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

Elastic and Plastic Behaviors of Laminated Ti-TiBw/Ti Composites

The novel laminated Ti-TiBw/Ti composites composed of pure Ti layers and TiBw/Ti composite layers have been successfully fabricated by reactive hot pressing. Herein, two-scale structures formed： the pure Ti layer and TiBw/Ti composite layer together constructed a laminated structure at a macro scale. Furthermore, TiBw reinforcement was distributed around Ti particles and then formed a network microstructure in TiBw/Ti composite layer at a micro scale. The laminated Ti-TiBw/Ti composites reveal a superior combination of high strength and high elongation due to two-scale structures compared with the pure Ti, and a further enhancement in ductility compared with the network structured composites. Moreover, the elastic modulus of the laminated composites can be predicted by H-S upper bound, which is consistent with the experimental values.

An Elasticity Model Considering Grain Boundaries and Tensile Orientations for Directionally Solidified Superalloys

In order to investigate the elastic properties of directionally solidified(DS)superalloys,an elasticity model called boundaries elastic model(GBE model),considering grain boundaries and tensile orientations,is proposed in this paper.Two assumptions are adopted in the GBE model:(1)The displacement of grains,which moves along the perpendicular direction,is restricted by the grain boundaries;(2)Grain boundaries influence region(GBIR)is formed around the grain boundaries.Based on the single crystal(SC)calculation method of elastic properties,the GBE model can well predict macroscopic equivalent elastic modulus(Young’s modulus)of DS superalloys under different tensile orientations effectively.To demonstrate the correctness of the GBE model,3D finite element simulation is adopted and tensile experiments on a Ni3Al?base DS superalloy(IC10)along five tensile orientations are carried out.Meanwhile,the grain boundaries are observed by light microscopy and transmission electron microscope(TEM).Therefore,the GBE model is proved to be feasible by comparing the simulated results with the experiments.

Composition effect on elastic properties of model NiCo-based superalloys

NiCo-based superalloys exhibit higher strength and creep resistance over conventional superalloys.Compositional effects on elastic properties of the γ and γ' phases in newly-developed NiCo-based superalloys were investigated by first-principles calculation combined with special quasi-random structures.The lattice constant,bulk modulus,and elastic constants vary linearly with the Co concentration in the NiCo solution.In the selected(Ni,Co)3(Al,W)and(Ni,Co)3(Al,Ti)model γ' phase,the lattice constant,and bulk modulus show a linear trend with alloying element concentrations.The addition of Co,Ti,and W can regulate lattice mismatch and increase the bulk modulus,simultaneously.W-addition shows excellent performance in strengthening the elastic properties in the γ' phase.Systems become unstable with higher W and Ni contents,e.g.,(Ni0.75Co0.25)3(Al0.25 W0.75),and become brittle with higher W and Co addition,e.g.,Co3(Al0.25 W0.75).Furthermore,Co,Ti,and W can increase the elastic constants on the whole,and such high elastic constants always correspond to a high elastic modulus.The anisotropy index always corresponds to the nature of Young's modulus in a specific direction.