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.

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.

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.

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.

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.

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.

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.

ELECTRIC FIELD EFFECTS ON YOUNG'S MOLULUS OF NANOWIRES

As an important component of nanodevices and nanomachine constructions, the mechanical performance of nanowires （NWs） has been a subject of intense research efforts due to gaining relevance in controlling functionality of nanoelectromechanical systems （NEMS）; meanwhile, one of the characteristics of the NEMS is the dependence of the functionality of the systems upon the applied electric field. The study of the electric effects on the Young＇s modulus of nanostructures is of certain usefulness in the design of NEMS and the precise measurement of mechanical properties of one-dimensional nanostructures. This paper reviews the origin of the size-dependence of the elastic property of NWs and the factors influencing the discrepancies and inconsistencies in the measured values of the Young＇s modulus for the NW, besides the surface effects, nonlinear effects, the electromechanical coupling effects as a possible effect responsible for the differences in quantitative and qualitative performance of the measured Young＇s modulus for the NWs versus the diameter are clarified.

Elaboration and Characterization of a Hybrid Composite Material with Two Particles of the Same Size: Coco Shells and Palm Shells

This work aims to develop and characterize a hybrid composite material with two particles of the same size. As reinforcing particles, the hulls of palm nuts and coconut are chosen. Hybrid composite material composites in the form of specimens were produced by molding at 10%, 20% and 30% mass fractions in various sizes (0.63 mm, 1.25 mm and 2.5 mm). The samples were physically characterized (water absorption rate, moisture content, actual, theoretical and apparent density) and mechanical in 3-point flexion. The main results are: the highest and minimum water absorption rate are respectively 3.57% and 0.67% for respectively particle sizes 1.25 mm (sample P10C30) and 0.67% in the size of 0.63 mm (sample P10C10). The moisture content varies from 0.64 to 7.14% respectively for the P20C20 (2.5 mm) and P10C30 (2.5 mm) samples. The maximum and minimum real density are 1340,518 Kg/m3 and 1055.981 Kg/m3, for respectively the composites of particles sizes 1.25 mm (P20C10) and 0.63 mm (sample P20C20). The minimum real density is Its maximum theoretical density is 1194.949 Kg/m3 (for samples P20C10, P10C10 and P30C10);however, the minimum is 1189.966 Kg/m3 (P10C20 and P20C20). The bulk density varies from 933.28 Kg/m3 to 1176.1 Kg/m3, respectively, in sizes from 2.5 mm (P10C30) to 0.63 mm (for P10C30). As for the mechanical characteristics, the Modulus of Elasticity (MOE) varies from 25.664 GPa to 25.759 GPa, respectively, the samples P10C10 (1.25 mm) and P10C20 (2.5 mm). The MOE values describe a parabola whose peak is reached when the palm shell loads are 20%, that is to say P20C10, whatever the particle size distribution. In resilience, samples with small particles are more resilient with a maximum value of 22.49 J/cm2 and a minimum value of 4.45 J/cm2 to verify the principles of Hall-Petch’s law.

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.

Various admixtures to mitigate the long-term strength retrogression of Portland cement cured under high pressure and high temperature conditions

In order to investigate the problem of long-term strength retrogression in oil well cement systems exposed to high pressure and high temperature(HPHT)curing conditions,various influencing factors,including cement sources,particle sizes of silica flour,and additions of silica fume,alumina,colloidal iron oxide and nano-graphene,were investigated.To simulate the environment of cementing geothermal wells and deep wells,cement slurries were directly cured at 50 MPa and 200?C.Mineral compositions(as determined by X-ray diffraction Rietveld refinement),water permeability,compressive strength and Young’s modulus were used to evaluate the qualities of the set cement.Short-term curing(2e30 d)test results indicated that the adoption of 6 m m ultrafine crystalline silica played the most important role in stabilizing the mechanical properties of oil well cement systems,while the addition of silica fume had a detrimental effect on strength stability.Long-term curing(2e180 d)test results indicated that nano-graphene could stabilize the Young’s modulus of oil well cement systems.However,none of the ad-mixtures studied here can completely prevent the strength retrogression phenomenon due to their inability to stop the conversion of amorphous to crystalline phases.

Topological Design of Microstructures of Materials Containing Multiple Phases of Distinct Poisson’s Ratios

A methodology for achieving the maximum bulk or shear modulus in an elastic composite composed of two isotropic phases with distinct Poisson’s ratios is proposed.A topology optimization algorithm is developed which is capable of finding microstructures with extreme properties very close to theoretical upper bounds.The effective mechanical properties of the designed composite are determined by a numerical homogenization technique.The sensitivities with respect to design variables are derived by simultaneously interpolating Young’smodulus and Poisson’s ratio using different parameters.The so-called solid isotropicmaterial with penalizationmethod is developed to establish the optimization formulation.Maximum bulk or shearmodulus is considered as the objective function,and the volume fraction of constituent phases is taken as constraints.Themethod ofmoving asymptotes is applied to update the design variables.Several 3D numerical examples are presented to demonstrate the effectiveness of the proposed structural optimization method.The effects of key parameters such as Poisson’s ratios and volume fractions of constituent phase on the final designs are investigated.A series of novel microstructures are obtained fromthe proposed approach.It is found that the optimized bulk and shearmoduli of all the studied composites are very close to the Hashin-Shtrikman-Walpole bounds.

Vibration analysis of foam plates based on cell volume distribution

In this paper, vibration analysis of irregular-closed-cell foam plates is per- formed. A cell volume distribution coefficient is introduced to modify the original Gibson- Ashby equations of effective Young＇s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa- rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.