Effective Elastic Moduli Research Articles

Effects of Initial Defects on Effective Elastic Modulus of Concrete with Mesostructure

Effects of Initial Defects on Effective Elastic Modulus of Concrete with Mesostructure

Fabrication and electroadhesion properties of parylene-coated carbon fiber arrays

Parylene-coated carbon fiber (CF) arrays with tunable inclination angles and heights were fabricated using oxygen plasma etching of composite wafers with embedded parallel CFs, followed by parylene coating via chemical vapor deposition. The effective elastic modulus of the CF arrays was found to decrease approximately in proportion to the square of the fiber length (5-60μm), with the parylene coating (∼2μm) further slightly reducing the modulus. Both experimental measurements and finite element simulations indicated that CF arrays with inclination angles below 75° exhibit ideal contact with glass wafers during electrostatic adhesion. However, the measured electrostatic adhesion between CF arrays and A4 paper was significantly lower than the predicted value for ideal contact, likely due to the porous nature of the paper. Electrostatic chuck prototypes based on the parylene-coated CF arrays demonstrated effective pick-and-place capabilities for A4 paper, plastic films, and glass wafers at voltages ranging from 500 to 900 V, without causing surface damage or leaving residue. These results highlight the potential of the parylene-coated CF arrays for applications in high-precision manufacturing and automated handling systems.

Surface Engineering of Polymeric Colloidal Crystals by Temperature - Pressure Annealing.

Polymer colloidal crystals (PCCs) have been widely explored as acoustic and optical metamaterials and as templates for nanolithography. However, fabrication impurities and fragility of the self-assembled structures are critical bottlenecks for the device's efficiency and applications. We have demonstrated that temperature-assisted pressure [ annealing results in the mechanical strengthening of PCCs, which improves with the annealing temperature. Here, the enhancement of elastic properties and morphological features of self-assembled PCC's is evaluated using Brillouin light scattering and scanning electron microscopy. The pressure-induced effects on the vibrational modes of PCCs are also illustrated at temperatures well below the polymer glass transition. While the PCCs colloid constituents display reversibility, the PCC material is strongly irreversible in the performed thermodynamic cycle. The effective elastic modulus enhances from 0.7GPa for the pristine sample to 0.8GPa, solely by pressure annealing at room temperature. [ annealing at higher temperatures leads to a maximum effective elastic modulus of 1.7GPa, more than twice the value in the pristine sample. Above a cross-over pressure, 725bar at 348K), the PCCs respond elastically and, hence, reversibly to pressure changes.

Yield surface of multi-directional gradient lattices with octet architectures

In this paper, a theoretical method is developed to delineate the effective elastic properties and yield surface of the gradient cellular structure. Additionally, a technique is presented for the construction of multi-directional gradient lattices, and two novel tri-directional gradient lattices (TD-GLs) by assembling octet unit cells with side lengths following specified gradient topological parameters serve as an illustrative example. Their effective elastic properties and yield surfaces are systematically investigated with the aid of theoretical, experimental, and finite element methods. It is found that the effective elastic modulus of the proposed TD-GLs exceeds by 48.80% as compared to that of conventional uniform octet lattices. Moreover, the normalized yield surfaces are proposed to emphasize the predominant role of structural topological features by eliminating the influence of the relative density on the yield behavior of TD-GLs, and this method that also can be extrapolated to other tension-dominated lattices. Subsequently, a theoretical model is developed to establish closed-form yield functions for characterizing the yield behavior of TD-GLs. The predicted yield surfaces from the proposed theoretical model demonstrate good agreement with the simulated results. Finally, the proposed TD-GLs demonstrate outstanding yield performance in various directions deviating from their orthogonal principal axes or planes, compared to lattices with uni- or dual-directional gradient topological configurations. In summary, the proposed multi-directional gradient lattices in this study exhibit the exceptional stiffness and outstanding yield performance in various directions, offering valuable insights for the structural design and engineering applications of lattice structures.

The implementation of M-integral in cross-scale correlation analysis of porous materials

The damage analysis caused by mesoscopic pores has attracted much attention in the development and application of porous materials. In this study, a novel application of M-integral is presented to establish a cross-scale correlation analysis of damaged porous materials. The multiscale damage analysis featured here can be proposed in two main steps. In detail, the first step is to construct a quantitative relationship between M-integral and porosity, where the values of M-integral for different porosity are calculated numerically. Subsequently, it applies the variation of M-integral with the material damage represented by a decrease in effective elastic modulus, and a cross-scale correlation between porosity and effective elastic modulus of porous material can be provided. In addition, an example is discussed to illustrate the specific application of this bridging parameter M-integral. The results confirm that M-integral can be an effective parameter bridging mesoscopic porosity and macroscopic damage, and is expected benefit to propose a convenient damage model of porous material. The findings should be of value in investigating the multiscale damage analysis of porous materials.

The Anisotropic Mechanical and Tribological Behaviors of Additively Manufactured (Material Extrusion) Implant-Grade Polyether Ether Ketone (PEEK)

In this study, we investigated the mechanical and tribological properties of the layer-by-layer structure of additively manufactured implant-grade Polyether Ether Ketone (PEEK) through the Material Extrusion (ME) process as a potential substitute for artificial joints. The effective elasticity modulus of the anisotropic 3D-printed PEEK was determined to be 2.505 GPa along the vertical and horizontal build orientations. The lubricated friction and wear performance were assessed using a pin-on-disk test under various loads, including 14, 30, 50, and 70 N, with a sliding speed of 50 mm/s over a total distance of 1 km at 37 °C. The contact parameters between the hemispherical steel pin and 3D-printed PEEK disks, involving contact pressures over the circle of contact, were observed to increase as the load increased. The results indicated that the wear coefficient exhibited a rise from 1.418 × 10−5 to 2.089 × 10−1 as the applied loads increased, signaling a shift from mild to severe wear regimes. Fetal Bovine Serum (FBS) as a lubricant exhibited a mixed mechanism, ascertained through the Stribeck curve, as well as a minimum fluid film thickness of 1.346 nm under an isoviscous–elastic regime, as calculated by the maximum load. Moreover, the mechanism governing wear during sliding, influenced by both normal axial and shear loads, primarily involved adhesion.

Formation of Structural-Phase State and Elastic and Durometric Properties of Biocompatible Cold-Rolled Titanium Ti–Nb–Zr-Based Alloys during Aging

The methods of scanning electron microscopy, X-ray diffraction analysis, and microindentation are used to study the effect of alloying with zirconium (within 3 to 6 at %) and complex Zr + Sn and Zr + Sn + Ta additions on the evolution of the structure, phase composition, and properties (effective modulus of elasticity, hardness, and wear-resistance parameters) of quenched biocompatible β-titanium (at %) Ti–6% Nb–% Zr, Ti–6% Nb–% Zr, Ti–6% Nb–% Zr, Ti–6% Nb–% Zr–% Sn, and Ti–6% Nb–% Zr–% Sn–0.7Ta alloys during aging (at 400°C for 4, 16, and 64 h) after multipass cold rolling with a total degree of strain of 85%. As compared to the quenching, the cold rolling of the studied Ti–b–r alloys is shown to suppress the occurrence of the β → ω transformation in the course of aging and to favor the acceleration of the decomposition of β solid solution with the formation of nonequilibrium αl phase in the course of aging. The increase in the zirconium content from 3 to 6 at % in the cold-rolled ternary Ti–6% Nb –х% Zr alloys and introduction of complex Zr + Sn and Zr + Sn + Ta additions to the Ti–6% Nb alloy instead of only zirconium addition hinder the decomposition processes of the β phase during aging; this impacts the intensity of variations of the effective modulus of elasticity and microhardness. The aging of the cold-rolled alloys under study was found to allows us to obtain the higher values of the parameters H/Er and (Н is the hardness and Er is the resolved modulus of elasticity) associated with the wear resistance as compared to those for the widely used medical Ti–Al–V alloy. The compositions of the alloys and conditions of their treatment are determined, which allow us to obtain the combination of the highest-level properties.

Mesoscale models for effective elastic properties of carbon-black/ultra-high-molecular-weight-polyethylene nanocomposites

In this paper, we apply mesoscale numerical modeling to predict the effective elastic properties of conductive carbon-black/ultra-high-molecular-weight-polyethylene nanocomposites. The models are based on X-ray microcomputed tomography images. The images show that for the considered range of carbon additive weight fractions, the conductive carbon black (CB) particles are distributed around the ultra-high-molecular-weight-polyethylene (UHMWPE) granules forming a carbon-containing layer of a thickness on the order of 1–2 μm.Finite element models of representative volume elements (RVE), incorporating the CB-containing layer, are developed. The RVEs are generated based on the size and shape statistics extracted from processed microcomputed tomography images with further incorporation of the CB-containing layer by a custom image processing code. The layer is modeled analytically as a 2-phase composite consisting of spherical CB inclusions distributed in the UHMWPE matrix. Elastic moduli predicted in the models are compared to experimental data. Results show that the numerical simulations predict effective elastic moduli within the confidence intervals of the experimental measurements up to 7.5 wt % of CB inclusions.

تطوير معامل المرونة الفعال للخرسانة الصديقة للبيئة القائمة على مسحوق الزجاج

This study aims to develop an effective modulus of elasticity for eco-concrete using glass powder. Various theoretical models, including VOIGT and REUSS-VOIGT, are compared with experimental results. The REUSS-VOIGT model proved most accurate, particularly for cement replacement (5%-20%) and fine aggregate replacement (up to 25%). The REUSS-VOIGT model closely matches experimental results, especially after 56 days. To achieving sustainable development in the production of Portland cement by conserving natural resources and rationalizing their consumption for future generations. Keywords: Homogenization, Effective Modulus of Elasticity, Eco-concrete, Glass Powder, REUSS/VOIGT Model.

Microstructure and corrosion properties of CrMnFeCoNi high entropy alloy coating by temperature field-assisted laser cladding

The CrMnFeCoNi high entropy alloy coatings were prepared on the surface of Q345 steel using a temperature field-assisted laser cladding process, and the effects of the applied temperature field on the cladding coatings were studied. The microstructures and corrosion morphologies of the coatings were observed, and the elemental distribution, hardness, effective elastic modulus, electrochemical corrosion performance, and corrosion products of different coatings were analyzed. The results show that the porosity of the HEA coatings prepared with a temperature field is reduced to below 50 % of the initial level. The microstructure of the coating changed, with the nanoindentation hardness of the coating increasing by up to 0.55 GPa, enhancing the mechanical properties. Among all the coatings, the coating prepared at 250 °C temperature field exhibited the best corrosion resistance, with corrosion potential and current density of −0.27 V and 0.15 μA/cm2, respectively, improving the corrosion potential by 0.1 V and reducing the current density by 1.08 μA/cm2 compared to the sample prepared at room temperature. After incorporating the temperature field, the stability of the passive film on the coating during corrosion improved, and the nucleation rate of pitting decreased. Therefore, incorporating an appropriate temperature field during laser cladding can effectively enhance the overall performance of the CrMnFeCoNi HEA coating.

استخلاص معامل الليونة الافتراضي للخرسانة المحتواة على مسحوق الزجاج الناعم

This work compares three theoretical models with experimental results to identify the most accurate model for estimating the effective modulus of elasticity (Eeff) of eco-concrete made with glass powder. The models are Ruess-Voigt, mixture law, and Ishai and Cohen. Validation is based on scientific studies of this eco-concrete. The study concludes that glass powder can replace 20% of cement, with the Ruess-Voigt model being the most accurate. If glass powder replaces up to 30% of fine aggregates, both the Ruess-Voigt and mixture rule models are closely accurate. Keywords: Homogenization, Effective Elasticity Modulus, Glass Powder. Ruess/Voigt Model. Mixture Law Model. Ishai and Cohen model.

A peridynamic-based reconstruction and analysis method for short-fiber reinforced composites

Abstract As the complex microstructure, predicting the effective elastic properties and damage mechanisms of Short-Fiber Reinforced Composites (SFRC) continues to pose a challenge. This study presents a new reconstruction and analysis method based on PeriDynamics (PD) for SFRC. The reconstruction of the surface profiles of short-fibers obtained from Micro-CT (Micro-Computed Tomography) scanning resulted in a PD computational model that accurately reflects the actual microstructure of SFRC. The results predicted the effective elastic modulus of SFRC while fiber volume fraction and distribution have impact. Micro-cracks emerge at stress concentration regions near the fiber-matrix-fiber interfaces between two adjacent fibers, and with increasing load, these cracks gradually propagate, interact, and merge with each other. Eventually, major cracks form, leading to material failure.

Analytic solutions for effective elastic moduli of isotropic solids containing oblate spheroid pores with critical porosity

AbstractAccurate characterization for effective elastic moduli of porous solids is crucial for better understanding their mechanical behaviour and wave propagation, which has found many applications in the fields of engineering, rock physics and exploration geophysics. We choose the spheroids with different aspect ratios to describe the various pore geometries in porous solids. The approximate equations for compressibility and shear compliance of spheroid pores and differential effective medium theory constrained by critical porosity are used to derive the asymptotic solutions for effective elastic moduli of the solids containing randomly oriented spheroids. The critical porosity in the new asymptotic solutions can be flexibly adjusted according to the elastic moduli – porosity relation of a real solid, thus extending the application of classic David‐Zimmerman model because it simply assumes the critical porosity is one. The asymptotic solutions are valid for the solids containing crack‐like oblate spheroids with aspect ratio < 0.3, nearly spherical pores (0.7 < < 1.3) and needle‐like prolate pores with > 3, instead of just valid in the limiting cases, for example perfectly spherical pores (= 1) and infinite thin cracks (0). The modelling results also show that the accuracies of asymptotic solutions are weakly affected by the critical porosity and grain Poisson's ratio , although the elastic moduli have appreciable dependency of and . We then use the approximate equations for pore compressibility and shear compliance as inputs into the Mori–Tanaka and Kuster–Toksoz theories and compare their calculations to our results from differential effective medium theory. By comparing the published laboratory measurements with modelled results, we validate our asymptotic solutions for effective elastic moduli.

Evaluating predictive scheme for thermomechanical properties of Si-diamond composites.

A novel, parameter-independent multiscale correlational constitutive model has been devised to predict thermomechanical properties of Si-diamond-SiC and Si-diamond composites, including the effective elastic modulus, effective bulk modulus, effective shear modulus, effective Poisson's ratio, average coefficients of thermal expansion as well as thermal conductivity. Based on this model, the effective thermomechanical response of two kinds of composites was simulated, and the underlying mechanisms of thermomechanical coupling between constituents were also critically evaluated. The findings were shown that the effective elastic properties of composites, including effective elastic modulus, effective bulk modulus, effective shear modulus, increased with diamond and SiC, and that the introduction of dispersed diamond with highly thermal conductivity and lowly thermal expansion significantly enhanced thermophysical properties of Si-diamond-SiC composites. The thermomechanical coupling of these composites was influenced by the effective elastic properties of composites and the disparity in the intrinsic properties of constituents.

On effective surface elastic moduli for microstructured strongly anisotropic coatings

The determination of surface elastic moduli is discussed in the context of a recently proposed strongly anisotropic surface elasticity model. The aim of the model was to describe deformations of solids with thin elastic coatings associated with so-called hyperbolic metasurfaces. These metasurfaces can exhibit a quite unusual behaviour and concurrently a very promising wave propagation behaviour. In the model of strongly anisotropic surface elasticity, strain energy as a function of the first and second deformation gradients has been introduced in addition to the constitutive relations in the bulk. In order to obtain values of surface elastic moduli, we compare dispersion relations for anti-plane surface waves obtained using the two-dimensional (2D) model and three-dimensional (3D) straightforward calculations for microstructured coatings of finite thickness. We show that with derived effective surface moduli, the 2D model can correctly describe the wave propagation.

A nonlinear elastic-plastic model describing the bending and fracture behavior of Caragana korshinskii Kom. branch wood

ABSTRACT Caragana korshinskii Kom. branch (CKB), a vital biomass source in northwest China, has not been thoroughly studied in terms of its bending fracture mechanics. This research aims to establish a nonlinear constitutive model that clarifies the fracture behavior of CKB when subjected to bending loads. The nonlinear bending fracture process of CKB was characterized through a three-point bending test, revealing stages of elastic deformation, elastic-plastic transition, and plastic fracture. A power-enhanced elastic-plastic model combined with continuous damage mechanics theory was used to develop an intrinsic bending fracture model, from which the equations governing bending damage evolution were derived. The model's accuracy was validated with simulations in Abaqus/Explicit, showing that CKB from various growth sites demonstrated distinct nonlinear bending behaviors. At the critical damage strain, cumulative damage led to a reduction in the effective elastic modulus, with the bending fracture curve exhibiting a power function trend. The parameters of the nonlinear elastic-plastic constitutive model were derived through curve fitting, yielding coefficients of determination (R²) exceeding 0.99. The consistency between the trends observed in actual tests and simulations, along with a peak bending force error of 7.7%, validated the finite element model's reliability and confirmed the intrinsic model's accuracy.

Stress-deformation analysis of the cracked elastic body

A new analytical plane Elastic Fracture Mechanics (LEFM) model of the effective elastic moduli exhibited by an isotropic elastic cracked solid in tensile and compressive stress fields is presented. The effective Young’s modulus and Poisson’s ratio E¯,v¯, respectively, relate the stresses applied to the cracked solid with its macroscopic deformation. In the case of a compressive stress field the effective elastic moduli depend solely on properly oriented cracks that are either open or closed. This model is then used for the stress and displacement estimations around a circular axisymmetric hole under internal pressure and external hydrostatic stress. The creation of the hole alters the stresses in its neighborhood, and induces a deterioration of the elastic moduli. In this manner, the effective elastic moduli depend on the radial distance from the hole’s boundary. The validation of the algorithm was done against Kirsch’s analytical solution of the axisymmetric hole problem for nearly zero density of cracks as well as for large values of the friction angle. The model predicts a lower tangential stress concentration at the wall of the hole compared to that predicted by the constant linear elasticity solution and a maximum stress concentration that is not necessarily located at the wall of the hole. This apparent enhancement of rock strength adjacent to the wall is more pronounced for larger concentrations of open cracks.

Static bending analysis of pressurized cylindrical shell made of graphene origami auxetic metamaterials based on higher-order shear deformation theory

Static bending responses of a pressurized composite cylindrical shell made of a copper matrix reinforced with functionally graded graphene origami are studied in this paper. The kinematic relations are extended based on a new higher-order shear and normal deformation theory in the axisymmetric framework. The constitutive relations are extended for the composite cylindrical shell where the effective modulus of elasticity, Poisson's ratio, thermal expansion coefficient and density are estimated using the Halpin-Tsai micromechanical model and the rule of mixture. Some modified coefficients are employed for correction of the mentioned material properties in terms of the volume fraction and the folding degree of graphene origami, characteristics of copper and graphene nanoplatelets and thermal loads. The principle of virtual work is used to derive governing equations through computation of strain energy and external work. The static bending results including radial and axial displacements, circumferential strain and stress are presented along the longitudinal and radial directions in terms of volume fraction, folding degree and distribution of graphene origami. The results show an increase in radial displacement and circumferential strain with an increase in folding degree and a decrease in volume fraction of graphene origami. The main novelty of this work is investigating the effect of foldability parameter and various distribution of graphene origami on static results of short cylindrical shell.

Effect of sample dimensions on the stiffness of PA12 Lattice materials fabricated using Powder Bed Fusion

Powder Bed Fusion fabrication techniques, including selective laser sintering, have made the fabrication of lattice meta-materials consisting of periodic cells formed by interconnected struts possible. It is generally observed that cell size has a strong influence on the lattice’s effective Young’s modulus, following in the case of typical polymers used for printing a trend of the smaller the softer. However, there is no clear understanding of the origin of the effective elastic modulus reduction with lattice cell size. In this paper, an integrated study is performed to unravel the reasons behind this effect. The analysis performed encompasses mechanical characterization (compression tests and nanoindentation), microstructure characterization (X-ray tomography, DSC, SAXS, and WAXS), and numerical analysis of the effect of defects (FFT and Finite element simulations of cells with roughness and defects) of PA12 printed single cells of different sizes and full lattice specimens containing many cells. It is found that the effect of porosity and roughness is not enough to explain the reduction of the effective elastic modulus with the cell size, suggesting that this effect is necessarily a combination of the defects, incomplete melting of particles and the changes of PA12 nanostructure induced by the different printing conditions as function of full specimen size . The results of the micro- and nanostructure characterization validate this assumption.

Early detection of fatigue-induced material changes by modulation of ultrasound in dynamically loaded structures

In this work, an ultrasonic approach for early detection of fatigue-induced material changes in an aluminium alloy plate under dynamic loading is developed and validated. Material degradation followed by the emergence and growth of a crack was created by a fatigue machine while monitoring the modulation of sinusoidal ultrasonic wave packets sent along the plate around high- and low-load instants in the fatigue cycle. The determined wave parameters and the difference between their high- and low-load values were found to be very sensitive not only to the emergence of the crack but also to the plastic deformation, which, according to digital image correlation monitoring, preceded the crack formation and changed the effective elastic modulus felt by A0 and S0 Lamb mode contributions to the wave packets. Experimental analysis and simulations showed that the high sensitivity to microstructural changes was resulting from their substantial effect on the propagation velocity of the arriving A0 and S0 wave packet contributions, which in turn had a strong influence on their interference.