Reuss Model Research Articles

Modeling of ice-matrix composite fracture

This article discusses the results of a study that used the structural approach to conduct multiscale modeling of composite materials. These materials are composed of an ice matrix that has been enhanced with high-strength basalt fibers. The research involved numerical modeling to analyze the fracture process of composite materials made by freezing fresh water with added basalt fibers. The analysis included experimental data from samples of pure ice and composites with different amounts of filler. The effective modulus of elasticity of the composites was determined by considering the quantity of basalt fiber reinforcement. The discrepancy between the strength obtained by finite element complex ANSYS numerical calculation and the experimental data was revealed by a series of macroscopic test calculations of the composite material sample, according to which the effective modulus of elasticity of the composite was recalculated and corrections were introduced into the Voight and Reuss models, taking into account the non-uniform distribution of the fibers and the non-ideal adhesion between the fibers and water ice. A stochastic model of crack growth at the micro level was also used with the data on the diameter and length of basalt fibers and their random distribution in the layers of the composite material. Using the newly acquired effective elastic moduli and the SmartCrackGrowth algorithm, a satisfactory agreement of the crack growth rate with the obtained by stochastic calculation was achieved. The refined method of effective elastic moduli and multilevel model of stress-strain state calculation of composite materials are recommended for assessing the strength of ice cover and designing winter roads with high load-bearing capacity and long operational duration in the Arctic and Subarctic environments.

Spatial reconstruction, microstructure-based modeling of compressive deformation behavior, and prediction of mechanical properties in lightweight Al-based entropy alloys

Lightweight Al-based entropy alloys are newly emerged materials with promising potential for structural applications; however, their modeling and strengthening prediction require further exploration. In this study, the spatial distributions of various phases in three Al-based entropy alloys were investigated. A closely interconnected intermetallic compound (IC) network comprising Al2Cu and Al45Cr7 phases was identified. Finite element (FE) modeling was conducted based on the reconstructed three-dimensional microstructure to simulate compressive deformation behavior. The IC network served as the main stress bearer during deformation. Thin sections in the Al2Cu network were the weak sites where stress concentration and damage first occurred. However, the breakage of this limited region contributes to relatively coordinated deformation and extended plasticity. The breakage of large particles accounts for the final alloy failure. The results of the FE model were compared with the experimentally measured stress–strain behavior and mechanical properties, showing very good agreement. Given the non-uniform distribution of strain and stress during deformation, a strengthening model, merging the Voigt and Reuss models, was also developed to predict the mechanical properties of Al-based entropy alloys with the aim of facilitating Al-based entropy alloy development.

A Comparative Study of Micromechanical Analysis Models for Determining the Effective Properties of Out-of-Autoclave Carbon Fiber-Epoxy Composites.

This study aims to critically assess different micromechanical analysis models applied to carbon-fiber-reinforced plastic (CFRP) composites, employing micromechanics-based homogenization to accurately predict their effective properties. The paper begins with the simplest Voigt and Reuss models and progresses to more sophisticated micromechanics-based models, including the Mori-Tanaka and Method of Cells (MOC) models. It provides a critical review of the areas in which these micromechanics-based models are effective and analyses of their limitations. The numerical analysis results were confirmed through finite element simulations of the periodic representative volume element (RVE). Furthermore, the effective properties predicted by these micromechanics-based models were validated via experiments conducted on IM7/5320-1 composite material with a fiber volume fraction of 0.62.

Various homogenisation schemes for vibration characteristics of axially FG core multilayered microbeams with metal foam face layers based on third order shear deformation theory

This study assesses the significance of homogenisation models in theoretically analysing the vibrations of three-layered microbeams with a core composed of axially functionally graded (AFG) material and with upper and lower face layers composed of metal foam material, especially when the third order shear deformation beam theory and the modified couple stress theory are used. The material of the core is assumed to vary following a power gradation profile. The range of homogenisation schemes, including the Voigt model, Reuss model, Voigt-Reuss-Hill model, Tamura model, Mori-Tanaka model, lower and upper bounds of Hashin-Shtrikman, and the local representative volume element (LRVE) model, are utilised to approximate the material properties of the AFG core. The upper and lower layers of metal foams are modelled using the closed-cell and open-cell solid porosity models. The coupled motion equations are solved for the natural frequencies of the system for the transverse, rotational and axial directions. A software-based finite element analysis (FEA) study of two simplified macrobeam systems was undertaken and the agreement between the FEA and numerical results, using the presented theoretical method, is found to be excellent. It has been confirmed that the homogenisation schemes have a notable effect on the mechanical properties of the AFG core, and hence on the coupled translational-rotational motion's natural frequencies. The largest difference in natural frequencies between different homogenisation schemes is found with a power gradation constant of approximately 0.53. A larger disparity of natural frequencies between different homogenisation methods was seen with an increase in the thickness of the AFG core and the microbeam's length-scale parameter of multilayered porous microbeam. The results of this study highlight the significance of homogenisation scheme employed when investigating the vibrations of a multilayered microbeam with an AFG core and metal foam porous face layers.

Predicting the acoustic characteristics of seafloor sediments containing cold spring carbonate rocks

The acoustic and physical properties of two valuable marine cold spring carbonate rock samples gathered from the Chaoshan Depression in the South China Sea were measured. The Wyllie time-average equation was applied to analyze the measured sound speeds and their trend under different porosities, and the sound speeds of marine cold spring carbonate rocks were found to be consistent with those of terrestrial carbonate rocks. The Voigt model, Reuss model, and Voigt-Reuss-Hill model were used to predict the characteristics of the sound speed for four states of seafloor sediments containing cold spring carbonate mineral particles or rocks. For these four states of marine cold spring carbonate mineral particles existing on or in seafloor sediments, the sound speed and reflection coefficient of a mixture of seafloor surface sediments containing cold spring carbonate mineral particles or rocks decrease with an increase in the volume ratio of the seafloor sediment. This method for predicting the reflection coefficient provides evidence to explain the high and low reflection coefficients observed in Chirp sub-bottom profiles of cold spring seepage areas.

Numerical Modeling of the Dynamic Elastic Modulus of Concrete.

This article introduces simulations of theoretical material with controlled properties for the evaluation of the effect of key parameters, as volumetric fractions, elastic properties of each phase and transition zone on the effective dynamic elastic modulus. The accuracy level of classical homogenization models was checked regarding the prediction of dynamic elastic modulus. Numerical simulations were performed with the finite element method for evaluations of the natural frequencies and their correlation with Ed through frequency equations. An acoustic test validated the numerical results and obtained the elastic modulus of concretes and mortars at 0.3, 0.5 and 0.7 water-cement ratios. Hirsch calibrated according to the numerical simulation (x = 0.27) exhibited a realistic behavior for concretes of w/c = 0.3 and 0.5, with a 5% error. However, when the water-to-cement ratio (w/c) was set to 0.7, Young's modulus displayed a resemblance to the Reuss model, akin to the simulated theoretical triphasic materials, considering matrix, coarse aggregate and a transition zone. Hashin-Shtrikman bounds is not perfectly applied to theoretical biphasic materials under dynamic situations.

Experimental Study of Mechanical Properties and Failure Characteristics of Coal-Rock-like Composite Based on 3D Printing Technology.

Coal contains cracks and has strong heterogeneity, so the data dispersion is large in laboratory tests. In this study, 3D printing technology is used to simulate hard rock and coal, and the rock mechanics test method is used to carry out the coal-rock combination experiment. The deformation characteristics and failure modes of the combination are analyzed and compared with the relevant parameters of the single body. The results show that the uniaxial compressive strength of the composite sample is inversely proportional to the thickness of the weak body and directly proportional to the thickness of the strong body. The Protodyakonov model or ASTM model can be used as a verification method for the results of a uniaxial compressive strength test of coal-rock combination. The elastic modulus of the combination is the equivalent elastic modulus, and the elastic modulus of the combination is between the elastic modulus of the two constituent monomers, which can be analyzed using the Reuss model. The failure of the composite sample occurs in the low-strength material, while the high-strength section is rebounding as an extra load on the low-strength body, which may cause a sharp increase in the strain rate of the weak body. The main failure mode of the sample with a small height-diameter ratio is splitting, and the failure mode of the sample with a large height-diameter ratio is shear fracturing. When the height-diameter ratio is not greater than 1, it shows pure splitting, and when the height-diameter ratio is 1~2, it shows a mixed mode of splitting and shear fracture. The shape has a significant effect on the uniaxial compressive strength of the composite specimen. For the impact propensity, it can be determined that the uniaxial compressive strength of the combination is higher than that of the single body, and the dynamic failure time is lower than that of the single body. It can hardly determine the elastic energy and the impact energy of the composite with the relationship to the weak body. The proposed methodology provides new cutting-edge test technologies in the study of coal and coal-like materials, with an exploration of their mechanical properties under compression.

木材パルプ／バイオプラスチック積層複合材料の表面処理による力学特性の改善

In this study, wood-pulp／bio-based poly (butylene succinate) (Bio-PBS) laminated composites were made by using papermaking techniques. Wood-pulp fibers were treated with 3-aminopropyltrimethoxysilane (APTMS) and poly (vinyl alcohol) (PVA) to improve the interfacial adhesion between the wood-pulp fibers and Bio-PBS. Wood-pulp fibers without being processed (PF), wood-pulp fibers treated by APTMS (PF-Si), and wood-pulp fibers treated by both APTMS and PVA (PF-Si/PVA) were converted to sheets by the papermaking technique. Those sheets and Bio-PBS films were used to make wood-pulp/Bio-PBS laminated composites by hotpressing and cut into test pieces. Tensile testing and the heat distortion temperature measurements were conducted with those samples. As a result, the tensile strength of composites was close in value to that expected by the Reuss model when the volume fraction of wood-pulp was 12％ and 24％. Furthermore, the tensile strength of composites containing PF-Si/PVA was higher than that of composites containing PF and PF-Si. The heat distortion temperature of the composites was higher than that of Bio-PBS, although the effects of surface treatment on the heat distortion temperature were not confirmed. Microscopy observations of composite fractures indicated that the surface treatment of wood-pulp fibers enhanced interfacial adhesion between the woodpulp fibers and Bio-PBS.

Experimental and theoretical studies of effective piezoelectric coefficients of 2-2 connectivity AlN/AlScN composite piezoelectric films

Aluminum nitride (AlN) and Sc-doped AlN have become the most popular piezoelectric thin-film materials in the fields of RF and smart sensing. AlN/AlScN composite films based on 2-2 connectivity exhibit stronger interaction and better lattice matching between AlN and AlScN, resulting in improved nucleation, growth kinetics, crystal quality, piezoelectric response, and surface morphology. In this work, a method for predicting the effective coefficients of AlN/AlScN composite piezoelectric thin films is proposed and validated. This prediction method is based on first-principles calculations, the Reuss model theory, and the Mori-Tanaka (MT) method. It also conforms to the mean strain and stress theory of the micromechanical approach. The precise compliance, dielectric and piezoelectric properties (Sij, ε, dij) of AlN/Al0.8Sc0.2N composite film with different thickness ratios are calculated. Through the deflection measurement of piezoelectric cantilever with proof mass based on AlN/Al0.8Sc0.2N composite film, the experimental piezoelectric stress coefficient (d31) is calculated. The correctness of the prediction method is verified by comparing the theoretical calculation (d31* = −3.1pC/N) and experimental data (d31 = −3.4pC/N), showing excellent agreement within experimental error. Meanwhile, the voltage sensitivity of the accelerometer is significantly enhanced by the AlN/AlScN composite piezoelectric film. It is believed that this work will broaden the theoretical study and application of the AlN/AlScN composite piezoelectric film.

Micromechanics predictions of effective elastic, piezoelectric and dielectric properties of composite piezoelectric films

Knowledge of the effective elastic, piezoelectric and dielectric properties facilitates the design of radio frequency devices, for example film bulk acoustic resonators (FBARs). Based on the Reuss model and Eshelby–Mori–Tanaka micromechanics theory, this paper predicts the effective properties of bilayer composite piezoelectric film consisting of AlN film and vertical compound ScAlN film. The evaluated material coefficients and original material parameters are substituted into the FEM simulation to investigate the performance of FBARs, respectively. The consistent resonant frequencies of FBARs demonstrate the accuracy of Reuss model in calculating the effective parameters of bilayer composite piezoelectric film.

Thin film combinatorial sputtering of Al-Ce alloys: Investigating the phase separation of as-deposited solid solutions and determining the coefficient of thermal expansion

AlxCe100−x thin films with a composition range of ~75.0 < x < 99.5 at% (36.5 < x < 97.5 wt%) were synthesized via combinatorial co-sputtering from an Al and an Al50Ce50 target. The crystal structure, phase fraction, film morphology, electrical resistivity, and temperature-dependent coefficients of thermal expansion (CTE) are all correlated to the AlxCe100−x composition. The as-deposited films form a metastable solid-solution, and annealing leads to the formation of the thermodynamically stable two-phase system of Al and the α-Al11Ce3 intermetallic. Temperature dependent x-ray diffraction (XRD) reveals that the two phases expand independently of one another, and the thin film Al temperature-dependent CTE is similar to bulk Al. The thin film Al11Ce3 intermetallic phase has a nearly constant CTE of ~1.5 × 10−5/°C within the temperature range studied (25–550 °C). To confirm the thin film Al11Ce3 results, bulk stoichiometric Al11Ce3 and +/- 1 wt% Ce samples were prepared and the CTE of each was measured with the same conditions. A Rietveld analysis of the bulk data enabled an estimation of the CTE in each of the 3 orthorhombic lattice parameters, which displayed anisotropic behavior. The thin film and bulk CTE measurements were in very good agreement. Estimations of the temperature dependent CTE of the two-phase alloys are made via the Reuss and Voigt models. By demonstrating the efficacy of the approach, more complex multi-component rapid materials discovery of low CTE Al-alloys can be pursued via the combinatorial thin film synthesis and XRD measurement.

Determination of the residual stress in texture Cu-Ni-Si-Co alloy with HEXRD

This work uses high-energy synchrotron X-ray diffraction (HEXRD), atomic force microscope (AFM), nanoindentation and EBSD technology to explore a new method for measuring residual stress in strong R {124} 〈211〉 texture alloys, and the distribution of residual stress and Young's modulus in different crystal orientations. Compared with the traditional Voigt and Reuss model, for the textured Cu-Ni-Si-Co alloy, a local Voigt and Reuss inter-grain interaction model based on HEXRD diffraction technology is established, which can more accurately characterize the residual stress of superficial layer (230 μm). The local stress model provides a new X-ray diffraction method for testing the residual stress of textured materials. Aiming at the textured Cu-Ni-Si-Co alloy with compressive stress, the quasi-in-situ method combining EBSD and nanoindentation is used to characterize the residual stress of different crystal orientations in the microdomain. The hard orientation [111] grain direction has the highest residual stress, and the soft orientation [100] grain direction has the lowest residual stress, and the residual compressive stress in the hard orientation is about twice that of the soft orientation. In addition, the Young's modulus of the material is also the largest on [111] hard-oriented grains and the smallest on [100] soft-oriented grains.

Microstructure and properties of high entropy alloy reinforced titanium matrix composites

In this paper, CoCrFeNiMo 0.2 high entropy alloy (HEA) particles reinforced titanium matrix composites were prepared by hot pressing sintering in the vacuum. The microstructure and composition of the composites at 700 °C ~ 900 °C were studied through X-ray diffraction (XRD), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA). Also, the mechanical properties of the composites were studied by microhardness tester, nano-indentation and uniaxial compression experiment. The results show that the interface layer of different thicknesses is formed between the particles and the matrix in the composites under different sintering temperatures. At 700 °C ~ 850 °C, the mechanical properties of the composites increase with the increase of temperature, which is related to the diffusion of HEA particles and the formation of the interface layer. When the sintering temperature is 850 °C, the hardness is 402.6 HV, the yield strength is 928.2 MPa, and the compressive strength is 2032.6 MPa. However, the high entropy alloy particles have a greater degree of dissolution and diffusion at 900 °C, the strengthening effect of the particles is weakened, so the mechanical properties of the composites are correspondingly reduced. • High entropy alloy reinforced titanium matrix composites were prepared. • The composites has high compressive strength (2032.6 MPa), due to the strength and toughness of the HEA and good interfacial bonding. • Young's modulus of the interface layer is a transition between the matrix and the particles, and the interface layer has the greatest hardness. • Macro-micro mechanical properties of composites are compared through a hybrid computational model, in which is much close to the Reuss model.

Assessment of Reuss, Tamura, and LRVE models for vibration analysis of functionally graded nanoplates

Assessment of Reuss, Tamura, and LRVE models for vibration analysis of functionally graded nanoplates

The Effect of Micromechanics Models: 2D and 3D Numerical Modeling for Predicting the Mechanical Properties of PP/Alfa Short Fiber Composites

In the present work, we propose to confront two modeling techniques for predicting the macroscopic properties of short alfa fiber-reinforced polypropylene composites. The first modeling was a micromechanical analysis using the Mori-Tanaka, Self-consistent, Diluted, Voigt, Reuss, and Neerfeld-Hill models. The second modeling was digital, using a specific finite element technique called the Projected Fiber (PF) approach. In the framework of this study, both 2D and 3D finite element analyses based on the PF approach were used. First, we proposed an inverse approach using these analytical and finite element models to predict the Young’s modulus of alfa fiber. Then, we compared the obtained results with the experiment values available in the literature. This comparison showed that the micromechanical models underestimated the alfa fiber’s Young’s modulus, while the finite element approach, PF, allowed for good framing of the experimental values. Moreover, we investigated the effect of fiber content on the predicted elastic properties of a polypropylene (PP) matrix reinforced with randomly distributed short alfa fibers. We noticed that the Diluted model was more accurate than the Mori-Tanaka and Self-consistent methods. As for the PF approach, its estimations were close to the experimental values. For example, the Young’s modulus for the PP/alfa with a 30 wt% of fiber content was underestimated with an error of 4.3%. It is shown that the 2D PF approach can provide calculated results with sufficient prediction accuracy.

Generalized homogenization model of piezoelectric materials for ultrasonic transducer applications

Although piezocomposite (PC) materials have increasingly attracted researchers, there is still a need to properly and easily derive their properties. We develop a generalized homogenization model (GHM) that accounts for Smith and Cha approaches to evaluate the equivalent characteristics of piezocomposites. This method could be applied to all connectivities patterns, but restricted herein to 2-2 and 1-3 piezocomposites for comparison with Smith (1-3) and Cha (2-2) analytical results. In the proposed GHM is a parameter θ, is changed for various connectivities. The 1-3 and 2-2 PZT-7A/Araldite D (PCs) data are used and equivalent characteristics of these Pcs are determined as function of volume fraction of PZT-7A piezoelectric. Results show that the electromechanical coefficients are well fitted by Voigt and Reuss models. Results obtained for some parameters show that the proposed GHM is consistent with the analytical existing models used for the 1-3 and 2-2 connectivities and is in line with measured values from Chan and Unsworth (1989). Based on the GHM 2-2 configuration results of piezocomposite materials, the electroacoustic responses of transducers having some of these properties are simulated using the KLM model. A performance trade-off was chosen, resulting in an improved thickness coupling coefficient and a lowered acoustical impedance, and a similar approach as that on a pure PZT-7A.

Micromechanics-Based Prediction Models and Experimental Validation on Elastic Modulus of Recycled Aggregate Concrete

Elastic modulus is one of the most important mechanical properties of concrete (including recycled aggregate concrete), and it has a notable guiding significance for engineering. There is a lack of micromechanical research on the elastic modulus of recycled aggregate concrete. This paper adopts four models based on micromechanics, including the Voigt model, Reuss model, Eshelby method, and Mori–Tanaka method, to predict the elastic modulus of recycled aggregate concrete. The optimal model is determined by comparing the results of the four models with the experimental data. On this basis, some previous prediction methods for the elastic modulus of concrete are employed to be compared with the most satisfactory models in this paper. Several experimental data from the open literature are also utilized to better illustrate the reliability of the prediction models. It is concluded that the Mori–Tanaka method unfailingly produces more accurate predictions compared to other models. It gives the best overall approximation for various data and has extensive effects in predicting the elastic modulus of RAC. This work may be helpful in promoting the development of micromechanics research in recycled aggregate concrete.

Magnetoelasticity of Fe1−xGax thin films on amorphous substrates

In this work, we study the magnetoelastic behavior of ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ga}}_{x}$ ($0.11&lt;x&lt;0.19$) thin films, grown on glass and oxidized Si(100) amorphous substrates, that present an isotropic crystalline texture in the film plane. The magnetoelastic coupling coefficients are obtained through the cantilever deflection technique. We find that the magnetoelastic response is larger for samples grown on glass with respect to those grown on Si(100), and such a response increases for larger Ga concentrations for both substrates used. Furthermore, the increasing substrate temperature during growth does not appear to have a significant effect on magnetoelastic behavior of samples grown on Si(100). From a model that takes into account the elastic grain interaction for isotropic systems, we are able to describe the experimentally observed behavior. We find that the magnetoelastic response of the samples grown on glass are well described by the Voigt model, while the samples on Si(100) present an intermediate response between the Voigt and Reuss models.

Isotropized Voigt-Reuss model for prediction of elastic properties of particulate composites

Voigt and Reuss models do not make any assumption regarding composite microstructure, but they are only able to estimate bounds rather than values of composite properties. To enable the models to predict elastic properties of particulate composites, we isotropized Voigt and Reuss models based on the equivalence of normal and shear strain energy respectively in a representative volume element, and derived a set of simple and uncoupled equations for the prediction of composite Young’s modulus and shear modulus. Composite bulk modulus and Poisson’s ratio can then be determined either by the elasticity relationships or by generalization of the isotropized Voigt-Reuss equations. Validation with reported experimental data show that, for composites with phase properties of either small or large contrast, isotropized Voigt-Reuss model has similar accuracy as the widely used micromechanical models, for the prediction of Young’s modulus and shear modulus.

Computer Exploration of the Ice Samples Strength Using Different Numerical Methods

The exploration of the Arctic region is a very challenging and important problem today. One of the problems, connected with the Arctics’ investigation, is the ice strength change and measurement during the whole year. In this paper we present the results of the ice strength study using different numerical methods on the unstructured and structured grids. We carry out the computations of the ice strength using the discontinuous Galerkin method on unstructured grids and the Prandtl–Reuss model. For this, we compute the model, imitating the interaction between an ice field and a vertical bearing. In addition, we calculate the ice strength after the uniaxial compression and bending using the discontinuous Galerkin method. Then, we present the result strength distribution in the ice sample, computed with the help of the grid-characteristic method on the structured grids. The results demonstrate the possibility of the application of the grid-characteristic method on structured grids to the problem of the ice strength study.