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This work has explored surface/interface theory-based torsional wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer on top of a functionally graded elastic substrate. PFRC is assumed to be composed of piezoelectric fiber and epoxy matrix. Micro-mechanical investigations have been performed to determine the coefficients of PFRC using strength of materials (SM) and rule of mixtures (RM) techniques. The dispersion relation for the torsional wave under nonclassical boundary conditions is determined using surface/interface theory. The effects of surface/interface, fiber volume fractions, and heterogeneities on the phase velocity and the mode shapes of the wave have been demonstrated graphically. [ABSTRACT FROM AUTHOR]

AbstractTo investigate the effect of the structural gradient of oil palm wood (OPW) on the variation in drying collapse, OPW specimens prepared from different locations along the trunk radius and trunk height were kiln-dried at 80 °C to a final equilibrium moisture content of 4%. The effects of anatomical characteristics and the fraction of vascular bundles on the cross-sectional strain due to drying collapse were investigated. Along the trunk radius, there is a critical fraction of vascular bundles above which the drying collapse of OPW becomes exceedingly small. Below the critical value, the drying collapse of OPW linearly increases with a decrease in the fraction of vascular bundles following a rule of mixtures. Microstructural examination reveals that the thickness of the cell wall and the arrangement of cells between fiber cells in the vascular bundles and parenchyma cells at the interface area are effective against parenchyma cell collapse during drying. The decrease in cell wall thickness and the increase in space at the interface between these cells with trunk height correspond to an increase in the critical value of the fraction of vascular bundles from the lower bottom to the upper top zones of the trunk height. [ABSTRACT FROM AUTHOR]

In the present article, firstly, the micro-mechanical model of piezomagnetic fiber-reinforced composite (PMFRC), composed of CoFe $ _{2} $ 2 O $ _{4} $ 4 fiber-epoxy matrix combination, is presented employing the Strength of Materials (SM) and Rule of Mixtures (RM) techniques. Secondly, the impacts of varying fiber-volume fractions ( $ \Omega _{f} $ Ω f ) on the energies carried by different reflected waves in the PMFRC are analytically studied. Due to the incidence of a quasi-longitudinal wave, three reflected waves viz. quasi-longitudinal (qP), quasi-transverse (qSV), and magneto-acoustic (MA) waves are generated in the PMFRC half-space. Propagation angles of all reflected waves are analyzed considering incident qP and qSV waves, and the existence of critical angles is established for the latter case. The closed-form expressions of amplitude ratios of all reflected waves are derived by employing appropriate magneto-mechanical boundary conditions and using Cramer's rule. In order to validate the numerical results, the expressions of energy ratios of all reflected waves and interaction energy are derived, which exhibit the influence of existing parameters. In doing so, the Law of Conservation of Energy is also established. The existence of a critical value of $ \Omega _{f} $ Ω f is discovered in the range $ (0.6,0.8) $ (0.6 , 0.8) , beyond which the magnitudes of energies carried by the reflected waves change drastically. [ABSTRACT FROM AUTHOR]

The tensile characteristics of a novel TWARMAT hybrid fabric with a weight of 600 g/m2, comprising aramid and E-glass fibers were assessed. Additionally, a conventional 205-g/m2 plain glass and 160-g/m2 plain carbon fiber fabrics were also tested for comparison. The results obtained reveal that TWARMAT exhibited superior stiffness and density ratios. To confirm these experimental results, the rule of mixtures was utilized. The close agreement between the two sets of data, with mean relative errors of 5.5 and 1.05% for Young's modulus and density respectively, confirms the reliability of the methods applied. [ABSTRACT FROM AUTHOR]

In this study, a constitutive model applied to predict the tensile properties and fracture behavior of well‐bonded multilayered metal composites is extended. The equivalent single‐layer model, as a convenient method, is introduced into finite‐element simulations by combining it with an improved Xue–Wierzbicki damage plasticity model that considers material anisotropy. The steel use stainless (SUS) 430/Al1050/SUS430 laminated sheet fabricated by cold rolling is selected as the research material. The quasistatic uniaxial tests and Nakazima tests are operated to verify the accuracy of the proposed method. The mean errors in tensile stress and fracture forming limit strains are 2% and 3%, respectively. A load‐sharing mixture rule is proposed to assess the effects of the volume fraction, strength coefficient, and hardening exponent of the constituent materials on the mechanical properties of the laminates. In the results, it is indicated that the laminate exhibits sufficient elongation and remains markedly enhanced in tensile strength, reaching 470 Mpa when the ductile Al layer is combined with the higher strength and hardenability steel layer. In this research, it is aimed to clarify the formability characteristics in laminated composites for optimal sheet configuration design and development. [ABSTRACT FROM AUTHOR]

The spacecraft and space shuttles demand novel engineering materials to meet the required properties. This can be accomplished by altering the material properties in more than one direction. The introduction of inplane bidirectional functionally graded materials with porosity are expected to exhibit these properties. This paper presents the buckling analses of inplane bidirectional (2-D) functionally graded porous plates (IBFGPPs) considering uniform porosity distribution in uni-axial and bi-axial compression. The effective modulus of elasticity of the material is varied in in x-and y-axes by employing the rule of mixtures. The higherorder theory used for the study of buckling response meets the nullity requirements at plate’s upper and lower surface and derived the equations of motion thru Lagrange equations. The displacement functions are formulated in simple algebraic polynomials, incorporating admissible functions to satisfy the simply supported conditions in both axial and transverse directions. The components of admissible functions are derived by Pascal’s triangle. Accurateness of this theory is judged by comparing it to existing numerical data in the literature. The effect of thickness ratio’s (a/h), aspect ratio’s (b/a), exponents (ζ1and ζ2) in η1 and η2-direction, and the porosity on the buckling response of IBFGPPs are examined comprehensively. The numerical findings provided here serve as reference solutions for evaluating diverse plate theories and for comparing them against results obtained through alternative analytical and finite element techniques. From the obtained results, it can be inferred that the proposed theory facilitates the assessing of buckling tendencies of in-plane bi-directional porous FG plates produced through sintering process and could be deemed as a pivotal in the process of optimizing the design of the IBFGPPs. [ABSTRACT FROM AUTHOR]

Magnesium chips were coated with silicon powder using a binder, and injection molding was performed using silicon-coated chips as the raw material. Microstructural analysis of the products revealed that all added silicon (Si) precipitated as Mg2Si particles, with no voids present at the interfaces between the Mg2Si particles and the matrix. Furthermore, the hardness and Young's modulus of the products increased with higher Si content. The Young's moduli followed the rules of mixtures. [ABSTRACT FROM AUTHOR]

Magnesium chips were coated with a high concentration of graphite using a binder and were used as the raw material for injection molding. The microstructure of the magnesium injection-molded product with added graphite exhibited a dispersion of needle-like graphite particles. No significant voids were observed at the interfaces between the graphite and the matrix. The addition of more than 0.5 mass% graphite decreased the proof stress and tensile strength of the injection-molded products. The Young's modulus of the graphite-added products tended to decrease with an increase in the graphite content, which is consistent with the lower limit of the rule of mixtures. The thermal conductivity of the 6.9 mass% graphite-added product increased compared with that of the AZ91D magnesium alloy and the coefficient of linear thermal expansion decreased. Both values are within a range that satisfied the rules of mixtures. [ABSTRACT FROM AUTHOR]

Abstract A tensile test program of Moso bamboo samples was carried out in order to obtain information on the radial distribution of elastic and strength properties. In accordance with previous studies, the elastic modulus and the tensile strength were found to increase outwards in the radial direction. This spatial dependence was compared with the distribution of the fibre content of the layers and found excellent correlation suggesting that the fibres are the main load bearing components. The fibre content was quantified using regression analysis in the radial direction as 0.1 (inner layer), 0.19 (middle-1 layer), 0.28 (middle-2 layer) and 0.44 (outer layer). The Rule of Mixture theory allowed the estimation of the elastic modulus and the tensile strength of the main individual components, the fibres and the parenchyma matrix. Article Highlights Radial distribution of bamboo fibres across the culm wall and stiffness properties obtained from tensile test parallel to fibres were compared. The radial distribution of bamboo fibres was analysed in layers using image analysis software. The tensile failure mechanisms of bamboo samples were identified and found to depend on fibre content.

In this work, the effect of coal-fly ash (CFA) reinforcements on the physio-mechanical properties of iron metal matrix composites (IMMCs) are predicted and compared with the experimental results. The IMMCs were synthesized by reinforcing different amounts (0, 0.15, 0.28 and 0.38 vol. %) of CFA particulates to the iron matrix through powder metallurgy technique (P/M). The iron powder/CFA mixtures were compacted at a load of 10 ton followed by sintering in inert environment at 1150 ℃ for 90 min. Structural, morphological, and elemental characterisation of iron/CFA and IMMCs were performed using X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM) and Energy Dispersive X-Ray spectroscopy (EDS) respectively. Sufficient diffusion among the iron particles, uniform distribution of CFA particulates and clear interfaces between matrix and reinforcements have been observed in the FESEM micrographs. The trends of experimental results of sintered density and microhardness of the IMMCs has been found in line with the theoretical results predicted using rule of mixtures (ROM). Furthermore, the effects of increased vol.% of CFA inclusions on the elastic modulus (E) , yield strength (σ y ) and ultimate tensile strength (σ u) of the IMMCs have been conceived using Ramberg–Osgood (RO) model, under tensile loading. A significant reduction of 32% in sintered density and 42% increment in microhardness of the IMMCs have been observed. The RO model demonstrated significant enhancements of 51% in E and 42% in σ y . On the other hand, whereas 44% reduction in ultimate tensile strength of IMMCs has been observed on increased amount of CFA (0–0.38 vol.%). The load transfer strengthening mechanism has been found dominating the Hall–Petch followed by Taylor's strengthening mechanism. Further, the various specific properties of the IMMCs were compared with prevalent literature. The specific properties of IMMCs such as microhardness, E , σ y and σ u are found comparable with the established aluminium based MMCs. [ABSTRACT FROM AUTHOR]

Deflection and stress calculated from an experimentally validated, high-fidelity finite element model (FEM) of a photovoltaic module experiencing mechanical load was compared to results from a simplified FEM treating the module laminate as a homogenized composite using a rule of mixtures approach, and further compared to analytical calculations treating the module as a Kirchoff-Love flat plate. The goal of this study was to determine the error incurred by analyzing module mechanics with varying levels of simplification, since resolving the aspect ratios of a module is computationally expensive. Homogenized FEMs were found to underpredict peak deflection under a 1.0 kPa load by between 13 and 19% for lower and upper bound application of the rule of mixtures. However, module shape was captured, implying that a useful replication of a resolved model could be achieved with a reduced, calibrated material stiffness. Homogenized stress results captured glass layer tensile stress components to within 46 to 52% at a sample location of interest, though agreement was poor through the remainder of the laminate due to the lack of material resolution. For plate theory, deflection was overpredicted by 45 to 67% for upper and lower bound homogenizations, and frame-adjacent module shapes were not adequately replicated. Stress results mirrored FEM trends but magnitudes were not well correlated to resolved model values. These results support the use of homogenized laminate models for module shape derivation, though resolved models remain necessary for stress analyses. The accuracy of plate theory was found to be inadequate for most applications. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of the thermal fracture of a functionally graded coating (FGC) on a homogeneous substrate (H), i.e., FGC/H structures. The FGC/H structure was subjected to thermo-mechanical loadings. Systems of interacting cracks were located in the FGC. Typical cracks in such structures include edge cracks, internal cracks, and edge/internal cracks. The material properties and fracture toughness of the FGC were modeled by formulas based on the rule of mixtures. The FGC comprised two constituents, a ceramic on the top and a metal as a homogeneous substrate, with their volume fractions determined by a power law function with the power coefficient λ as the gradation parameter for the FGC. For this study, the method of singular integral equations was used, and the integral equations were solved numerically by the mechanical quadrature method based on the Chebyshev polynomials. Attention was mainly paid to the determination of critical loads and energy release rates for the systems of interacting cracks in the FGCs in order to find ways to increase the fracture resistance of FGC/H structures. As an illustrative example, a system of three edge cracks in the FGC was considered. The crack shielding effect was demonstrated for this system of cracks. Additionally, it was shown that the gradation parameter λ had a great effect on the fracture characteristics. Thus, the proposed model provided a sound basis for the optimization of FGCs in order to improve the fracture resistance of FGC/H structures.

The usage of additive manufacturing techniques has increased dramatically in recent years. Fabricated parts are no longer simple prototypes, but rather structural components whose mechanical characteristics must be understood before printing. One of the weaknesses of 3D printing is the high variability of dimensional, geometric, and mechanical properties, which is due to the combination of various printing parameters, including the number of walls, roofs, and floors, filling patterns, and printing layer thickness.This study aims to predict the mechanical properties of onyx printed parts as a function of the number of walls and a solid pattern through an analytical approach based on the rule of mixtures and numerical finite element simulation. The influence of the number of walls on the mechanical properties of onyx printed parts was characterised by uniaxial tensile tests. The results show that walls have a significant impact on the final mechanical properties of the parts. The study found that the higher the number of walls, the greater the mechanical properties of the parts. The rule of mixtures approach allowed us to predict the mechanical properties with good accuracy, with prediction errors observed ranging from 1% to 10% depending on the number of walls in the parts. The numerical simulation using finite elements was carried out using the properties of the walls and the solid pattern obtained from tensile testing, enabling a comparison between the experimental test and the rule of mixtures. The results show that the mechanical properties obtained by the rule of mixtures and numerical simulation are consistent with the physical tensile test.

In long period stacking ordered (LPSO) phase containing Mg-Zn-Y alloys, high elastic modulus and deformation kinks of LPSO phase considerably enhance the tensile yield strength, with slight detriment of or benefit to the ductility depending on its volume fraction. In present work, uniaxial tensile tests and fracture toughness tests are carried out using Mg99.2Zn0.2Y0.6, Mg97Zn1Y2, Mg89Zn4Y7 and Mg85Zn6Y9 (at%) materials with different extrusion ratios. Extrusion processing enhances both strength and ductility due to the recrystallization of Mg grains. Variable plastic deformation mechanisms are activated depending on volume fraction of Mg and LPSO phase as well as their relative size during bending. {101¯2} tensile twins in Mg grains and deformation kinks in LPSO phase are observed, which dissipate large amount of deformation energy favoring for toughness. However, inherently brittle LPSO phase is detrimental to toughness. Microstructure-motivated empirical models for yield strength and fracture toughness prediction based on rule of mixtures are calibrated by experimental data. Energy release rates of individual mechanisms are estimated, which quantitatively indicate strong Mg/LPSO interaction.

In recent decades, the construction of statistically similar representative volume elements (SSRVEs) of materials for use in numerical analyses has been accomplished utilizing various methods, tools, and frameworks. Such a framework is introduced in this work, where the creation of 3D SSRVEs of metal matrix composites was investigated to assess their mechanical properties with reference to the material's microstructure. The material studied was a composite based on AA7075 alloy reinforced with carbon fibers, with volume fractions of 0%, 4%, 8%, and 12%. The statistics of the alloy's microstructure were extracted by segmenting an SEM image and fitting the precipitate particles' sizes with respect to a lognormal distribution. The open-source software DREAM.3D was used to construct 3D ensembles and the Abaqus FEA software was employed for the mechanical testing simulations. By plotting the tensile stress–strain curves for the composites, it was found that the elastic modulus increased with the fibers' volume fraction, obeying the rule of mixtures for discontinuous fibrous composites. The fiber efficiency factors were also calculated. The yield stresses of the composites were found and compared to the ones expected according to the shear-lag model, indicating major differences. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of the thermal fracture of a functionally graded coating (FGC) on a homogeneous substrate (H), i.e., FGC/H structures. The FGC/H structure was subjected to thermo-mechanical loadings. Systems of interacting cracks were located in the FGC. Typical cracks in such structures include edge cracks, internal cracks, and edge/internal cracks. The material properties and fracture toughness of the FGC were modeled by formulas based on the rule of mixtures. The FGC comprised two constituents, a ceramic on the top and a metal as a homogeneous substrate, with their volume fractions determined by a power law function with the power coefficient λ as the gradation parameter for the FGC. For this study, the method of singular integral equations was used, and the integral equations were solved numerically by the mechanical quadrature method based on the Chebyshev polynomials. Attention was mainly paid to the determination of critical loads and energy release rates for the systems of interacting cracks in the FGCs in order to find ways to increase the fracture resistance of FGC/H structures. As an illustrative example, a system of three edge cracks in the FGC was considered. The crack shielding effect was demonstrated for this system of cracks. Additionally, it was shown that the gradation parameter λ had a great effect on the fracture characteristics. Thus, the proposed model provided a sound basis for the optimization of FGCs in order to improve the fracture resistance of FGC/H structures. [ABSTRACT FROM AUTHOR]

• Temperature effects on mechanical properties of 3D printed C CFRP composites. • Temperature effects on failure mechanism of 3D printed C CFRP composites. • Tension and shearing experiment tests for 3D printed C CFRP composites. • Classical laminate theory and rule of mixtures to the 3D printed C CFRP composites. Design for safety of 3D printed continuous carbon fiber reinforced polymer (C CFRP) composites remains challenging for accommodating harsh service environments with a wide range of temperatures. To investigate thermal effects on mechanical properties and failure mechanism of C CFRP materials, this study carried out a series of experimental tests on the laminates with layups of [0] n , [90] n and [0/90] n for tension, as well as [±45] n for in-plane shearing. The application of classical laminate theory and rule of mixtures to the 3D printed C CFRP composites under varying temperatures is then evaluated. The results indicate that the transverse elastic modulus/strength and in-plane shear modulus/strength increase at a low temperature, but all the mechanical properties decrease at a high temperature. Notably, an unexpected decrease in strength of [0/90] n laminates is observed when the temperature drops from −10 °C to −40 °C. Significant strain concentrations are visualized during tensile experiments at high temperature through the digital image correlation (DIC) technique. With increasing temperature, the [0] n laminates undergo a transition from an explosive to a jagged failure mode, while the [90] n laminates shift from brittle to ductile failure. The alteration is attributed to decrease in the mechanical properties of both the matrix and the matrix fiber interface, as revealed by scanning electron microscopy (SEM) analysis. It is found that although the classical laminate theory exhibits an acceptable prediction accuracy for the 3D printed C CFRP composites under varying temperature conditions, the rule of mixtures is not applicable. For this reason, the new formulations for the rule of mixtures are then proposed to enable accurate predictions for 3D printed C CFRP composites under different temperatures. This study is anticipated to provide insightful understanding on mechanical properties and failure mechanisms for 3D printed C CFRP composites at different temperatures. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) has inherent mechanical strength inconsistencies when the build orientation changes. To address this issue, theoretical models, including analytical and numerical models, can be developed to predict the material properties of additively manufactured materials. This study develops a systematic finite element (FE)-based multiscale numerical model and simulation process for the polymer acrylonitrile butadiene styrene (ABS). ABS samples are fabricated using fused deposition modelling (FDM) to determine the material properties and mechanical behaviours. For macroscale analysis, good agreement between the numerical and experimental tensile strength of transverse samples proved that the FE model is applicable for applying a reverse engineering method in simulating the uniaxial tension of samples. The FE modelling method shows its capability to consider infill density effects. For mesoscale analysis, two methods are developed. The first method is a representative volume element (RVE)-based numerical model for all longitudinal samples. The second method is analytical and based on the rule of mixtures (ROM). Modified rule of mixtures (MROM) models are also developed, which demonstrate an improvement compared to the original ROM models. The research outcomes of this study can facilitate the AM process of parts in various engineering fields. [ABSTRACT FROM AUTHOR]

In long period stacking ordered (LPSO) phase containing Mg-Zn-Y alloys, high elastic modulus and deformation kinks of LPSO phase considerably enhance the tensile yield strength, with slight detriment of or benefit to the ductility depending on its volume fraction. In present work, uniaxial tensile tests and fracture toughness tests are carried out using Mg 99.2 Zn 0.2 Y 0.6 , Mg 97 Zn 1 Y 2 , Mg 89 Zn 4 Y 7 and Mg 85 Zn 6 Y 9 (at %) materials with different extrusion ratios. Extrusion processing enhances both strength and ductility due to the recrystallization of Mg grains. Variable plastic deformation mechanisms are activated depending on volume fraction of Mg and LPSO phase as well as their relative size during bending. { 10 1 ¯ 2 } < 10 1 ¯ 1 ¯ > tensile twins in Mg grains and deformation kinks in LPSO phase are observed, which dissipate large amount of deformation energy favoring for toughness. However, inherently brittle LPSO phase is detrimental to toughness. Microstructure-motivated empirical models for yield strength and fracture toughness prediction based on rule of mixtures are calibrated by experimental data. Energy release rates of individual mechanisms are estimated, which quantitatively indicate strong Mg/LPSO interaction. [ABSTRACT FROM AUTHOR]

Soft magnetic composites (SMCs) are consolidated ferromagnetic powders covered with polymers. Ultra-thin flat powder can effectively reduce eddy current loss of SMCs, even at the frequency at which next-generation semiconductor devices are driven. In this study, pure iron powders were processed with ball-milling to obtain the ultra-thin powder and prepare the SMC. The effect of aspect ratio of the powder on the mechanical strength of SMC was investigated. Although the maximum bending stress of SMC made of iron particles with an aspect ratio of 1140 reached 60% of the strength of sintered iron powder, the increase in the maximum bending stress with increasing aspect ratio slowed down when the aspect ratio exceeded 100. The reason for the slowdown was assumed to be a decrease in insulating film coverage on the particle at high aspect ratio ranges due to the stacking and welding of particles during the ball milling process. [ABSTRACT FROM AUTHOR]

Adhesives are extensively used in the automotive and aeronautical industries as they enable the creation of durable and light weight joints, with exceptional strength to weight ratios. The constant search for the means of adapting the mechanical performance of adhesives to each application has led to the use of several types of fillers to change their properties. Following a study on the effect of inorganic fillers, i.e., hollow glass beads, in the failure mechanisms of single lap joint's (SLJ), this work focuses on the response of the strength and fracture properties of structural adhesives to this filler. To this end, their tensile strength and mode I fracture properties were thoroughly analyzed by performing bulk tensile and double-cantilever beam (DCB) tests, at a quasi-static speed. The specimens were manufactured by adding different %v/v of filler to two epoxy-based crash resistant adhesives. Both adhesives have shown a negligible effect on the tensile strength, a decrease in strain at failure and critical energy release rate in mode I, as well as an increase of the Young's modulus, for higher % in volume of hollow glass beads. These phenomena were further analyzed recurring to scanning electron microscopy, and the concept of rule of mixtures. [ABSTRACT FROM AUTHOR]

Recent investigations have highlighted the multi-resolution and high throughput characteristics of the spherical indentation experimental and analysis protocols. In the present work, we further demonstrate the capabilities of these protocols for reliably extracting indentation stress-strain (ISS) responses from the microscale constituents as well as the bulk scale of dual phase materials exhibiting bimodal microstructures. Specifically, we focus on bimodal microstructures produced in an α–β Ti6242 sample. Combining the multi-resolution indentation responses with microstructural statistics gathered from the segmentation of back-scattered electron images from the scanning electron microscope allowed for a critical experimental evaluation of the commonly utilized Rule of Mixtures based composite model for the elastic stiffness and plastic yield strength of the sample. The indentation and image analyses protocols described in this paper offer novel research avenues for the systematic development and critical experimental validation of composite material models. [ABSTRACT FROM AUTHOR]

In this research, a method is examined by which the behavior of continuous carbon fiber reinforced additive manufacturing may be simulated using Finite Element Analysis. This technique is used in a simulated tensile test experiment in which the findings are compared to results determined from theoretical calculations according to the Rule of Mixtures method and from existing mechanical testing results. Four different fiber reinforcement configurations are examined with fiber volume fractions ranging from 4% to 32%. It was found that for fiber volume fractions of 11%, the simulation results closely match those predicted theoretically by the Rule of Mixtures as well as the mechanical testing results published in existing research. Lower fiber volume fractions near 4% yield less accurate results, with a 20% error due to the fact that the anisotropic behavior of the polymer matrix is the dominant material trait. Simulation of higher volume fractions near 32% closely approximate theoretical predictions, however neither the theoretical results nor the simulation results accurately reflect real world mechanical testing, indicating that nonideal condition factors such as the effect of micro-voids between the start and end of the fiber reinforcements play a significant role in the overall strength of the material. Thus, for fiber volume fractions near 11%, this simulation method can accurately be used to predict the behavior of end-use components, but more study must be done to increase simulation accuracy in low and high fiber volume fractions. [ABSTRACT FROM AUTHOR]

In recent decades, the construction of statistically similar representative volume elements (SSRVEs) of materials for use in numerical analyses has been accomplished utilizing various methods, tools, and frameworks. Such a framework is introduced in this work, where the creation of 3D SSRVEs of metal matrix composites was investigated to assess their mechanical properties with reference to the material’s microstructure. The material studied was a composite based on AA7075 alloy reinforced with carbon fibers, with volume fractions of 0%, 4%, 8%, and 12%. The statistics of the alloy’s microstructure were extracted by segmenting an SEM image and fitting the precipitate particles’ sizes with respect to a lognormal distribution. The open-source software DREAM.3D was used to construct 3D ensembles and the Abaqus FEA software was employed for the mechanical testing simulations. By plotting the tensile stress–strain curves for the composites, it was found that the elastic modulus increased with the fibers’ volume fraction, obeying the rule of mixtures for discontinuous fibrous composites. The fiber efficiency factors were also calculated. The yield stresses of the composites were found and compared to the ones expected according to the shear-lag model, indicating major differences.

Abstract Analyzed the influence of normal/shear initial stresses and rotation on reflection/transmission characteristics of waves propagating at the interface of two distinct micro-mechanically modeled piezomagnetic fiber-reinforced composite(PMFRC) half-spaces composed of CoFe2O4 fiber-epoxy matrix combination. An incident quasi-longitudinal(qP) wave generates reflected/transmitted quasi-longitudinal(qP), quasi-transverse(qSV), and magneto-acoustic(MA) waves, whose propagation directions are illustrated graphically. Transmitted qP wave has critical angles for considered initial stresses and rotation. Energy ratios of reflected/transmitted waves, interaction energy, and net energy are obtained, which satisfy the Law of Conservation of Energy, thereby validating this problem. Influences of incident angle, initial stresses, and rotation on amplitude/energy ratios are meticulously analyzed. [ABSTRACT FROM AUTHOR]

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications. [ABSTRACT FROM AUTHOR]

Waste from hundreds of thousands of tons of non‐recyclable end‐of‐life wind turbine blades will be generated within the next decades. This work studies the effect of recycled fiber categories on the tensile properties of reinforced polylactic acid (PLA) specimens made by fused filament fabrication 3D printing. Three different fiber categories, that is, virgin, ground, and pyrolyzed, are examined and compared experimentally and analytically using micromechanical models. Tensile tests are performed on different PLA specimens prepared with the three fiber categories and two fiber contents of 5% and 10% per ASTM D638. Compared to virgin fibers, both recycled fibers, that is, ground and pyrolyzed fibers, exhibit higher strength and stiffness values. Ground recycled fibers showed higher ultimate tensile strength compared to the pyrolyzed ones, while higher stiffness values were obtained for pyrolyzed fibers. Single fiber tensile tests, pull‐out interfacial strength tests, thermal analysis, and microscopic imaging are performed to evaluate parameters used in the micromechanical models. The Halpin‐Tsai and Cox models showed good agreement with the experimental modulus results with errors less than 5% for pyrolyzed fibers, while the minimum prediction error was 24.1% for strength results. [ABSTRACT FROM AUTHOR]

The practicality of implantable biomedical materials depends on the design of size and function to meet the needs of personal customization. This paper used fused deposition modeling 3D printing process to make composite materials, and studied the performance of 3D printed samples through different matrix molecular weights, print filling settings, additives, and their contents. Mechanical properties, thermal analysis, structural characterization, surface hydrophilicity, and functional verification of PCL‐based 3D printed composites were discussed. We found that 80% print filling and 10% SA addition could greatly improve the work of fracture of the tensile sample. Furthermore, the efficacy and content of CS was also verified and analyzed. These resulting information are helpful for structural design and functional matching of medical composites. [ABSTRACT FROM AUTHOR]

Thermal barrier coatings (TBCs) represent a relatively thin layer of ceramic with the favourable insulating properties, which are generally used to improve the temperature stability of the engineering component such as turbine blades. One of the prime prerequisites of TBCs is to determine the optimised coating configuration with the desired thermo-mechanical properties and enhanced service life. In a typical functionally graded coating structure, this could be achieved by having a trade-off between the thermal insulation and fatigue toughness offered by ceramic in top coat and metal towards the substrate, respectively. In this work, a computational method was used to analyse and optimise the parameters pertaining to thermo-mechanical evaluation of the slurry spray-coated (SST) mullite–nickel ASTM 1018 steel. The composite material properties have been predicted using the classical mean-field micromechanics model and rule of mixtures and the finite element simulation package ANSYS. Experimental validation has been performed to analyse the relative thermal and structural properties of the composite layers of the coatings using transient plane source (TSP)-based thermal constants analyser. The predicted and experimental results were further analysed and optimised for various process parameters using response surface optimisation and multi-objective genetic algorithm, which evaluated the optimum results considering the boundary conditions with a temperature reduction of nearly 306 °C. Further, the research results indicate that suitable thickness of the coating configuration of the slurry-sprayed mullite–nickel TBC system included coating thickness of 57.2 μm, 147.1 μm, and 143.9 μm for bond, intermediate, and top coats, respectively. The material properties were found dependent on the coating composition across the FG structure, and the predicted, computed, and experimental results were in reasonable agreement. [ABSTRACT FROM AUTHOR]

• Study investigates transverse material property gradient through bamboo culm wall. • Transverse behaviour does not behave as a fibre-reinforced composite material. • Variation if morphology through culm wall identified using microscopy. • Culm wall morphology coupled with material property assessment. Performance of full-culm bamboo structures is dominated by longitudinal splitting behaviour, often exacerbated by connection details. This behaviour is a function of the transverse properties of this highly orthotropic material. Considerable study of the longitudinal properties of bamboo is available in which it is often concluded that bamboo may be considered as a fibre-reinforced composite material and material properties may be assessed using rule-of-mixture methods. Nonetheless, few studies have addressed the transverse properties of the bamboo culm wall, despite these largely governing full-culm behaviour. This study investigated the transverse material property gradient through the culm wall and attempts to connect the mechanical results to physical observations and phenomena. Most importantly, the study demonstrates that the complex transverse behaviour of bamboo does not appear to behave as a classic fibre-reinforced composite material in the direction transverse to the fibres. In this study, five different bamboo species, Phyllostachys edulis , Phyllostachys bambusoides , Phyllostachys meyeri , Phyllostachys nigra, and Bambusa stenostachya were tested using a modification of the flat-ring flexure test to obtain a measure of the transverse tensile capacity of the bamboo. Microscopy analyses are used to qualitatively describe the culm wall architecture and to quantitatively assess the failure modes through the culm wall thickness. [ABSTRACT FROM AUTHOR]

Rule of mixture models are usually used in the tensile properties prediction of polymer composites reinforced with synthetic fibres. They are less utilized for natural fibre/polymer composites due to natural fibres physical and mechanical properties variability which reduces rule of mixture model's prediction values accuracy compared to the experimental values. This had led to studies conducted by various researchers to improve the existing rule of mixture models to give a better reflection of the true natural fibres properties and enhance the rule of mixture models prediction accuracy. In this paper, rule of mixture model's utilization includes the existing rule of mixture models as well as proposed rule of mixture models which have one or more factors incorporated into existing rule of mixture models for natural fibre/polymer composites tensile properties prediction are reviewed. [ABSTRACT FROM AUTHOR]

Mechanical parameters of Scots pine wood (Pinus sylvestris L.) of low (about 8%) and high (higher than the fiber saturation point) moisture content (MC) subjected to tensile stress along the grains were studied. The measurements were performed for microtome samples sliced from either earlywood or latewood and for samples containing both earlywood and latewood. The effect of MC on the mechanical properties of earlywood and latewood of Scots pine was different. The MC was found to have greater influence on the tensile strength and modulus of elasticity in latewood than in earlywood, but its effect on strain at failure was greater in earlywood. As determined individually for earlywood and latewood, the tensile strength, modulus of elasticity, and the strain at failure that were calculated from the rule of mixtures (the weighted mean for earlywood and latewood) did not differ significantly from the values found in the samples containing both zones. This similarity was observed at low and high MC.

In this research, the influence of adding micro- and nano- sized calcium carbonate powders to nylon-66 was investigated. Mechanical properties of micro and nano- composites, including tensile strength, elongation, and Young’s modulus, before and after ageing, were determined and analyzed. For this purpose, micro- and nano-sized CaCO3 particles were used as fillers to prepare micro-composites (conventional composites) and nano-composites via a polymer solution method. It was observed that tensile strength and young’s modulus increased and elongation decreased with increasing CaCO3 particles in the composites. Also, nano-composites had higher strength and modulus than micro-composites. Theoretical prediction of elastic modulus was carried out using rule of mixtures, Guth, Nicolais–Narkis, Hashin–Shtrikman, and Halpin–Tsai equations. Calculated results show that these equations are not suitable for accurate prediction for the work carried out. However, these models can be used with confidence for the prediction of elastic modulus because experimental results are higher than the calculated values.

A lower bound of the longitudinal elastic modulus of polymer composite materials reinforced with unidirectional continuous fibres is obtained by means of a Differential Calculus approach. In the mathematical derivations, the concept of interphase between the fibre and matrix was also taken into consideration. The three phases are considered as isotropic. The results obtained from the proposed formula were compared with those arising from some reliable and accurate theoretical models as well as with experimental data found in the literature, and a reasonable agreement was observed. [ABSTRACT FROM AUTHOR]

A new material tailoring method for spherical and cylindrical vessels made of functionally graded materials (FGMs) is presented. It is assumed that the FG material is composed of an Al-SiC metallic-matrix composite. A uniform ratio of in-plane shear stress to yield strength [φr] is used as the design criterion to utilize the maximum capacity of the vessel. The aim is to find a distribution of SiC particles in the radial direction, i.e., fr, that achieves a uniform index φr=const. through the wall thickness of the internally pressurized spherical or cylindrical vessel. Both the Mori-Tanaka and rule-of-mixtures homogenization schemes are used to express the effective elastic module and Poisson’s ratio. Moreover, the strength of the composite is expressed based on the rule of mixtures. Besides, finite element simulation is carried out to verify the accuracy of the analytical solution. The effects of input parameters such as the internal pressure, strength of the SiC particles, ratio of in-plane shear stress to effective yield strength, and choice of homogenization scheme on the tailored distribution of the SiC volume fraction in the radial direction are also investigated. [ABSTRACT FROM AUTHOR]

Fish scales are an interesting natural structural material and their functionality requires both flexibility and toughness. Our previous studies identified that there are spatial variations in the elastic properties of fish scales corresponding to the anatomical regions, and that they appear to be attributed to changes in the microstructure. In the present study, a model is proposed that describes the elastic behavior of elasmoid fish scales in terms of the relative contributions of the limiting layer and both the internal and external elasmodine. The mechanical properties of scales from the Megalops atlanticus (i.e. tarpon) were characterized in tension and compared with predictions from the model. The average error between the predicted and the experimental properties was 7%. It was found that the gradient in mineral content and aspect ratio of the apatite crystals in the limiting layer played the most important roles on the elastic modulus of the scales. Furthermore, misalignment of plies in the external elasmodine from the longitudinal direction was shown to reduce the elastic modulus significantly. This is one approach for modulating the fish scale flexibility for a high mineral content that is required to increase the resistance to puncture. [ABSTRACT FROM AUTHOR]

The present study aims at investigating the delamination behavior of laminated composites in different loading modes within a homogenization theory of mixtures. The delamination damage phenomenon is introduced at the bulk level by eliminating the explicit representation of interfaces. Potential delamination planes are identified according to the developed interfacial stresses, and damage evolution is computed for each mode independently through a stress-based formulation. An arc-length strategy is employed to solve equilibrium equations owing to the snap-back effects. Reliability of the adopted mixing theory, as a framework for integrating the delamination theory into, is assessed by comparing the results with the ones obtained from micromechanical models in a fiber metal laminate structure. Considering delamination, a good agreement is observed in mode I, mode II and mixed mode configurations by evaluating the results against available numerical and experimental data in thermoset and thermoplastic composite systems. The present method has the capability to be used in the conventional finite element codes with the number of elements kinematically needed in the thickness, regardless of the number of layers, which dramatically reduces the computational cost in modeling composites with large number of layers. The proposed approach is not intended to replace other exact methods at the coupon scale, however, its main application would be in modeling delamination on large scale systems with minimum loss of accuracy. [Display omitted] [ABSTRACT FROM AUTHOR]