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The XYZ 3-dimensional thermal conductivities of the C/C up to 2000 °C were measured by a laser flash method. Carbon fiber-reinforced carbon composites (C/C) were generally developed for aerospace missions due to their excellent thermal resistivity at ultrahigh temperature. C/C must endure harsh environments such as thousands of degrees Celsius without degradation of its mechanical properties. To solve this problem, among the passive thermal protection system, we suggest a method of conducting more heat through the mono-axial direction, which resulted in ease of the thermal rise in the heat receiving part. For example, the X-43A flight applied unbalanced C/C (UCC) with different carbon fiber orientation ratios according to the XY direction in the leading edge part. To investigate the difference in thermal conductivity between unbalanced C/C (UCC) and balanced C/C (BCC), unbalanced and balanced preforms were prepared by a needle punching process, and then they were densified by pitch infiltration and a carbonization process. We compared and analyzed the effects of unbalanced C/C(UCC) and balanced C/C (BCC) structures on the thermal conductivity. We also designed the “rule of mixtures” equation for calculating thermal conductivities of each C/C using reported data of carbon fiber and graphite matrix. Our calculations of thermal conductivity ratio match the ratio of real data.

In this study, a meshfree approach using a naturally stabilized nodal integration (NSNI) integrated with a higher-order shear deformation theory (HSDT) for free vibration analysis of multilayer functionally graded graphene platelets reinforced composite (FG GPLRC) plates with complicated shapes is presented. Four different patterns of graphene platelets (GPLs) including uniform and functionally graded distributions are exampled. The rule of mixtures and modified Halpin–Tsai model are respectively used to compute the Poisson's ratio, density and Young's modulus. Based on the principle of virtual work, discretize governing equations of FG GPLRC plates are derived. These equations are solved by a moving Kriging (MK) meshfree method to determine natural frequencies of the FG GPLRC plates. The advantage of moving Kriging shape function is content with the Kronecker delta function property, thus essential boundary conditions are simply imposed as in the finite element method. In addition, the present meshfree approach uses the direct nodal integration with an additional augmentation of stability components to reduce the computational cost as compared to the high-order Gauss quadrature scheme. As observed in numerical examples, natural frequencies of FG GPLRC plates are impressed by the geometries, boundary conditions and distributed patterns of GPLs. It is also seen that the present approach is simply, stable and good predictions for FG GPLRC plates.

This work explores the possibility of tailoring the thermal conductivity and thermal expansion of rare earth monosilicates through the introduction of multiple rare earth cations in solid solution. Six rare earth monosilicates are studied: Sc2SiO5, Y2SiO5, Nd2SiO5, Dy2SiO5, Er2SiO5, and Yb2SiO5. Four equimolar binary cation mixtures and a five-cation equimolar mixture were characterized. Thermal expansion was measured up to 1200 °C with X-Ray Diffraction (XRD) and bulk thermal conductivity was measured by Hot Disk technique. The linear coefficient of thermal expansion (CTE) of mixed-cation systems followed a rule of mixtures, with average linear CTEs between 6 - 9 × 10−6 /°C. Scandium monosilicate showed a lower linear CTE value as well as a notably lower degree of CTE anisotropy than other rare earth monosilicates. Thermal conductivity was found to decrease below rule of mixtures values through increasing heterogeneity in rare earth cation mass and ionic radii, as expected for the thermal conductivity of solid-solutions. The five-cation equimolar RE2SiO5 (RE=Sc, Y, Dy, Er, and Yb) shows a thermal conductivity of 1.06 W/mK at room temperature, demonstrating that multi-component rare earth silicates are strong candidates for novel dual-purpose thermal and environmental barrier coatings.

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.

For QSTE700 high-strength steel rectangular welded tube, the mechanical properties of the weld zone vary with the distance from the centerline of the weld. Therefore, the accurate description of constitutive relationship of the weld zone is of great significance for the study of formability of QSTE700 rectangular welded tube. Firstly, the mechanical properties of parent and mixed specimens containing weld zone and parent zone were obtained by uniaxial tensile test. And based on the microhardness test, the width and the microhardness distribution of the weld zone were determined. Secondly, by subdividing the weld zone into several small areas, and combining with the rule of mixtures and nanoindentation test, the continuous functional relationships of strength coefficient K, hardening coeffecient n and elastic modulus E were obtained, and then, the continuous constitutive relationship of QSTE700 rectangular welded tube was established. Finally, the validity and reliability of the continuous constitutive relationship of welded tube were verified by nanoindentation test and rotary draw bending of rectangular welded tube. Besides, it was found that the finite element model of rotary draw bending of QSTE700 rectangular welded tube established by using the continuous constitutive relationship can well simulate the cross section deformation and wall thickness variation.

The article provides a brief overview of studies on crystalline materials with negative Poisson’s ratio (crystalline auxetics) with cubic anisotropy. It has been demonstrated that 1/4 part of all cubic crystals has auxetic properties. Even more auxetics are found among chiral nano/microtubes with cubic cylindrical anisotropy. It has been established that chiral nano/microtubes made of cubic crystals exhibit linear Poynting’s effect under torsion, in contrast to the known nonlinear effect for isotropic materials. In the case of longitudinal tension of two-layered composites, it is shown that Voigt’s rule of mixtures is violated in the presence of a layer of auxetic materials.

In this paper, the free damped vibration behavior of doubly curved panels is investigated, while reinforcements are aligned and straight single-walled carbon nanotubes with uniform and functionally graded distributions under four different patterns through thickness. The extended rule of mixtures is employed to achieve effective material properties. Hamilton principle and third-order shear deformation theory of Reddy are used for governing equations of motions of spherical, cylindrical, hyperboloid and paraboloid panels resting on visco-Pasternak medium. A semi-analytical approach with an iterative numerical algorithm is implemented to figure out frequencies and modal loss factors of eigenvalue problem. To verify, the present results are compared with those that are obtained via first-order shear deformation theory for flat, cylindrical, and spherical panels. Also, the influence of shallowness, thickness, curvature, aspect ratios, distribution and content of carbon nanotubes, and viscoelastic medium on natural frequency and damping capability of panels are examined via numerical examples. For the first time, the crossing phenomena of natural frequencies and modal loss factors of FG-CNT–reinforced composite panels with external damping under higher-order theory assumptions are presented. Results show that hyperboloid panels with high aspect, shallowness, and low thickness ratios are susceptible to follow inharmonic motion rather than a harmonic one.

This article presents the free vibration frequencies of composite plates reinforced with single-walled carbon nanotubes by using a refined simplified two-variable nth-higher-order theory. Four kinds of distribution of uniaxially aligned reinforcement material are presented. The most famous one is the uniform; in addition, three types of functionally graded distributions of carbon nanotubes in the through-thickness direction of the plates are investigated. The effective physical properties of composite media are given according to a refined rule of mixtures approach that contains the efficiency parameters. Exact closed-form formulation based on a refined simplified two-variable nth-higher-order plate theory that can be adapted to the vibration of such plates is investigated. Accuracy of presented approach is validated by comparing its results with those given by other investigators

A topologically heterogeneous microstructure design is introduced in a Cu/Zr nanolayered composite, in which each soft 100 nm Cu or Zr layer is surrounded on both sides by several hard 10 nm Cu/Zr bilayers. This design aims to impose a full geometrical constraint on all of the soft layers. Micropillar compression tests demonstrate that the composite deforms in a compatible fashion among the layers, in which no extrusion of the soft layers occurs. An elevated strength of 730 MPa is achieved in the composite compared with the strength prediction based on the linear rule of mixtures.

In this research, electrically characteristics of a graphene nanoplatelet (GPL)-reinforced composite (GPLRC) microdisk are explored using generalized differential quadrature method. Also, the current microstructure is coupled with a piezoelectric actuator (PIAC). The extended form of Halpin–Tsai micromechanics is used to acquire the elasticity of the structure, whereas the variation of thermal expansion, Poisson’s ratio, and density through the thickness direction is determined by the rule of mixtures. Hamilton’s principle is implemented to establish governing equations and associated boundary conditions of the GPLRC microdisk joint with PIAC. The compatibility conditions are satisfied by taking perfect bonding between the core and PIAC into consideration. Maxwell’s equation is employed to capture the piezoelectricity effects. The numerical results revealed the important role of ratios of length scale and nonlocal to thickness, outer-to-inner ratio of radius ( $$R_{\text{o}} /R_{\text{i}}$$ ), ratio of piezoelectric to core thickness (hp/h), and GPL weight fraction ( $$g_{\text{GPL}}$$ ) on the critical voltage of the system. Another important consequence is that by increasing $$R_{\text{o}} /R_{\text{i}}$$ , the critical voltage of the smart structure increases more intensely in comparison with the $$g_{\text{GPL}}$$ .

In this article, buckling analysis of a porous nanocomposite cylindrical shell reinforced with graphene platelets (GPLs) using first-order shear deformation theory is carried out. Internal pores and GPLs are scattered uniformly and/or nonuniformly in the thickness direction. The mechanical properties such as the effective modulus of elasticity through the thickness direction are computed by the modified Halpin–Tsai micromechanics approach, whereas density and Poisson ratio are in accordance with the rule of mixtures. The Rayleigh–Ritz method is employed to obtain a critical buckling load of the graphene-reinforced porous cylindrical shell. The accuracy of the obtained formulation is validated by comparing the numerical results with those reported in the available literature as well as with the software ABAQUS. Moreover, the effects of patterns of internal pores and GPLs distribution, GPLs weight fraction, density and size of internal pores, different boundary conditions, geometric factors such as mid-radius to thickness ratio and shape of graphene platelets on the buckling performance of the functionally graded graphene platelet-reinforced composite porous cylindrical shell are explored.

The main objective of this work is to present a finite element model for the stability analysis of functionally graded material thin plates subjected to uniaxial and biaxial loads. This model is developed using the classic thin plate’s kinematics of von Karman. Static equilibrium equations are established by means of the principle of stationary potential energy. The formulation is made without any homogenization technique or rule of mixtures; thus, the stress and strain vectors are split into two parts: a membrane part and a second bending part. For the elastic behavior matrix, it is written in dimensionless form. The finite element discretization is done using a four-node quadrilateral element with five degrees of freedom per node. Lagrange bilinear shape function are adopted for the membrane components, and Hermite’s high-degree shape function are adopted for the flexural component. The critical buckling loads are established by solving the eigenvalue problem. The efficiency of the model is tested on several examples of buckling plates under different types of loading. In the present study, specimens of rectangular and perforated plates were tested in three different loading conditions: uniaxial compression, biaxial compression, and compression–traction.

Motivated by the recent use of friction stirring in the manufacture of in-situ composites, a new additive manufacturing method for design and manufacture of tailor-made functionally graded composites is presented. A numerical analysis of Aluminium 6061 T6 alloy and SiC in-situ metal matrix was developed with Friction stir processing. Functionally graded material (FGM) possess gradual change in Composition and structure over the entire volume, which results in corresponding changes in its material properties. A geometrical model of Aluminium 6061 T6 alloy of thickness of 6 mm is generated. SiC nanoparticles is filled in the pre-drilled linear fashioned successively centre distance holes on aluminium base metal. Mori-Tanaka method and the rule of mixtures aid to determine the material properties of the model from the elementary constituents. A moving coordinate which produce heat input from both the tool shoulder and the tool pin is introduced to make modelling the moving tool easier. The temperature distribution of the FG plate was analysed across various regions of the path from material flow in addition to the evaluation of process efficiency by 3 dimensional finite element method using COMSOL multi-physics.

This paper describes the research performed within the scope of H2020 project FIBRESHIP in the development and validation of a thermo-mechanical model to assess the fire performance of composite structures. A one-dimensional thermal model with pyrolysis is used to obtain the temperature profile across the thickness, and later, introduced in the thermo-mechanical model with a quadrilateral shell element approach. The composite constitutive model employed is the so-called Serial/Parallel Rule of Mixtures (SPROM) which has been modified to introduce the effect of the thermal deformation. A set of experimental tests are then used to validate the correctness of the numerical method proposed. The experimental data used to validate the thermal model is the classic Henderson experimental test. The thermo-mechanical coupling is validated against an original vertical furnace test of an FRP ship's bulkhead, following on the 2010 FTP Code standards. These validations demonstrate the correctness and accuracy of the proposed decoupled thermo-mechanical formulation.

A multi-scale framework for modelling of fibre reinforced polymer composite structures with intrinsic self-healing ability is presented in this work. At the microscale, matrix constituent is modelled using the micro-damage-healing constitutive model developed and validated in [1]. In this model damage variable reduces the material’s elasticity modulus, whereas the healing variable causes its restoration. Reinforcing fibres are considered transversely isotropic and linear elastic. Hashin failure criterion and progressive damage model are used for modelling of fibre failure and post-failure behaviour. Rule of Mixtures equations for homogenised mechanical properties are used as a means of homogenisation. On the other hand, the Voigt and Reuss approximations for the strain tensor are applied to perform the localisation. The Voigt (iso-strain) approximation is used in the direction of the reinforcing fibres, whereas the Reuss (iso-stress) approximation is used at other components of the strain tensor. In [2] the aforementioned model was implemented into the Abaqus/Standard user material subroutine UMAT and validated with experimental results of the three-point flexural tests. Inhere, the model is implemented into the Abaqus/Explicit user material subroutine VUMAT and is validated with experimental results of the low-velocity impact (LVI) tests, available in [3]. Composite plates consisted of woven glass fibres as reinforcements and a polymer blend as the matrix constituent. The blend consisted of diglycidyl ether bisphenol A (DGEBA) epoxy resin and poly(ε- caprolactone) thermoplastic polymer. Woven fibre warp and weft yarns are approximated with unidirectional plies. The impact is simulated in Abaqus/Explicit using the VUMAT subroutine, whereas the healing is simulated in Abaqus/Standard using the UMAT subroutine, validated in [2]. Preliminary results are presented in Figure 1 where experimentally obtained and simulated contact forces between the composite plate and the impactor are compared. Validation proved the model’s applicability to simulate healing of micro-damage induced during a low-velocity impact. Provided that the proper set of parameters is used, the model could be used for simulation of other types of composite structures with intrinsic self-healing ability. References: [1] Smojver, Ivica ; Ivančević, Darko ; Brezetić, Dominik ; Haramina, Tatjana (2022): Constitutive modelling of a self-healing composite matrix polymer material. In International Journal of Damage Mechanics, 0(0): 1-18. [2] Smojver, Ivica ; Ivančević, Darko ; Brezetić, Dominik (2022): Modelling of micro-damage and intrinsic self-healing in unidirectional CFRP composite structures. In Composite Structures, 286: 1-10 [3] Cohades A, Michaud V. Damage recovery after impact in E-glass reinforced poly(ε- caprolactone)/epoxy blends. Composite Structures. (2017) 180: 439–447.

In this work, a multi-scale framework is used for modelling of Low Velocity Impact (LVI) and post- impact healing of woven intrinsically self-healing FRP composite structures. The matrix constituent is modelled using the elastic-plastic micro-damage healing model. Furthermore, the reinforcing fibres are modelled as linear elastic with Hashin failure criterion and progressive damage model. The employed micromechanical model is the Rule of Mixtures (ROM). The developed model is implemented into Abaqus/Explicit user material subroutine VUMAT and validated using the LVI experimental results available in the literature. Tested specimens consisted of a self-healing epoxy resin and woven E-glass fabric as the matrix constituent and reinforcement, respectively. Validation results by comparing contact forces have shown that the model accurately predicts damaging mechanisms in the specimen. Additionally, prediction of fibre damage is in satisfactory agreement with experimental results. Finally, prediction of damaged and healed areas corresponds to experimental ultrasonic measurements.

In this work, the influence of a compliant hyperelastic polymeric phase infiltrated inside stiff auxetic lattices is studied through experimental and numerical approaches. Samples were fabricated using material jetting technology (MJT). The design principle mimics examples of biological materials which combine stiff and compliant materials to attain high superior mechanical properties exceeding the rule of mixtures of both constituent. Two negative Poisson’s ratio lattice designs are considered, namely Hexaround and Warmuth cell. Their effective elasto-mechanical properties are investigated through finite element method (FEM) using a homogenization strategy with periodic boundary conditions. A comparison of mechanical properties between lattices and composite lattices, for multiple lattice/matrix volume fractions is discussed and numerical models are validated through a series of compression tests. Results suggest that filling lattices could increase Young’s modulus, peak stress, plateau stress and delayed densification of the lattice, hence improving both specific energy absorption (SEA) and absorption efficiency of the considered architectured materials. The improvements are attributed to the presence of the matrix acting as a structural support, modifying lattice failure mode from layerwise to shear band breaking. These results expand the design principles for new energy absorption devices based on architectured materials. France–Australia Science Innovation Collaboration program. ANR JCJC SCOLASTIC project (grant no.16-CE08-0009). Rod Rickards Fellowship from the Australian Academy of Science.

A multifunctional efficiency metric is developed using mean-field micromechanics solutions to quantify the multifunctionality of the multifunctional composite anodes. Multifunctional efficiency metrics evaluate the volume and/or mass savings or performance increase when structural and functional materials are replaced by multifunctional materials [1]. The proposed methodology compares the total energy associated with different functionalities, such as elastic strain energy and electric charge energy of the multifunctional materials with the total energy of the single function structural and functional material. To achieve volume and mass savings, the energy of different functionalities is set to be the same between the multifunctional and traditional single- functional materials, and, at the same time, the volume and/or mass of the multifunctional composite needs to be smaller than that of the combination of single- functional materials. The volumes and/or mass savings can be expressed using the properties of multifunctional and traditional single-functional materials. In this work, structural anodes made from silicon nanoparticles, reduced graphene oxide, and aramid nanofibers are used as an example to calculate the mass savings compared to a traditional anode with structural support. The existing multifunctionality metrics are based on the rule of mixtures method, which is adequate for certain geometries and loading conditions, such as in-plane directions for laminate composites. However, if multifunctional composite materials involve multiple phases, material property variation during the charging process, and complex geometries or orientations of the structural and functional phases, a more comprehensive method is required to accurately capture the multifunctional efficiency. The multifunctional efficiency varies significantly during the charging and discharging process. This new metric can provide both upper and lower bounds of multifunctional efficiency. This new multifunctional efficiency metric will help optimize the selection and arrangement of different phases in the multifunctional and quantify the optimization results.

This study presents a meshfree approach using a naturally stabilized nodal integration (NSNI) combined with a higher-order shear deformation theory (HSDT) for buckling analysis of functionally graded graphene platelets reinforced composite (FG GPLRC) plates. Various types of distributed graphene platelets (GPLs) consisting of uniform and functionally graded are considered. The Poisson’s ratio, density and Young’s modulus are calculated by using the rule of mixtures and modified Halpin–Tsai model, respectively. Discretize governing equations are deduced from the principle of virtual work and solved by a moving Kriging (MK) meshfree method to determine the buckling load factor of the FG GPLRC plates. Due to using the direct nodal integration and augmenting of stability components, the computational cost is reduced when comparing to the high-order Gauss quadrature scheme. Through numerical examples, the buckling load factor of FG GPLRC plates is affected by the geometries, boundary conditions and distributed patterns of GPLs.

In the present study, a buckling analysis of laminated composite rectangular plates reinforced with multiwalled carbon nanotube (MWCNT) inclusions is carried out using the finite element method (FEM). The rule of mixtures and the Halpin–Tsai model are employed to calculate the elastic modulus of the nanocomposite matrix. The effects of three critical factors, including random dispersion, waviness, and agglomeration of MWCNTs in the polymer matrix, on the material properties of the nanocomposite are analyzed. Then, the critical buckling loads of the composite plates are numerically determined for different design parameters, such as plate side-to-thickness ratio, elastic modulus ratio, boundary conditions, layup schemes, and fiber orientation angles. The influence of carbon nanotube fillers on the critical buckling load of a nanocomposite rectangular plate, considering the modified Halpin–Tsai micromechanical model, is demonstrated. The results are in good agreement with experimental and other theoretical data available in the open literature.

The local repair of a damaged composite structure has the potential to restore the performance of the structure without replacing it. In this work, the tensile behavior of a patch repaired composite laminate is analyzed in detail using experimental and numerical studies. A 4-ply composite laminate is prepared by using E-glass chopped fiber mat as the reinforcement and Epoxy L12 as the matrix material. The damage is created in the laminate by drilling a hole of 8 mm at the center. The laminate is then repaired by adhesively bonding the same material as an external patch on both sides. Tensile tests have been carried out on healthy, damaged, and repaired specimens. It is found that the load carrying capacity is restored with the external patch repair. The longitudinal stiffness and the load carrying capacity are restored by 75% and 90%, respectively. A three-dimensional finite element modeling of the tensile tests has been carried out to analyze the stress distribution in all three specimens. A brief literature review is also presented about the mathematical models used to estimate mechanical properties of the chopped fiber strand mats. In this work, the elastic properties of the random fiber chopped strand mat are estimated using the modified rule of mixtures. From the results of the numerical study, it is found that the stress concentration around the damage is reduced by 70% with the patch repair. The present study is mainly useful for maintenance engineers.

It is shown that the simple rule of mixtures describes correctly the elastic modulus of polymer/carbon nanotubes nanocomposites, if the real characteristics of the nanofill are used instead of the nominal ones. These characteristics are determined by the structure of carbon nanotubes in the polymer matrix. The factor of effective length (aspect ratio) of carbon nanotubes pays the main contribution to nanocomposites stiffness.

This paper presents a bi-directional closed-form analytical solution, in the framework of nonlinear soft composites mechanics, for top-down hyperelastic characterization of brain white matter tissue components, based on the directional homogenized responses of the tissue in the axial and transverse directions. The white matter is considered as a transversely isotropic neo-Hookean composite made of unidirectional distribution of axonal fibers within the extracellular matrix. First, two homogenization formulations are derived for the homogenized axial and transverse shear moduli of the tissue, based on definition of the strain energy density function. Next, the rule of mixtures and Hashin-Shtrikman theories are used to derive two coupled nonlinear equations which correlates the tissue shear moduli to these of its components. Closed-form solutions for shear moduli of the components are then obtained by solving these equations simultaneously. In order to validate the hyperelastic characteristics of components obtained in previous step, they are used in a bottom-up approach in a micromechanical model of the tissue with the aim of predicting the directional homogenized responses of the tissue. Comparison of model predictions with the experimental test results reported for corona radiata and corpus callosum white matter structures reveals very good agreements with the experimental results in both directions. The model predictions are also in good agreement with the analytical solution obtained by the iterated homogenization technique. Results indicate that axonal fibers are almost ten times stiffer than the extracellular matrix under large deformations.

In this study, Fe and 316L powders with two different particle sizes were used as the feedstock. They were also premixed using different mixing ratios and combinations: (i) either 316L or Fe powder with large particles blended with small ones and (ii) a blend of 316L and Fe powder using three particle size combinations. Both single-component and mixed powders were deposited by cold spray, and the deposition efficiencies (DEs) were calculated and discussed. The results show that the DE of a mixture of large and small particles of the same powder follows the Rule of Mixtures, whereas the variation of the DE of the 316L and Fe mixture depends on the particle size combinations; specifically, mixtures with smaller-sized particles show better DEs than the respective Fe powder. The difference in the DEs of different Fe/316L mixtures can be explained by the particle–particle interactions (i.e., tamping and retention) upon impact. In addition, a relationship between the average particle size and density is proposed to determine the occurrence of particle–particle interactions in cold spray of mixed generic powders. The industrial significance of the knowledge of particle–particle interactions is finally explained in the context of the fabrications of metal matrix composites.

Purpose The purpose of this study is to confirm that the stiffness of fused filament fabrication (FFF) three-dimensionally (3D) printed fiber-reinforced thermoplastic (FRP) materials can be predicted using classical laminate theory (CLT), and to subsequently use the model to demonstrate its potential to improve the mechanical properties of FFF 3D printed parts intended for load-bearing applications. Design/methodology/approach The porosity and the fiber orientation in specimens printed with carbon fiber reinforced filament were calculated from micro-computed tomography (µCT) images. The infill portion of the sample was modeled using CLT, while the perimeter contour portion was modeled with a rule of mixtures (ROM) approach. Findings The µCT scan images showed that a low porosity of 0.7 ± 0.1% was achieved, and the fibers were highly oriented in the filament extrusion direction. CLT and ROM were effective analytical models to predict the elastic modulus and Poisson’s ratio of FFF 3D printed FRP laminates. Research limitations/implications In this study, the CLT model was only used to predict the properties of flat plates. Once the in-plane properties are known, however, they can be used in a finite element analysis to predict the behavior of plate and shell structures. Practical implications By controlling the raster orientation, the mechanical properties of a FFF part can be optimized for the intended application. Originality/value Before this study, CLT had not been validated for FFF 3D printed FRPs. CLT can be used to help designers tailor the raster pattern of each layer for specific stiffness requirements.

The objective was to obtain a quantitative relationship between the multiscale structural parameters and the elastic modulus of rice stem. Anisotropic elastic properties of rice stem were calculated via multiscale simulation. The elastic constants of the sub-layers of cell wall were calculated by the Halpin-Tsai equations and the rule of mixtures. Cellular structure of stem cross section was reconstructed via a skeletonisation method and used to create the finite element models. The influence of multiscale structural parameters, including the volume fractions of skin and vascular bundle, the cell wall thickness of different types of cells, the volume fraction and stiffness of compound composition, the volume fraction of S2 layer and the microfibril angle (MFA) in the layer, on the overall stiffness of rice stem was determined. Numerical results showed that if the volume fraction and stiffness of each cell wall component are assumed to be constant, increasing the volume fraction of the mechanical tissue layer, thickening the fibre cell wall and decreasing the MFA in S2 layer are the most effective ways to increase the longitudinal tensile modulus of rice stem. Changing the cell wall thickness and the volume fraction of vascular bundle is useful for controlling the tangential modulus. However, more effective is to change the cell wall thickness of parenchyma cell and the volume fraction of the vascular bundle for controlling the radial tensile modulus of rice stem.

We newly design a high-entropy-alloy(HEA)-cored multi-layered sheet (MLS) containing AISI 304 stainless steel (STS) surface layers (HEA/STS MLS) by using a commercial roll-bonding procedure, and property-enhancing mechanisms such as TWinning Induced Plasticity (TWIP), TRansformation Induced Plasticity (TRIP), and geometrically necessary dislocation (GND) generation were analyzed. This MLS well satisfied a rule of mixtures because the HEA and STS layers were strongly bonded to show similar deformation mechanisms of TWIP and TRIP at both room and cryogenic temperatures. The HEA layer demonstrated synergic effects of homogenization and maximization of TWIP and TRIP mechanisms with the STS layers. In particular, very high strain hardening and persistent elongation (about 50%) as well as very high tensile strength over 1.5 GPa are quite unique and interesting results because they have not been reported in the FCC-based HEA areas yet. Our findings also demonstrate that the HEA-cored MLS fabrication can be an attractive route to a new HEA design strategy for cryogenic applications.

Commercially pure zirconium was processed by the surface mechanical attrition treatment (SMAT), and the microstructure observation showed that a gradient structure was induced. Nanoindentation measurements were taken to obtain the load–displacement curves at different depths below the treated surface. Using dimensional analysis, the local yield stress, hardness, strain hardening exponent, and elastic modulus at the corresponding depths were derived. The results showed that the yield stress and hardness varied with depth, while the strain hardening exponent and elastic modulus were approximately invariable. The finite element method was used to simulate nanoindentation at different depths below the treated surface to verify the derivation of the local elastic–plastic constitutive relationship. Stress–strain curves were computed for the treated samples through the rule of mixtures, and they agreed well with the experimental results. The analysis showed that the surface and subsurface hardening layers as well as the transition layer shared a high load applied to the samples, even though their volume fraction was small.

The high tensile strength of polymer matrix composites is derived primarily from the high strength of the carbon fibers embedded in the polymer matrix. However, their compressive strength is generally much lower due to the fact that under compression, the fibers tend to fail through micro-buckling well before compressive fracture occurs. In this work, we consider multi-walled carbon nanotube (MWNT) sheets wrapped around carbon fiber at room temperature to improve fiber/matrix interfacial properties which, in turn, influences compressive strength of the composite. To investigate the effect of the wrapping of MWNT sheet on composite strength, Molecular Dynamics simulations were performed on an atomistic model of the interface region between the epoxy, carbon fiber and the scrolled MWNT sheets. The compressive strength of the unidirectional composite was computed using a novel hierarchical multi-scale model comprising of the rule of mixtures at the microscale, and the modified Argon’s formula for composites at the macroscale. Model predictions were benchmarked through comparison with experimental data for different volume fractions of MWNT sheet.

The paper provides a theoretical analysis of axially stretched rectangular thin plates composed of two differently oriented layers of cubic crystals. In one layer, the crystal has its principal crystallographic orientations parallel to the plate edges, and in the other, the crystal is oriented at a certain angle to the plate plane. The analysis shows that more than fifty cubic crystals with positive anisotropy can form two-layered plates whose effective Young’s modulus is greater than the moduli of both layers, which violates the well-known Voigt’s rule of mixtures. The anomalous behavior of effective Young’s modulus and Poisson’s ratios in the plates depends on the properties of their constituent crystals: the sign and value of anisotropy coefficients and Poisson’s ratio, ratio of Young’s moduli, relative orientation angle, and layer thickness ratio.

In this study, for the first time, a size dependent computational model based on the modified strain gradient theory (MSGT) and higher-order shear deformation theory (HSDT) for free vibration analysis of multilayer functionally graded graphene platelet-reinforced composite (FG GPLRC) microplates is proposed. To capture size effects of microstructures, three material length scale parameters (MLSPs) are considered and used. The effective Young's modulus for each layer of the FG GPLRC microplate is computed according to the Halpin–Tsai model, while the effective density and Poisson's ratio are computed by the rule of mixtures. Four different types of graphene platelets (GPLs) distributions, which are either uniform or functionally graded (FG), are considered. The principle of virtual work is used to derive discretize governing equations which are then solved by an isogeometric analysis (IGA). In addition, thank to continuous higher-order derivatives of NURBS basis functions in IGA, it is suitable for a numerical implementation of the present size dependent model within required third-order derivatives in the weak form. Besides, the present size dependent model can be recuperated into the modified couple stress theory model (MCST) or classical HSDT model when two or all MLSPs in the theory are taken equal to zeros, respectively. The rectangular and circular FG GPLRC microplates with different boundary conditions, distributed types of GPLs and MLSPs are exampled to evaluate natural frequencies. Numerical results have shown that the difference of the natural frequency predicted by the MSGT, the MCST and classical HSDT are large when the plate thickness approaches the MLSPs, however, this difference decreases with a rise of the plate thickness.

A novel cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields. The domain is discretized with arbitrary polygons and on each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The plate is made of functionally graded material with effective properties computed using the rule of mixtures. The influence of various parameters, viz., the plate aspect ratio and the material gradient index on the static bending response and the first fundamental frequency is numerically studied. It is seen that the proposed element: (a) has proper rank; (b) does not require derivatives of shape functions and hence no isoparametric mapping required; (c) independent of shape and size of elements and (d) is free from shear locking.

In this study, a NURBS formulation based on the four-variable refined plate theory (RPT) for free vibration , buckling and static bending analyses of multilayer functionally graded graphene platelets reinforced composite (FG GPLRC) plates, for the first time, is proposed. The distributions of graphene platelets (GPLs) in the polymer matrix either uniformly or non-uniformly including different patterns are considered. The Young’s modulus of the nanocomposites is predicted by the modified Halpin–Tsai model, while the Poisson’s ratio and density mass are implemented by the rule of mixtures. Governing equations are derived and the NURBS formulation is employed to obtain natural frequencies, critical buckling loads and deflections of multilayer FG GPLRC plates. Thanks to continuous higher-order derivatives of NURBS basis functions in isogeometric analysis (IGA), the present approximation is easy to satisfy the C1-continuty requirement of the RPT model. In addition, a rotation-free technique is applied to eliminate the bending and shear slopes in the case of clamped boundaries. Effects played by GPLs weight fraction, GPLs distribution patterns, number of layers, thickness-to-length ratio are investigated. Numerical results indicate that the inclusion of GPLs can significantly improve the stiffness of plates.

The contribution of a reinforcement to the tensile strength of a composite can be evaluated by different micromechanics models. Nonetheless, one of the main difficulties is the evaluation of the intrinsic properties of the reinforcements. The literature shows experimental and model-based methodologies to estimate such intrinsic properties, and few are based on single fiber tensile test in combination with a Weibull analysis. This paper proposes using henequen strand to prepare polypropylene-based composites. Henequen fibers show a high cellulose content that allows obtaining strong interfaces when a coupling agent is added to the composite formulation. The novelty of this work is based on a simplified methodology to evaluate the intrinsic tensile strength of the reinforcements and its contribution to the tensile strength of the composite. A percentage of coupling agent that returns the highest tensile strength is identified with a strong interface. Then, typical values for a coupling factor and interfacial shear strength are used with a modified rule of mixtures and a modified Kelly and Tyson models to obtain the orientation factors. The prediction of composite behavior from fiber properties is necessary to anticipate the correlation between experimental and the back-calculated parameters.

To simplify the analysis and characterisation of composite laminates, an invariant-based approach to stiffness that takes the trace of the plane stress stiffness matrix as a material property was recently proposed. In the present work, a study based on micro-mechanical models brings new insight to this invariant-based approach. The Rule of Mixtures and the Halpin-Tsai models are used to establish the relations between the fibre volume fraction, the fibre/matrix stiffness ratios, and the trace-normalised engineering constants of unidirectional laminae and multidirectional laminates. For sufficiently high longitudinal fibre/matrix stiffness ratios and for fibre volume fractions between 50% and 70%, typical of advanced CFRPs, the variation of the trace-normalised longitudinal Young's modulus is within 6% for unidirectional laminae and within 1% for multidirectional laminates, supporting the definition of an invariant-based approach to stiffness based on a Master Ply concept and laminate factors derived thereof, defining clearly a domain of applicability of the invariant theory and confirming the empirical observations of the past.

The proportion of latewood varies from species to species and from site to site. To understand the stiffness of wood structures, it is necessary to accurately determine the modulus of elasticity (MOE) of the wood. In this paper, a digital image correlation method was used to analyze the surface strain of wood specimens during tensile testing and calculate the Poisson’s ratios of latewood and earlywood. Digital image analysis (DIA) and X-ray densitometry (XrD) techniques were employed to determine the latewood proportion. Good agreement was observed between the DIA and XrD results for the sapwood proportion. Based on the rule of mixtures, the effective MOE was calculated based on the MOEs of earlywood and latewood.

Recent investigations have focused on the evaluation of the effective elastic properties of microcapsules-based composites theoretically by assuming the constituents’ mechanical properties. The aim of this study is to investigate the effective elastic properties of self-healing microcapsules-based composites (SHMC) theoretically and validate them experimentally. The elastic modulus of the matrix material was evaluated using dynamic mechanical analysis (DMA) of neat polymer samples. Furthermore, the self-healing microcapsules (SHM) elastic modulus was determined through single-microcapsule compression testing followed by finite element modeling. The determined constituents’ elastic properties were used in modeling of SHMC to determine their effective elastic properties analytically. An analytical model, based on Eshelby and Mori–Tanka (E&M–T) two-constituent models, was reformulated and extended to be suitable for a hierarchical approach for solving core–shell–matrix three-constituent SHMC. The results were compared with predictions of the differential-effective medium theory and the rule of mixtures. Finally, all analytical models were compared to experimental results obtained from DMA of 5, 10, and 20 vol% urea-formaldehyde/dicyclopentadiene (UF/DCPD) SHM embedded in epoxy matrix. Good agreement was achieved and the reformulated E&M–T model successfully predicted the elastic properties of SHMC. It was found that the effect of the test uncertainty, the microcapsule geometric parameters for the same batch, and the shell elastic modulus for a given load–deformation curve on the effective elastic properties of SHMC is insignificant. The effective elastic properties depend only on the microcapsules volume fraction up to a certain limit.

Present research deals with the large amplitude thermally induced vibrations of an annular plate made of functionally graded materials (FGMs). One surface of the plate is subjected to rapid surface heating while the other surface is either thermally insulated or kept at reference temperature. The material properties of the constituents are assumed to be temperature dependent. The rule of mixtures is used to obtain the properties of the graded media. With the aid of the von Karman kinematic assumptions and first order shear deformation theory, the governing equations of motion and the associated boundary conditions are obtained. With the aid of the generalized differential quadrature (GDQ) method, these equations are transformed into a set of nonlinear algebraic equations which are solved iteratively using the Newton-Raphson method and Newmark time marching scheme. The temperature profile across the plate thickness is also obtained using the iterative Crank-Nicolson and the GDQ methods. Numerical results are devoted to the effects of temperature dependency, plate thickness, power law index, and boundary conditions of the plate on the large amplitude thermally induced vibrations. It is shown that for thin plates thermally induced vibrations take place and the quasi-static response can not be considered as the true response of the plate under thermal shock.

Dense TiC-ZrC-Cr3C2 composites with various TiC content from 19.6 mol% to 78.4 mol% have been fabricated by hot-pressing sintering at 1950 °C using 2.0 mol% Cr3C2 as sintering aid. The effect of TiC content on the microstructure, mechanical and thermal properties of TiC-ZrC-Cr3C2 composites are investigated systematically. The single (Zr, Ti, Cr)C solid solution is obtained when TiC content is 19.6 mol%, while with increasing TiC content, the composites begin to consist of Zr-rich (Zr, Ti)C solid solution and Ti-rich (Ti, Zr, Cr)C solid solution phase. SEM and EDS analysis confirm that Cr element is not favorable to diffuse into ZrC lattice to form (Zr, Cr)C solid solution. Flexural strength and Vickers hardness increase gradually with increasing TiC content, but fracture toughness does not improve significantly. Fracture toughness are in the range of 3.34–4.01 MPa∙m1/2 for all composites, and the optimum value reaches 4.01 MPa·m1/2 with 49.0 mol% TiC. Experimental results of the thermal expansion coefficient reveal that the addition of TiC raises the thermal expansivity of TiC-ZrC-Cr3C2 composites. Noticeably, the thermal conductivities of TiC-ZrC-Cr3C2 composites show a decrement trend with increasing TiC content, not as theoretical predicting by the rule of mixtures. For instance, the thermal conductivity at 25 °C ranges from 18.0 W/m∙K for 8Z2T2C composite down to 10.6 W/m∙K for 2Z8T2C composite.

This paper unprecedentedly reports the effect of metal (nickel) coating on the stress-dependent electric permittivity, piezoelectricity and piezoresistivity of carbon fiber. Both permittivity (2 kHz) and DC conductivity of carbon fiber are increased by nickel coating. For 7-μm diameter carbon fiber, nickel coating (0.25-μm thickness) increases the relative permittivity from 12,200 to 63,200, and decreases the resistivity from 1.5 × 10−5 to 1.5 × 10−7 Ω.m. The relative permittivity of the nickel coating (Rule of Mixtures) is 404,600 - similar to 405,300 for nickel wire (160-μm diameter). The resistivity of the nickel coating (Rule of Mixtures) is 2.0 × 10−8 Ω.m - lower than 8.8 × 10−8 Ω.m for the nickel wire - probably because of the higher degree of preferred crystallographic orientation in the nickel coating. The nickel structure affects the conduction more than polarization. The piezoelectric and piezoresistive effects are diminished by the nickel coating, which governs these effects. The nickel coating changes the stress dependence of the permittivity (for capacitance-based self-sensing) from positive to negative and changes the piezoresistivity (for resistance-based self-sensing) from negative (gage factor −1830) to positive (gage factor +1650). The piezoelectricity of the nickel-coated carbon fiber and nickel wire are similar, but the piezoresistivity is weak for the latter (gage factor +30).

This study investigated the compressive response of ice-templated composites and provides an understanding of their mechanical behavior based on the properties of templated ceramic and epoxy. Results suggested a dependence of properties on the microstructure of the templated porous ceramic, whereas more interestingly composites exhibited catastrophic and progressive types of failure. Compressive strength was found to be markedly greater relative to the strength of templated ceramic and polymer, and irrespective of the failure type, strength was greatly enhanced under dynamic loading relative to quasistatic loading. Compressive strength was also calculated based on the rule of mixtures and mode of failure in ice-templated ceramic. The analysis suggested that the axial mode of failure was not dominant in composites, and failures resulted from the fracture of lamella walls, possibly due to elastic instability. Fragments of the composite specimens were analyzed using scanning electron microscopy to study the fracture characteristics and rationalize the catastrophic and progressive types of failure.

Nanodomained heterogenous structures characterized by randomly dispersed nanograins (NGs) embedded in the coarser grains (CGs) have demonstrated an exciting potential to break the strength–ductility trade-off, providing high strength without the loss of ductility. Here, using a combination of discrete crystal plasticity finite element (discrete-CPFE) model and dislocation density-based CPFE model, we study the effects of grain size, volume fraction of nanograins on the strength and deformation in nanodomained materials. Our analysis shows that the overall flow stresses of nanodomained samples are equal or higher than the strengths predicted by rule of mixtures. Smaller NGs or higher volume fraction of NGs can make the nanodomained samples stronger, as they can be more effective to promote the dislocation accumulations inside the CGs and eventually raise the critical resolved shear stress for each slip system during the plastic flow. Areas surrounding NGs stored higher dislocation densities and less plastic strain, due to the restricted dislocation motion. Furthermore, NGs grain embedded in the CGs can effectively reduce the anisotropy of strength in the nanodomained samples.

Results of measurements of the specific heat and the thermal conductivity of concrete with blended special aggregate for neutron and gamma radiation shielding are presented. Experimental tests were performed on concrete with heavyweight aggregate (magnetite, barite), hydrogen-bearing aggregate (serpentine) and amphibolite aggregate. The thermal properties of concrete were determined using a nonstationary method. The highest specific heat was found for concrete with serpentine aggregate. Simple models for predicting the specific heat and the thermal conductivity on the basis of concrete mix design were evaluated to include the blends of heavyweight and hydrogen-bearing aggregates. The thermal conductivity of concrete was found to be linearly dependent on the concrete density in the range from 2200 to 3500 kg/m3. Its increase due to water saturation of concrete was not dependent on the open porosity of concrete. It was found that the specific heat can be fairly well predicted using the rule of mixtures formula. The thermal conductivity of concrete can be approximately predicted using a parallel model in the case of water-saturated concrete. The thermal conductivity prediction for dry concrete is also discussed.

In this work, a bottom-up multiscale modeling approach is developed to estimate the effective elastic moduli of Carbon NanoTube (CNT)-reinforced polymer composites. The homogenization process comprises two successive steps, including an atomistic-based computational model and a micromechanics approach at the nano- and micro-scales, respectively. Firstly, the atomistic-based finite element model defines a cylindrical Representative Volume Element (RVE) that accounts for a carbon nanotube, the immediately surrounding matrix, and the CNT/polymer interface. The carbon-carbon bonds of the CNT are modeled using Timoshenko beams, whilst three-dimensional solid elements are used for the surrounding matrix. Through the application of four loading conditions, the RVEs are homogenized into transversely isotropic equivalent fibers by equating the associated strain energies. Secondly, the equivalent fibers are employed in a micromechanics approach to estimate the macroscopic response of non-dilute composites. This is performed using both the analytical Mori-Tanaka model and a computational RVE model with a hexagonal packing geometry. A wide spectrum of single- and multi-walled carbon nanotubes are studied, as well as two different polymeric matrices. Furthermore, the so-called efficiency parameters, imperative for the application of the simplified extended rule of mixtures, are characterized by polynomial expressions for practical filler contents. Finally, detailed parametric analyses are also provided to give insight into the sensitivity of the macroscopic response of CNT-reinforced polymer composites to microstructural features such as filler volume fraction, chirality or aspect ratio.

We studied the effect of embedded nanograins on the strength and deformation of nanodomained heterogeneous nickel (Ni) via a novel discrete-crystal plasticity model. Nanodomained structures exhibited higher strength than those of heterogeneous lamella structures and rule of mixtures. Due to the mismatch of strengths between the nanograins and coarse grains, geometrically necessary dislocations (GND) accumulated around nanograins and increased with the strain. In addition, smaller nanograins are more effective to generate GND in both nanodomained and heterogeneous lamella structures. These findings shed light on the role of dislocation mechanisms in the plasticity of heterogeneous nanostructured metals.