Three-dimensional Random Orientation Research Articles

Serendipitous relationship between discrete distribution models representing random orientations of fillers in composite materials and the golden ratio

The purpose of this study is to establish simple discrete distribution models capable of expressing the two and three-dimensional random orientation states of fillers in composite materials. Initially, a new method is proposed to divide the elastic constants into isotropic and anisotropic parts. Employing this method, for the composite material containing ellipsoidal fillers with various orientations in the material, the macroscopic elastic constants and thermal expansion coefficients of the material are derived based on the Mori–Tanaka method. Subsequently, the analysis of the macroscopic properties is performed for fillers oriented two and three-dimensional discrete distributions. As a result, it is found that when both angular pitches of the azimuth angle and the rotational angle of the fillers in a plane are at most 72°, the macroscopic elastic constants and the thermal expansion coefficients of the material exhibit in-plane isotropy, leading to the realization of a two-dimensional random state. Furthermore, if the angular distribution of the zenith angle and azimuth angle corresponds to the vertices of the regular dodecahedron and icosahedron, and the angular pitch of the rotational angle of the fillers is at most 72°, the macroscopic properties of the material become isotropic, resulting in a three-dimensional random state. Notably, the angle of 72° and the orientation angles of the vertices of the regular dodecahedron and icosahedron are associated with the golden ratio. Therefore, this analysis suggests a serendipitous relationship between the golden ratio and the angular pitch that simplifies the random orientation distribution of fillers.

Optical transmittance and electrical conductivity of silica glass with biserial and hierarchical network structures made of carbon nanofibers

Silica glass composites, with biserial and hierarchical percolative network made of carbon nanofibers (CNFs), was fabricated using a layer-by-layer technique and spark plasma sintering to obtain high optical transmittance and electrical conductivity. Owing to the network, the critical volume fraction, Vc, for the CNF percolation in the silica glass-matrix composite (0.5–0.7 vol%), when the electrical conductivity of the composite drastically increased with change from insulator (∼10−10 S/m) to conductor (∼10−1 S/m), is smaller than theoretical Vc predicted for the three-dimensional random orientation of CNFs (2.6 vol% for the CNF aspect ratio of 30). The conductivity of the composite with above the Vc of CNFs (∼10 S/m) is higher than that reported for the polymer-matrix composite (∼10−5–∼10−3 S/m). Furthermore, high optical transmittance was observed for the electrically conductive composite with Vc of CNFs.

Efficiency of nanoparticle reinforcement using finite element analysis of titanium alloy mandible plate.

Nanoparticles in the form nanotubes and nanoplatelets have been compared for von Mises stresses by using them as low-composition reinforcements in titanium alloy-based mandible plate for different compositions and orientations. A finite element model has been designed to reconstruct a fractured human mandible with a titanium alloy mandible plate. A 500 N compressive force was applied on the mandible, and stress distribution across the plate sections was analysed for aligned two-dimensional random and three-dimensional random orientations for both tubes and platelets. Carbon material as graphene has been used for tube and platelet in the form of nanotubes and nanoplatelets, respectively. Using properties of graphene as the filler in titanium alloy plate, for both nanoplatelets and nanotubes, the stresses reduced between 5% and 25% for nanoplatelets and nanotubes graphene-titanium composite plates in comparison to non-reinforced plates, at critically stressed sections. Nanotubes exhibited stress reduction of nearly 23.4% for aligned configurations, while nanoplatelets exhibited stress reduction up to 21.2% for two-dimensional and three-dinemsional random configurations in comparison to non-reinforced titanium plates. Hence, it has been suggested that nanotubes exhibited superior mechanical reinforcement potential beyond that of aligned nanoplatelets, while nanoplatelets provided enhanced mechanical reinforcements for random configurations. Therefore, for biomedical implant applications nanocomposite materials can be designed with the same dimensional form but with lower compositions of filler materials by simply manipulating the appropriate orientations.

Analytical model for the prediction of the piezoresistive behavior of CNT modified polymers

Abstract In this work a theoretical and experimental study is carried out on the piezoresistive behavior of CNT modified polymers. A novel and easy-to-be applied analytical model is developed, to predict the piezoresistive response of CNT modified polymers, where the conductive network of CNTs within the polymeric matrix is modelled accounting for the three-dimensional random orientation of the nanofiller, the CNT waviness and entangling, and the electrical properties of the material in the undeformed state. Then, the analytical estimations are compared with the results from new experimental tests on specimens made of multi-walled CNT modified thermosetting matrix as well with data taken from the literature, showing a good agreement.

Spectrally Consistent Scattering, Absorption, and Polarization Properties of Atmospheric Ice Crystals at Wavelengths from 0.2 to 100 μm

Abstract A data library is developed containing the scattering, absorption, and polarization properties of ice particles in the spectral range from 0.2 to 100 μm. The properties are computed based on a combination of the Amsterdam discrete dipole approximation (ADDA), the T-matrix method, and the improved geometric optics method (IGOM). The electromagnetic edge effect is incorporated into the extinction and absorption efficiencies computed from the IGOM. A full set of single-scattering properties is provided by considering three-dimensional random orientations for 11 ice crystal habits: droxtals, prolate spheroids, oblate spheroids, solid and hollow columns, compact aggregates composed of eight solid columns, hexagonal plates, small spatial aggregates composed of 5 plates, large spatial aggregates composed of 10 plates, and solid and hollow bullet rosettes. The maximum dimension of each habit ranges from 2 to 10 000 μm in 189 discrete sizes. For each ice crystal habit, three surface roughness conditions (i.e., smooth, moderately roughened, and severely roughened) are considered to account for the surface texture of large particles in the IGOM applicable domain. The data library contains the extinction efficiency, single-scattering albedo, asymmetry parameter, six independent nonzero elements of the phase matrix (P11, P12, P22, P33, P43, and P44), particle projected area, and particle volume to provide the basic single-scattering properties for remote sensing applications and radiative transfer simulations involving ice clouds. Furthermore, a comparison of satellite observations and theoretical simulations for the polarization characteristics of ice clouds demonstrates that ice cloud optical models assuming severely roughened ice crystals significantly outperform their counterparts assuming smooth ice crystals.

Percolation threshold of conducting polymer composites containing 3D randomly distributed graphite nanoplatelets

An improved analytical model is developed based on the average interparticle distance (IPD) concept to predict the percolation threshold of conducting polymer composites containing disc-shaped nanoparticles with high aspect ratios. Two different conditions were taken into account in the model in terms of particle distribution, namely two- and three-dimensional random orientations. A 10 nm interparticle distance is adopted as the electrical conducting criterion according to the tunneling mechanism, and the percolation threshold is estimated as a function of geometric shape of the nanoparticle. A parametric study suggests that the thickness and diameter of fillers are important factors that determine the percolation threshold of conducting nanocomposites. The accuracy and the applicability of the present IPD model are verified by comparing with several existing models and experimental data for graphite nanoplatelet reinforced polymer nanocomposites. It is shown that the current model presents much better agreement with experimental results than existing models.

Laminated nanocrystalline soft underlayers for perpendicular recording

Media with laminated [Fe(Ta,Ti,Nb)C/Ta]n=2–4 soft magnetic underlayers (SULs) were prepared, and the effect of lamination on spike noise was investigated. Cross-sectional transmission electron microscopy observation revealed that nanocrystalline layers, composed of α-Fe grains with three-dimensional random orientation, were physically separated by 2.5-nm-thick Ta layers. Laminated SULs had low coercivities, i.e., less than 0.2 Oe, when the total thickness of the SUL ranged from 200 to 400 nm and the thickness of each nanocrystalline layer was more than 50 nm. These low coercivities are probably due to magnetostatic interaction between adjacent nanocrystalline layers. The medium with a laminated SUL showed much lower spike noise than the medium with a single-layer SUL. It is thought that magnetostatic interaction can reduce the stray field from the SUL, and result in a decrease in spike noise.

Some closed-form solutions for effective moduli of composites containing randomly oriented short fibers

This investigation presents an approach to obtain the effective moduli of both two- and three-dimensional, randomly oriented composites in terms of the shape and volume fraction of fibers. The composite fiber is treated as an spheroidal inclusion that enables its geometry ranging from short fiber to continuous fiber. To simulate spatial fiber orientation, a probability density function controlled by two Euler angles is introduced. Furthermore, based upon the Mori-Tanaka mean-field theory to account for the interaction between the fibers and matrix, an analytical approach is developed to assess the effective moduli of composites containing randomly oriented short fibers. In particular, when the fibers are uniformly distributed over a given region, closed-form solutions for the effective moduli of a two-phase composite are obtained for four special distributions of fiber orientations. Both two- and three-dimensional random orientations, resulting respectively in a transversely isotropic and a fully isotropic composite, are analyzed explicitly. Numerical examples have been given for an E-Glass/Epoxy composite. Analysis results indicate that the effective moduli are strongly affected by the volume fraction, the aspect ratio, and the orientation of fibers.

Some direction-dependent properties of matrix-inclusion type composites with given reinforcement orientation distributions

A Mori-Tanaka mean-field approach for predicting the overall thermoelastic properties of multi-phase composites with given orientation distributions of the inclusion phases is used to study the influence of the inclusion orientation distribution on the effective material properties. The aim of this study is primarily to understand the effects of the inclusion orientations in short-fiber-reinforced composites and to identify the basic mechanisms of interaction between the phases which govern the overall thermoelastic behavior. Perfectly aligned discontinuous fibers, various orientation distributions as well as two-dimensional and three-dimensional random orientations of the inclusions are studied. The overall Young's moduli, shear moduli and coefficients of thermal expansion, as well as the onset of yielding of the matrix phase under thermal and mechanical loading conditions, are calculated. The results are evaluated both in terms of the orientation distributions of the inclusions and in terms of the direction dependences of the predicted overall moduli. From these findings useful information on the appropriate requirements for the design of composite materials and composite structures can be obtained.

Leaf anatomy and ultrastructure of the Crassulacean-acid-metabolism plant Kalanchoe daigremontiana

Light-microscopic analysis of leaf clearings of the obligate Crassulacean-acid-metabolism (CAM) species Kalanchoe daigremontiana Hamet et Perr. has shown the existence of unusual and highly irregular venation patterns. Fifth-order veins exhibit a three-dimensional random orientation with respect to the mesophyll. Minor veins were often observed crossing over or under each other and over and under major veins in the mesophyll. Paraffin sections of mature leaves show tannin cells scattered throughout the mesophyll rather evenly spaced, and a distinct layer of tannin cells below the abaxial epidermis. Scanning electron microscopy showed that bundle-sheath cells are distinct from the surrounding mesophyll in veins of all orders. Transmission electron microscopy demonstrated developing sieve-tube elements in expanded leaves. Cytosolic vesicles produced by dictyosomes undergo a diurnal variation in number and were often observed in association with the chloroplasts. These vesicles are an interesting feature of cell ultrastructure of CAM cells and may serve a regulatory role in the diurnal malic-acid fluctuations in this species.

Effective Stiffness of Randomly Oriented Fibre Composites

This paper is concerned with the theoretical derivation of the effective stiffness properties for two types of randomly oriented fibre systems: (a) A system with completely three-dimensional random orientation of fibres in an isotropic matrix phase; (b) A system with two-dimensional (planar) random orientation of fibres in an isotropic matrix phase, appropriate to thin sections in a state of plane stress. The formulas derived predict the effective isotropic properties of the composite in terms of the elastic properties of each phase and the volume concentration of the fibre phase. These results provide the theoretical limits with which experimental results can be compared to assess the effectiveness of bonds, dispersion of fibres and any other factors which may affect the performance. In the last section a comparison is made with experimental results. In addition, the relation of the present study to pre vious work on this topic is discussed.

Effective Stiffness of Randomly Oriented Fibre Composites

This paper is concerned with the theoretical derivation of the effective stiffness properties for two types of randomly oriented fibre systems: (a) A system with completely three-dimensional random orientation of fibres in an isotropic matrix phase; (b) A system with two-dimensional (planar) random orientation of fibres in an isotropic matrix phase, appropriate to thin sections in a state of plane stress. The formulas derived predict the effective isotropic properties of the composite in terms of the elastic properties of each phase and the volume concentration of the fibre phase. These results provide the theoretical limits with which experimental results can be compared to assess the effectiveness of bonds, dispersion of fibres and any other factors which may affect the performance. In the last section a comparison is made with experimental results. In addition, the relation of the present study to pre vious work on this topic is discussed.