Rotation statistics of fibers in wall shear turbulence

In this paper, the rotation of rigid fibers is investigated for the reference case of turbulent channel flow. The aim of the study is to examine the effect of local shear and turbulence anisotropy on the rotational dynamics of fibers with different elongation and inertia. To this aim, statistics of the fiber angular velocity, Ω, are extracted from direct numerical simulation of turbulence at shear Reynolds number Re _τ = 150 coupled with Lagrangian tracking of prolate ellipsoidal fibers with Stokes number, St, ranging from 3 to 100 and aspect ratio, λ, ranging from 1 to 50. Accordingly, the fiber-to-fluid density ratio ranges from ${S \simeq 7}$ S ? 7 (for St = 1, λ = 50) to ${S \simeq 3, 470}$ S ? 3 , 470 (for St = 100, λ = 1). Statistics are compared one to one with those obtained for spherical particles to highlight effects due to elongation. Results for mean and fluctuating angular velocities show that elongation is important for fibers with small inertia (St ≤  5 in the present flow-fiber combination). For fibers with larger inertia, elongation has an impact on fiber rotation only in the streamwise and wall-normal directions, where mean values of Ω are zero. It is also shown that, in the center of the channel, the Lagrangian autocorrelation coefficients of Ω and corresponding rotational turbulent diffusivities match the exponential behavior predicted by the theory of homogeneous dispersion. In this region of the channel, the probability density function of fiber angular velocities is generally close to Gaussian, indicating that particle rotation away from solid walls can be modeled as a diffusion process of the Ornstein–Uhlenbeck type at stationary state. In the strong shear region (comprised within a distance of 50 viscous units from the wall in the present simulations), fiber anisotropy adds to flow anisotropy to induce strong deviations on fiber rotational dynamics with respect to spherical particles. The database produced in this study is available to all interested users at https://www.fp1005.cism.it.     

Numerical Study of Particle Dispersion in the Wake of Two Tandem Square Cylinders Using Discrete Vortex Method

This study has been conducted to investigate numerically the particle dispersion in the wake of dilute particle-laden gas flows past two identical square cylinders in tandem arrangement at Reynolds number of 10,000,000. In the numerical method, the discrete vortex method is employed to calculate the gas flow fields, and the Lagrangian approach is applied to track individual solid particles. A dispersion function is defined to represent the lateral dispersion scale of particles. The wake vortex patterns and the distributions of particles with various Stokes numbers ranging from 0.01 to 10 are obtained. The numerical results reveal that: (1) the particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas the particles with St = 1.0, 10 congregate mainly around the vortex periphery; (2) the particles with St = 0.01, 0.1 are trapped by the vortices into the gap between the two square cylinders, while very few particles with St = 1.0, 10 are distributed within the gap; (3) the particle's dispersion intensity along the lateral direction decreases greatly as St is increased from 0.01 to 10.     

Surface modification of fiber reinforced polymer composites and their attachment to bone simulating material

The purpose of this study was to investigate the effect of fiber orientation of a fiber-reinforced composite (FRC) made of poly-methyl-methacrylate (PMMA) and E-glass to the surface fabrication process by solvent dissolution. Intention of the dissolution process was to expose the fibers and create a macroporous surface onto the FRC to enhance bone bonding of the material. The effect of dissolution and fiber direction to the bone bonding capability of the FRC material was also tested. Three groups of FRC specimens (n = 18/group) were made of PMMA and E-glass fiber reinforcement: (a) group with continuous fibers parallel to the surface of the specimen, (b) continuous fibers oriented perpendicularly to the surface, (c) randomly oriented short (discontinuous) fibers. Fourth specimen group (n = 18) made of plain PMMA served as controls. The specimens were subjected to a solvent treatment by tetrahydrofuran (THF) of either 5, 15 or 30 min of time (n = 6/time point), and the advancement of the dissolution (front) was measured. The solvent treatment also exposed the fibers and created a surface roughness on to the specimens. The solvent treated specimens were embedded into plaster of Paris to simulate bone bonding by mechanical locking and a pull-out test was undertaken to determine the strength of the attachment. All the FRC specimens dissolved as function of time, as the control group showed no marked dissolution during the study period. The specimens with fibers along the direction of long axis of specimen began to dissolve significantly faster than specimens in other groups, but the test specimens with randomly oriented short fibers showed the greatest depth of dissolution after 30 min. The pull-out test showed that the PMMA specimens with fibers were retained better by the plaster of Paris than specimens without fibers. However, direction of the fibers considerably influenced the force of attachment. The fiber reinforcement increases significantly the dissolution speed, and the orientation of the glass fibers has great effect on the dissolving depth of the polymer matrix of the composite, and thus on the exposure of fibers. The glass fibers exposed by the solvent treatment enhanced effectively the attachment of the specimen to the bone modeling material.     

考虑纤维方向分布的玻纤增强PP复合材料拉伸性能

纤维方向及其分布对玻纤增强PP复合材料的力学特性具有至为关键的影响。提出了一种快速获取纤维数量及每根纤维方向的方法。通过引入方向张量, 利用Moldflow软件进行玻纤增强PP树脂注塑成型模拟获得纤维方向的平均分布, 结合显微方法观察判断特定点的纤维沿厚度方向的分层情况及定量判断纤维方向的分布。对轿车玻璃纤维增强注塑仪表板的纤维方向相对一致处取与纤维方向呈0°、45°、90°的样条, 通过拉伸实验测得拉伸模量, 利用所提出的方法研究了仪表板内玻纤方向的分布及其对拉伸模量的影响。研究结果表明: 玻纤增强注塑仪表板的力学性能是各向异性的, 其沿厚度方向纤维按方向大致可分为三层。     

Prediction of fiber orientation structure for injection molded short fiber composites

Structure of fiber orientation in injection molded short fiber composites is predicted by the numerical analysis. To analyze the packing stage as well as the filling stage, a compressible generalized Hele-Shaw model is adopted. A numerical scheme free from coordinate transformation is developed for three-dimensional shell-like geometry. Flow-induced fiber orientation can be predicted by solving evolution equations for the orientation tensor with a suitable closure approximation. Fibers are mainly oriented toward the flow direction near the top cavity wall due to high shear rates, while they are randomly oriented near the centerline of cavity where low shear rates prevail. Thus, the molded parts show the skin-core structure of orientation. Structure of fiber orientation continues to change during the packing stage due to additional velocity gradients – which are likely to align fibers more towards the flow direction. Electronic Publication     

Synthesis of organ-soluble copolyimides by one-step polymerization and fabrication of high performance fibers

A series of organ-soluble copolyimides (co-PIs) were synthesized from 3,3′,4,4′-benzophenonetetracarboxylic dianhydride (BTDA), 2,2′-bis(trifluoromethyl)-4, 4′-diaminobiphenyl (TFMB), and 2-(4-aminophenyl)-5-aminobenzimidazole (BIA) via a one-step polymerization in N-methyl-2-pyrrolidone (NMP). The polyimide solutions were used to fabricate as-spun polyimide fiber by a wet-spinning process. SEM images of the round cross-section of the fibers indicated that a homogeneous and dense fibrous structure was produced in the coagulation bath of H₂O/NMP = 90/10 (v/v) and many microfibrils appeared on the surface. The drawn fibers exhibit excellent mechanical properties, and the strength and modulus of BTDA/TFMB/BIA co-PI fibers (TFMB/BIA = 50/50) reached 2.25 and 102 GPa with a draw ratio of 3.0. The 5 % weight loss temperature of the co-PI fibers in thermogravimetric analysis spectra achieved 548–563 °C in an air atmosphere. The glass transition temperatures were found to be between 340 and 366 °C according to the DMA results. Annealed BTDA/TFMB/BIA co-PI fibers displayed distinct wide-angle X-ray patterns, and crystallinity and crystal orientation with various draw ratios were observed.     

Characterization of fiber orientation in short fiber reinforced composites with an image processing technique

An experimental method is developed to measure the three-dimensional fiber orientation in short fiber reinforced composites by utilizing an image processing technique. The second order orientation tensor can be calculated with geometrical data that were obtained from two parallel planar cross-sections. The orientation state of individual fibers is determined from the geometry of the elliptical cross-sectional shape on the polished surface. The basic concept in determining the three-dimensional fiber orientation tensor is to slice the composite sample twice in the same direction within a small distance. The tensor is determined by using a digital image processing technique and a computational code which calculates the tensor from the geometrical characteristics obtained for the elliptical fiber cross-sections. Experiments are performed to measure the three-dimensional orientation tensor of composite specimens and good results are obtained by using the method proposed in this study Electronic Publication     

Direct Monte Carlo simulation of turbulent drag reduction by rigid fibers in a channel flow

A two-way coupled simulation technique for a dilute suspension of rigid fibers in turbulent flows is proposed. It is based on an Eulerian direct numerical simulation of the incompressible Navier–Stokes equations and a Lagrangian direct Monte Carlo simulation of the fiber orientational conformation. The numerical methods are explained in detail. The developed simulation tool is employed to study the turbulent drag reduction by rigid fibers in a fully developed channel flow at a nominal shear Reynolds number Re _τ = 180. We use 128³ grid cells to resolve the Eulerian field and 6.55 × 10⁷ Lagrangian particle clusters each of which containing 100 fibers to compute the fiber conformation. This results in a total number of 6.55 × 10⁹ fibers. Turbulence statistics of the fibrous drag-reduced channel flow using a direct solver are reported for the first time. Previously reported features of a fibrous drag-reduced channel flow are confirmed by our simulation. We present the mean flow quantities. In particular, turbulence intensities are investigated by considering the probability density function of the fluctuating velocities.     

A study of a flexible fiber model and its behavior in DNS of turbulent channel flow

The dynamics of individual flexible fibers in a turbulent flow field have been analyzed, varying their initial position, density and length. A particle-level fiber model has been integrated into a general-purpose, open source computational fluid dynamics code. The fibers are modeled as chains of cylindrical segments connected by ball and socket joints. The equations of motion of the fibers contain the inertia of the segments, the contributions from hydrodynamic forces and torques, and the connectivity forces at the joints. Direct numerical simulation of the incompressible Navier–Stokes equations is used to describe the fluid flow in a plane channel, and a one-way coupling is considered between the fibers and the fluid phase. We investigate the translational motion of fibers by considering the mean square displacement of their trajectories. We find that the fiber motion is primarily governed by velocity correlations of the flow fluctuations. In addition, we show that there is a clear tendency of the thread-like fibers to evolve into complex geometrical configurations in a turbulent flow field, in fashion similar to random conformations of polymer strands subjected to thermal fluctuations in a suspension. Finally, we show that fiber inertia has a significant impact on reorientation timescales of fibers suspended in a turbulent flow field.     

Fatigue behavior and modeling of short fiber reinforced polymer composites including anisotropy and temperature effects

Effects of anisotropy and temperature on cyclic deformation and fatigue behavior of two short glass fiber reinforced polymer composites were investigated. Fatigue tests were conducted under fully-reversed (R = −1) and positive stress ratios (R = 0.1 and 0.3) with specimens of different thicknesses, different fiber orientations, and at temperatures of −40 °C, 23 °C, and 125 °C. In samples with 90° fiber orientation angle, considerable effect of thickness on fatigue strength was observed. Effect of mold flow direction was significant at all temperatures and stress ratios and the Tsai–Hill criterion was used to predict off-axis fatigue strengths. Temperature also greatly influenced fatigue strength and a shift factor of Arrhenius type was developed to correlate fatigue data at various temperatures, independent of the mold flow direction and stress ratio. Micromechanisms of fatigue failure at different temperatures were also investigated. Good correlations between fatigue strength and tensile strength were obtained and a method for obtaining strain–life curves from load-controlled fatigue test data is presented. A fatigue life estimation model is also presented which correlates data for different temperatures, fiber orientations, and stress ratios.     

Flow-induced fiber orientation in gas-assisted injection molded part

Polyamide 66 with 33 wt.% glass fiber (DuPont, Zytel 70G33) was molded by gas-assisted injection molding (GAIM). Scanning electron microscope (SEM) micrographs indicated that fibers orientated notably in the core layer and slightly in the region near the mold wall, but aligned disorderly in the region near the gas channel. However, fibers orientated remarkably in the center of the thickness of the GAIM part, which was greatly different from the fiber orientation behavior in the samples molded by the conventional injection molding (CIM) and the water-assisted injection molding (WAIM) as reported in the literatures. Combining with a previous simulation dealing with gas penetration, the mechanisms for fiber orientation in the GAIM part are also discussed.     

Fiber distribution and orientation in UHP-FRC beams and their effect on backward analysis

In this study 23 ultra-high performance fiber reinforced concrete (UHP-FRC) notched beams were tested in order to investigate the effect of fiber orientation and distribution on the bending behavior. Due to the small fiber diameter and high fiber volume fraction used in UHP-FRC, the number of fibers crossing a 150 × 150 mm (6 × 6 in.) beam section can be as high as 26,000. An opto-analytical method was used to investigate the number and orientation of the fibers near the critical crack in each test beam. For the casting method used, which was in accordance with the recommendation of Association Francaise de Genie Civil (AFGC) and Service d’etudes techniques des routes et autoroutes (SETRA), a high degree of uniformity in fiber distribution and orientation was found over the beam cross section. Based on the analytically determined fiber orientation and distribution, shape functions were derived that take into account variations over the beam height. The proposed shape functions were incorporated in a backward analysis of the results from bending tests to estimate the uniaxial tensile behavior of the UHP-FRC used. The sensitivity of the backwardly calculated tensile behavior of UHP-FRC to variations in fiber density and orientation was evaluated. Based on the bending test results of the notched beam specimens, and for the casting method used in this research, the influence of these variations on the backwardly calculated tensile strength was found to be small, with a maximum stress variation of ~5 % for any given crack width.     

Electrospinning highly oriented and crystalline poly(lactic acid) fiber mats

In recent years, there has been an increased focus on sustainable, green alternatives with similar properties to conventional petroleum-based polymers. Poly(lactic acid) (PLA) is a biodegradable biopolymer which exhibits mild piezoelectric properties and has good processability which gives it potential for use in numerous existing and novel applications. The purpose of this study was to produce highly oriented and crystalline PLA electrospun fiber mats for piezoelectric applications. In order to yield a high piezoelectric constant, high crystallinity and fiber orientation are necessary. A two parallel collector set up was used to mechanically orient the fibers in the space between two copper electrodes. Voltage and feed rate were adjusted to produce smooth, oriented fibers with average diameters ranging 0.73–1.19 μm. Crystallinity and orientation were increased via hot drawing of the fiber mats and were maximized between 40 and 50 % and greater than 50 %, respectively.     

Asymptotic analysis of the viscous micro/nano pump at low Reynolds number

The steady viscous parabolic flow past an eccentrically placed rotating cylinder is studied in the asymptotic limit of small Reynolds number. It is assumed that the flow around the rotating cylinder undergoes boundary slip described by the Navier boundary condition. This involves a single parameter to account for the slip, referred to as the slip length ?, and replaces the standard no-slip boundary condition at solid boundaries. The streamlines for ? > 0 are closer to the body than for ? = 0, and it is discovered that the loss of symmetry due to the rotation of the cylinder is significantly reduced by the inclusion of slip. This arises as a result of a balance between the rotation velocity and the slip velocity on that portion of the cylinder which rotates opposite to the free-stream flow. Streamline patterns for nonzero eccentricity partially agree with Navier–Stokes simulations of the viscous pump; the small discrepancy is primarily due to the fact that here wall effects are not explicitly considered. Expressions for the frictional drag and the torque on the cylinder are obtained. The expression for the torque agrees well with the lubrication solution for the flow past a rotating cylinder placed symmetrically in a fully developed channel flow. The results presented here may be used to validate numerical schemes developed to study the viscous pump.     

Optimal fiber distribution for tensile properties of injection molded composite

The survival rate of a composite is the residual fiber length divided by the initial fiber length, and it decreases with the initial fiber length and fiber volume content (V_f) during injection molding processes. The degree of damage is higher for carbon fiber than for glass fiber, and the survival rate increases with a hyperbolic tangent relationship as the nozzle diameter increases. Higher survival rate corresponds to a stronger material. Five different lengths of fiber with 29 different size fibers were selected based on the distribution and shape of residual fiber in experimental works. These were examined to study the effects of fiber distribution on the tensile properties of a short-fiber reinforced composite (SFRC). Compared with the experimental results, the modulus predicted using the Halpin-Tsai relation shows reasonable agreement with the prediction obtained using the residual fiber length instead of the initial fiber length. It was found that the tensile modulus and strength generally differ by a factor of up to 3.2, depending on the fiber distribution patterns with V_f = 30%, and the trend is more significant as the fiber aspect ratio increases. The interactions between the fiber and matrix and the staggered-type distribution are the most important factors in the reinforcement of the SFRC. With the same combination of short fiber length, an optimized fiber distribution pattern is suggested.     

Bearing strength of commingled boron/glass fiber reinforced aluminum laminates

The bearing properties of recently developed hybrid fiber/metal laminates, or COmmingled Boron/glass fiber Reinforced Aluminum laminates (COBRA), are investigated in this study. The bolt-type bearing tests on GLass REinforced aluminum laminates (GLARE), non-commingled hybrid boron/glass/aluminum fiber/metal laminates (HFML) and COBRA were carried out as a function of e/D ratio, metal volume fraction, fiber volume fraction, and fiber orientation. Experimental results show that with the same joint geometry and metal volume fraction, the commingling of boron fibers improves the bearing strength of fiber/metal laminates. Observations show the boron/glass fiber prepreg, transverse to the loading direction, results in a bearing mechanism that effectively increases the bearing strength. The bearing strength of COBRA with longitudinal fibers is lower than that with transverse fibers due to the fact that shearout failure takes place before maximum bearing strength is reached. The experimental results show that, with only either transverse fiber orientation or longitudinal fiber orientation, COBRA with 18% boron fiber volume fraction possesses a higher bearing strength when compared to HFML with 6% boron fiber volume fraction. In addition to the properties in COBRA with parallel-plies commingled prepreg, the bearing properties of various COBRA with [0°/90°] and [0°/90°/90°/0°] cross-ply commingled prepregs are also discussed.     

Stokes shape factor for lactose crystals

The alpha-lactose crystal has a tomahawk shape which needs to be accounted for when designing settling equipment. A shape factor can be used to achieve this. A variety of shape factors have been used for lactose crystals in the literature. This paper sets out to experimentally determine a shape factor for lactose. Large undamaged tomahawk shaped lactose crystals were grown in a lactose agar gel and then recovered for use in settling experiments. Typical industry produced crystals were also tested for comparison. Settling experiments enabled the calculation of a Stokes settling diameter, the diameter of a sphere with the same density and settling velocity as the tomahawk shaped lactose crystal. Using crystal mass to calculate equivalent particle volume and Stokes diameter, the Stokes shape factor for lactose gel-grown crystals was calculated to be 0.99. A Stokes height factor (B_St) was formulated which, when multiplied by the height of the lactose crystal, gives the Stokes settling diameter. The lactose B_St value was determined to be 0.595 ± 0.007 and 0.643 ± 0.008 for gel-grown and plant-grown lactose crystals, respectively.     

Effect of hot stretching graphitization on the structure and mechanical properties of rayon-based carbon fibers

The influence of hot stretching graphitization on the structure and mechanical properties of rayon-based carbon fibers was studied. It was observed that the Young’s modulus of the treated fibers increased with heat treatment temperature (HTT) and hot stretching stress, to 173 GPa by 158.2 % through hot stretching at 2700 °C under stress of 270 MPa compared to that of the as-received carbon fiber. Meanwhile the tensile strength increased to 1.75 GPa by 73.3 % through hot stretching at 2700 °C under 252 MPa. The field emission scanning electron images showed markedly increased roughness on the external surface and bigger and more compacted granular morphologies on the cross section of the treated fibers with increasing HTT. The preferred orientation of graphitic layers was improved by hot stretching, and the higher the HTT, the stronger the effectiveness of the hot stretching. The crystallite sizes grew and the crystallite interlayer spacing decreased obviously with increasing HTT but changed just slightly with increasing stretching stress. The analysis based on uniform stress model and shear fracture theory proposed that the improvement of tensile strength and Young’s modulus for rayon-based carbon fiber was mainly due to the increased preferred orientation and nearly unchanged shear modulus between planes with increasing HTT during hot stretching graphitization, which was much different from polyacrylonitrile-based carbon fibers.     

Fatigue of a 3D Orthogonal Non-crimp Woven Polymer Matrix Composite at Elevated Temperature

Tension-tension fatigue behavior of two polymer matrix composites (PMCs) was studied at elevated temperature. The two PMCs consist of the NRPE polyimide matrix reinforced with carbon fibers, but have different fiber architectures: the 3D PMC is a singly-ply non-crimp 3D orthogonal weave composite and the 2D PMC, a laminated composite reinforced with 15 plies of an eight harness satin weave (8HSW) fabric. In order to assess the performance and suitability of the two composites for use in aerospace components designed to contain high-temperature environments, mechanical tests were performed under temperature conditions simulating the actual operating conditions. In all elevated temperature tests performed in this work, one side of the test specimen was at 329 °C while the other side was open to ambient laboratory air. The tensile stress-strain behavior of the two composites was investigated and the tensile properties measured for both on-axis (0/90) and off-axis (±45) fiber orientations. Elevated temperature had little effect on the on-axis tensile properties of the two composites. The off-axis tensile strength of both PMCs decreased slightly at elevated temperature. Tension-tension fatigue tests were conducted at elevated temperature at a frequency of 1.0 Hz with a ratio of minimum stress to maximum stress of R = 0.05. Fatigue run-out was defined as 2 × 10⁵ cycles. Both strain accumulation and modulus evolution during cycling were analyzed for each fatigue test. The laminated 2D PMC exhibited better fatigue resistance than the 3D composite. Specimens that achieved fatigue run-out were subjected to tensile tests to failure to characterize the retained tensile properties. Post-test examination under optical microscope revealed severe delamination in the laminated 2D PMC. The non-crimp 3D orthogonal weave composite offered improved delamination resistance.     

Effect of chromium carbide coating on thermal properties of short graphite fiber/Al composites

A chromium carbide coating was synthesized onto graphite fibers by molten salts method to improve the interfacial bonding and thermal properties of short graphite fiber/Al composites which were fabricated by vacuum pressure infiltration technique. The graphite fiber/Al composites with different thicknesses of chromium carbide coatings were prepared through varying plating times to investigate the influence of chromium carbide layer on the microstructures and thermal properties of the composites. The combined Maxwell–Garnett effective medium approach and acoustic mismatch model schemes were used to theoretically predict thermal conductivities of the composites. The results indicated that the chromium carbide coating formed on graphite fiber surface in molten salts consists mainly of the Cr₇C₃ phase. The Cr₇C₃-coating layer with plating time of 60 min and thickness of 0.5 μm was found to be most effective in improving the interfacial bonding and decreasing the interfacial thermal resistance between graphite fiber and aluminum matrix. The 40 vol% Cr₇C₃-coated graphite fiber/Al composite with Cr₇C₃ thickness of 0.5 μm exhibited 45.4 % enhancement in in-plane thermal conductivity of 221 W m^?1 K^?1 compared to that of uncoated composite, as well as the coefficient of thermal expansion of 9.4 × 10^?6 K^?1, which made it as very interesting material for thermal management applications.