Fiber Volume Fraction Distribution Research Articles

A scale-span method to characterize the mechanical property of BCF/PEEK considering uncertain structural characteristics

The focus of this study is exploring a scale-span characterization method to predict the mechanical properties of Braided Carbon Fiber Reinforced Poly Ether Ether Ketone (BCF/PEEK) considering structural uncertainty. Firstly, a complicated micro-scale Representative Volume Element (RVE) model that considers the random position and size of fiber was established via the developed Python script. Analogously, a mathematical expression adopted by the trust region algorithm was proposed to accurately describe the detailed cross-sectional shapes and fluctuation amplitude characteristics of BCF/PEEK for the sake of establishing the precision meso-scale RVE model. Then, the corresponding elastic properties that consider fiber volume fraction and fiber distribution location were characterized via the span-scale characterization method. Meanwhile, the influence of fiber bundle fluctuation amplitude and fiber volume fraction on the mechanical properties was investigated as well. In addition, the mechanical properties of BCF/PEEK with the change of the braid angle between warp and weft yarn were predicted via the established meso-scale RVE model. Finally, a series of experiments have been carried out. The maximum and minimum absolute prediction deviation of all elastic property parameters were only 4.07 % and 1.41 %, respectively, which verified the proposed scale-span characterization method can predict the mechanical properties of composites well.

A micromechanical study on shear performance of unidirectional composites with randomly distributed fibers in the transverse cross‐section

AbstractThe properties of unidirectional (UD) composites has been investigated by analyzing their elastic and strength characteristics under shear loading. The UD fiber‐reinforced polymer (FRP) composites usually consist of fibers randomly dispersed throughout the cross‐section in the transverse direction which is generally not accounted for. A micromechanical model based on finite element analysis (FEA) approach is utilized here to examine these properties. The study begins by identifying micro scale unit cells or repetitive unit cells (RUCs) at the micro scale, as well as representative volume elements (RVEs). The distribution of fiber volume fraction (Vf) varies among various micro scale unit cells positioned in the transverse cross‐section. The elastic properties and strength are estimated by considering the properties of the matrix and fibers, and the configuration of micro scale unit cells, which feature a fiber arrangement which is categorized as hexagonal and varying Vf at different locations (from 0.35 to 0.75). However, the overall Vf for the UD composite remains constant at 0.65. Studies are also carried out with the random distribution of fibers at micro scale unit cells. The findings reveal that the random distribution of fibers significantly impacts the shear behavior of the composite. This investigation provides valuable insights into how the mechanical properties of the UD composite are subjective by the distribution of fiber, thereby contributing to the design and development of this light weight high‐performance material.Highlights Elastic and strength analysis of UD composites is presented. Emphasis is on fiber dispersion in transverse plane. Microscale unit cells, RUCs and RVE are identified. Studies are carried out based on micromechanical model. Influence of fiber distribution on shear behavior is investigated.

Accounting for mesoscale geometry and intra-yarn fiber volume fraction distribution on 3D angle-interlock fabric permeability

Understanding resin flows within 3D interlock fabrics involves addressing a dual-scale flow problem. Indeed, the fluid can flow through inter-yarn channels, characterized by a unit cell mesoscale morphology, but also within yarns considered as homogeneous equivalent porous media. The former is assumed to follow the Stokes’ law while the latter be related to the Darcy’s law, directly linked to the microscopic intra-yarn fiber volume fraction (FVF) field. In this work, a coupled Stokes–Darcy steady-state flow within a 3D woven textile, modeled at mesoscale, is solved through a finite element monolithic approach with a mixed velocity-pressure formulation, stabilized by the Variational MultiScale Method (VMS) and implemented in the Z-set software. The fabric permeability tensor is then computed without any assumptions on its nature and analyzed both through its diagonal components, its eigenvectors and eigenvalues. The main contribution of this study lies in examining the influence of variations of the inter-yarn porous medium morphology, through textile compaction and geometrical reduction to prevent edge flows, and the intra-yarn permeability (from complete field to unique value) on the overall fabric permeability.

Effect of distribution of fiber volume fraction and resin-rich layer through thickness on stiffness of composite lattice structures

Effect of distribution of fiber volume fraction and resin-rich layer through thickness on stiffness of composite lattice structures

Self-consistent homogenization-based parametrically upscaled continuum damage mechanics model for composites subjected to high strain-rate loading

This paper develops a Parametrically Upscaled Continuum Damage Mechanics (PUCDM) model for carbon fiber/epoxy matrix composites subjected to high strain-rate loading. The PUCDM model for predicting high strain-rate induced deformation and damage evolution at the macroscopic scale, explicitly incorporates microstructural morphology and micro-inertia in its constitutive coefficients. It is developed using self-consistent homogenization that uses a concurrent multiscale model to account for the effect of micro-inertia and stress wave interaction with the microstructure. The concurrent model embeds a statistically equivalent representative volume element (SERVE) of the microstructure in an exterior domain, whose constitutive and damage response are described by the PUCDM model. Micromechanical modeling for the composite microstructure involves a unified cohesive zone enhanced phase-field damage model for fiber-matrix interface debonding, fiber breakage, and matrix cracking. The PUCDM model parameters for the upscaled domain are determined through micro-macro-scale energy equivalence, along with traction reciprocity and displacement continuity at the SERVE-exterior domain interface that are enforced using a Lagrange multiplier-based approach. Simulations using the concurrent model analyze stress wave propagation and damage evolution in composite microstructures with three different fiber volume fractions at multiple strain rates in the range of 102 − 105 s−1. The fiber volume fraction and spatial distributions affect the overall stiffness and damage evolution in the PUCDM model. Results of the analysis demonstrate the need for representation of micro-inertia, strain rates and microstructure morphology in the PUCDM-based stiffness and damage model parameters for high strain-rates above [Formula: see text].

A universal transfer-learning-based detection model for characterizing vascular bundles in Phyllostachys

A comprehensive understanding of vascular bundles is the key to elucidate the excellent intrinsic mechanical properties of bamboo. This research aims to investigate the gradient distribution of fiber volume fraction and the gradient changes in the size of vascular bundles along the radial axis in Phyllostachys. The inter-nodes of twenty-nine kinds of Phyllostachys were collected, which the cross section was sanded by sanding pads with 320 mesh and scanned with a resolution of 9600 ppi. A universal transfer-learning-based vascular bundle detection model with high precision of up to 96.97% were built, which can help to obtain the characteristics of vascular bundles quickly and accurately. The total number of vascular bundles, total fiber sheath area, the length, width and area of fiber sheath of individual vascular bundles within the entire cross-section were counted and analyzed. The results showed that these parameters had a strongly positive linear correlation with the outer circumference and wall thickness of bamboo culms, but the fiber volume fraction (25.50 ± 3.51%) and the length-to-width ratio of the vascular bundles (1.226 ± 0.091) were relatively constant. Furthermore, the cross section of bamboo were divided into multi-layer sheet along the wall thickness direction and the characteristics of vascular bundle were counted in each layer. The results showed that the fiber volume fraction decreased exponentially along the radial direction from skin to core, the length-to-width ratio of vascular bundle decreased quadratically along the radial direction from skin to core, the width of vascular bundle increased linearly along the radial direction from skin to core. The trends of the gradient change in vascular bundle’s characteristics were found highly consistent among bamboo species in Phyllostachys.

A parameterized unit cell model for 3D braided composites considering transverse braiding angle variation

In this paper, a parameterized unit cell model for 3D braided composites considering transverse braiding angle variation is proposed, to assist the mechanical characterization of such materials. According to the geometric characteristics of 3D braided composites, a method for automatically generating textile geometries based on practical braiding parameters, including the main braiding angle, the transverse braiding angle, and the fiber volume fraction, is established and implemented in a CAD software package. In this model, the addition of transverse braiding angle educes a more flexible control of fiber volume fraction distribution, and with the combination of control parameters according to the actual fiber distribution needs of users, it can suggest the appropriate parameters for the unit cell. The generated unit cell models are used in finite element analysis and the results are validated against experiments for a number of 3D braided composites in terms of fiber volume fraction and elastic constants, and good agreement is observed. Based on the parameterized unit cell model, the effects of main braiding parameters on the elastic properties of 3D braided composites are discussed.

Intelligent analysis technology of bamboo structure. Part II: The variability of radial distribution of fiber volume fraction

Scientific and reasonable utilization of bamboo is strongly related to the radial distribution of the fiber volume fraction. In this paper, the K-means clustering algorithm was applied to set separate thresholds for individual vascular bundles, to solve the problem that the bamboo ring cannot be binarized well. We introduced a layered model based on the WEB coordinate system, programmed via JavaScript, to layer the cross-section within the entire bamboo conveniently and accurately. It allowed uniform layering of sample areas of any thickness, any width, and any number of layers. Furthermore, this research systematically studied the bamboo rings at the breast height of Moso bamboo [Phyllostachys edulis (Carr)H. de Lebaie] grown in 12 major producing areas of China and the 50-internode sections from base to top of one bamboo with the method mentioned above. The results indicated that the thickness of a single layer should not be higher than 0.4 mm while examining the gradient structure of bamboo. The radial distribution of fiber volume fraction from 12 areas all followed the ExpDec1 function, and the mean goodness of fit (R2) was 0.988. The radial distribution of fiber volume fraction in the first 45 sections from the base to the top corresponded to the ExpDec1 function. It provided a theoretical basis for the functional improvement of bamboo and the development of new bamboo-based smart materials.

Modeling the effective viscoelastic properties of PEEK matrix reinforced by arbitrary oriented short glass fibers

The aim of this work consists in estimating and modeling the viscoelastic behavior at small strain of KetaSpire® KT-880 PEEK fiber composites reinforced with short glass fibers. The viscoelastic behavior of the PEEK matrix is identified from a series of DMA tests at different temperatures. The principle of time–temperature superposition is used to build a master curve in order to identify the parameters of a generalized 13-branch Maxwell model. The composite’s master curves are constructed by using virtual DMA experiments. These master curves are used to identify a generalized, transversely isotropic Maxwell spectral law. The modulus of each branch of the model is linked to the characteristic time of the branch by a normal distribution function (spectral law), which allows drastically reducing the number of material parameters. Finally, a metamodel is built to estimate the behavior of the composite as a function of the microstructural parameters: fiber volume fraction and fiber orientation distribution function.

Experimental and computational analysis of structure-property relationship in carbon fiber reinforced polymer composites fabricated by selective laser sintering

A fundamental understanding of structure-property relationship of carbon fiber reinforced polymer (CFRP) composites fabricated by selective laser sintering (SLS) is essential to provide guidance to improve the mechanical properties in this promising additive manufacturing process. In the present study, we propose a new computational framework to evaluate the mechanical behavior of SLSed CFRP based on the representative volume element (RVE) model. Firstly, a new voxel-based fiber packing algorithm is proposed with the three-dimensional fiber orientation tensor to describe the fiber distribution. The porosity generated in the manufacturing process is also considered by adding spherical voids in the matrix region. In order to remove the artificial stress concentration induced by the voxel-based algorithm, a python script is developed to regenerate the geometries of different phases with conforming mesh. Meanwhile, the constitutive models of different phases in SLSed CFRP, i.e., matrix, fiber and interface, are established according to the material characteristics. Next, the proposed computational framework of SLSed CFRP is validated by the X-ray computed tomography (XCT) measurements and tensile tests of a representative SLSed carbon fiber/polyamide 12 (CF/PA12) composite. The effects of fiber volume fraction and fiber orientation distribution on the mechanical behavior of SLSed CF/PA12 composite are further quantitatively explored and ranked with regards to their influence on stiffness and failure strength.

Nonlinear thermal stability of temperature-dependent metal matrix composite shallow arches with functionally graded fiber reinforcements

The present article aims to study the non-linear equilibrium paths of an Al2O3 reinforced metal matrix composite (MMC) shallow arch in a thermal environment. The structure is made up of applicable industrial materials having temperature-dependent thermomechanical properties. In order to describe the configuration of shallow arch, two different geometrical models are implemented in which the first model has a symmetrical configuration but the second model has an unsymmetrical one. The concept of symmetric functionally graded (FG) material is implemented in the laminated composite arch by changing the volume fraction of fibers in each lamina. The elasticity tensor is created based on the plane-stress assumption and implementation of the rule of mixture. The mathematical modeling is developed using first-order shear deformation beam theory under specific assumptions i.e., geometrical nonlinearity, neutral axis concept, and uniform temperature gradient. Next, an analytical procedure is established to solve the three coupled nonlinear equilibrium equations for both clamped-clamped and simply-simply supporting conditions. The obtained exact solutions are capable of determining the critical temperature, in which the perturbed pitchfork bifurcation occurs, as well as the thermal equilibrium path of the structure. The influences of geometrical parameters (i.e., the initial curvature shape and amplitude, the thickness-to-length ratio, and the lamination sequences) as well as physical elements (i.e., matrix materials, fiber volume fraction distribution patterns, and temperature dependence of materials) on the thermal behavior of the system are examined. Eventually, in order to verify the analytical results presented in this study, a finite difference method-based numerical solution (bvp4c in Matlab software) is utilized to solve simultaneously the three coupled nonlinear governing equations.

Micro-computed tomography analysis of natural fiber and bio-matrix tubular-braided composites

There is an increasing demand for the use of “green”-based materials as reinforcement and matrix materials in composites. However, the ability of these natural-based materials to perform as consistently and reliably as conventional materials is still relatively unknown. A key importance in the viability of these materials is the evaluation of the content of voids and imperfections, which may affect the properties of the entire composite. In this study, the microstructure of tubular-braided composites manufactured from cellulose fibers and a partially bio-derived resin was studied with the use of micro-computed tomography. These methods were used to determine the effect of modifying braid angle, resin type, and curing method on fiber volume fraction, void volume, and void distribution. It was determined that the void content increased with the increase in braid angle, and vacuum-bagging reduced the total void content. The sample with the smallest braid angle produced with vacuum-bagged curing contained a void fraction of 1.5%. The results of this study proved that the materials used could be viable for further testing and development and that micro-computed tomography imaging is valuable for identifying how to improve consistency and minimize imperfections to create more accurate and reliable natural fiber-braided composites.

Effect of heterogeneous interphase on the mechanical properties of unidirectional fiber composites studied by FFT-based method

Based on representative volume element (RVE) with interphase region between fiber and matrix, the microscopic mechanical behavior of transversely randomly distributed unidirectional (UD) carbon fiber reinforced polymer composites is studied by using fast Fourier transforms (FFT) simulation. The change of mechanical properties across interphase region can be described by an exponential function. By using FFT method, the effect of fiber volume fraction and interphase properties distribution on the effective material properties and the damage development mechanism of the composites are investigated. The effect of heterogeneous behaviors of carbon fiber with core/shell like behavior and interphase is also discussed. Compared to the traditional finite element model with zero-thickness interface, the stress-strain results obtained by the present computational approach are in good agreement with experimental data. This study can be helpful for interface design and manufacturing of fiber reinforced composites.

Fiber migration in shear flow: Model predictions and experimental validation

Understanding transient flow behavior of polymer composites is crucial for improving the predictions of final composite properties in polymer processing operations. This work is aimed at measuring concentration migration of fiber reinforcing particles in addition to fiber orientation evolution during simple shear flow. Center‐gate injection molded samples using Nylon‐6 containing 33 wt% short glass fibers (PA6‐33GF) were prepared. Samples were imaged using X‐ray computed tomography (X‐CT) to obtain fiber orientation tensors and fiber volume fraction distributions after different strain units were imposed. With higher applied strains, the orientation of fibers evolved from a shell–core structure typical of injection molded composites to a preferential alignment in the shearing direction. As for fiber concentration, an initial shell–core concentration profile established during injection molding was found to diminish towards a uniform concentration distribution upon shearing. This experimentally observed concentration migration was modeled using the suspension balance model (SBM) which predicts concentration changes based on changes in particle stress contributions. The SBM uses a particle stress contribution model that is designed for spherical particles. Predictions from this model gave reasonably accurate steady state results and the evolution of the concentration profile. A modified fiber stress model that incorporates fiber orientation effects was also tested for its applicability for fiber‐filled systems. Predictions from this model yielded reasonable agreement with measured concentration evolution data but with a slower attainment of a uniform concentration profile. Further investigation on the empirical constants used in the fiber stress model warrants a rheological assessment to improve concentration evolution predictions for use in constitutive rheological modeling. POLYM. COMPOS., 40:3573–3581, 2019. © 2019 Society of Plastics Engineers

Numerical analysis on the flow–compaction behavior and the effect of interface permeability in thick composite plates during autoclave processing

A multi-field coupled model was developed to simulate the flow–compaction behavior of thick composite laminates manufactured by the autoclave process based on Darcy’s law and the effective compaction stress theory. The model was verified by comparing the predictions with the experiment results of a thick unidirectional laminate. The results show that the resin flow and compaction of fiber bed start from the top surface and gradually spread into the interior region, and the non-uniform resin flow along the thickness direction causes a gradient distribution of fiber volume fraction in the thick composite part. A cross-plied composite laminate model with a thin interlaminar layer was constructed, and the effect of the interlaminar transverse permeability on the flow–compaction behavior of the thick cross-plied laminate was numerically analyzed. The results indicate that the thick cross-plied composite laminate with high interlaminar transverse permeability has the similar flow–compaction process with that of the thick unidirectional laminate. An interlaminar layer with low transverse permeability impedes the resin flowing out from the interior of the thick cross-plied composite laminate and causes a lower fiber volume fraction compared with that in a unidirectional laminate.

Theoretical determination of the fiber volume fraction distribution for natural fiber fabric reinforced polymer composite

The present work attempts to understand the inter-relation between the spun yarn fiber volume fraction and the fabric fiber volume fraction when adapted in the reinforced polymer composite. The yarn diameter of the natural fiber spun yarn has a great heterogeneity that affects the fiber volume fraction at the different basic units of the fabric. That in turn creates a rich fiber or rich polymer point in the final composite, resulting in the composite with varied reinforcement which has a crucial impact on the stress transfer between yarns and matrix and the composite fracture mechanism. The model was developed to express the effect of the lay out of the yarns in warp and weft directions with their real measured diameters. The fiber volume fraction of each basic weave unit was targeted to calculate the minimum, average, and maximum values of the fabric's fiber volume fraction distribution. The developed model predicts of the effect of yarn fiber volume fraction and warp and weft densities for weave fabric on its final fabric volume fraction, taking into consideration the actual variation of the yarn diameter along its length, to accomplish suitable structural performance for a composite material.

Role of fiber distribution and air evacuation time on capillary driven flow into fiber tows

Composite materials are created by reinforcing a matrix material with fibers. In Liquid Composite Molding (LCM) processes, dry fiber preforms are impregnated with resin to form the composite. The fiber preforms usually contain fiber tows and resin impregnation into the tows is driven by the applied pressure gradient and the capillary pressure. The fiber tows are usually less permeable than the regions in between them hence the resin will typically flow around the fiber tows at much faster rate than into them. Due to the dual scale nature of the pore structure, there are often microvoids within fiber tows that result from air and volatiles being trapped. This paper introduces a novel methodology to include both capillary and void pressure in the prediction of tow filling. The methodology allows for addressing the effect of non-uniform fiber volume fraction distributions within the tow on void distribution. The time dependent applied pressure experienced by the tow is also taken into account. The method is used to study the effect of wetting properties and the length of air evacuation time on void entrapment.

多相複合材料に対する確率均質化法に関する研究

Advanced materials such as fiber reinforced composite materials show high stiffness and strength and therefore they are widely spread in industries. However, those mechanical properties are sometimes largely scattered because of physical and geometrical uncertainties at the microscale depending on the manufacturing process. To this end, there is a growing need for the stochastic multiscale simulation to predict the scattered properties. Hence, this paper proposed a first-order perturbation based stochastic homogenization method for multi-phase composite materials using many random parameters for elastic tensor of constituent materials. A demonstrative numerical example is shown for plain glass woven fabric reinforced plastic fabricated by hand layup using 62 random parameters when the distribution of fiber volume fraction was considered.

Flow property of fiber suspension in a turbulent channel flow under considering both Brownian and turbulent diffusions

The issue of fiber suspension flow has received great substantial attention in the last decades. In contrast with the abundant researches of normal size fiber suspensions flow, this paper is devoted to the small size fiber suspension composed of water and polyarmide fiber where Brownian motion plays an important role and thus cannot be neglected. The spatial distribution and orientation of fiber, streamwise mean velocity profile, turbulent kinetic energy, Reynolds stress and rheological property of fiber suspension in a turbulent channel flow are obtained and analyzed both numerically and experimentally. To simulate the small fiber suspension flow well, the well-known Reynolds averaged Navier-Stokes (N-S) equation governing the suspension flow is modified in consideration of the effect of fibers on base flow. The equation describing the probability density functions for fiber orientation is derived in view of the rotary Brownian diffusion. The general dynamic equation for fibers is reshaped in the effect of spatial Brownian diffusion. For the sake of the closure of the N-S equation, the turbulence kinetic energy and turbulence dissipation rate equations with fiber term are employed. The conditional finite difference method is adopted to discrete these partial differential equations. And the diffusion term and convective term are discretized by the central finite differences and the second-order upwind finite difference schemes, respectively. The second and fourth-order orientation tensors are integrated by the Simpson formula. Experiment is also performed to validate some numerical results. The results show that most fibers tend to align parallelly to the flow direction in the flow, especially in regions near the wall. Such a phenomenon is more obvious with the decreases of Reynolds number and fiber concentration, and with the increase of fiber aspect ratio. Fiber volume fraction distribution is non-uniform across the channel, and becomes more uniform with increasing Reynolds number, and with reducing fiber aspect ratio. The changes of fiber orientation distribution and spatial distribution are not sensitive to fiber aspect ratio for 5. Streamwise mean velocity profile in fiber suspension has a steeper slope than that in single phase flow, and the steepness increases as the fiber concentration and fiber aspect ratio increase, and as the Reynolds number decreases. The presence of fiber will reduce the turbulence kinetic energy and Reynolds stress. The effect of fiber on the turbulence suppression becomes more obvious with the increases of fiber concentration and aspect ratio, and with the decrease of Reynolds number. The first normal stress difference is less than 0.05 and much less than the shear stress. From the wall to the center of the channel, the shear stress increases while the first normal stress difference decreases. Both the shear stress and the first normal stress difference increase with increasing fiber concentration and aspect ratio. Shear stress increases while the first normal stress difference decreases with increasing Reynolds number. The effects of fiber concentration on the shear stress and the first normal stress difference are larger than the fiber aspect ratio.

Effect of Pre-Molding Process and Additive of Injection Molded Wood/PP Composites

Abstract Injection molded composites are becoming more widespread in recent years because of their high quality and low cost. However, compared to synthetic fiber composites, it is difficult to maintain a constant fiber volume fraction and uniform distribution for natural fiber composites during the direct injection process. This is mainly because natural fibers are more easily twisted during feeding into the injection machine, owing to their rough surfaces. These feeding difficulties are particularly due to the low bulk densities of natural fibers, especially natural fillers. Additional challenges to the injection process include the concentration and, especially for natural filler reinforced composite. To address these problems, the current study investigates the mechanical properties and morphologies of polypropylene (PP) reinforced by wood powder. Two pre-molding processes, dry-blending and compounding, were compared, and the effects of an additive (crystalline polyalpha olefin (CPAO)) on the mechanical properties of the wood/PP composites were investigated. This investigation is based on tensile, three point bending, and Izod impact tests, and scanning electron microscope (SEM) observation of the fracture surfaces. Results indicated that the composites molded through compounding exhibited better mechanical properties than the samples molded through the direct dry-blending process. In addition, the tensile and bending properties of the composites produced through compounding were found to increase with the addition of CPAO content, because of improved wood powder distribution in the PP matrix.