Tow Cross-section Research Articles

A parametric modeling method for 3D woven composites considering realistic meso-structural characteristics

The precision of mesoscale simulation for three-dimensional woven composites (3DWCs) is intricately linked to the fidelity of the geometric representation. This paper aims to present a novel parametric modeling approach for generating representative volume element (RVE) of the 3DWCs while considering its realistic meso-structural characteristics. The real architecture of 3DWCs is defined to consider the squeezed surface warp tow. Tow geometry is specified, accounting for torsion of tow cross-section and crimp of weft tow path. The RVEs of the composites are geometrically assembled via a specific translational symmetry. The tensile response of the composites with the novel geometry is scrutinized utilizing a progressive damage model, compared with that of the ideal geometry. Additionally, the impact of weft tow size on the tensile response of the composites is explored.

Effect of intra-tow flow on plain woven fabric permeability using virtual fiber-voxel element method

A geometric modeling platform based on the virtual fiber-voxel element is proposed to characterize textile reinforcement in a cost-effective way, which could reflect the systemic local changes of the tow path and tow cross-section. The finite volume method is used to solve the governing equation of the boundary value problem, and the permeability of the fabric is calculated by using the flow field data obtained from the model. The flow field analysis and pressure drop in flow direction of different thickness unit cells suggest that the size of inter-tow channels play a vital role in determining the overall in-plane permeability values. The flow channels of the inter tow in warp direction were found to be greater than in the weft direction, which causes the overall permeability to be anisotropic.

Resin Capacity of Technical Woven Fabrics: Pore Volume and Pore Shape Simulation

Nowadays, technical woven fabrics are broadly utilized as reinforcement of composites. Resin capacity of woven fabric is one of the main challenges in laminate fabrication. Resin diffusion during fabrication of the composite is extremely depended on fabric micro-morphology. The geometry of weave unit cell and its pore are fundamental factors in evaluating resin capacity and resin diffusion within fabrics. The main attempt of this study was obtaining an approach to evaluate resin capacity of a woven fabric via simulating pore shape and pore volume. For this purpose, four basic unit cells for all kind of weaves were simulated with the two shapes of tow cross-section: lens and racetrack. Afterwards, 3D shape and volume of their pores were simulated using this approach. The proposed approach is established on the base of initial data of fabric such as tow setts, tow titers, planar density and thickness of a technical fabric. To assess the simulation, three types of woven fabrics namely, plain, twill and satin were impregnated by epoxy resin using vacuum infusion process. The volume fractions of the matrix and fibers of real composites were compared with simulated ones. It was demonstrated that the approach with racetrack assumption led to high degree of convergence with experimental results. The maximum relative error of pioneered method to evaluate volume of the pore in this condition exceeded up to 1.43 %. Suitable correlation between volume fractions of the pore and void was observed in experimental data. It is experimentally demonstrated that the void volume fraction of composite will be increased with decrease of pore volume due to difficulty of wetting. In this paper, it is illustrated that the resin capacity of a woven fabric is a function of vacuum level in vacuum infusion process. For instance, resin capacity of a certain plain fabric could be reduced up to 10 % under 60 kPa (0.6 bar) of vacuum in contrast with steady state of fabric at room atmosphere.

Influence of the lateral confinement on the transverse mechanical behavior of tows and quasi-unidirectional fabrics: Experimental and modeling investigations of dry through-thickness compaction

Fibrous textiles are subjected to dry through-thickness compaction during most of the composites manufacturing processes. Usual tow models implemented in textile numerical simulations do not reproduce the tow widening occurring during the compaction. Nonetheless, this widening (that can reach 10%) would influence the internal microstructure of the considered fabric and its mechanical behavior. This paper proposes a simple mechanical approach to reproduce the width and thickness evolutions experimentally measured during through-thickness compaction of E-glass and carbon tows. Once the material parameters identified on laterally free tows, the tow cross-section model is employed to study the influence of the tow lateral confinement on the transverse mechanical behavior of its corresponding quasi-unidirectional fabric. It is observed that the lateral confinement depends on the quasi-unidirectional stitch tension. This confinement induces a densification of the tows leading to a stiffening of the quasi-unidirectional transverse behavior. This stiffening is well predicted by the proposed modeling approach.

Stress analysis of a plain orthogonally woven textile composite under tension along the warp direction

A non-idealized finite element model of a plain orthogonally woven textile composite was subjected to tension along the warp direction, and the predicted stress state was investigated. The effect of refining the geometry and mesh on the volume average stresses and the percentage of each constituent at different stress levels was explored. For the particular textile architecture considered, which consisted of large reinforcement tows and complex tow cross sections, it was shown that the typical mesh refinement in the literature might suffice for volume average stresses, but a higher mesh refinement is needed to accurately capture stress concentrations. The locations of stress concentrations within each constituent were identified. For the three types of tows, [Formula: see text], transverse normal stress in the local coordinate system, in the wefts was predicted to be the most severe component of stress. For the layers of wefts that are crossed over or under by a binder, stress concentrations developed where the warps were the most distorted. Whereas, for the interior layer of wefts, stress concentrations developed where a binder came closest to the weft. In the matrix, [Formula: see text], the normal stress in the direction of the load, concentrations developed where a binder came close to a warp or weft. The locations of peak cross-sectionally averaged stresses along the tow paths were shown to match the locations of local stress concentrations. However, it was observed that many of the stress concentrations might be sensitive to the method used to create the finite element model, boundary conditions, or accounting for the variation of local fiber-volume fraction that results from a variation of cross-sectional area.

Numerical investigation on the effect of tow tension on the geometry of three-dimensional orthogonally woven fabric

The fabric geometry determines the mechanical performance of a textile composite. This paper investigates the effect of tow tension on the fabric geometry during the weaving process. A numerical model at the fiber scale was established by representing the fiber as a chain of truss elements connected by fully flexible hinges and having strong tensile modules. Fabric samples were woven on a homemade loom under different tension configurations to verify the numerical model. The model results with respect to the tow cross-section and path are in good agreement with observations of the homemade fabric sample. The tow cross-section deformation is the consequence of fiber rearrangement due to the transverse force originating from Z-binder tension. It is also found that the crimps of weft tows are different to those of warp tows. For weft tows, appreciable crimping is found in the regions of intercrossing with the Z-binder tow. Meanwhile, fibers undulate at the edges and remain straight in the middle of warp tows.

Influence of filament distribution on transverse tow permeability: Model predictions and experimental validation

In the past, various analytical and semi-analytical permeability models have been implemented for process modeling of flow through single scale fabric with reasonable success. However, characterization of permeability for a dual scale fabric is relatively more complex requiring specification of permeability at tow and fabric length scales. In the current work, a semi-analytical model for transverse tow permeability is developed taking into consideration the details of microstructural filament arrangements within a single tow by conducting detailed scanning electron microscopy (SEM) of a cured tow cross-section. The current analysis indicates that by explicitly accounting for said local fiber volume fraction and its distribution, the transverse tow permeability predictions improve when compared to existing analytical results. In addition, a new experimental methodology for transverse tow permeability characterization has been developed and presented. The predictions considering locally varying fiber volume fractions were found to match well with the experimentally evaluated tow permeability.

Effect of Z-binder tension and internal micro-structure on damage behavior of 3D orthogonal woven composite

The main goal of this study was to investigate the effect of tow tension and related internal micro-structure on the damage behavior of 3D orthogonal woven composites under tensile loading. For representing the internal micro-structure of the composite with respect to varying tow cross-section and the unregulated undulated path which are introduced by Z-binder tension, a dynamical method at filament level which simulates an interlacing process was used to obtain the fabric architecture. Then, an element recognition algorithm was proposed to convert a representative unit cell of 3D woven fabric architectures into a finite element model with 8-node solid elements consisting of four kinds of sets in terms of warp, weft, Z-binder tows and resin matrix. In addition, filament trajectory was also extracted from fabric architecture to serve as a local material orientation. Comparative simulations under tensile loading were conducted on the FEA models generated by this work and texgen software, respectively. An experiment was also carried out to verify the simulation results. The stress–strain curve in the proposed model was found to be closer to the experiment data. The results show that the tensile modulus and strength reduce due to the diverged warp tow path which is induced by the interaction between the tows during the weaving process. Moreover, the irregularity and compressed weft tow cross-sections nearby the intercross point are more likely to generate the transverse damage which would result in the non-linear tensile behavior of the composite material.

Evolution of single carbon and glass fibrous tow cross-sections in dry and lubricated states during compaction perpendicular to the fibers

Abstract Fibrous fabrics are used in a variety of applications, among them, for structural composites. Most fabrics are efficiently manufactured from tows or yarns. During textile manufacturing or during fiber reinforced composites manufacturing, the fabrics and tows undergo several movements and deformations. Although there have been several attempts by different authors to model micro structural mechanical behavior of fabrics, they often suffer from unknown geometric dimensions at various loads or unknown materials' mechanical parameters. This paper presents a method for measuring and comparing tows (or yarns) geometrical evolution during compaction perpendicular to the fibers. The tows are compacted and dimensions are continuously measured using confocal chromatograph. Fabrics and tows of the study are composed of glass or carbon fibers, in dry or lubricated states. Volume, compacity evolutions and Poisson's ratio are extracted for a wide range of compaction levels. Tables of material characteristics and experimental data are also provided for a further use or analysis.

On the stochastic variations of intra-tow permeability induced by internal geometry variability in a 2/2 twill carbon fabric

This study investigates the stochastic variation of tow cross sections in a 2/2 twill carbon fabric and intra-tow permeability. A large sampling of tow cross sections (720 per layer) done by X-ray Micro-Computed-Tomography of a 7-layer composite plate is used to validate the use of the following statistical distributions of the random geometrical parameters: tow thickness (normal), tow width (log-logistic), intra-tow fibre volume fraction (log-normal) – and intra-tow permeability (gamma). The intra-tow fibre volume fraction and permeability variables are auto-correlated with a correlation length of ca. 3mm, which corresponds to a correlation length of the out-of-plane tow centroid coordinates and is close to the spacing of the warp and weft yarns. The findings can serve as guidelines in doing Monte Carlo modelling of woven preforms variability and continue previously published work on inter-tow geometry and permeability.

Stochastic characterisation methodology for 3-D textiles based on micro-tomography

A recently developed framework to quantify variability of common textile reinforcements of unit cell size is extended to allow for a stochastic description of complex three-dimensional (3-D) textile architectures spanning multiple unit cells. The reinforcement geometry is characterised from synchrotron micro-tomography images in terms of centroid coordinates and tow cross-section. The statistical information includes an average trend, standard deviation and correlation information. A general representation of correlation information is proposed to account for the different tow correlations depending on the location inside the 3-D architecture.The methodology is applied to the characterisation of a 3-D carbon fabric considered for NASA’s Adaptive Deployable Entry Placement Technology (ADEPT) system. Determining geometrical variability in the weave is of importance during the process of setting design margins and risk analysis. Statistical analysis demonstrates strong dependency on the crossover positions for the average trends and correlation data, with a substantially higher variation for the Z-interconnecting tows.

Entrapment and venting of bubbles during vacuum bag prepreg processing

During composites manufacturing with partially pre-impregnated fibers (i.e. “prepregs”) in Out-of-Autoclave processes, non-impregnated fabric cross-sections serve as air pathways to evacuate entrapped bubbles of air, moisture, or volatiles. The bubbles trapped within a laminate during processing lead to decreased structural performance. In this work, the motion of resin and bubbles during the processing of a characteristic prepreg is directly visualized in situ. This is performed utilizing a previously developed flow visualization technique under known pressure and temperature conditions. This study investigates the processing conditions under which a bubble succeeds or fails to meet and coalesce with available air pathways in order to escape the laminate. A key finding of this study is that tunable process parameters, such as pressure and temperature, are less important for successful bubble removal as compared to the initial state of resin impregnation in the prepreg. Prepregs with initially high states of resin impregnation will often fail to draw bubbles into air pathways through the center of fiber tow cross sections, whereas prepregs with initially low states of resin impregnation have clear pathways for bubbles to meet local resin flow fronts, coalesce, and escape. The relevant literature on the motion of bubbles in confined spaces is discussed. It is observed that small Capillary number theory (i.e. Ca < 0.01) under predicts the relative velocity of bubbles, and the faster than expected bubble transport is likely due to effects given by the bubble aspect ratio via the fibrous micro-channel geometry.

A multi-scale finite element approach for modelling damage progression in woven composite structures

A significant challenge in the numerical modelling of composite structures with a multi-axis fibre architecture is the reproducibility of the textile mechanics [1]. A numerical analysis procedure for woven composite structures using a multi-scale finite element approach has been developed, and is presented in this paper. The approach is demonstrated for a flat two-dimensional woven glass/epoxy laminate. Digital microscopy is used to estimate tow cross-section and path, and quantify the amount of variation of these parameters. This data is used to generate both a meso-scale model of a single unit cell as well as a macro-scale model of the complete structure. Numerical results from the proposed approach are compared to experimental stress–strain data, which show good agreement in the lower strain range.

Parametric constitutive model of uni-directional fiber–matrix composite

A computational model that allows to explicitly determine transversely isotropic elastic constants of uni-directional fiber–matrix composite tow as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic RVE is employed. The technique is enhanced by introduction of averaging procedure over different shapes of the 2D fiber layout pattern in the tow cross-section. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.

Microscopic Investigation of Quartz Fiber Fabrics: Geometry Model

In response to the relationship between perform structural parameters and the composites properties, a newly geometrical modeling of 2D biaxial orthogonal woven fabric was established in this paper. Based on the yarn’s true configuration, the SEM image of the yarn cross-section was taken, geometrical parameters (the individual tow geometry and weaving pattern of the fabrics) are introduced in order to describe the general families of woven fabrics. The tow waviness can be described by combinations between undulated and straight segments and the tow cross-section can be described by lenticular shape. When the geometrical model was used to predict the structural properties of the fabric, the predicted values show good agreement with the measured ones. The geometrical model proposed here is intended as the foundation for further design and analytical of the mechanical properties of the composite materials reinforced with these fabrics.

3D Geometrical Model of Plain Weave Fabrics for Finite Element Analysis

Woven unit-cell geometry functions are presented for a balanced plain weave fabric. Based on the functions, a 3D geometrical model applying to a meshing preprocessor for 3D finite element is proposed. The geometry model takes into account the existence of the space between tows, the undulation of the tow, and the actual tow cross-section shape. The internal geometry of model is from micrographs of sectioned laminates, which is helpful to define the accurate and actual 3D geometrical model. The section shape of the yarn remains unchanged along the trajectory. This model can be easily identified using three parameters measured on a real fabric. An accurate hexahedral mesh developed using these geometry model is presented. This is an important point for 3D finite element simulation of fabric model, which is a powerful method to investigate the mechanical behavior and also the composites made from it.

Mesh generation and geometrical modelling of 3D woven composites with variable tow cross-sections

The modelling of 3D woven composites represents a key part in both material and component design. Current modelling techniques can struggle to mesh correctly accurate unit cell models and apply the complex but necessary periodic boundary conditions required, often with sacrifices made in idealisation of the weave architecture. An automated voxel meshing technique suitable for modelling failure in 3D woven composite unit cells has been developed, which is generic in nature and allows incorporation of architectural deformities within weaves, including tow rotations and misalignments. The model requires node points with only five independent variables to define the unit cell geometry. Application of a smoothing algorithm to the tow/matrix interface voxels produces a suitable surface for modelling tow/matrix debonding, leading to a more accurate representation of the stress field.

Modelling of moisture diffusion in multilayer woven fabric composites

Advanced woven fibre reinforced composites have wide applications in industries. However, the mechanical performance of this kind of composites is significantly affected by the moisture absorption of the polymer matrix. This paper presents a numerical investigation on the moisture diffusion taking place in multilayer woven fabric composites. The transient diffusion process of moisture is examined based on the repeating Representative Unit Cell (RUC) of woven fabrics. Using finite element analysis methods, the microscopic heterogeneity of RUC is described in terms of the tow size, tow cross-section shape and tow weaving configuration of fabrics. The model is then applied to simulate the moisture diffusion within the composites of varied number of plies. Finally, by using a data fitting function for the modelling results, a simple predicting model for moisture saturation time with the increase of the number of plies is proposed for the purpose of practical applications.

Flexural and torsional behaviour of biaxial and triaxial braided composite structures

This paper presents a systematic investigation of flexural and torsional properties of biaxial and triaxial braided composites, with one or more layers, at different braid angles. Braided tubes were impregnated with vacuum infusion process to produce void free samples. Flexural and torsional tests were conducted using special attachments to an Instron test machine. Assuming a lenticular geometry for the tow cross-section, a modified laminate analysis was performed by computing reduced tow properties due to the presence of tow waviness (crimp). The results obtained from the laminate analysis were used in the macro-analysis of the braided tube in order to compute the flexural and torsional properties. The experimental results were in good agreement with the computed values.

Micromechanics modeling of moisture diffusion in woven composites

Woven composite structures are expected to experience a range of hygrothermal environmental conditions during their service life. Since moisture can cause plasticization of the polymer matrix, alter the stress state and degrade the fiber/matrix interface, understanding of moisture absorption and desorption behavior is critical for predicting long-term material and structural performance. This paper focuses on the effect of weave microstructure on the moisture diffusion behavior of polymer matrix woven composites. The effect of tow architectural parameters on the through-the-thickness moisture diffusion behavior is investigated using finite element subcell models with appropriate boundary conditions. The results are presented and discussed in terms of the tow waviness, tow cross-section shape and weave pattern. Simulations of moisture diffusion tests are also conducted for 3-ply woven hybrid composite laminates consisting of uni-weave and 4-harness satin weave, in which the tow fiber volume fractions are determined from image analysis. The results from the simulation are in good agreement with the available test results.