Mechanics of textile composites: Micro-geometry

Textile fabric geometry determines textile composite properties. Textile process mechanics determines fabric geometry. In previous papers, the authors proposed a digital element model to generate textile composite geometry by simulating the textile process. The greatest difficulty encountered with its employment in engineering practice is efficiency. A full scale fiber-based digital element analysis would consume huge computational resources. Two advances are developed in this paper to overcome the problem of efficiency. An improved contact-element formulation is developed first. The new formulation improves accuracy. As such, it permits a coarse digital element mesh. Then, a static relaxation algorithm to determine fabric micro-geometry is established to replace step-by-step textile process simulation. Employing the modified contact element formulation in the static relaxation approach, the required computer resource is only 1–2% of the resource required by the original process. Two critical issues with regards to the digital element mesh are also examined: yarn discretization and initial yarn cross-section shape. Fabric geometries derived from digital element analysis are compared to experimental results.     

Nonlinear Multi-Scale Modelling,Simulation and Validation of 3D Knitted Textiles

Three-dimensionally (3D) knitted technical textiles are spreading into industrial applications, since their geometric, structural and functional performance can be tailored and optimized on fibre-, yarn- and fabric levels by customizing yarn materials, knit patterns and geometric shapes. The ability to simulate their complex mechanical behaviour is thus an essential ingredient in the development of a digital workflow for optimal design and manufacture of 3D knitted textiles. Here, we present a multi-scale modelling and simulation framework for the prediction of the nonlinear orthotropic mechanical behaviour of single jersey knitted textiles and its experimental validation. On the meso-scale, representative volume elements (RVEs) of the fabric are modelled as single, interlocked yarn loops and their mechanical deformation behaviour is homogenized using periodic boundary conditions. Yarns are modelled as nonlinear 3D beam elements and numerically discretized using an isogeometric collocation method, where a frictional contact formulation is used to model inter-yarn interactions. On the macro-scale, fabrics are modelled as membrane elements with nonlinear orthotropic material behaviour, which is parameterized by a response surface constitutive model obtained from the meso-scale homogenization. The input parameters of the yarn-level simulation, i.e., mechanical properties of yarns and geometric dimensions of yarn loops in the fabrics, are determined experimentally and subsequent meso- and macro-scale simulation results are evaluated against reference results and mechanical tests of knitted fabric samples. Good agreement between computational predictions and experimental results is achieved for samples with varying stitch values, thus validating our novel computational approach combining efficient meso-scale simulation using 3D beam modelling of yarns with numerical homogenization and nonlinear orthotropic response surface constitutive modelling on the macro-scale.     

Attachment mode performance of network-modeled ballistic fabric shielding

A central issue in the use of ballistic fabric shielding is the mode of attachment to the structure that it is intended to protect. In order to investigate this issue, a discrete multi-scale yarn-network model is developed for structural fabric undergoing ballistic impact, based on work found in Zohdi and Powell [Zohdi TI, Powell D. Multiscale construction and large-scale simulation of structural fabric undergoing ballistic impact. Comput Meth Appl Mech Eng 2006;195:94–109] and Zohdi [Zohdi TI. Modeling/simulation of progressive penetration of multilayered ballistic fabric shielding. Comput Mech 2002;29:61–7]. The model is comprised of a network of yarn with stochastic properties determined by smaller-scale fibrils, which are randomly misaligned. The effects of stochasticity on the overall response are explored, and the model is compared against macro-scale experiments. The key feature of the model is the fact that it does not depend on phenomenological parameters, and can be calibrated by simply measuring the properties of an individual, smallest-scale, fibril. The properties of a fibril are easily ascertained from a simple tension test. The response of the overall fabric model and ballistic experiments are in excellent agreement. The model indicates that fabric which is attached by being pinned at the corners generally absorbs more energy, relative to fabric clamped along the sides. The basis for this result is discussed at length in the body of this work. Furthermore, it is observed that a uniform-yarn model, one which ignores the stochastic nature of the yarn, over-estimates the amount of energy absorbed.     

Numerical prediction of in-plane permeability for multilayer woven fabrics with manufacture-induced deformation

A unit cell based Computational Fluid Dynamics model is presented for predicting permeability of multilayer fabric structures. In Liquid Composites Moulding processes, fabric lay-ups undergo significant manufacture-induced deformation, combining compression, shear, and inter-layer nesting. Starting from the configuration of un-deformed fabric, the deformation is simulated geometrically by accounting for self-imposed kinematic constraints of interweaving yarns. The geometrical modelling approach is implemented in the open-source software TexGen. The permeability tensor is retrieved from flow analysis in ANSYS/CFX, based on TexGen voxel models. Using only measured geometrical data for un-deformed fabrics, deformed plain weave fabric and twill weave fabric lay-ups were modelled and their permeability tensors predicted. Comparison with experimental data demonstrates the generally good accuracy of predictions derived from the proposed numerical method.     

Unit cell modelling of textile laminates with arbitrary inter-ply shifts

Deformation and failure mechanisms of textile laminates are strongly affected by mutual shift of the plies. To model arbitrarily stacked laminate within a traditional framework of multi-scale modelling, one must construct a representative volume element (RVE), which includes all the plies. This is a time consuming and computationally expensive work. As an alternative, the paper suggests a technique that allows setting problems on one unit cell of a single ply, i.e. a volume smaller than RVE of the laminate. The technique approximates the stress field in a ply by combination of stress fields obtained in two additional problems. Boundary conditions (BC) in these problems imitate the interaction of the unit cell with surrounding media. Once these problems are solved, the solution for arbitrary number of plies is composed analytically. The proposed technique respects inter-ply configurations, accounts for the number of plies, distinguishes the ply position, and reproduces the meso stress state with a good accuracy. The technique is validated against reference solutions obtained for the entire laminate.     

Modelling microscopic flow in woven fabric reinforcements and its application in dual-scale resin infusion modelling

A physical unit cell impregnation model is proposed for the micro-scale flow in plain woven reinforcements. The modelling results show a characteristic relationship between tow impregnation speed, the surrounding local macro-scale resin pressure and the tow saturation within the unit cell. This relationship has been formulated into a mathematical algorithm which can be directly incorporated into a continuum dual-scale model to predict the ‘sink’ term. The results using the dual-scale model show a sharp resin front in inter-tow-pore spaces and a partially saturated front region in intra-tow-pore spaces. This demonstrates that the impregnation of fibre tows lags behind the resin front in the macro pore spaces. The modelling results are in agreement with two reported experimental observations. It has been shown that the unsaturated region at the flow front could increase or have a fixed length under different circumstances. These differences are due to the variation in tow impregnation speed (or the time required for the tow to become fully impregnated), the weave architecture and the nesting and packing of plies. The modelling results have also demonstrated the drooping of the inlet pressure when flow is carried out under constant injection rates. The implementation of the algorithm into a dual-scale model shows coherence with a single-scale unsaturated model, but demonstrates an advantage in flexibility, precision and convenience in application.     

Consistent Finite Element mesh generation for meso-scale modeling of textile composites with preformed and compacted reinforcements

A new automated method to generate smooth Finite Element meshes for the meso-scale representation of textile composites unit cells with preformed and compacted reinforcements is presented. The reinforcement geometry is obtained from textile geometry preprocessors or by modeling of the preforming step. It is then transformed into a geometric model of the entire composite unit cell, taking into account the real yarn shape after preforming and compaction, the contact interactions between the yarns, as well as the resulting local variations of fiber volume fraction. A consistent mesh of the complete cell, conformal between the parts, is ensured, without the need for inserting artificial matrix layers between the yarns. The methodology is illustrated by mechanical modeling of the representative unit cell of a multi-layer composite with a compacted and nested woven reinforcement.     

Computational up-scaling of anisotropic swelling and mechanical behavior of hierarchical cellular materials

The hygro-mechanical behavior of a hierarchical cellular material, i.e. growth rings of softwood is investigated using a two-scale micro-mechanics model based on a computational homogenization technique. The lower scale considers the individual wood cells of varying geometry and dimensions. Honeycomb unit cells with periodic boundary conditions are utilized to calculate the mechanical properties and swelling coefficients of wood cells. Using the cellular scale results, the anisotropy in mechanical and swelling behavior of a growth ring in transverse directions is investigated. Predicted results are found to be comparable to experimental data. It is found that the orthotropic swelling properties of the cell wall in thin-walled earlywood cells produce anisotropic swelling behavior while, in thick latewood cells, this anisotropy vanishes. The proposed approach provides the ability to consider the complex microstructure when predicting the effective mechanical and swelling properties of softwood.     

Modelling of Woven Fabrics with the Discrete Element Method

The mechanical behaviour of woven fabrics is dominated by the kinematics of the constituents on the microscopic scale. Their macroscopic response usually shows non-linearities which are due to the mobility of the interlaced yarns. The major deformation mechanisms of fabrics, i.e. the crimp interchange in case of biaxial tension and the trellising motion of the yarns in case of shear, reflect the dependency of the macroscopic material behaviour on the microstructural deformation mechanisms.
We present a novel modelling approach for woven fabrics which is capable to represent directly and locally the microstructure and its kinematics at yarn level. With only a small set of assumptions on the micro-scale the complex macroscopic material behaviour can be directly obtained. The proposed model uses the Discrete Element Method (DEM) for the representation of the fabric's microstructure. It is intrinsically dynamic since the equations of motion are solved numerically for every mass point through an application of an explicit finite difference technique. The model covers the full mobility of the fabric's microstructure while being efficiently enough to model macroscopic patches of the material.
With this model we can study the influence of the different material features of the micro-scale on the macroscopic material behaviour. With some further extensions accounting for coatings or embeddings, the range from pure fabrics to fabric reinforced membranes and composites can be covered. Problems related to large deformations and localization as well as damage can be addressed with the presented modelling approach.     

基于自由变形技术的二维机织物细观模型

为了避免理想化织物模型横截面恒定、纱线间相互渗透的问题,生成具有真实感的二维机织物三维细观模型,提出一种基于自由变形技术的几何变形方法。首先通过理想化的纱线中心线轨迹、横截面建立织物初始几何模型,然后应用自由变形技术对纱线进行变形。在变形过程中,所有纱线横截面在空间位置和参数的约束下进行自由变形,所有横截面变形后的控制网格组成纱线的控制网格,以驱动纱线的整体变形,最终生成具有真实感的织物细观模型。变形过程中纱线间的接触应用基于射线的碰撞检测技术处理。该方法可以扩展并应用于其他织物结构,且可以输出到其他软件中进行模拟计算。      

Effect of statistical yarn tensile strength on the probabilistic impact response of woven fabrics

The probabilistic impact response of flexible woven fabrics can be described through the V₀–V₁₀₀ or probabilistic velocity response (PVR) curve which describes the probability of fabric penetration as a function of projectile impact velocity. One source of variability that affects the probabilistic nature of fabric impact performance is the statistical distribution of yarn tensile strengths. In this paper the effects of the statistical yarn strength distribution characteristics on the probabilistic fabric impact response are computationally studied using five different strength distributions with differing mean strengths and distribution widths. Corresponding fabric PVR curves are generated for each strength distribution using a probabilistic computational framework that involves randomly mapping yarn strengths onto the individual woven yarns of a fabric finite element model and then running a series of impact simulations for the case of a four-sided clamped fabric impacted at the center by a spherical projectile.     

Strength prediction in CFRP woven laminate bolted double-lap joints under quasi-static loading using XFEM

The current paper is concerned with modelling damage and fracture in woven fabric composite double-lap bolted joints that fail by net-tension. A 3-D finite element model is used, which incorporates bolt clamp-up, to model a range of CFRP bolted joints, which were also tested experimentally. The effects of laminate lay-up, joint geometry, hole size and bolt clamp-up torque were considered. An Extended Finite Element (XFEM) approach is used to simulate damage growth, with traction–separation parameters that are based on previously reported, independent experimental measurements for the strength and toughness of the woven fabric materials under investigation. Good agreement between the predicted and measured bearing stress at failure was obtained.     

Homogenization of braided fabric composite for reliable large deformation analysis of reinforced rubber hose

High pressure rubber hose is in the lamination structure composed of pure rubbers and braided fabric composite layers to have the sufficient strength against the excessive radial expansion and the large deformation, in which the braided fabric layer is woven with wrap and fill tows inclined to each other with the predefined helix angle in the complex periodic pattern. The consideration of detailed geometry of braided fabric layer in the numerical analysis leads to a huge number of finite elements so that the braided fabric layer has been traditionally simplified as an isotropic cylindrical one with the homogeneous isotropic material properties of braid spun tread. However, this simple model leads to the numerical prediction and design with the questionable reliability. In this context, this paper addresses the development of an in-house module, which is able to be interfaced with commercial FEM code, for the reliable large deformation analysis of the reinforced rubber hose with the element number at the level of the traditional simple model. The in-house module is able to not only automatically generate 3-D unit cell (or RVE) model of the braided fabric layer but evaluate the homogenized orthotropic material properties by automatically performing a serious of unit cell finite element analyses based on the superposition method. The validity of the in-house module and the reliability of the homogenization method are verified through the illustrative numerical experiments.     

Analysis of three-dimensional textile preforms for multidirectional reinforcement of composites

A mathematical model has been developed to describe the structural geometry of three-dimensional textile preforms made by the two-step braiding process. These structures consist of parallel yarns, interconnected with braiding yarns, that lie in complex spatial orientations. The model predicts structural features such as fibre orientation, fibre volume fraction, and interyarn voids from the key process variables of braiding pattern, advance rate, and yarn geometry. The limiting geometry was computed by establishing the point at which yarns jam against each other. Using this factor makes it possible to identify the complete range of allowable geometric arrangements for this type of preform. Experiments of several bare and impregnated samples confirmed the theoretical predictions and demonstrated that very high fibre loadings (above 75% fibre volume fraction) could be achieved. The modelling technique used a “unit cell” approach, which can be applied to many other types of preform for advanced composites.     

An inverse method for material parameters determination of titanium samples under tensile loading

Different approaches used for the simulation of woven reinforcement forming are investigated. Especially several methods based on finite element approximation are presented. Some are based on continuous modelling, while others, called discrete or mesoscopic approaches, model the components of the fabric. A semi discrete finite element made of woven unit cells under biaxial tension and in-plane shear is detailed. In continuous approaches, the difficulty lies in the necessity to take the strong specificity of the fibrous material into account. The yarn directions must be strictly followed during the large strains of the fabric. This is the main goal of the non-orthogonal model and of the hypoelastic constitutive model based on the yarn rotation presented in this paper. In the case of discrete and semi-discrete approaches the directions of the yarns are “naturally” followed because the yarns are modeled. Explicitly, however, modeling each component at the mesoscopic scale can lead to high numerical cost.     

Three-scale modeling and numerical simulations of fabric materials

Based on the underlying structure of fabric materials, a three-scale model is developed to describe the mechanical behavior of fabric materials. The current model assumes that fabric materials take on an overall behavior of anisotropic membranes, thus the membrane-scale is taken as the macroscopic scale of the model. Since fabric materials exist only as thin structures and there is no corresponding bulk material having a similar constitutive property, the direct approach of the mechanics of surfaces is employed. Following the membrane-scale, a yarn-scale is introduced, in which yarns and their weaving structure are accounted for explicitly. Yarns are modeled as an extensible elasticae. A unit cell consisting of two overlapping yarns is used to formulate the weaving patterns and the interaction between the yarns, which governs the nonlinear constitutive behavior of fabric materials. The third scale, named fibril-scale, accounts for the fibrils constituting a yarn and incorporates their mechanical properties. Via a coupling (handshake) process between these three scales a couple model is introduced. The overall behavior and performance of various fabric products becomes predictable by the knowledge of the material properties of a single fibril and the weaving structure of the fabrics. In addition, potential damage during deformation is also captured in the current model through breakage of fibrils in the fibril-scale.     

Properties of yarn pull-out in para-aramid fabric structure and analysis by statistical model

The aim of this study is to analyze and determine the pull-out properties of para-aramid woven fabrics. Para-aramid Kevlar29® and Kevlar129® woven fabrics were used to conduct the pull-out tests. They have high and low fabric densities. A yarn pull-out fixture was developed to test various fabric sample dimensions. Data generated from single and multiple yarn pull-out tests in various dimensions of Kevlar29® and Kevlar129® woven fabrics included fabric pull-out forces, yarn crimp extensions in the fabrics and fabric displacements. The regression model showed that yarn pull-out forces depend on fabric density, fabric sample dimensions and the number of pulled ends in the fabric. Yarn crimp extensions depend on the crimp ratios of the fabric and fabric density. Fabric displacements depend on fabric sample dimensions and the number of pulled yarns.     

Effect of fabric compaction and yarn waviness on 3D woven composite compressive properties

3D-woven fabrics incorporate through-thickness reinforcement and can exhibit remarkable inter-laminar properties that aid damage suppression and delay crack propagation. However, distortions in the internal architecture such as yarn waviness can reduce in-plane properties, especially in compression. The degree of yarn waviness present in a 3D woven fabric can be affected by a range of factors including weave parameters and manufacturing-induced distortions such as fabric compaction. This paper presents a thorough analysis of the effect of fabric compaction and yarn waviness on the mechanical properties and failure mechanisms of an angel-interlock fabric in compression. Tests were conducted on coupons moulded to different volume fractions and data compared to previous measurements of local yarn angle. Major findings show the importance of yarn straightness on compressive strength and how this can be affected by optimising moulding thickness. Failure initiation was also found to be heavily influenced by weave style and yarn interlacing.