Yarn Extension Research Articles

Evaluation of Poisson’s ratio of textiles from mesoscopic models

The magnitudes of Poisson’s ratios can attain some peculiar values for woven fabrics, in contrast to conventional engineering materials, leading to unusual stress–strain relationships. A mesoscopic discrete model of dry fabric has been presently developed at the scale of the armor, accounting for the yarn–yarn interactions at the yarns crossing points. From a mechanical viewpoint, yarns are modeled as elastic straight bar elements representing stretching springs connected at frictionless hinges by rotational springs. The motion of each node along the yarn is described by a lateral displacement and a local rotation. The reaction force exerted by the transverse yarns at the contact points is calculated from Timoshenko theory, and the work of the reaction forces is incorporated into the structure potential energy. The equilibrium shape of textile structures submitted to external loading is identified as configurations achieving the minimum of the potential energy; a genetic search algorithm has been implemented for the determination of the global minimum of the total potential energy. The transverse behavior of plain weave fabric is evaluated in terms of the Poisson’s ratio, based on virtual simulations at the mesoscopic scale of analysis. Poisson’s ratio first increases towards a maximum due to the rapid shrinkage of the sample in the transverse direction, and decreases thereafter when the crimp changes are exhausted, with yarn extension as the main deformation mechanism. The influence of the mechanical properties of both warp and weft on Poisson’s coefficient is assessed. Scaling laws of the equivalent elastic properties of plain weave versus characteristic geometrical parameters (as the pick spacing) of the plain weave armor are determined. The predictions of the mesoscopic models provide a guideline for the design of woven fabrics.

MESOSCOPIC MODELS OF WOVENS: A GENERAL STRATEGY BASED ON THE MINIMIZATION OF THE POTENTIAL ENERGY INVOLVING GENETIC ALGORITHMS

Mesoscopic discrete models of dry fabric have been developed based on a discretization of the yarn geometry, accounting for the yarn–yarn interactions at the yarns crossing points. From a mechanical viewpoint, yarns are modeled as elastic straight bar elements representing stretching springs connected at frictionless hinges by rotational springs. The motion of each node along the yarn is described by a lateral displacement and a local rotation. The expression of the reaction force exerted by the transverse yarns at the contact points is assessed from Timoshenko beam theory. In a general situation, the reaction force is obtained by solving a linear system of equations involving all the nodal displacements at the contact points (with the transverse yarns) for each yarn. The equilibrium shape of the woven is obtained as the minimum of its total potential energy, accounting for the work of the reaction forces due to the transverse yarns. The finding of the absolute minimum of the structure’s total potential energy is achieved by a genetic algorithm, based on an initial guess of the solution relying on beam mechanics. Simulations of the fabric response under uniaxial tension evidence the effect of yarn-yarn interactions due to the increase of the reaction forces, as well as the effect of the transverse yarn properties. Plain weave has a nonlinear response due to the crimp change, whereas serge shows a quasi linear response due to yarn extension being the dominant deformation mechanism.

The low-stress tensile behaviour of single worsted yarns

A geometrical model is proposed to explain the conformational change of fibres in a single yarn during extension in the low-stress region, assuming that fibre slippage and fibre elongation do not occur. The key parameters affecting the yarn low-stress extension are the yarn twist factor and the yarn packing fraction. On extension, a yarn is compressed diametrally and a limit of low-stress extension is attained when the yarn packing fraction reaches an assumed maximum value of 0.76. Using the Van Wyk theory of compression of fibre assemblies, a relationship between the tensile stress and the yarn extension is derived and the load-extension curve of a single yarn in the region of low-stress extension is defined. Equations are also derived enabling calculation of the yarn packing fraction from the low-stress load-extension curve of a yarn. This work establishes a first step towards the more complex models to characterise the low-stress extension of twofold yarns and woven fabric.

Advanced material model for coated fabrics used in tensioned fabric structures

An accurate and reliable material model for plain weave coated fabrics used in the construction of Tensioned Fabric Structures (TFS) is developed in this paper. The paper begins with an account of the material response of these fabrics, furnishing an understanding of the key elements that a successful material model should encompass. The paper also contains a review of existing models, which has highlighted the need for an accurate, reliable and fully calibrated material model. The proposed material model consists of a series of nonlinear elastic elements, frictional elements and rigid links to model the yarns, and an isotropic plate to model the coating. The high degree of accuracy and reliability attained is demonstrated through comparison against experimental results. This is attributed to faithfully capturing the major deformation mechanisms that prevail in TFS, which include crimp interchange, yarn extension and crushing, friction, coating extensions and fabric shear. The success of this work paves the way for accurate and reliable analysis of TFS, providing better control and assessment of stress states encountered in the field.

Analysis of a Novel 3D Hybrid Woven/Knitted Fabric Structure

In Part I of this series, a geometric model was developed to predict loop length, yarn consumption, and thickness of a novel 3D hybrid woven/knitted fabric structure. In this part, a mechanical model is generated for estimating the Young's modulus and extension of the 3D hybrid woven/knitted fabric structure. Castigliano's theorem is used to derive the relations. The compression, extension, and bending energies of yarns are considered for the total strain-energy formula of the fabric. The mechanical model is verified for the fabric Young's modulus. There is reasonable agreement between theory and experiment considering the assumptions made and the complexity of the 3D fabric structure. The deviation is less with high performance multifilament fibers in the warp and bias yarns.

A Constitutive Model for Blended Yarn Extension with Fragmented Low-Elongation Fibers

A simple micromechanical model is developed for the interactions in a parallel square-stacked mixed array of elastic fibers representing the microstructure of a blended yarn undergoing axial extension. The mixed array consists of a small fraction of relatively high modulus, low elongation-to-break (LE) fibers dispersed among high elongation-to-break ((HE) fibers. The LE fibers are assumed to break into fragments, and the LE fiber fragments are assumed to slip relative to neighboring fibers in regions near the fragment tips. The fiber array experiences lateral compression arising from the remote tension on the twisted yarn, and frictional forces acting at slipping fiber-to-fiber contact surfaces are assumed to obey Amontons' law. Solutions of a dimensionless boundary value problem for deformations in a unit cell of the fiber array are presented. Dimensionless parameters involving the constituent LE and HE fiber properties are identified and their influence on blended yarn tensile behavior is illustrated.

On Thermo-mechanical Coupling and Heat Transfer in the High-strain-rate Extension of Continuous Filament Yarns

The effect of thermo-mechanical coupling arising from fiber plasticity on the load–extension behavior of continuous filament yarns extended at high-strain rates is investigated using an analytical approach. The plastic deformation behavior of the fibers is assumed to follow a simple constitutive relation incorporating linear thermal softening and linear strain hardening. A micromechanical model for fiber-to-fiber heat conduction is developed and used lo analyze heat transfer within the yarn. Fiber-to-fiber heat conduction is shown to be quite sensitive to the size of the fiber contact region. Results are presented for the temperature rise and tension in a single 0.72 tex nylon fiber and a simulated 195 tex nylon yarn during extension at a variety of strain rates. The nylon yarn exhibits a significant thermal softening effect when extended at strain rates of 0.1s−1 and higher. Fiber temperatures are seen to vary significantly from the interior to the surface of the yarn at a strain rate of 0.1s−1, but at higher rates, say 5s−1, the temperature distribution is seen to be nearly uniform. The analysis here and in previous work is used to interpret some literature experimental results on high-strain-rate extension of nylon yarns.

Modelling Fabric Mechanics

Mechanics of textile fabrics by modelling of equilibrium of forces is difficult to apply broadly in practical applications. An alternative, which offers more promise for industrial utility in computer-aided design, is the energy-based approach described by Hearle and Shanahan (1978 a, b). The paper reviews the basic principles and considers the ways of introducing appropriate energy terms to cover yarn extension, yarn bending, yarn flattening, and friction at crossovers. The main discussion is given for the elastic response of simple, plain-weave fabrics, based on several different geometric models, but the ways to deal with other fabrics and conditions are also suggested. The paper provides a protocol for advancing the subject from academic research to commercial use.

Prediction of statistical strengths of twisted fibre structures

A new approach, based on Daniels' statistical model for a parallel fibre bundle and the recent results on yarn mechanics by the present author, is introduced to predict the strengths of twisted yarns including the effects of interfibre friction and the fibre fragmentation mechanism during yarn extension. By calculating the lateral pressure in a twisted yarn, the critical fibre length of the fibre fragmentation process has been determined, and was found to decrease together with the increasing yarn strain. This, according to the Weakest link theorem, will lead to a substantial increase of fibre strength. Incorporating this conclusion into Daniels' result yielded a more realistic prediction of the strength and its boundary for a twisted fibre structure. The key differences between a filament yarn and a short-fibre yarn and their effects on strengths are also discussed. The major results from the study are illustrated schematically.

Development of a Constitutive Theory for Short Fiber Yarns Part II: Mechanics of Staple Yarn With Slippage Effect

A general constitutive theory governing the mechanical behavior of staple yarns and including the effect of fiber slippage during yarn extension is presented in this paper. A differential equation describing the stress transfer mechanism as well as the slippage influence in a staple yarn is applied by which both the distributions of fiber tension and lateral pressure along a fiber length are derived. A so-called fiber slippage ratio λ is defined in terms of fiber and yarn properties to specify the length along both ends of a fiber that is slipping during yarn extension. Factors such as fiber dimensions and properties, the effect of the discontinuity of fiber length within the structure, and fiber orientations in the yarn are all included in the theory. The slippage effect is incorporated into the results obtained in Part I of this study, so that the tensile and shear moduli as well as Poisson's ratios of the yarn with slippage effect are theoretically determined. Comparisons of these properties in both cases with and without the slippage mechanism are provided in this paper.

Development of a Constitutive Theory for Short Fiber Yarns: Mechanics of Staple Yarn Without Slippage Effect

This article reports an attempt to develop a general constitutive theory governing the mechanical behavior of twisted short fiber structures, starting with a high twist case, so that the effect of fiber slippage during yarn extension can be ignored. A differential equation describing the stress transfer mechanism in a staple yarn is proposed by which both the distributions of fiber tension and lateral pressure along a fiber length during yarn extension are derived. Factors such as fiber dimensions and properties and the effect of the discontinuity of fiber length within the structure are all included in the theory. With certain assumptions, the relationship between the mean fiber-volume fraction and the twist level of the yarn is also established. A quantity called the cohesion factor is defined based on yarn twist and fiber properties as well as on the form of fiber arrangement in the yarn to reflect the effectiveness of fiber gripping by the yarn. By considering the yarn structure as transversely isotropic with a variable fiber-volume fraction depending on the level of twist, the tensile and shear moduli as well as the Poisson's ratios of the structures are theoretically determined. All these predicted results have been verified according to the constitutive restraints of the continuum mechanics, and the final results are also illustrated schematically.

LOCAL IRREGULARITY MEASUREMENTS ON THE PERIODIC STRUCTURE OF WOVEN FABRICS UNDER UNIAXIAL TENSION

The uniaxial extension behavior of a woven fabric has been observed using optical diffraction method. By measuring intensity distributions, we have obtained the average spacings between neighboring two yarns within an accuracy of the order of 1% and their local irregularity as a statistical deviation over a range of 2 to 8% in the warp and filling directions. The point of inflexion on the load-extension curve, which indicates the initial point of the yarn extension, has been determined directly by detecting the maximum of the diffracted intensity as a function of the yarn extension. The first part of the extension has also been analyzed by the crimp interchange model.

A nonlinear elastic constitutive model for coated fabrics

A nonlinear elastic constitutive model for coated fabrics is developed. The model which accounts for the basic mechanisms of yarn rotation, yarn extension and coating extension is obtained by expressing the equations of equilibrium for a unit cell of the material in terms of effective continuum stresses and strains. A systematic method of determining the model parameters is proposed. Based on the parameters obtained from a single biaxial test, theoretical curves are plotted for various biaxial loading states and compared with experimental results for several commercially available structural fabrics.

Optimization of fiber drawing processes in terms of the filament state variables

AbstractA new method of optimizing the fiber drawing process involving the feed roll, the heated elements and the take‐up roll is presented. In this method, the process is described in terms of the filament temperature and filament extension in the drawing zone. This is in contrast to the conventional approach in which the machine control variables such as the heated element temperature, fiber feed velocity and the total draw ratio were used to describe the process. It is shown that the drawing process seldom proceeds by a simple yielding mechanism and that a one‐step drawing process usually involves a yield draw followed by a post‐yield stretching. Using the drawing of nylon 6 fibers as an example, it is shown that the most critical factors related to achieving the highest fiber strength in drawing from a given precursor are the yarn temperature and yarn extension at yielding and during the post‐yield drawing.

Modified Equations for the Energy Analysis of the Plain Weave, Including Yarn Extension—Reply

Modified Equations for the Energy Analysis of the Plain Weave, Including Yarn Extension—Reply

Modified Equations for the Energy Analysis of the Plain Weave, Including Yarn Extension

Modified Equations for the Energy Analysis of the Plain Weave, Including Yarn Extension

Finite extension of a viscoelastic multiple filament yarn

This paper is concerned with the investigation of finite extension of a viscoelastic multiple filament and single layered yarn subjected to axial forces and twisting moments. The filament in the yarn is considered as a linear viscoelastic slender curved rod with circular cross section and helical configuration. The theory of slender curved rods is employed in the analysis whereby the curvature of the filament is assumed to be sufficiently small such that the cross section of the filament perpendicular to the axis of the yarn is approximately elliptical. In our study, we have also assumed that there is slipping between filaments during deformation of the yarn. Geometrical nonlinearity in introduced by the resuctions in helical angle and cross section of the filament. In order to illustrate the technique introduced here, in our numerical analysis, the extensional relaxation modulus of the filament is derived from a model of three-element solid and Poisson’s ratio of the filament is regarded as constant. Examples are presented for the extensions of yarns with fixed ends and yarns with free ends.

Temperature as a factor in the strength and breaking extension of filament yarns subjected to a tensile shock load

Temperature as a factor in the strength and breaking extension of filament yarns subjected to a tensile shock load

39—AN ENERGY ANALYSIS OF WOVEN-FABRIC MECHANICS BY MEANS OF OPTIMAL-CONTROL THEORY PART I: TENSILE PROPERTIES

The general energy analysis of fabric mechanics by means of optimal control presented in a previous publication is applied to the woven-fabric structure for deformations whereby the yarns remain in the same plane. The three-dimensional equations of the general theory are reduced to two-dimensional form, the boundary conditions are evaluated for the plain-weave fabric in biaxial tension, and an important mechanism of woven-fabric extension, which was not included in the general analysis, namely, the possibility of yarn extension, is introduced into the theory. The fabric load–extension curves and yarn-decrimping curves for the plain-weave construction are computed for a realistic range of input parameters: the yarn extension rigidity, weave crimp, degree of set, lateral yarn compression, and ratio of the curvilinear length of yarn in the warp direction to that in the weft direction of the fabric. The computed results are discussed in terms of the following dimensionless parameters: the applied tension per thread and the interaction force on the crossing thread (divided by the yarn bending rigidity), the relative fabric extension (the fabric extension divided by the yarn crimp), the initial relative fabric tensile rigidity, the Poisson's ratio of the fabric, and the initial tensile rigidity of the crimped yarn unravelled from the fabric. The tensile properties of plain-weave fabrics in both the grey state and the finished state are illustrated by reference to the computed results, which are also employed to explain the behaviour of yarns during the extension of woven fabrics.

On the Extension of Elastic Two-Ply Filament Yarns

This paper deals with the small extension of linearly elastic two-ply filament yarns. Each filament is treated as a long slender curved rod with circular cross section and helical configuration. Analysis is based on the linear theory of slender curved rods. Two problems are investigated, namely, the extension of a yarn with fixed ends and the extension of a yarn with free ends. In comparison with a previous study of a similar problem, it is found that the method adopted in this paper can provide more accurate results and better geometrical and physical insights into the problem. In this study, the yarn elongation and the filament stress are determined for yarns with various helical angles. The effect of the superposition of a twisting moment on the axial extension is also investigated.