W. Denney Freeston

Mechanics of Elastic Performance of Textile Materials Part XVIII. Stress-Strain Response of Fabrics Under Two-Dimensional Loading1

A theoretical analysis of the load-elongation behavior of idealized plain-weave fabrics subjected to biaxial stresses is presented. Fabric strains resulting from both crimp interchange and yarn extension are considered. The analytical expressions de rived have been solved with the aid of a digital computer for both linearly elastic and elasto-plastic materials. Time effects, although not explicitly included, are discussed. Generalized plots of the results are presented for the two extremes of initial fabric structure: (1) equal crimp distribution in both sets of yarns and (2) one set of yarns noncrimped (straight). The predicted and measured response of model fabrics are compared.

Mechanics of Elastic Performance of Textile Materials Part XVI: Bending Rigidity of Nonwoven Fabrics

Theoretical analyses of the effects of fiber diameter, fiber tensile and torsional stiff ness, fiber distribution and fabric density on the bending rigidity of nonwoven fabrics are presented. The fibers are assumed to exhibit linear tensile and shear stress-strain behavior. The two extreme cases of complete freedom and no freedom of relative fiber motion are analyzed. A comparison is made between the predicted and experimentally observed bending rigidities of a waterlaid, nonwoven fabric composed of short, straight viscose rayon fibers.

Strain-Wave Reflections During Ballistic Impact of Fabric Panels

A numerical model is presented which describes the strain level build-up in yarns due to multiple strain wave reflections from yarn crossover intersections in a woven fabric subject to ballistic impact. Crossing yarns present barriers from which strain waves are partially reflected. The maximum yarn strain occurs at the point of impact and decays with distance along the yarn away from this point. The rapidity of decay is governed by the crossover reflection coefficient. Using observations of the deformation cone size of ballistically impacted fabric panels, it is concluded that the reflection coef ficient is small (approximately 0.01). The strain increases with time at different rates for different reflection coefficients until failure at the impact point. Extensions of this model to other fibrous structures are discussed.

Crack propagation in woven fabric

The occurrence of crack propagation in flexible fiber assemblies, specifically woven fabric, is studied. The speed of propagation of a strain wave down a constrained filament is analyzed. Expressions for the strain energy released as the crack propagates and the kinetic energy and shear energy of the retracting material are developed, and the physical significance and relationships between the various forms of energy are studied. The effects of fiber and yarn properties, fabric construction, and coating properties on fabric resistance to crack propagation are analyzed. The analysis developed shows that high‐modulus fibers woven into fabrics with shear stiffness, e.g., long float weaves, can support the greatest applied load without propagating a crack. In the case of coated fabric, a coating with a low modulus at high shear rates applied in a manner whereby it does not penetrate the fabric structure gives the best performance. However, the most promising method for preventing the propagation of crack in c...

Geometry of Bent Continuous-Filament Yarns1

Expressions are derived for determining theoretically the number of filaments accommodatable in successive con centric rings in a multifilament yarn cross section as a function of yam twist and filament diameter. Increasing filament ellipticity with increasing twist is considered. Numerical values are tabulated for several typical filament diameters and a range of yam twists. The yarn packing factor is also given. Photomicrographs of model yarns illustrate that migra tion of filaments occurs with increasing twist; filaments are forced outward from one ring to the next as their ellipticity is increased. Photographs of bent, multifilament model yams show evidence of an increase in helix angle of the filaments on the inside of the bend and a decrease of those on the outside of the bend. A change of filament packing density upon bending is also evident. An increase in packing density on the inside of the bend and a decrease on the outside is observed for some degrees of bending; however, for severe bending the packing density appears to decrease throughout. Analytical results are presented graphically for the curvature and change in curvature of the filaments in a bent, twisted yam as a function of filament position in the yam cross section, yam twist, and radius of curvature. The most significant findings relate to the locations within the yam cross section of the maximum and minimum curvature and changes in curvature. A discussion of the classic geometrical model of a bent yarn as it relates to fiber mobility is included.

Mechanics of Elastic Performance of Textile Materials Part XVII: Torsional Recovery of Filaments and Singles Yarns, and Plied-Yarn Balance

Theoretical analyses of the torsional recovery of filaments and singles yarns and the ply back-twist required to give balanced plied yarns are presented. The methodology employed parallels that previously reported for filament bending recovery [4]. The filaments are assumed to be linearly elastic for shear stresses below the yield stress, to have a sharply defined yield point, and to exhibit linear work-hardening beyond the yield. Time effects, although not explicitly included, are discussed. The torsional behavior of small-diameter metal wire and some polymeric filaments is, approximated by these assumptions. The effects of bending stresses and tensile stresses imposed on fibers during spinning or throwing are neglected. The yarn torque which develops from the application of a tensile stress to a twisted singles yarn, which would otherwise not exhibit any residual torque, is also neglected. However, the magnitudes of the possible effects of tension on filament torque, and filament bending on yarn torque are noted. The analytical expressions obtained for the twist recovery of filaments as a function of filament diameter, material properties, and initial twist are verified experimentally. The analytical expressions for the twist recovery of singles yarns and the ply back- twist required to give balanced plied yarns are experimentally investigated. The causes of differences between the theoretical and experimental results are discussed.

Mechanics of Elastic Performance of Textile Materials Part XV: Filament Bending Recovery

Recovery from bending is an important end use requirement of most textile struc tures, being directly related, for example, to crease recovery of apparel fabries. Al though fabric bending recovery is influenced by yarn and fabric geometry, filament bending recovery plays a significant role. Thus, an understanding of the influence of filament properties on filament bending recovery is essential to the understanding of fabric bending recovery. An analysis of the bending recovery of filaments is presented. The filaments arc assumed to be linearly elastic for tensile stresses below the yield stress, and to have a sharply defined yield point. The filaments are further assumed to exhibit linear work-hardening beyond the yield, and to have the same properties in compression as in tension. Time effects, although not explicitly included, are discussed. The tensile behaviur of fine-diameter metal wire and several polymeric filaments is approximated by these assumptions. The analytical expressions obtained for the recovered radii of curvature of circular filaments as a function of the filament diameter, material properties, and initial radius of curvature are verified experimentally. The rigidity and bending recovery of ribbon and circular filaments of the same material and tensile strength are compared. Future publications, the basic work for which has been completed, will extend the analysis to twisted singles yarns, and woven and nonwoven fabrics.

Bending Rigidity of Random Webs

In reference [1], the authors presented a theoretical analysis of the influences of fiber diameter, fiber tensile and torsio~al stiffness, fiber distribution, and fabric density on the bending rigidity of nonwoven fabrics. The fibers were assumed to exhibit linear tensile and shear stress-strain behavior. The two extreme cases of complete freedom and no freedom of relative fiber motion were analyzed. Many of the nonwoven fabrics of current interest are essentially random webs. The fiber distribution in a unit cell in these fabrics is approximated by the assumption that the same number of filaments lie at each angle, i.e., the fiber angular frequency distribution can be taken as constant. The bending rigidity of such a unit cell is given in reference [1] by Equations 29 through 32 for the case of complete freedom of relative fiber motion and Equation 44 for the case of no freedom of relative fiber motion. L’tilization of these expressions requires the determination of Nf, the total number of fibers contained in the circle inscribed in a unit cell. However, it is not necessary to actually count the number of fibers in the inscribed circle. As shown in the appendix of this letter I

Filament Bending Recovery and Fabric Crease Recovery

I rthts III the 1&dquo;( It I t .111’ 11111’1 mtHnnnm.~tu)!~ )nht)<)r<! I I I I 111 (0% III(’ nx’nw’t ’ ’ t’nt’ht~Omn III 11 N I g I I I I I(’. I I It 1 4 t I t’ I ’1,,&dquo;1.....IIII( III pI&dquo; 11111 I .111 I t. BI 11. 111 ~-, <’) II B ’11’BB, 1111 I jhtpots pi 1’B 11111&dquo;’’’ ~u)ths)h’<! I III I I I I t .1 1 )It I It. I I. I i<11«1 , .111’ 11111 I suhttothd III 1 1 ( I I I I I . I II t % itBB .. I I I ( the ( .111 t I ii )I , ,1&dquo;’’’’&dquo;1111 I t liill I 1I&dquo;’HllhlhilllB hll’ 1111111111,1111111 g I % I III IIplllillll I cBt’wssct) I