Theory of the Shear Deformation of Fibrous Assemblies

Abstract

The initial response of the unit fibrous cell to an externally applied shear stress is assumed to involve both the bending of fiber sections and slippage at contact points. The criterion used to determine whether a contacting fiber will bend the contacted fiber section or whether it will slip along it depends on the relative angles of the two fiber sections to the external stresses. The total proportion of slipping and nonslipping contact points is thus derived using the density function of fiber orientations within the unit fibrous cell. The derived modulus values for shear behavior are related to the moduli derived earlier for compression behavior. The symmetry rules for selected idealized orientation distributions ( e.g., random) of the fibers in the unit cell provide a check on the validity of the derivations.The use of continuum mechanics to model the behavior of assemblies of fibers remains restricted by inadequate knowledge of the constitutive properties of the unit fibrous cell. In the last three years since we first raised this issue [4], a number of papers have appeared that have improved our understanding of how the unit cell responds in tension [ 2 ] and compression [ 3,8 ] . This understanding includes a prediction [ 3,8 ] of the various Poisson's ratio terms so that algorithms are now available for estimating many of the tangent compliance terms in the general material properties matrix.While these recent analyses of tension and compression have been able to draw on a long established legacy of published research dating back at least to the theories of Grosberg [ 5 ] and van Wyk ( I 1 ] , respectively, the same does not apply to shear behavior. Indeed while it has long been recognized that shear between layers of fibers in yarns [ I ] or fabrics [ 5 ] does occur, the theoretical treatment of shear as a continuum strain has received only minimal attention. Where it has been modeled, the shear deformation has been treated as frictional slippage between layers of fibers. As such there has been no consideration of the low-strain response of the assembly under shear stress, no elastic strain energy due to shear has been calculated, and only the inelastic mechanisms associated with catastrophic shear failure ( i.e., massive slippage) have been dealt with.It is cert.ainly true that such simple textile deformations as twisting a yarn [9] or bending a fabric [ 5 ] involve almost immediate shear failure, because the ' essentially parallel fibers slide past each other with almost no restraint in accommodating large deformations of the yarn or fabric. The simplest way of treating this problem is to assume a high initial linear shear stiffness [ 5 J ( e.g., equal to the fiber modulus) up to a small critical shear stress. Thereafter, the assembly may be considered to shear via frictional slippage with no increase in shear stress. The work done against friction must be accounted for in the energy equations, but the tangent compliance in shear for initial shear stresses above the threshold level may in fact be rega...

Physical properties of twisted structures. II. Industrial yarns, cords, and ropes

“…However, Grosberg and Smith 34,91 have shown that if one pulls a fiber from a twistless sliver, the withdrawal force WF per unit length of fiber required is given by WF ϭ ЈP ϩ WFo (17) where P is the external pressure applied to the fiber mass; Ј is the equivalent frictional coefficient but with dimensions of length, and WFo is the value for WF when P ϭ 0, that is, the cohesion force. This conclusion has been utilized by Carnaby and Pan 75,86 to predict the compressional hysteresis and the shear modulus of fiber assemblies.…”

“…On the other hand, the existing fiber contact point will also abate the free volume of the fiber mass, and consequently increase the chance for successive fibers to make new contacts. Some of the research results in this area have been applied to study the compressional 75,83 and shear 86 behavior of general fiber assemblies, as well as the prediction of nonwoven products, 77 leading to considerable progress in those areas.…”

Adhesive contact in filaments

“…By denoting a and b as the semi-axes of the ellipse of the contact zone, the peak pressure can be determined by (11) from which we have (12) In the above P is the compressive force that is actually the resultant adhesive force between two filaments in contact. The peak pressure is 1.5 times the average pressure on the contact surface, and a is related to the compressive force P and the semi-axes of the ellipse a and b [29] such that (13) where the semi-axes a and b are determined as (14) In the above, coefficients m and n are numbers depending only on the ratio (B -A) to (A + B) as tabulated in the literature [28]. Now, let us consider the compressive force induced by surface adhesion between filaments in contact.…”

Change of Yarn Hairiness during Winding Process: Analysis of the Protruding Fiber Ends

“…Figure 2 Contacting illustration between the tension disk and the yarn. where is the effective aspect ratio of the fiber within the contacting area of the tension disk, and n c1 is the mean number of fiber contacts over the length L e1 , and other parameters can be obtained from Hickie and Chaikin [3] and Pan [6]. The fiber length L e2 , which is outside the acting area of the tension disk, can be calculated as:…”