Theory of the Compression Hysteresis of Fibrous Assemblies

Abstract

An analysis of a fibrous assembly at large deformations has been explored as a means of predicting the compressional behavior, especially the compression hysteresis. The essential principle is to classify all the fiber contact points in the assembly as either slipping or nonslipping, so they can be dealt with separately. The compressional modulus and Poisson's ratio are derived and shown to be dominated by the mechanical properties and the directional distribution of the individual fibers within the assembly. An iterative algorithm, in which the system geometry is updated on successive incre ments, is developed to cope with large and nonlinear deformations. A comparison between the theoretical prediction and the experiment has indicated reasonable agree ment. An improvement could probably be achieved by including the contribution of fiber viscoelasticity to the total hysteresis.

Compressibility of carbon fabrics with needleless electrospun PAN nanofibrous interleaves

“…cycle, then a certain part of the deformation is not recovered when the load is released, and the thickness under given load decreases for each successive cycle. This hysteresis behavior is studied in [28]. Typically after the third cycle the differences between the subsequent cycles become negligible.…”

“…Compression behavior of random fibrous assemblies is controlled by a number of factors as fiber bending rigidity and friction and fiber orientation and density in an assembly. Descriptive and to certain extent predictive theories for compression resistance can be found in [28,29]. So far as the listed properties of two different fiber assemblies are close, one can expect that the compression response of these assemblies is close as well; the differences of these properties lead to different compression resistance.…”

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

“…The peak pressure p 0 is located at the center of the contact zone. 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].…”