W. James Lyons

Theoretical Values of the Dynamic Stretch Moduli of Fiber‐Forming Polymers

Employing concepts first applied to textile fibers by Meyer and Lotmar in calculating the elastic stretch modulus of the crystalline domain of cellulose, the moduli of crystalline polyhexamethylene adipamide (α form), and polyethylene terephthalate have been derived. The treatment employs interatomic force constants for the stretching and bending of primary valence bonds, applied to molecular geometries deduced from the crystal structures of these polymers as determined by Bunn and co‐workers. The modulus of the crystal cell of the first material (nylon 66) is calculated to be 15.7×1011 dyne cm−2, while that of the second is 14.6×1011 dyne cm−2. Supposedly these are approximately the modulus values which fibers having perfectly oriented, efficiently packed molecules would have. In both cases the theoretical value is at least an order of magnitude larger than that found experimentally for actual production samples.

Fatigue Fracture in Fibrous Polymers as a Brittle, Crack‐Nucleation Process

An interpretative analysis of experimental results on the failure of synthetic fibers in fatigue under cyclic tension leads to the conclusion that rupture is of a brittle nature. Although molecular rearrangement undoubtedly takes place during longitudinal fatiguing, rupture itself cannot be regarded as a viscous, laminar flow process. Failure is localized; the undamaged sections of the specimens show relatively less important effects of the fatiguing. Lifetime cannot be predicted from measurements of fiber tenacity, modulus, or rate of creep. A theory of fatigue rupture, based on the observation of cracks in specimens strained to breakage, is formulated. The treatment involves the assumption that a crack grows by a nucleation process up to a critical size. At a slightly larger size, the crack becomes unstable and propagates spontaneously, to produce rupture. The theory leads to an expression for lifetime as a function of stress that is in substantial agreement with experimental data on a number of samples.

Statistical Treatment of Data and Extreme-Value Theory in Relation to Fatigue in Textiles

The use of central measures of lifetime to characterize fatigue behavior is misleading, and more attention should be paid to early failures and expected minimum life. Differences in the dispersions of lifetimes between samples may lead to faulty conclusions if these are based on mean lifetimes. The possible dependence of dispersion on stroke is considered. Because of dispersion in fatigue data, it is necessary to test large numbers of specimens to make reliable predictions. The inadequacy of observed central values as bases for judging the applicability of a distribution is discussed. Criticism leveled against the commonly used logarithmic-normal distribution is cited. Criteria are presented for the development of a lifetime distribution that takes into account the physical realities of the fatigue process. Analytical expressions for a number of concepts in the statistics of fatigue are reviewed. The theory suggesting the application of the third asymptotic distribution is outlined. The distribution has been adapted to accumulated fatigue data on an acrylic fiber sample.

Fatigue in Textile Fibers Part I. General Considerations; Fatiguing by Cyclic Tension: Instrumentation and Fatigue Lifetimes

Equipment on which six fiber specimens can be simultaneously fatigued in cyclic tension, at one common strain amplitude, has been developed and constructed. Fre quencies are continuously variable from zero to 18 cycles/sec, and the total stroke is adjustable from zero to 1 in. Provisions are made for the automatic taking up of the slack resulting from growth in each fiber and stopping of the machine at the conclusion of a test. The growth in each specimen and the time to rupture are recorded on a strip chart. Results on two viscose samples and one experimental acrylic sample suggest that the growth that occurs during the fatiguing has two phases, in both of which the increase in extension is substantially linear with the logarithm of time. The rate of extension (per unit log time) in the initial phase is at least twice as great as in the later phase. In a third viscose sample, of high crystallinity, in which the growth rate of extension and the extensions at break were both low, the distinction between the two phases prac tically vanishes. Fatigue lifetimes of the acrylic sample appear, from plots on probability paper of the individual lifetimes of the specimens, to conform better to a logarithmic normal distri bution than to the normal.

Influence of Fiber Geometry on the Mechanical Properties of Assemblies During Processing Part I : Polyester Fibers in Webs and Slivers

Samples of polyester fibers have been processed on the worsted system from raw stock through the 4th pin-drafting stage. The samples consisted of all combinations of two widely-differing levels of each of the following fiber variables: (a) surface roughness, (b) cross-sectional shape, (c) linear density, (d) crimp, and (e) staple length. Laboratory evaluations were conducted the cohesion, elasticity, and resilience of card webs, and for the static and dynamic cohesion, evenness, and fiber orientation of slivers. In general, the important conclusions were that staple length and crimp are the most highly significant factors controlling the cohesion and related properties of the fiber assemblies; the other variables are statisti cally significant at lower levels. Additionally, three pertinent fiber properties were measured on specimens removed from a number of subsample assemblies. The results of tests on specimens removed from 4th pin-drafting slivers showed that the rough and smooth fibers retain their distinctive surface characteristics through the successive stages of drafting. Crimp measurements indicated that this characteristic is retained through the opening and carding operations, but is substantially removed during pin drafting. Length analysis of fibers from 4th pin-drafting slivers showed that some breakage occurred in 6-in. samples during processing.

Fatigue in Textile Fibers Part III: Fatiguing by Biaxial Rotation

A single-station machine on which a fiber can be fatigued in a localized region, by being axially rotated in a bent configuration, has been built. The test fiber, on either side of the bend, is mounted on shafts at 90° to each other, driven at the same rotary speed. Speeds up to 550 rpm are attainable. Nylon 66 and nylon 6 monofils in a number of diameters from 8 to 28 mils have been fatigued in biaxial rotation on this machine, in a fourfold range of rotary velocities and for periods of 15, 30, and 45 min. They were then tested for residual breaking tenacity and extension. A few fibers have been fatigued for other periods of time, or to rupture, for microscopic examination of the fatigued region. In most samples the rupture properties decrease with increasing rotary velocity, for any given fatiguing period. The rate of this decrease tends to be lower in the range of higher velocities. The shapes of the breaking-extension curves are largely determined by those of the breaking-tenacity curves, reflecting the near-linearity of the tenacity- extension relationship. The monofils of smaller diameter, especially those of nylon 6, are less affected by the increase in rotary velocity. In most of the samples, the residual breaking tenacity appears to be largely determined by the total number of revolutions sustained by the specimen, with no consistent influence of rotary velocity on the results. Monofils of the higher draw ratios and those that had been heat-set show a much sharper decline in residual properties with increasing rotary velocity than do the non- heat-set samples of lower draw ratio. However, the breaking tenacities of the heat-set samples retain their relatively higher positions after fatiguing under most conditions. Representative photomicrographs of monofils fatigued at various velocities and for different periods short of rupture show progressive development of diagonal fissures in the fatigued regions, especially in the nylon 66, and of a bulbous expansion in the nylon 6 specimens. Photomicrographs of the broken ends of monofils fatigued to rupture indi cate that the breakage in nylon 6 occurs across planes coinciding with the diagonal fissures. In nylon 66 the breakage appears to occur in a roughly transverse plane.

Fatigue in Textile Fibers Part XI: Fatiguing by Cyclic Tension: Effects of Temperature, Stroke, and Frequency on Lifetimes

Supplementing earlier studies, experiments have been conducted on polyester (PET), aromatic polyamide (APA), and polypropylene (PP) fiber samples at various strokes and at temperatures ranging from 23° to 90°C. In the PET, at a reduced stroke of 3.4%, a rise in logarithmic lifetime with increasing temperature was found; the same trend was exhibited by this material at higher strokes. In the APA and PP, at the strokes used, declines in lifetime with increasing temperature were observed. In all cases, the general level of lifetimes was raised with reductions in stroke. Considerable growth in the PP fibers during fatiguing was observed. Review of lifetime data on PET, nylon 66, and APA samples, at a number of strokes and temperatures, leads to the con clusion that the distributions of these data tend to conform to the Weibull third asymptotic pattern. Analysis of data on lifetime as a function of stroke, for six man- made fiber samples, reveals good agreement with an expression, originally proposed for metals, which relates these two variables. It is shown that results on an acrylic and two PET samples conform to an empirical formula which relates the frequency of cyclic loading to lifetime, and, furthermore, that this formula is a simplification of a theoretical expression developed in fatigue studies at TRI.

Fatigue in Textile Fibers Part V: Fatiguing by Cyclic Tension: Probability-Strain-Lifetime Relationships for a Polyester Sample

It is shown that fatigue data on a polyester sample. Type 52 Dacron, 2may reasonably be taken as conforming to the third asymptotic distribution. Expressions are derived for the probability of survival as a function of strain amplitude and fatigue lifetime (number of cycles to rupture), based on this distribution. A family of curves of strain amplitude vs lifetime, corresponding to various probabilities of survival, is presented for the polyester sample.

Concerning the Theory of Fatigue Failure in Textile Materials

A minor modification of the reaction rate theory of flow is proposed with the aim of accounting, in terms of molecular processes, for the observed dependence of dynamic properties, particularly fatigue, on the frequency of stressing. To this end a factor ϕ (v). which is a function of the frequency v. is introduced into the expression for the rate of breakage of bonds in the macromolecules of textile materials. It is shown that with this reasonable assumption of a frequency factor there results a general expression which, like earlier expressions, is compatible with the known dependence of fatigue life on tem perature and stress under dynamic as well as dead loads. The present development goes further, permitting the derivation of a specific expression which is in accord with the ob served frequency dependence of the fatigue life of a textile material.

Law of Cumulative Damage in the Fatigue of Textile Fibers1

In 1945 Miner [2], working in a non-textile field, proposed a relationship for the quantitative expression of the &dquo;cumulative damage&dquo; incurred by specimens fatigued under various levels of cyclic stress, in sequence. The underlying notion is that if a specimen is fatigued under certain conditions, the permanent, fractional damage sustained can be expressed as the ratio of the number of cycles to which the specimen had been subjected to the number of cycles to failure under the