Dusan C. Prevorsek

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.

Determination of Non-Flow Shrinkage Ratio in Oriented Fibers

A method for the determination of the non-flow shrinkage ratio of oriented fibers is described. The dimensional changes accompanying the transition of an oriented semi-crystalline molecular structure into a disoriented amorphous random coil structure are shown for various types of fibers. Irradiation and fatiguing had a pronounced effect on fiber shrinkage, both in the magnitude of shrinkage and in the temperature range where the shrinking process terminates. A previously derived theory of shrinkage was applied to obtain values for the average crystallite sizes in the fibers studied. These were found to be in accord with estimates made by others using x-ray methods.

Fatigue in Textile Fibers Part VI: Fatiguing by Cyclic Tension; Effects of Frequency on the Statistics of Lifetimes

Experimentation has meluded investigation of the effects of frequency on the hfetime distributions of an acrylic sample and Types 52 and 420 Dacron2 fibers. Increase of frequency of cyclic loading was found to result In an increase in the dispersion of life times (in number of cycles) in the acryhe sample. The effect of mereasing the frequency was to raise the general level of the lifetime distributions of both Types 52 and 420 Dac ron. In general, the scatter in lifetimes at any one frequency was found to be much smaller for these samples than it was for the acrylic. The distributions for the two Dacrons were observed to be virtually unimodal. The third asymptotic function was acordmgly assumed to be apphcable. Estimates of parameters of this distribution. at various frequencies, were caculated and tabulated. A noteworthy finding was that while Type 420 Dacron has higher average lifetimes at various frequencies than Type 52, the minimum lifetimes of both are effectively zero. The average number of cycles to failure was found to increase with frequency in all three samples, although not in expected accord with a simple linear relationship. A possible explanation for the deviations is offered. Auxiliary tests, made in an attempt to account for the large differences in fatigue behavior between Type 52 and 420 Dacron, showed the latter to have substantially higher molecular weight and better orientation.

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.

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

Fatigue in Textile Fibers Part VII: Fatiguing by Cyclic Tension; Considerations of Creep and Force Data

Creep measurements during fatiguing by cyclic tension have been made on an acrylic fiber and two types of Dacron,2 at various strokes and frequencies. The curves for creep extension vs fatiguing time in cycles for the acrylic sample were found to be concave downward, whereas those for the Dacron fibers are concave upward, suggesting basic differences in the original structures and the structural changes occurring during fatiguing. The results indicate that there exists an inverse relationship between the number of cycles to failure and the minimum creep rate in the case of acrylic fibers. Creep extension at break, in a number of fiber samples, was found to decrease as the average lifetime increases as a rsult of reductions in stroke, and also, in the acrylic sample, as a result of increases in cyclic frequency. Simultaneous measurements of creep and force in a number of samples indicate that most of the changes in the geometry and dynamic properties of the fiber specimens occur in a very short initial interval of the fatiguing period. These data are taken to indicate that creep is only an accon ni ment of fatiguing by cyclic tension, and not the immediate cause of final rupture, which is believed to be the result of crack propagation.

Endurance of Polymeric Fibers in Cyclic Tension

Abstract The performance characteristics of simple filaments in fatigue in cyclic longitudinal tension are reviewed and discussed in terms of a theory which assumes that the fracture is a result of the formation of an unstable crack. It is shown that the derived relationships are in qualitative agreement with observed effects of temperature, frequency, stroke, etc. In quantitative studies however, and especially with those intended to extract values of unknown parameters, it must be observed that the derived expressions apply only for the conditions where the effects of structural reorganization in front of the propagating crack are negligible in comparison with the effects associated in the formation of new crack surfaces. Thus, the theory is applicable primarily to highly oriented fibers which are ruptured at temperatures below Tg. In the analysis of the results of the fatigue experiments, it is also necessary to take into account the structural changes which take place during the initial period of load...

A Microscopical Method for the Study of Free Thermal Shrinkage in Oriented Polymers

Oriented polymers exhibit considerable dimensional change on heating. Since it is evident that the magnitude of the shrinkage and the temperature range in which it occurs mutt reflect the composition and structure of the fiber, it is believed that the study of fiber shrinkage, especially the nm.rimum non-flow shrink, as a function of temperature may be a fundamental and very useful method of charWterizing fibers. In fact,

Distribution of Measured Lifetimes

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