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 loading (mechanical conditioning). In this period the fibers change considerably in their properties (modulus, elongation at break, etc.) which in turn affects the fatiguing conditions. In the interpretation of data obtained in fatiguing at constant stress or strain amplitude, it must be observed that the theory also indicates that the severity of fatiguing conditions should be expressed in terms of strain-energy amplitude instead of the commonly used stress- or strain-amplitude arguments. This analysis is based on the appearance of the term σ2/E=σε in the expressions for lifetime. It is conceivable that our experimental data discussed in Experimental (fourth subsection) would not show the large difference between fatiguing at constant stroke and constant force-amplitude, if the results of both experiments were plotted as a function of σ∈. The most important goal of our study was to establish a method for predicting the potential endurance of fibers from their molecular structure. The derived equations include the three primary parameters which are affected by the molecular structure of the polymers: fracture surface energy, modulus, and activation energy associated with the processes involved in crack growth. The physical significance of these factors is discussed and methods to estimate their numerical values from known molecular parameters are reviewed. In correlating or predicting the fatigue behavior from molecular structure of the polymer, it must be remembered that the derived expressions hold for a perfectly oriented, flawless ensemble of molecules. The studies of fiber morphology on the other hand, show that the fibers consist of at least two phases differing primarily in the degree of order. Since the studies of mechanical coupling between phases indicate a poor load transfer between phases it is obvious that the morphological characteristics (e.g., chain folding) play a very important role in the overall mechanical behavior of the fibers and, therefore, must be considered. The studies of the effects of morphology on mechanical properties of fibers are still in an early stage of development. Further work is required to elucidate the fiber morphology and especially the structure of the phase boundary (crystal surfaces, concentration of tie-molecules, etc.). Developments are also necessary in a theory which would adequately describe the mechanical responses of such complex systems. If one considers that the strength of present “high tenacity” fibers is about 5–10 times lower than calculated values, assuming a flawless structure, then it is expected that functional modifications of fiber morphology should lead to significant increases in their strength, endurance, and modulus.
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