Summary
In fatigue of fibers, extreme value approaches do not always offer an adequate interpretation of the scatter encountered in observed lifetimes. Assuming that a considerable part of the scatter is associated with rate-controlling random processes involved in the initiation of brittle fracture, then the lifetime distribution can be derived from the expression for the rate of brittle fracture in oriented polymers. Shifts and changes in these distributions, resulting from changes in fatiguing conditions, are shown to be in agreement with experiment provided that the structural changes induced by mechanical action are taken into consideration.
Zusammenfassung
Bei Ermüdung von Fasern gestattet die Näherung für Extremwerte nicht immer eine adäquate Interpretation der Streuung in den beobachteten Lebenszeiten. Mit der Annahme, daß ein beträchtlicher Teil der Streuung mit geschwindigkeitsbedingten Zufallsprozessen, die in der Initiierung des Sprödigkeitsbruches eine Rolle spielen, verknüpft sind, kann die Lebenszeitverteilung aus dem Ausdruck für die Geschwindigkeit des Sprödbruches in orientierten Polymeren abgeleitet werden. Verschiebungen und Änderungen dieser Verteilungen, wie sie aus Änderungen in den Ermüdungsbedingungen folgen, lassen sich in Übereinstimmung mit dem Experiment darstellen, vorausgesetzt, daß die durch mechanische Wirkung induzierten Strukturänderungen in Betracht gezogen werden.
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Abbreviations
- B :
-
parameter, in number of cycles, associated with duration of healing process.
- D :
-
cumulative damage; the specimen fails whenD=1
- E :
-
Young's modulus
- ΔF * :
-
activation energy associated with the separation of polymer segments
- K :
-
normalizing factor
- N :
-
number of cycles
- N 0,N′0 :
-
parameters, in number of cycles, reflecting the duration of an initiation period when no damage is caused by fatiguing
- N v :
-
expected lifetime
- N′ v :
-
parameter, in number of cycles, associated with the increase in stress concentration during fatiguing
- R c :
-
rate of failure
- R N :
-
rate of crack growth per cycle
- T :
-
absolute temperature
- V :
-
volume of the specimen
- Z :
-
concentration of nucleation sites
- a :
-
dimensionless parameter related to the rate of decrease in stress concentration associated with a preexisting defect
- b :
-
ratio of static stress to the superimposed cyclic stress amplitude
- Δf r :
-
free energy associated with the formation of a crack of radiusr
- h :
-
Planck's constant
- k :
-
Boltzmann constant
- \(\hat k\) :
-
dimensionless parameter associated with the rate of cumulative damage
- k′:
-
dimensionless parameter associated with the rate of increase in stress concentration
- l :
-
average distance between polymer chains in direction perpendicular to the fiber axis
- r :
-
radius of a crack
- r * :
-
critical radius of a crack
- q :
-
stress concentration factor
- qd 0 :
-
stress concentration factor associated with the preexisting defect
- q′:
-
same as qd0 at the end of healing process
- q f :
-
stress concentration factor associated with fatigue induced defects
- v :
-
effective volume of the vacancy created by the separation of two polymer chain segments
- ɛ 0 :
-
cyclic strain amplitude
- ɛ s :
-
static strain
- ν :
-
frequency
- ϱ :
-
specific fracture surface energy
- σ 0 :
-
cyclic stress amplitude
- σ * :
-
critical local stress
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Work done in a project sponsored by a group of member companies of Textile Research Institute.
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Prevorsek, D.C., Withwell, J.C. Theory relating lifetimes statistics to molecular processes, in the fatigue fracture of fibrous polymers. Kolloid-Z.u.Z.Polymere 201, 27–38 (1965). https://doi.org/10.1007/BF01497076
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DOI: https://doi.org/10.1007/BF01497076