A study of the fatigue behavior of fiber reinforced nylons

A phenomenological model combining a Weibull distribution function with a kinetic equation for flaw growth has been used to describe the static tensile strengths and fatigue lives of short graphite-fiber reinforced nylon 66 materials. A simple Weibull function of the form \documentclass{article}\pagestyle{empty}\begin{document}$ P\left( {\sigma _b } \right) = \exp - \left( {{{\sigma _b } \mathord{\left/ {\vphantom {{\sigma _b } {\hat \sigma }}} \right. \kern-\nulldelimiterspace} {\hat \sigma }}} \right)^{9.5} $\end{document} described the distribution of static strengths. The scale factor \documentclass{article}\pagestyle{empty}\begin{document}$ {\hat \sigma } $\end{document} varies with the annealing treatment and, in general, is a function of environmental variables. The cumulative distribution of breaking times in fatigue can be characterized by a translated three parameter Weibull function \documentclass{article}\pagestyle{empty}\begin{document}$ P\left( {t_B } \right) = \exp - \left\{ {\left. {\left( {\frac{{\sigma _{\max } }}{{\hat \sigma }}} \right)^{16} + \frac{{t_B }}{{\hat t}}} \right\}} \right.^{0.59} . $\end{document} The average time to break (which is related to the time scale factor \documentclass{article}\pagestyle{empty}\begin{document}$ {\hat t} $\end{document}), appears to be a function of the flaw growth rate. The distribution equation has been found to predict the number of half cycle failures and is thus a valid model for the proof testing of large populations. An electrical resistivity method was developed to measure flaw growth rates in prenotched cantilever beams. Experimental data fit the following equation: ln (Δa/Δn) = ?88.88 + (12.46 ± 5.68) ln (K_eff)_max. The correlation coefficient was 0.81. From curve fitting of fatigue data it appeared that flaw growth rate varied with the ninth power of flaw length (Δa/Δn) = Ma⁹. The direct measure of flaw growth rate using electrical resistance gave Δa/Δn = Ma^6.23±2.84 with 90 percent confidence. The two measurements overlap within the 90 percent confidence bands, but predictions of fatigue life using the flaw propagation data were not good. Scanning electron microscope studies showed that specimens with a short fatigue life have glassy, fibrillated fracture surfaces while specimens with a long fatigue life exhibit a high degree of ductility in portions of the fracture surface. These differences are traced to differences in the size and shape of flaws.