Fatigue probability curves

ASTM Special Technical Publication No. 91 discusses in detail the important ramifications to be considered in the various statistical aspects of fatigue testing. Most often, the fatigue curves as well as the tabulated values of endurance strengths and endurance limits are based on the 50% probability curve. As a result, designers do not resort to using scatter-band... 

Several statistical techniques have been developed to specify fatigue life and fatigue limit in terms of probabilities. One convenient way of representing data treated in this manner is with a series of constant probability curves, several of which are plotted in Figure 8.21. The P value associated with each curve represents the probability of failure. 

If sufficient data are available, much more information can be provided when different curves for various percentages of failure are plotted. Where such data are available, reasonable design criteria would be based on some probability for failure, depending on how critical the effects of failure occur. If a large, expensive repair of a complex mechanism would result from the fatigue failure of one product, then a 10 or even 1 % probability of failure would be a more likely design criterion than the 50% suggested above. 

Based on the fatigue life data of TC21 titanium with EBW in ultra-high cycle fatigue regime, the probability distribution of fatigue life at certain stress level is discussed in Kolmogorov criterion method and the P-S-N curve is obtained by maximum likelihood estimation method, the conclusions are as follows ... 

The well-known S-N curves are - probably for historical reasons — the method most often used to describe fatigue behavior for fiber reinforced plastics. In this discontinuous (as defined in the previous section) procedure, the fatigue criterion is typically fracture, that is total failure of the test specimen. Statistic evaluation leads to statements regarding the probability of fracture P, Figure 1.65. 

Carbon steel specimens tested at four different stress amplitudes with maximum stress of 346, 324, 302 and 270 MPa, respectively, has yielded the fatigue lives listed in the following table. Using the Weibull distribution derive the 90 and 99.9 % probability S-N curves and that at 90 % probability of survival with 90 % confidence P(90)C(90). Analyzed with the Weibull procedure, already applied in the previous problem, the four different stress amplimde yield the results shown in Fig. 4.25. Also shown are the best-fitting fines with the relative equations. It is worth noting how the Weibull slope m decreases as the maximum stress decreases passing from m — 5.16 at 346 MPa Xo m — 1.0 at 270 MPa. 

The starting point is the determination of points A = (lOOO ) e B = (A 5y) of Fig. 5.17. The resulting fatigue curve may be considered a mean fatigue curve obtained by smooth, mirror-polished specimens. This curve shall be modified to take into consideration all factors affecting fatigue strength such as load factor (see Sect. 3.6), surface finish (see Sect. 3.3), size effect (see Sect. 3.5) and, eventually, also the requested probability of survival (1 — P). 

Figure 8.21 Fatigue S-N probability of failure curves for a 7075-T6 aluminum alloy P denotes the probability of failure. (From G. M. Sinclair and T. J. Dolan,...

FIGURE 4.12 Flexural fatigue curves for 90% and 50% probability of survival of glass reinforced epoxy laminates (181 Style S-901, room temperature, saturated humidity, 30 cps). (Adapted from Lockwood, P. A., Proc. 4th Annual Plastics Corf., Eastern Michigan University, September, 1969, pp. 74—99.)... 

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