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29.1.2 Constant-Stress-Level Testing If high-cycle fatigue strength in the range of 103 to 106 cycles is required and reliability (probability of survival) contours are required, then constant-stress-level testing is useful. A dozen or more specimens are tested at each of several stress levels. These results are plotted on lognormal probability paper to confirm by inspection the lognormal distribution, or a statistical goodness-of-fit test (Smirnov-Kolomogorov, chisquared) is conducted to see if lognormal distribution can be rejected. If not, then reliability contours are established using lognormal statistics. Nothing is learned about endurance limit. Sixty to 100 specimens usually have been expended. 29.1.3 Probit Method If statistical information (mean, standard deviation, distribution) concerning the endurance limit is needed, the probit method is useful. Given a priori knowledge that a knee exists, stress levels are selected that at the highest level produce one or two runouts and at the lowest level produce one or two failures. This places the testing at the knee of the curve and within a couple of standard deviations on either side of the endurance limit. The method requires exploratory testing to estimate the stress levels that will accomplish this. The results of the testing are interpreted as a lognormal distribution of stress either by plotting on probability paper or by using a goodness-of-fit statistical reduction to confirm the distribution. If it is confirmed, the mean endurance limit, its variance, and reliability contours can be expressed.The existence of an endurance limit has been assumed, not proven. With specimens declared runouts if they survive to 107 cycles, one can be fooled by the knee of a nonferrous material which exhibits no endurance limit. 29.1.4 Coaxing It is intuitively appealing to think that more information is given by a failed specimen than by a censored specimen. In the preceding methods, many of the specimens were unfailed (commonly called runouts). Postulating the existence of an endurance limit and no damage occurring for cycles endured at stress levels less than the endurance limit, a method exists that raises the stress level of unfailed (by, say, 107 cycles) specimens to the next higher stress level and tests to failure starting the cycle count again. Since every specimen fails, the specimen set is smaller. The results are interpreted as a normal stress distribution. The method s assumption that a runout specimen is neither damaged nor strengthened complicates the results, since there is evidence that the endurance limit can be enhanced by such coaxing [29.1]. 29.1.5 Prot Method This method involves steadily increasing the stress level with every cycle. Its advantage is reduction in number of specimens; its disadvantage is the introduction of (1) coaxing, (2) an empirical equation, that is, S = Se + K n
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See Ref. [29.2].
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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S = Se = K, n = =
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Prot failure stress at loading rate, psi/cycle material endurance limit material constants loading rate, psi/cycle
and (3) an extrapolation procedure. More detail is available in Collins [29.3].
29.1.6 Up-Down Method The up-down method of testing is a common scheme for reducing R. R. Moore data to an estimate of the endurance limit. It is adaptable to seeking endurance strength at any arbitrary number of cycles. Figure 29.1 shows the data from 54 specimens
FIGURE 29.1 An up-down fatigue test conducted on 54 specimens. (From Ransom [29.5], with permission.)
gathered for determining the endurance strength at 107 cycles. The step size was 0.5 kpsi. The first specimen at a stress level of 46.5 kpsi failed before reaching 107 cycles, and so the next lower stress level of 46.0 kpsi was used on the subsequent specimen. It also failed before 107 cycles. The third specimen, at 45.5 kpsi, survived 107 cycles, and so the stress level was increased. The data-reduction procedure eliminates specimens until the first runout-fail pair is encountered. We eliminate the first specimen and add as an observation the next (no. 55) specimen, = 46.5 kpsi. The second step is to identify the least frequent event failures or runouts. Since there are 27 failures and 27 runouts, we arbitrarily choose failures and tabulate Ni, iNi, and i2Ni as shown in Table 29.1. We define A = iNi and B = i2Ni. The estimate of the mean of the 107cycle strength is = S0 + d 1 A Ni 2 (29.4)
where S0 = the lowest stress level on which the less frequent event occurs, d = the stress-level increment or step, and Ni = the number of less frequent events at stress level i. Use +1 2 if the less frequent event is runout and 1 2 if it is failure. The estimate of the mean 107-cycle strength is
See Refs. [29.4] and [29.5].
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