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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.

(29.22) (29.23)

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For axial fatigue, the (Sax)103 ordinate in Fig. 29.8 is kc fSut and the (Sax)106 ordinate is kc 0.30Sut, where k c is determined by interpolation in Table 29.6. For torsional fatigue, the (Ssf)103 ordinate is kc fSut and the (Ssf)106 ordinate is kc 0.30Sut, where kc is taken from Table 29.7 or, for materials following the distortion-energy theory of failure closely, kc = 0.577.

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Many loading patterns depart from the sinusoidal character of smoothly rotating machinery and the convenient equation pair displayed as Eq. (29.17). In complicated patterns, characterization in the form of maximum force Fmax (or maximum stress max) and minimum force Fmin (or minimum stress min) is more useful. In fact, max-min (max/min/same max or min/max/same min) will avoid losing a damaging cycle. Consider a full cycle with stresses varying 60, 80, 40, 60 kpsi and another cycle with stresses 40, 60, 20, 40 kpsi, as depicted in Fig. 29.13a. These two cycles cannot be imposed on a part by themselves, but in order for this to be a repetitive block, it is necessary to acknowledge the loading shown by the dashed lines. This adds a hidden cycle that is often ignored. To ensure not losing the hidden cycle, begin the analysis block with the largest (or smallest) stress, adding any preceding history to the right end of the analysis block as shown in Fig. 29.13b. One now searches for cycles using max-min characterizations. Taking the hidden cycle first so that it is not lost, one moves along the trace as shown by the dashed line in Fig. 29.13b, identifying a cycle with a maximum of 80 kpsi and a minimum of 60 kpsi. Looking at the

12 9 11 10 16 2 8 3

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.

remaining cycles, one notes a cycle with a maximum of 60 and a minimum of 40 kpsi. There is another with a maximum of 20 and a minimum of 40 kpsi. Since failure theories are expressed in terms of a and m components, one uses Eqs. (29.17) and constructs the table below.

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Note that the most damaging cycle, cycle 1, has been identified because care was taken not to lose it. The method used is a variation of the rainflow counting technique. One is now ready to apply Miner s rule. Note that if the original cycles were doubled in the block, there would be five cycles, with the additional two duplicating cycles 2 and 3 above. Example 2. The loading of Fig. 29.13a is imposed on a part made of 1045 HR steel. Properties at the critical location are Sut = 92.5 kpsi, Se = 46 kpsi, strain-strengthening coefficient 0 = 140 kpsi, true strain at fracture f = 0.58, and strain-strengthening exponent m = 0.14. Estimate how many repetitions of the loading block may be applied if a Gerber fatigue locus is used. Solution. From Eq. (29.21), f= = From Eq. (29.22), a = From Eq. (29.23), b= 1 0.815(92.5) log = 0.0715 3 46 Se f Sut Se

1/2.1

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46 140(0.58)0.14 46 92.5

J1 J1-1 -2 -3 -4

= 0.815

(Sf)103 = fSut = 0.815(92.5) = 75.39 kpsi For cycle 1, which has a = 70 kpsi and m = 10 kpsi, using Eq. (29.18), Sf = a 70 = = 70.83 kpsi 1 ( m/Sut)2 1 (10/92.5)2

Since required endurance strength 70.83 kpsi is less than (Sf)103, the number of cycles exceeds 103. N1 = Sf a

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