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High Cycle Fatigue: A Mechanics of Materials Perspective part 48. The nomenclature used in this book may differ somewhat from what is considered standard or common usage. In such instances, this has been noted in a footnote. Additionally, units of measurement are not standard in many cases. While technical publications typically adhere to SI units these days, much of the work published by the engine manufacturers in the United States is presented using English units (pounds, inches, for example), because these are the units used as standard practice in that industry. The graphs and calculations came in those units and no attempt was made to convert. | 456 Applications and an effective stress ratio can then be defined as Reff K 8.16 Kmax eff Note that in this case AK does not change due to residual stresses but Reff decreases if Kres is a negative number. Since the residual stresses are compressive the computed Kres is negative. While it should be recognized that Kres being negative has no formal meaning a negative Kres is used to represent the contribution of the compressive loading across the crack surfaces. This in turn is added to the K of the applied loading. If closure is observed at a given crack length then the measured value of Popen corresponds to the point where Kmin overcomes Kres. In the reported investigation at the higher stress ratio test condition Rapplied K 8.17 7Ymax and Kmn 0-8Kmax 8.18 Since closure was absent in the load-displacement traces at R 0.8 with or without LSP then K Kres 0 8.19 and therefore combining Equations 8.18 and 8.19 yields Kres -0.8Kmax 8.20 Equation 8.20 implies that the magnitude of Kres is less than or equal to 80 Kmax during the R 0.8 test. For the case of R 0.1 testing where Kmax is the same as the R 0.8 test it follows from Equations 8.15 and 8.16 that n _ 0 1Kmax Krcs s Rf a Kr. 8 21 and 0.1Kmax - 0.8Kmax Reff K -08K 8.22 max max or Reff -3.5 8.23 HCF Design Considerations 457 Note that Reff equal to -3.5 is a limiting value or upper bound in magnitude because it is based on the assumption of Kres -0.8Kmax Equation 8.20 . The above calculations imply an apparent closure level of 80 during crack growth with Reff -3.5 at the crack tip. It is important to point out that closure contributions at a certain value of K and residual stresses producing a value of K at the crack tip are different and independent concepts. The effect of closure quantified by Equation 8.14 reduces the range of AK whereas residual stresses reduce the mean stress. The behavior of a cracked specimen that has a residual stress can be further understood with the aid of Figure 8.67 where compliance .
