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High Cycle Fatigue: A Mechanics of Materials Perspective part 43. 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. | 406 Applications Figure 8.27. Representation of straight line fits using SWT parameter for various values of R. by finding the best value of the exponent m using a least squares fit to a straight line representation of all of the lines in Figure 8.26. The resulting model has a value of m 0.34 and is shown in Figure 8.28. Here all of the lines are brought together in a single band but the degree of scatter is somewhat large. To illustrate the scatter on the original data of Figure 8.26 Figure 8.29 is drawn along with the best fit straight line shown as a solid line in the figure. While the single straight line seems to represent all of the data reasonably well the degree of scatter is quite broad. What these plots illustrate is that when data from different values of R are represented by a single function the Figure 8.28. Consolidation of straight line fits to data using Walker model. HCF Design Considerations 407 Figure 8.29. Consolidation of all data using Walker model. resulting scatter is a combination of the true scatter as illustrated in Figure 8.26 as well as the inability of the function to consolidate results obtained at different values of R. For the particular data sets shown here the data at R 0.8 are considered to be different than the other data because at this high value of R time-dependent behavior has been observed. The data at R -1 on the other hand may be represented by a different value of the exponent m in Equation 8.5 because it has been found that a different exponent can consolidate data at negative R better than the one used for positive R. In general this provides another degree of flexibility in representing data at various values of R with a single function. This becomes an exercise in curve fitting that has little or no physical significance. tf-eff - R m 8.5 The example above illustrates the issue of distinguishing between true material scatter and the capability of a model to represent data obtained under a variety of conditions or in
