High Cycle Fatigue: A Mechanics of Materials Perspective part 8. 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. | 56 Introduction and Background y P 4 2 15b o-u L V u J where e and g are either positive or negative constants. Because of the large number of terms most experimentally determined constant life data may be represented by proper selection of the constants. . JASPER EQUATION Of both practical and historical significance is the observation that Jasper 32 in 1923 proposed that fatigue life is related to the stored energy density range per cycle in a material when evaluating data obtained earlier by Haigh. Applying this concept to HCF conditions it can be assumed that all stresses and strains are elastic thus all equations represent purely elastic behavior. For purely uniaxial loading the shaded area in Figure illustrates schematically the stored energy for the cases where loading is purely tensile R 0 . The energy for the case where R 0 which involves tension and compression in a single cycle is illustrated in Figure by the shaded area. The stored energy density range per cycle is then given for uniaxial loading by C CTmax 1 C CTmax min E CTmin Characterizing Fatigue Limits 57 min max Figure . Stored energy shaded for elastic loading under reversed fatigue R 0 . 58 Introduction and Background since a Es E is Young s modulus. The energy can then be written as U - m 2E where the plus sign is for R 0 and the minus sign for R 0 see Figures and . For purposes of presenting the equation in the form of a Haigh diagram the stress limits are written in terms of mean and alternating stresses O max am a CTmin am - a where am and aa represent the mean and alternating stresses respectively. For the specific case of fully reversed loading R -1 the energy is written as U 2 -i 2E where a-1 represents the alternating stress maximum stress at R -1. For any other case of uniaxial loading the following equation is easily derived and can be used to obtain the value of the alternating stress on a Haigh diagram in terms of stress ratio R
