In a number of studies of data obtained from fatigue tests on various materials it has been shown that the number of cycles to failure is related to the strain range by a relationship of the form  
where N is the number of cycles to failure, ε the strain range, and m and c are constants. In the low cycle portion of the strain range versus cycles to failure curve, evidence has been presented by several investigators to show that the relationship should be  
where εp is the plastic strain range and c, the constant, can be related to tensile ductility. Some investigators have found the relation  
more useful. Here εt is the total strain range. As a result of a series of Pressure Vessel Research Committee investigations at Lehigh University, a large body of low cycle fatigue data has been obtained for a wide range of steels, microstructures, heat-treatments, and testing conditions. A study of these data has been undertaken, with special emphasis on the suitability of a relationship of this type for analysis and representation of fatigue data. As a result of this study the following conclusions have been drawn: (a) In the range of 5000 to 100,000 cycles a relation εtNm = c appears to be satisfactory. (b) Using this latter relation, an analysis of the low cycle fatigue behavior of structural steels reveals that they can be classified into three broad groups on the basis of their composition. Each group has a characteristic value of m and c which can be used to predict their behavior over the range 5000–100,000 cycles. (c) The value of m and the total strain for 5000 cycle life can be related to n, the strain hardening exponent, for the steels. The total strain for 100,000 cycle life is related to the ultimate tensile strength of the steels. Using these relationships, the fatigue curve for a structural steel can be estimated from tension test data. (d) The effect of microstructural variations for a steel within any one of the three groups was of secondary importance when compared to the compositional groupings, although some systematic effects of microstructural variations were noted.
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