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Fatigue failure can be divided into two phases—fatigue crack initiation and subsequent crack propagation. In the following sections, basic definitions and principles of fatigue and the history of fatigue investigations will be described in more detail. 1 History of Fatigue Investigations Studies of fatigue phenomena date back to first half of the nineteenth century . A German mining engineer named Albert was among the first who investigated metal fatigue. About 1830 he studied the fatigue behavior of iron chains.
35] attributed this different appearance of the S–N curves to the smaller test volume and to the stress gradient occurring in rotating bending tests (Fig. 13b). Accordingly, for a similar steel (NF 100C6) Marines et al.  observed a continuously decreasing shape of the S–N curve without any indication of a step and thus also proposed that the stepwise S–N curve rather represents the rotating bending behavior than the properties of the steel. These authors  also suggested that the specific appearance of the S–N curve originates from the stress gradient occurring in rotating bending tests.
These two researchers provided the first mathematical tool for quantitative modeling of brittle fatigue failure. The major drawback of their works was the incapability of the treatment of metal fatigue. In the 1950s Irwin showed that the amplitude of the stress singularity ahead of a crack could be expressed in terms of the so-called stress intensity factor. These works mark the beginning of the so-called linear elastic fracture mechanics. In the 1960s, Paris et al. found a relationship between fatigue crack propagation per stress cycle (da/dN) and the stress intensity factor DK during constant amplitude cyclic loading.