An Observation Concerning the Cycle Ratio in Cumulative Damage

Life estimates for structural components subjected to repeated loads of varying stress amplitudes are usually based on some cumulative damage hypothesis. Practical calculations have often used the suggestion by Palmgren (1) and Miner (2), that ΣiniNi=1 where ni is the number of cycles applied at a stress amplitude Si, while Ni is the fatigue life at this amplitude. In many situations, predictions on the basis of Eq 1 have been wrong by more than estimated experimental error (3,4). More complex relations for estimation of cumulative damage have been proposed (for example, (4,5, and 6)). Most of these have one or more of the following limitations: 1. No physical mechanism is so clearly defined as to give the relation useful identification with concepts applicable in design. 2. Too many experimental data are required for engineering application. 3. Mathematical calculations are cumbersome. The following discussion shows some interesting implications of considering cycle ratios in the light of two separate stages in the progress of fatigue: (1) damage to the initiation of a crack, and (2) propagation of the crack to failure of the specimen or component.