Cumulative damage analysis based on fatigue damage bounds

A cumulative damage analysis is presented based on damage curves derived in Ben-Amoz (2003) as bounds on mean fatigue damage in constant amplitude cycling. A detailed analysis is developed for two-stage high-low (H-L) and low-high (L-H) cycling based on single and two-mode bounds. The use of single-mode bounds is questionable as neither bound reflects a crack tip process whereas two-mode bounds reflect the actual process by the presence of both slip and opening-mode damage in each cycle. This leads to results in much closer agreement with experimental data. It is found that to ensure damage irreversibility in L-H cycling the presence of four discrete microstructure barriers obtained in Ben-Amoz (2003) is essential. As a result, two distinct sets of bounds apply: one for H-L another for L-H cycling. The barriers divide the fatigue process into three distinct macro stages while the entire range of lifetimes is divided into five ranges. In L-H cycling different sets of bounds apply to each interval between barriers, hence to each range of lifetimes. A statistical analysis based on an assumed log normal distribution of lifetimes is developed for two-stage H-L and L-H cycling. The bounds lead in a straightforward manner to a median while the variance can only be bracketed by the two-mode and single-mode variances due to exclusion of cyclic hardening as an additional random variable. Predicted residual lifetimes are in close agreement with experimental data in several metals notwithstanding the paucity of data. The two-stage analysis is then generalized to multi stage cycling.