抄録
A statistical nature of fatigue life (total life) Nf was studied by decomposing Nf into the crack initiation life Ni and crack propagation life Np. By assuming that both Ni and Np follow lognormal distributions and that the coefficient of variation is larger for Ni than for Np, the distribution of Nf was derived theoretically by using Monte Carlo simulation. Mutual independence of Ni and Np was also assumed. It was shown that Nf followed a composite log-normal distribution approximately. In the regions left of and right of the transition point, this composite distribution was similar to that of Np and to that of Ni, respectively (the “transition point” denotes the point at which plot of Nf breaks into two segments on log-normal probability paper). The transition point moved downwards with an increase in the average ratio of Ni to Np. When this ratio was significantly small or large, Nf followed actually a simple log-normal distribution similar to the distribution of Np or to that of Ni, respectively. By combining the above results with the well-known experimental fact that the ratio of the crack initiation life to the crack propagation life increases with a decrease in stress level, a new interpretation was presented to the stress level dependence of the fatigue life distribution. This interpretation is different from the conventional one which is based on the mixed distribution. The present theory was examined experimentally. The data on an aluminum alloy and a low carbon steel showed that both Ni and Np followed log-normal distributions approximately and that the coefficient of variation was larger for Ni than for Np. Furthermore, the distribution of Nf as derived by Monte Carlo simulation was in good agreement with the measured distribution of Nf.
