On the estimation of characteristic S–N curves with confidence

When fatigue test data for the number of cycles N to failure are limited, the estimation of the characteristic S–N curve, defined as the curve corresponding to the mean value of logN minus two standard deviations of logN, becomes uncertain. A study has been carried out to establish which confidence level in the estimation of the characteristic S–N curve from limited data is required in order to maintain the safety level equal to the safety level which is achieved under an assumption of perfect knowledge (infinitely many fatigue tests).Probability calculations for the situation with perfect knowledge as well as for the situation with limited fatigue test data are based on a first-order reliability method (FORM). Tolerance bound theory is used to calibrate the required confidence level from the results obtained from the FORM analyses.Calculations are carried out for assumptions of no uncertainty in the loading and unknown standard deviation of logN. Results are presented for a 10−2 requirement for the failure probability over the design life as well as for a 10−4 requirement for the failure probability in the last year of a 20-year design life that is typically used for design of marine structures. Variation cases are carried out to study the influence of uncertainty in the loading and to study the effect of assuming the standard deviation in logN to be known.The purpose of the paper is to demonstrate why and how to estimate characteristic S–N curves with confidence when the amount of data is limited. The results of the study provide a new way to optimize fatigue design whenever it is costly or time-consuming to achieve many reliable test data.

► Characteristic S–N curves are estimated with confidence when data are limited.
► We find the requirement for confidence so the achieved safety is the same as under perfect knowledge.
► We measure the safety achieved by the design in terms of the failure probability.
► Probability calculations are by a first-order reliability method and tolerance bounds.
► The results form a new way to optimize fatigue design when test data are limited.