1 Conservative Fatigue Life Estimation using Bayesian Update

In this paper, Bayesian update is utilized to reduce uncertainty associated with the fatigue life relation. The distribution for fatigue strain at a constant life cycle is determined using the initial uncertainty from analytical prediction and likelihood functions from test data. The Bayesian technique is a good method to reduce uncertainty and at the same time, provides a conservative estimate, given the distribution of analytical prediction errors and variability of test data. First, the distribution of fatigue model error is estimated using Monte Carlo simulation with uniformly distributed parameters. Then the error distribution is progressively updated by using the test variability as a likelihood function, which is obtained from field test data. The sensitivity of estimated distribution with respect to the initial error distribution and the selected likelihood function is studied. The proposed method is applied to estimate the fatigue life of turbine blade. It is found that the proposed Bayesian technique reduces the scatteredness in life by almost 50%, while maintaining the conservative life estimate at a given fatigue strain. In addition, a good conservative estimate of fatigue life prediction has been proposed using a knockdown factor that is obtained from the distribution of lowest test data. Moreover, Bayesian update has been utilized to update the parameters of strain – life curve for a case of constant strain amplitude Nomenclature t = total fatigue strain amplitude e = elastic strain amplitude p = plastic strain amplitude ef = co-efficient of fatigue ductility sf = co-efficient of fatigue strength c = exponent of fatigue ductility b = exponent of fatigue strength I