Probabilistic Analysis of Fatigue Crack Propagation Under Random Loading

In order to predict the fatigue crack growth curve under random loading, an analytical model is proposed in this paper. In addition to the mean crack growth curve, the model also considers the statistical variation of the crack growth curves under the same nature of random loading, as well as the material reliability after certain loading cycles are applied. To check the applicability of the prediction model, several fatigue experiments are performed. After comparing the analytical result with the experimental result, the following conclusions are drawn. (i) Under the same mean value and standard deviation for the stress amplitudes, the fatigue crack growth curves are influenced by the probability density function of the stresses. (ii) An “equivalent constant loading” and a crack closure model lead to better prediction than any other model. (iii) The variation of the crack growth curves can be predicted accurately for shorter crack lengths and conservatively for longer crack lengths. (iv) The prediction of the statistical variation can be improved by modifying the definition of the equivalent constant loading. (v) Fatigue reliability can be reasonably estimated. The foregoing conclusions can be taken into consideration in the design of pressure vessels which are frequently subjected to transients of random nature.