Search Results

A probabilistic distribution function roughly consists of two parts: the middle part and the tails. The fatigue life distribution at a stress/load level is often described with two-parameter lognormal or Weibull distribution functions, which are more suitable for modeling the mean (middle) behaviors. The domains of the conventional probabilistic distribution functions are often unbounded, either infinite small (0 for the two-parameter Weibull) or infinite large or both. For most materials in low- and medium-cycle fatigue regimes, the domains of fatigue lives are usually bounded, and the inclusion of the bounds in a probabilistic model is often critical in some applications, such as product validation and life management. In this paper, four- and five-parameter Weibull distribution functions for the probabilistic distributions with bounds are developed. Finally, the applications of these new models in fatigue data analysis and damage assessment are provided and discussed.

Life testing or test-to-failure method and binomial testing method are the two most commonly used methods in product validation and reliability demonstration. The two-parameter Weibull distribution function is often used in the life testing and almost exclusively used in the extended time testing, which can be considered as an accelerated testing method by appropriately extending the testing time but with significantly reduced testing samples. However, the fatigue data from a wide variety of sources indicate that the three-parameter Weibull distribution function with a threshold parameter at the left tail is more appropriate for fatigue life data with large sample sizes. The uncertainties introduced from the assumptions about the underlying probabilistic distribution would significantly affect the interpretation of the test data and the assessment of the performance of the accelerated binomial testing methods, therefore, the selection of a probabilistic model is critically important.