Prediction of component survival time by application of the asymptotic theory of extreme order statistics

Previous applications of fracture mechanics theories to predict component life during crack propagation have been developed without consideration of the statistical nature of fracture mechanics parameters. The statistical approach to fracture mechanics has been concerned mainly with the study of the size effect of brittle fracture strength distribution. This study, however, presents for the first time an approach to link the statistical approach to fracture mechanics and the laws of crack propagation to predict component survival time in order to investigate the effect of size temperature and strain rate on the expected component life. The asymptotic theory of extreme order statistics of the third kind for the smallest values (Weibull model) was used to study the effect of size, temperature, and strain rate on the fracture strength of identical specimens for both uniform and uniaxial bending stress fields. Then, these results were combined with crack propagation laws to develop the required relationships to predict component survival time and to investigate the effect of size, temperature and strain rate. These relationships were developed for the following cases: 1. The component subjected to uniaxial static uniform and bending stress fields. 2. The component subjected to constant amplitude, uniaxial, dynamic, uniform and bending stress fields with and without the mean stress effect. 3. The component subjected to a random uniaxial stress field. This study also presents a discussion of this approach to the following: a). The limitation of this statistical approach. b). The application to predict survival time in an aggressive environment. c). The application to predict survival time under a multiaxial stress field. d). The required experimental testing programs to support the validity of this statistical approach for studying the effects of size, temperature and strain rate on the mean fracture strength and the mean survival time for the uniaxial static uniform and bending stress fields.