13th International Conference on Fracture (ICF13) June 16–21, 2013, Beijing, China lower probability of failure or higher probability of failure to further validate this framework, and to test whether the populations described by the model are in agreement with experimentally observed populations. Additionally, sensitivity analysis studies are planned to understand the influence of the statistical distributions of the inputs with respect to the performance of the framework described. 5. Application to Fatigue Crack Growth in HCF An example application of the developed framework is illustrated for fatigue; similar concepts and applications can be extended for the combined SCC, pure fatigue and CF framework. For simplicity it is supposed that all solicitations have R=0, therefore only one Rratio is used for the Kitagawa diagram. Note that with appropriate material information and available data, this can be extended to any R-ratio level. It is here assumed that a component subjected to fatigue loading has an initial crack length a1. This component is subjected to HCF blocks of loading at constant R-ratio = 0. The blocks of loading are such that there is alternation of low amplitude stresses and higher amplitude ones. Within the framework of the Kitagawa diagram for fatigue the average point (, a), stress amplitude and crack length, will be moving from the safe zone into the fatigue crack propagation zone and vice versa frequently. This type of situation is illustrated in Figure 7, where the Kitagawa diagram for fatigue is shown with the failure diagram for static loading, whose bounds are the ultimate strength U and the fracture toughness for the material KIc. The blocks of loading are shown in the top right corner of Figure 7. As shown, the first block of cycles is well within the no-growth region of the Kitagawa diagram, therefore no crack propagation is expected. For the following block it is expected that fatigue crack propagation will occur, as the increase in stress level will bring the (, a) point outside the non-propagating area. The initial defect a1 grows in fatigue to a dimension a2 at the end of the block. In a similar way the third block will cause fatigue crack growth from a2 to a3. Note that at the time the defect has grown to a3, the stress is reduced to the same level of the first loading block. Given the different crack length a3, block 4 is near the limit condition described by the Kitagawa diagram. Nominally, no growth is expected for block 4 as well, but eventually the alternation of loading blocks of different stress amplitude will determine the (, a) point to lie outside the safe zone even for stress levels 1 and 4. Eventually the crack reaches the critical length for failure, i.e. when the (, a) point lies on the failure diagram for static loading. It is here proposed to use the developed stochastic framework for fatigue to calculate for each loading block a probability of crack propagation, PCP. Stress and crack length are taken as random variables within the current context, whose distribution needs to be estimated from available data. A probability of crack propagation can be calculated for each (, a) using the reliability methods described above and by considering for simplicity the correction factor Y constant and equal to unity. In the example described the PCP will be very small for the first loading block, and it is expected to be much higher for the second and third block. When the crack has grown to a3 however, even if the stress is decreased to a value equal to the one corresponding to the first block, the PCP is expected to increase.
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