13th International Conference on Fracture (ICF13) June 16–21, 2013, Beijing, China Figure 7: example of block loading and application of the developed framework for fatigue. By considering that for every loading block the probability of crack propagation can be estimated using the framework developed in this paper, a probability tree can be constructed where each branch event (or block) has an associated probability of crack propagation. Cracks are assumed to grow following Paris’ law at the K corresponding to the stress It is assumed that when (, a) lies within the “safe zone” of the Kitagawa diagram the crack will grow at the threshold level Kth. Each node of the tree will divide in two branches, one for a propagation event and one for a non-propagation event. By selecting consecutively at each node the branch with highest probability, a most probable crack growth path can be constructed. By selecting the branch that implies crack propagation at each node, no matter how probable the event is, a worst case scenario crack path can be constructed. Similarly a best case scenario can be constructed, by selecting the branch that implies no-propagation, creating an envelope for the most probable crack growth path. Figure 8: application example of the developed framework for subcritical crack growht in HCF block loading.
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