In my blog article What is the Difference between Low & High Cycle Fatigue? I explained that LCF is characterized by repeated plastic deformation (i.e. in each cycle). Essential here is that we talk about repeated plastic deformation. And that is the case if the nominal stress level exceeds the yield strength in each cycle, meaning we have plastic deformation on macro scale, so in the full net section of the structure.
The situation is completely different when only in a small area at a notch the yield strength is exceeded. If so, by applying a load cycle, only in that small area you will get plastic deformation. In the remaining net section, you will still have elastic deformation because stresses are lower. So you will have a redistribution of stresses over the net section. During unloding of the load, the complete distribution will be unloaded elastically, leading to a residual stress distributon after unloading. From that point on, with further cyclic loading, you will get elastic behaviour, i.e HCF (high cycle fatigue) and no repeated plastic deformation!
So, exceeding the yield strength locally at a notch will not lead to LCF but will merely lead to a stress redistribution.
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