The primary purpose of this work is to develop analytical solutions that could be used to assess the safety of irradiated nuclear reactor pressure vessels against unstable fracture during thermal shock events with repressurization present. This methodology makes use of a constraint straight beam model under combined tension and bending for simplicity. It will be shown that this model can represent the deep part-through circumferential crack in a cylindrical vessel under pressure and thermal load. The thermal load can be treated as an induced equivalent bending moment. Elastic and fully plastic solutions are presented for such deep cracks at the inner surface of the wall. The results show that such a crack would be stable under pressurized thermal shock load.
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