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In the present paper, we study specific features of crack propagation from surface flaws in full-scale sheets used in manufacturing pressure vessels for cryogenic applications. The process of crack propagation consists of several stages and terminates in stages of surface through or central through cracks under conditions of low-frequency repeated tension. The effect of a decrease in temperature from 292 to 77K on crack growth behavior was studied for sheets with a thickness of 2, 8, and 12mm. We describe a procedure for testing for crack-growth resistance at cryogenic temperatures and construct fatigue crack growth diagrams. It is shown that zones of influence of the front and rear faces of the specimen on the stress and strain fields near the crack front arise in the plane of a semielliptic crack. The shape of the interface of these zones can be approximated by a second-order curve. Variations in the thickness of the specimen and the test temperature affect the slope of the curve, i.e., the interface of the zones of influence. Specific features of the fracture process in the material of the plate with surface cracks manifest themselves most adequately at points of the crack front located on the indicated interface. We suggest a procedure for estimating the cyclic crack growth resistance of highly ductile stainless steels that is based on the use of the cyclic ΔJ-integral. We propose to regard the lengthl of the interface of the zones of influence of the front and rear faces of the specimen as a geometric parameter of the crack. It is used to construct kinetic fatigue crack growth diagrams for specimens with semielliptic surface cracks.