The influence of curvature of a cylindrical panel containing a crack on the value of the J-integral in the process of axial loading is investigated. We study the entire range of curvatures of the panel, namely, from a plate to a closed cylindrical shell. The critical values of the J-integral are determined numerically according to the experimentally obtained values of critical loads corresponding to the onset of crack propagation. The contributions of membrane and bending strains to the total value of the J-integral are evaluated. In the case of an almost plane panel, we analyze the influence of nonlinear bending (buckling) in the vicinity of the crack on the increase in the J-integral. The influence of crack length on the critical value of the J-integral is studied.Introduction. The investigation of regularities connected with the propagation of cracks in thin-walled structures is of high importance from the viewpoint of improvement of strength, reliability, and serviceability of these structures in the process of operation. It is known that, according to their nature, the parameters characterizing the process of crack growth belong to the following three groups: force parameters (stress intensity factors), deformation parameters (crack-tip opening displacement), and energy parameters (intensity of energy release and J-integrals).At present, the methods aimed at the investigation of fracture processes and evaluation of the crack resistance of materials and based on the application energy parameters are used more and more extensively. Note that the major part of available publications is devoted to the analysis of these parameters either for plates with through cracks in the plane stressed state or for massive bodies with internal or surface cracks (see, e.g., [1,2]). The investigation of fracture processes in thin-walled structures with cracks is complicated by the necessity of taking into account the influence of geometric nonlinearity affecting the deformation and fracture processes in the entire range of applied loads [3]. Moreover, it is reported that the parameters of fracture are not material constants [4].For thin-walled structures, the indicated parameters can strongly depend on the geometric shape and, in particular, on its changes in the process of deformation, which may be accompanied by the loss of stability and changes in the character of the stress-strain state. We do not know any direct theoretical results concerning the influence of the geometric nonlinearity of the process of deformation of thin-walled structures on the parameters of fracture. For plates with possibility of buckling and circular cylindrical shells, these problems are experimentally investigated in [5][6][7][8][9].The aim of the present work is to study the process of nonlinear deformation of a cylindrical panel containing a crack and analyze the influence of its curvature on the parameters of fracture in the process of insignificant crack growth.

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