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Sectioning method application to determine stress intensity factor along the front of a semi-elliptical transverse edge crack in a stretched flat bar

The article presents the developed method of analytic determination of the stress intensity factor distribution along the front of a semi-elliptical edge transverse crack in a flat bar stretched by constant stresses. The calculation is based on the method of sections. According to the method, the equilibrium equation for the normal force is written, which comes to the equality of the normal forces at the free end of the bar and in the plane of the crack. We show that between the values of the stress intensity factor at the deepest point and at the point coming to the surface, one can introduce a rigid constraint depending on the ratio of the crack depth to its half-length and the ratio of the crack depth to the bar thickness. The introduction of this connection allowed to use only one equilibrium equation in the calculation. To test the obtained data for a bar of infinite width, we compared this data and the results of calculating the stress intensity factor from the approximation formulae available in the reference literature. The possibility of using the developed methodology for a flat bar of finite width is justified by comparing the results of calculation by the proposed method with numerical values obtained in the process of solving the problem by the finite element method in the ANSYS software environment