Calculation model for assessing the durability of structural elements in the presence of holes and cracks

The problem of determining a number of cycles to failure for structural elements having technological holes of circular shape and weakened by cracks is considered. It is assumed that the structure is subject to cyclic loading (tension-compression) with given frequencies and amplitudes. A technique for determining stress intensity factors for the structural element with two symmetrical cracks adjoining a contour of hole has been developed. The problem of determining the stress intensity factor has been reduced to solving a singular integral equation. For the numerical solution of this equation, the boundary element method has been used. The formulas for the effective numerical simulation of singular integrals with singularities of the Cauchy and Hadamard type have been obtained. The solution accuracy of the considered singular equation is investigated. Boundary elements with different density approximations are considered. It has been established that the use of boundary elements with a cubic approximation of density leads to a significant increase in the solution accuracy. Densities appearing as unknown functions in the considered integral equations are used to calculate stress intensity factors. Comparison of the analytical and numerical solutions of the considered singular equation, as well as the analytical and numerical values of the stress intensity coefficients has been performed. The initial crack length starting crack development has been determined by using the threshold value of the stress intensity factor. The critical number of loading cycles leading to cracks of an unacceptable size has been calculated based on the Paris criterion. This critical number of cycles is a characteristic of durability. To compare the durability characteristics, the problems of determining the critical number of cycles for plates with single isolated cracks and with crack chains are considered. It has been established that at the same loading level, the smallest critical number of cycles corresponds to a structural element with cracks in the vicinity of technological holes.