Mathematical modeling of the processes of development of trunk cracks in the bodies of rotation of the complex structure taking into account the form-modification

Abstract

The step-by-step algorithm for determining of the trajectory of initial crack propagation in the bodies of rotation of the complex structure using FEM was developed and verified on the test examples. The result of calculation of the responsible object of modern technology are shown.Determining of the fracture mechanics parameters is an important, but partial problem of fracture mechanics. In practice, there are cases when a small initial small crack is known and it is necessary to determine the destruction conditions of the structure - the critical length of the crack at a given load. At the same time, the correctness of determining of the trajectory of initial crack propagation depends largely on the reliability of the calculation of fracture mechanics parameters along the trajectory. If it is not coinciding with the real one, it can lead to an incorrect assessment of the bearing capacity of the structure as a whole.It should be noted that a small number of papers are devoted to the modeling of the crack development using the FEM [3]. The effectiveness of the method in this case depends to a large extent on the effectiveness of the finite element base and the methods of determining of the fracture mechanics parameters. In this paper, the focus is on the use of universal finite element [7], which allows to optimize the FEM discrete model when calculating the bodies of a complex structure. Determination of the fracture mechanics parameters is realized by the modified method of reactions, the effectiveness of which in the case of mixed fracture is demonstrated in the works [2, 6].In this paper, we arrived at solutions of the new structure mechanics problems about the effect of form-modification on the life-time value and the fracture resistance of the structural elements of modern industry. It has been found that despite relatively small changes in the values of stress-strained state parameters the life-time of the stop valve has increased compared with the geometric linear calculation, which is essential for determining of the lifetime of this object.