Дослідження КІН двох взаємодіючих поверхневих півеліптичних тріщин методом скінченних елементів

Abstract

Проаналізовано існуючі методи визначення коефіцієнтів інтенсивності напружень (КІН) для поверхневих непівеліптичних тріщин уздовж їх контуру та літературні дані щодо взаємного впливу кількох тріщин на зміну величини КІН. Для уточнення КІН уздовж фронту однієї та двох взаємодіючих поверхневих напівелептичних тріщин здійснено їх моделювання за допомогою методу скінчених елементів. Наведено результати досліджень коефіцієнтів інтенсивності напружень уздовж фронту поверхневої тріщини за одновісного розтягу пластини скінчених розмірів на основі методу скінченних елементів, які добре узгоджуються з відомими рішеннями. Здійснено моделювання взаємного впливу двох колінеарних тріщин на розподіл КІН уздовж фронту поверхневих тріщин.

The authors present the results of the study of stress intensity factors along the front of surface crack and two collinear cracks under uniaxial tension of finite size plate basing on the finite element method. Surface cracks are a common phenomenon in structural elements of construction frequently as a result of high values of the stress in the body and availability of defects. Such defects can sufficiently reduce the service life of structural components causing their premature failure, especially under repeated loading. Definition of the stress intensity factors is one of the most important tasks for the residual life of structures estimation. In any linear elastic fracture mechanics (LEFM) problem, precise computation of stress intensity factors accurately is of great importance. The analysis of available methods for determining stress intensity factors for surface semi- elliptical cracks along their contour has been carried out and data on the mutual influence of several cracks on the change of SIF. In order to specify SIF along the front of one or two interacting semi-elliptical surface cracks, the problem of their evaluation using the finite element method was studied. First of all, the modeling of semi- elliptical surface crack in the prismatic sample under tensile pressure was carried out. A three-dimensional model of the sample with the global model elements and the model of crack area with a local mesh with tetrahedral elements were developed. Investigations were carried out for the surface semielliptical cracks with ratio a/t for the deepest crack point to the specimen thickness (a/t) in the range a/t=0,1...0,7 and different crack aspect ratios a/c = 0,2; 0,6; 1,0. For the chosen parameters the values of SIF K1 along the path of the semi- elliptical surface crack, well correlated with the known solutions, were obtained. The energy instability was found to be in the surface crack threshold of the contour areas when its semi-axes ratio amounts a/c=0,4...0,8. The authors modeled the mutual influence of two collinear cracks on the distribution of SIF along the surface cracks front basing on the similar research methods. The modeling of both commensurate cracks and those that are significantly different in size is also carried out. The mutual influence of cracks was found to start when the distances between the cracks are commensurate with the size of surface cracks. When the distance between the cracks is close to merger, the SIF K1 values for inside surface points of the crack contour significantly increase. The results obtained are of importance for the geometric schematization of defects and further estimation of the residual operating life of the construction parts.