Моделювання розкриття втомної тріщини в сплаві Д16Т за регулярного навантаження методом скінченних елементів

Abstract

Створено модель плоского зразка з центральною тріщиною в пружно-пластичній постановці за допомогою методу скінченних елементів. Обґрунтовано вибір розмірів скінченних елементів в околі вістря тріщини. Змодельовано закриття втомної тріщини за регулярного циклічного навантаження з урахуванням залишкових деформацій та напружень в її околі. Отримано задовільне узгодження результатів моделювання та експериментальних даних.

The aim of this study was to simulate fatigue crack opening using FE software complex ANSYS and compare it with experimental data. Using the FE simulation software the model of central cracked flat specimen was created. Only half of the specimen with enabled conditions of symmetry was modeled. The true strain diagram of D16T alloy at 20 °C was used for the simulations in order to reproduce the conditions of the experiment. FEM calculations were performed for the plane stress condition. For creation of the accurate computational model the size of finite element mesh in the crack tip was adapted using software experiment. The finite element mesh size for the finite element analysis of the stress strain state of the flat specimen with a central crack under uniaxial tension was found. Fatigue crack closure effect was modeled under constant amplitude cyclic loading considering residual strain and stresses in the crack tip. For software determination of the crack opening a macro that allows to calculate displacement of nodes of the model for a given load step was developed. The node, in which at this moment the crack tip was located, was determined with the help of software and two nodes on both sides of the crack plane at a distance r from its tip and the base b were selected. To maintain constant b and r during each crack growth the points of measurement were upgraded using software. Previous experiments proved that in order to reduce the error of determining opening stress intensity factor the measurement of the crack opening should be performed at the minimum values of b and r. Therefore, according to the experimental data r=0,02 mm and b=0 were used that is, directly on the shore of the crack. The method for determining the moment of crack opening has been chosen. It has been found that the moment of crack opening corresponds to the point of the greatest curvature of diagram efforts – opening of crack tip. For this purpose the derivative approximation by finite differences with a constant increase in stress was used. Results of modeling and experiment were compared.