关键词: 分形, 断裂韧性, 裂纹扩展力, 断裂能

Abstract:

In this paper, first, four parameters including the critical fracture stress, the fracture toughness, the crack extension force and the fracture energy of an infinite plate with a solitary fractal crack of mode I under one- way tension are investigated based on the fraetal geometry. Next, the boundary of the crack domain is constructed with standard Koch fractal curve, and the elastic strain energy of the plate is deduced according to the perimeter- area relationship of the fractal crack domain. Then, the critical fracture stress of the plate is obtained according to the Griffith fracture criterion, and theoretical equations of the fracture toughness, the crack extension force and the fracture energy are consequently derived, which are utilized to generalize the G criterion to the fractal crack case. Finally, numerical simulations are conducted to analyze the influences of various factors on the four above-mentioned parameters. The results indicate that the fracture toughness of the material negatively correlates with the crack length, that the relationship between the fracture toughness and the fractal dimension varies with the yardstick length, and that the fracture energy increases with the length and roughness of the crack. In addition, the growth of a crack is proved unsmooth in the paper.

Key words: fractal, fracture toughness, crack extension force, fracture energy