Analysis of Mixed-Mode Fatigue Crack Growth
Using Element-Free Galerkin Methods
Nam Kyu Ahn
This paper presents an iterative modeling scheme of mixed-mode fatigue crack growth using Element-Free Galerkin (EFG) methods. In EFG methods, a crack is modeled by piecewise continuous lines expressing discontinuities, and double nodes are placed on both sides of the crack surface. The domain of influence near the crack tip is determined by the diffraction method. An accurate solution of the crack growth can be easily obtained by mesh refinement near the crack tip since it is possible to arrange the nodes arbitrarily.
The increment and the direction of the fatigue crack growth are calculated based on stress intensity factors, which are estimated from the J-integral. The 2-dimensional and the 3-dimensional J-integral are studied considering the decrease in total potential energy for a virtual crack extension. In 2-dimension the path independency of J-integral in the curved or kinked crack is investigated.
The path of fatigue crack growth as well as initial geometry of kinked or curved crack is discretized using straight lines. The calculated crack increment and direction may be deviated from those of the actual crack if the crack is assumed to grow to the initial increment and direction. In the proposed modeling scheme, the path of the fatigue crack growth is supposed to be a parabola and the increment and direction of that are updated iteratively. Through numerical examples, J-integral is calculated exactly and the fatigue crack growth is simulated more accurately.
Element-Free Galerkin Method, Stress intensity factors, J-integral, fatigue crack growth