A Modified Quadtree Algorithm for Automatical Mesh Generation as Applied to Computational Crack Path Prediction

Abstract

One of the recent advances in fracture mechanics is the crack path prediction whose need stems mainly from two reasons. One is the understanding of the micromechanical toughening mechanisms of non-metallic materials such as ceramics and advanced composites due to noncollinear crack extension, while the other is the growing concern of the critical assessment at fracture and the related fracture control of potentially dangerous engineering structures. Several computational methods have been proposed for crack path prediction based on the finite element methods and the boundary integral equation methods, respectively, combined with appropriate crack path criteria.
Considering a finite element approach, the step-by-step analysis requires mesh generation and nodal numbering at each incremental curved crack extension, which may be one of the most important procedures of the simulation method. In order to improve the computational efficiency and capability, an automated mesh generating method so called the modified quadtree method is applied to the computational crack path prediction proposed by the first author. In the method, the object of interest is first placed inside a square having an integer coordinate system. This square is subdivided into four quadrants, which are again subdivided into four subquadrants. This procedure is continued until the mesh density reaches some desired level, where the quadrants placed along the object boundaries are appropriately cut to approximate curved boundaries. After correcting the nodal location, the finite element mesh subdivision is completed. In order to apply this technique to crack problems, special treatments are introduced both for the identification of the two crack surfaces occupying same coordinates, and for the shape and size control of the mesh in the neighbourhood of a crack tip.
The present method is applied to crack path prediction along a butt-weld plate made of mild steel. Numerical simulations are performed by taking into account of the effects of applied stresses and residual stresses. Although the initial crack is located along the toe of weldment, once the crack begins to extend, it is sharply curved to the base metal due to the tensile residual stress, and it continues to propagate in the base metal. This kind of crack propagation behavior qualitatively agrees with experimental results observed by several researchers.