A Computational Approach for the Prediction of Fatigue Crack Growth along Non-collinear Paths

Abstract

Proper understandings of fatigue crack propagation behavior with adequate accuracy are extremely important for the evaluation of ship structural strength and performance, where the prediction of a crack path is prerequisite. A step-by -step finite element approach has been proposed for fatigue crack path prediction, in which a cracked domain is remeshed by an automatic mesh generation algorithm and the stress field ahead of the current crack tip is analyzed by applying the method of superposition of analytical and finite-element solutions. Using the stress field parameters ahead of the crack tip, a curved crack increment can be determined by the first order perturbation solution together with the local symmetry criterion. The crack tip then extends for a certain increment size and the procedure is repeated for next steps.Since the modified quadtree algorithm previously implemented has some difficulties in dealing with geometric boundary, several improvements in the computational code have been made in this research so that the possibility of erroneous meshing on boundary line, boundary corner and crack line is significantly reduced. A circular region around a crack tip with a prescribed regular mesh pattern is introduced, and an integer coordinate system, which naturally fits for the global geometry of the domain, is chosen so that quadrilateral elements with nearly square shape almost cover the whole domain except in the vicinity of curved boundaries.Simple non-collinear fatigue crack propagation experiments are carried out. The stress intensity factors along measured crack paths are evaluated and the validity of the local symmetry criterion, on which the crack path prediction of this approach is based, is examined. It seems that the criterion is not regorously satisfied, but can be used as an approximate condition. Based on numerical data from computational experience a proper selection of an increment size in each step is discussed. It is observed that, for example, if KII/KI is kept below 2-3 % for a reasonable crack path prediction, the increment size should be chosen to be less than 20-25 % of the minimun distance from the current crack tip to the boundary.Once a fatigue crack is initiated in a welded structure, its propagation path is believed to be governed by a macroscopic stress distribution. Particularly in the case of biaxial stress distribution, it is possible that the initial crack propagation direction could be much changed as it extends for some distance. In this research the propagation behavior of a crack at a stress concentrated corner of a cruciform specimen is studied. Numerical crack path predictions are carried out for various external loading conditions (biaxial tension, biaxial in-plane bending, tension-bending), with various biaxial stress range ratios.