PSI - Issue 13

Masataka Aibara et al. / Procedia Structural Integrity 13 (2018) 1148–1153 Masataka Aibara/ Structural Integrity Procedia 00 (2018) 000 – 000 proposed a simple method to determine 0 with sufficient accuracy. However, the physical meaning and controlling factors of 0 are still uncertain. To clarify the underlying physics, it is necessary to investigate the relationships among mechanical conditions at a crack tip, microstructural factors, and FCGRs. In this study, two factors affecting the local FCGR are discussed: local microstructural and mechanical factors. The former cause a variation of fatigue crack front shape, and the shape of the fatigue crack front synergistically affects the mechanical condition at a crack tip inside the specimen. The crack-shape-dependent local mechanical condition causes a scatter in FCGRs; however, an irregularly shaped crack front can mechanically stabilize fatigue crack growth behavior. More specifically, even when a portion of the crack front locally propagates, the mechanical driving force at the crack tip of the local region (local growth part) decreases with increasing crack length. However, the driving force on the other portion of the remaining crack front (equilibrium growth part) increases with the local crack growth. This normalizes the fatigue crack growth behavior. This consideration implies that 0 or associated parameters can be understood in terms of the mechanics of a fatigue crack front with an irregular shape. More specifically, an attempt is made to analyze a stress intensity factor K , as a driving force for local fatigue crack growth, from the fatigue crack front with the irregular shape. Because K at the local growth part is different from that of the equilibrium growth part, the FCGR varies somewhat, even at a fatigue crack length longer than 0 . However, as mentioned above, K at the equilibrium growth part becomes relatively high with increasing dimensional ratio of the local growth part to the equilibrium growth part. Therefore, the effect of microstructure-induced scatter of FCGRs can be accommodated by the difference in K between the equilibrium and local growth parts. In this regard, in a simple model, factors affecting the mechanical accommodation capacity are the distribution of microstructural strength, remote stress, and sizes of the equilibrium and local growth parts. For further simplification, in this study, two dimensional factors are considered: the sizes of the equilibrium and local growth parts. As an analysis method, a finite-element method (FEM) is used to characterize the effects of the crack front shape on fatigue crack growth mechanically. Then we investigated the stress intensity factor values along the tip of the crack including a part of the locally grown crack front. And we propose a concept of force caused by a stable growth part which prevents local growth parts from growing. 2. Numerical analysis procedure 2.1. Analysis method for calculating stress intensity factor and its validation To analyze the mechanical conditions at a crack tip with a complicated front shape, a three-dimensional model for FEM analysis is needed. Specifically, when the mechanical condition at the local growth part is analyzed, a three dimensional FE model is indispensable. To avoid the effect of errors between exact and analytical solutions, a simple model is analyzed, and the analytical results are compared with a corresponding exact solution that has already been reported. As a simple model, a penny-shaped crack was prepared for the FE analysis. Based on the analytical results, the error from the exact solution was obtained. Then, it was assumed that the error between the analytical solution and exact solution is nearly constant as long as the meshing near the crack tip is the same. According to this assumption, an accurate K at a complicated shape of a crack tip can be obtained by correcting the analytical results using the relationship between exact and analytical solutions in the simple model. In general, K is calculated by using the stress distribution ahead of the crack tip and the displacement extrapolation method, but, here, only the stress at a point ahead of the crack tip was used for the present method to reduce the simulation cost. 2.2. Validation of the analysis method As a method to obtain an accurate solution (1976), a pressure was applied on the crack surfaces, which is equivalent to the loading remote stress. The analyses of the penny-shaped cracks mentioned above were performed with crack radii of 0 .5 μm (crack S) and 1.0 μm (c rack T). The pressure 0 on the crack surfaces, Young's modulus, and Poisson ratio were set to be 100 MPa, 206 GPa, and 0.3, respectively. Figure 1 shows the analysis model of crack T. Figures 2(a) and (b) show overviews of the analysis models for c racks S and T. Figures 2(a′) and (b′) show magnified images that present details of the meshing near the tips of cracks S and T. K values at cracks S and T are denoted as K S and K T , respectively. Here, an attempt was made to calculate K T using the proposed method as validation (although K T also can be obtained the same way with K S , as mentioned below). The exact solution of K S was calculated by Eq. (1) expressing the K when the remote stress σ acts on the penny-shaped crack with crack radius a . 1149 2