PSI - Issue 13

Masataka Aibara et al. / Procedia Structural Integrity 13 (2018) 1148–1153 Masataka Aibara/ Structural Integrity Procedia 00 (2018) 000 – 000

1151

4

Fig. 3. Schematic of the initial crack model.

3.2. Fatigue crack growth simulation We analyzed fatigue crack growth with the initial crack shown in Fig. 3 to investigate influence irregular crack front shape on fatigue life. The radii a 0 and b 0 of crack 1 were 10 and 2 μm, respectively. Figure 4(a) shows the analysis model of crack 1, which is the one-fourth entire symmetrical model. The pressure p 0 on the crack surfaces, Young's modulus, and Poisson ratio were set to be 350 MPa, 206 GPa, and 0.3, respectively. Figure 4(a) shows the analysis model of crack 1. Figure 4(b) shows the overviews of the analysis model for crack 1. Figure 4(b ′ ) shows magnified images that present details of the meshing near the tip of crack 1. In this analysis, a small-scale yielding condition was assumed to be satisfied, and the FCGRs follow the Paris law. Table 1 lists the number of load cycles. The K values at points A and B are denoted as K A and K B . Fatigue crack growth simulation was continued until K B approaches to 95% of K A . In other words, when the effect of local growth part became negligible for crack growth, the fatigue crack growth simulation was completed. In this analysis, the FCGR estimated by the Paris law is assumed to be constant during a certain number of cycles. The FCGRs were estimated by using the initial K at each stage shown in Table 1. After crack growth in each stage, the crack shape was reconstructed. Specifically, points A, B, and C were redefined on the crack front positions after the propagation. Then, the equilibrium growth part and the local growth part were approximated by circles that pass re-defined points A and C, and B and C, respectively. Figure 5 shows the schematic of the fatigue crack growth simulation. The growth direction at point C was determined to be vertical to the common tangent line of the equilibrium growth part and the local growth part for each growth stage.

Fig. 4. (a) Top and (b) side views of a crack model with the local growth part and (c) corresponding FEM model. (the inset indicates the magnified image of the region highlighted by the red squared. The unit is μ m)

Table.1. Number of load cycles in each crack.