PSI - Issue 13

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

1150

3

=

2 √

(1) Then, the analytical solution of K T was calculated by Eq. (2). and express each stress in the z-direction at the distance r = 0.02 μm from the crack tip at the crack s S and T. T = S ⋅ T S (2) As a result, the exact solution of K S obtained using Eq. (1) was 7.98 MPa√m . Analysis results of the stress in the z -direction at the distance r = 0.02 μm from the tips of cracks S and T were = 0.241 MPa and = 0.346 MPa . The analytical solution of K T using Eq. (2) was 11.5 MPa √m . Because the exact solution of K T is 11.3 MPa√m , the error between the analytical solution and the exact solution for K T is approximately 1.6%. Hence, the proposed method is viable.

Fig. 1. Schematics of the crack model: top and side views of the model containing the crack. (the unit is μ m)

Fig. 2. Overviews of the analytical models for (a) crack S and (b) crack T; (a’, b’) corresponding meshing around the crack tips .

3. Method of fatigue crack growth simulation 3.1. Calculation of stress intensity factor at a corner

Figure 3 shows the shape of the three-dimensional internal crack that contains the local growth part. This crack is referred to as crack 1. The shapes of the equilibrium growth part and the local growth part were approximated by circles with different radii. The radii of the equilibrium growth part and the local growth part are denoted as 0 and 0 , respectively. Points A and B in Fig. 3 indicate representative points of the equilibrium growth part and the local growth part. Point C is the connecting point of the crack fronts of the equilibrium growth part and the local growth part. Because K at the corner cannot be defined, stress of approximately the same distance from the crack tips was used for calculating K at points A, B, and C.