(a) High density pores : Nf = 1.99×105 Casting surface Initiation site Surface scratch Micro pores 50 mm (a) High density pores : Nf = 1.99×105 Initiation site Casting surface 100 mm (b) No defects : Nf = 2.47×106 Fig. 1 SEM micrographs of fracture surface. Fracture surfaces have been classified into four types according to fatigue crack initiation sites. High density micropores are observed in (a), while no obvious defects are observed in the crack initiation site in (b).

-4 -3 -2 -1 1 2 ln(Nf) ln(-ln(Ps)) 19 13 15 17 11 9 Surface scratch (1.19) LD (0.69) HD (Clustered) (0.82) HD (Isolated) (1.10) Polished surface (0.46) Fig. 2 Weibull plots of fatigue lives tested at 160 MPa. Forty specimens have been tested in total, which have been classified into five types, according to the kind and level of the fatigue crack initiation site. The Weibull modulus is shown for each type in the figure.

Casting surface 195 mm Air 100 mm Aluminum (Not displayed) Micro pores that caused the crack Other micro pores 85 mm 0 cycle Fatigue crack 230,000 cycles x y z 240,000 cycles Fig. 3 3D views of the fatigue crack initiation from micropores in the rectangular cuboid in specimen A. Note that one crack was initiated in the field of view. Micropores from which the fatigue crack has been initiated are highlighted in red. The air surrounding the specimen has been segmented and shown in gray, while the underlying aluminum has been removed in order to visualize the fatigue cracks.

Other micro pores (8,140 pores) 0.1 1 10 100 1000 Other micro pores (8,140 pores) Micropores that caused cracks (50 pores) Distance to a casting surface, dsurface / mm 1 5 10 40 Diameter of micro pores, dpore / mm Fig. 4 Relationship between the diameter of micropores and the distance to the casting surface. All the micropores contained in the 21 in-situ fatigue specimens are shown. Micropores from which fatigue cracks were initiated are shown in red.

Table 1 Results of the 3D image analysis of micropores contained in the 21 in-situ fatigue specimens. Micropores from which cracks were initiated have been analyzed separately. Micro pores from which cracks are initiated The region of interest analyzed* Whole region Number of specimens, nspecimen Number of micro pores, npore Number of micro pore pairs**, npair Number density of micro pores, r / ×1012 m-3 Volume fraction of micro pores, Vf (%) Mean diameter of micro pores, dpore / mm Maximum diameter of micro pores, dpore / mm Mean distance to casting surface, ssurface / mm Mean distance between paired micro pores, s / mm * The region in which only micropores closest to the casting surface exist. ** Micropore pairs defined as < 9.7 m between gravity centers 21 19118 6662 4.0 0.014 3.1 24.3 166.6 6.8 21 8140 3069 6.8 0.035 3.5 24.3 6.5 6.9 7 50 22 0.1 0.003 6.1 12.5 3.0 6.6 max

Table 2 Summary of contribution rates, R2, between each independent variable pair. x1 1 0.3898 0.0165 0.0109 0.0069 0.0001 x2 0.0291 0.0458 0.0292 0.0005 x3 0.7484 0.0030 0.0019 x4 0.0015 x5 0.0469 x6 Independent variables Diameter of a single micro pore, x1 Mean diameter of paired micro pores, x2 Distance to a casting surface, x3 Mean distance to a casting surface, x4 Distance between paired micro pores, x5 Angle to the horizontal axis, x6

0.06 0.03 Principal component 2 0.00 -0.03 -0.06 Principal component 1 x2 x1 x3 x4 x5 x6 Fig. 5 Principal component score distribution of principal components 1 and 2. The arrows indicate eigenvectors.

1 x4 < 0.7998 x2 < 0.6745 x5 < 0.4322 x6 < 0.5598 x3 < 0.8216 x2 < 0.7864 Fig. 6 Schematic illustration of the tree-based model obtained using CART.

Other micro pores (3069 pairs) -0.04 0.00 0.04 0.08 Predicted value, Y4 Micro pores that caused the crack (22 pairs) 0.0 0.5 1.0 0.0 0.5 1.0 Mean diameter of pores, x2 Dependent variable, y Fig. 7 Relationship between predicted value, Y4, dependent variable, y, and independent variable, x2.

Micro pores that caused the crack Other micro pores Casting surface 155 mm S1 Air P4 P5 40 mm P2 P3 P1 S2 Fatigue crack 50 mm 80,000 cycles x y z Aluminum (Not displayed) 98,000 cycles Fig. 8 3D views of magnified fatigue crack initiation behavior in specimen B. Note that the fatigue crack has been initiated from the large micropore pairs located in the sub-surface region. The white lines indicate micropore pairs that have dp larger than the statistical maximum value defined at 99 %.

Mean dia. of micro pore pair, dp / mm 1 2 3 4 5 6 Other pores (31 pairs) Statistically max. dia., dpmax = 5.4 mm P2 Mean dist. to casting surface, ℓp / mm Pores that caused a crack (10 pairs) P5 P1 P3 P4 Geometrically min. dist., ℓpmin = 1.8 mm 2 4 6 8 10 Mean dia. of micro pore pair, dp / mm Fig. 9 Relationships between the mean diameter of paired micro pores, dp and the mean distance to the casting surface, ℓp for the micro pores shown in Fig. 8. Micropore pairs from which the fatigue crack was initiated are shown in red.

2a=16 mm 2a=8 mm Surface A 2a=0 Pore Fatigue crack (a)　Single pore (b)　Pore pair Fig. 10 Schematic illustration of fatigue crack initiation from (a) a single pore, and (b) a micro pore pair. Three different stages of fatigue crack growth (i.e., surface crack length, 2a, of 0, 8 and 16 mm) are drawn.