PSI - Issue 7

Taizo Makino et al. / Procedia Structural Integrity 7 (2017) 468–475 Taizo Makino et Al./ Structural Integrity Procedia 00 (2017) 000–000

472

5

More specimens of S49 material used as the data originating from inclusion in Table 1 were tested under the same test conditions. Fig.3 presents the Weibull probability distribution of flaking life obtained from the reciprocating-type RCF test. “A” and “B” in the figure, which correspond to those originating from inclusion in Table 1, were the probability of failure of 65 % and 30 % respectively. This result suggests that the shape and size of inclusion being the crack origin affect the variability of flaking life.

Table 1. Vertical crack initiation and flaking life originating from artificial defect and inclusion in the reciprocating-type RCF test using plate specimens of 1.0mm in thickness.

99.99

99.0

90.0

Origin of flaking Size of origin [μm] *

Vertical crack initiation life N i

Flaking life N f

N i /N f

10.0 20.0 Cumulative probability F ( N f ), % 30.0 50.0 70.0

A

Artificial defect

0.02 0.78

Φ15×L58 Φ11×L25 Φ15×L55

6.00×10 3 7.50×10 6 6.00×10 6

2.92×10 6 9.65×10 6 7.57×10 6

Inclusion A Inclusion B

B

0.79 * Φ: Diameter on a plane parallel to the rolling contact surface, L: Length in depth direction

Vertica l inclusion S0.049mass%

1.0

10 6

10 7

10 8

Number of cycles to flaking N f , cycle

Fig.3. Weibull probability distribution of flaking life obtained from reciprocating-type RCF test. S49 material, t=1.0mm specimen.

3.2. Finite element model We performed finite element analysis (FEA) to simulate the stress states around artificial defects and inclusions. A numerical finite element (FE) model for the RCF test was developed as shown in Fig.4. The FE model comprises a rectangular block for the disc specimen and a hemisphere for the ball specimen taking symmetry into account. The size of model and loading conditions were the same as those of the Mori-type RCF test employed in our previous paper (Makino et al., 2014, 2016). A cylinder model with a diameter of 15 μm and a length of 200 μm was embedded at the centre and on the symmetry surface of the disc specimen (rectangular model). Existence or non existence of the cylinder model and variation of its physical property enable the modelling of artificial defects (circular holes), inclusions and non-inclusions/defects. The minimum length between nodes was 1.25 μm on the boundary between the cylinder and the matrix model. The FE model was validated in advance in terms of the accuracy of Hertzian stress. ABAQUS was used for the FE analysis. The elastic modulus and Poisson’s ratio were 205.8 GPa and 0.3, respectively in the disc specimen and the ball except the cylinder model. Plastic deformation was not considered in this paper. In the cylinder model, the following three cases were assumed. In the case of “Without (W/O) defect”, the same values as those of the matrix material of the disc specimen were employed. In the case of “Soft inclusion”, the elastic modulus and Poisson’s ratio of 100 GPa and 0.3 respectively considering sulphide were employed. In the case of “Circular hole defect”, the cylinder model was removed. Moreover, the “Soft inclusion” case was classified into two conditions; one condition was inclusion and matrix were fully bonded (Bonded interface), the other condition was inclusion and matrix were separated (Separated interface). We refer to “Soft inclusion” and “Circular hole defect” as “Defect” inclusively. Friction coefficients between the ball and disc specimen model, between crack faces and of the separated interface were zero with consideration of the oil lubrication. A vertical force was applied to obtain the same Hertzian stress p max (5.22 GPa) as that in the experiment, then the half-width of the contact patch a was 0.346 mm. The ball specimen model moved 8 mm across the defect on the disc specimen model along the symmetric surface.