PSI - Issue 7

Sho Hashimoto et al. / Procedia Structural Integrity 7 (2017) 453–459 Sho Hashimoto / Structural Integrity Procedia 00 (2017) 000–000

456

4

(1)

*

π 2

K

r

= τ

⋅

II

xz

where, r is the distance between each node and the crack-tip. K II was determined by extrapolating the values of K II * at r = 0. It is noted that K II * at the nodes located very close to the crack-tip were excluded from the extrapolation, owing to the deviation from true value, due to a singularity of stress-field. In this FEM analysis, the friction between the crack faces was not considered, i.e. the coefficient of friction was set to zero. 2.2. Results The variation in K II, drill at Point A in Fig. 5 is exhibited in Fig. 6. K II, drill was seen to vary from the negative peak to the positive peak, while the rolling element also displayed movement. The difference between the negative and positive peaks was calculated as ∆ K II, drill for the respective d , h ′ and q max . Figure 7 exhibits examples of the analytical results, with ∆ K II,drill as a function of defect size at h ′ = 0.100 mm. In Fig. 7, the SIF range for a penny-shaped crack in an infinite body under uniform shear, ∆ K II0 , is also indicated by a solid line, given by the following equation (Kassir and Sih, 1966):

4

(2)

π 2

K ∆ = II0

a

∆ ⋅ τ

(

)

2

π

ν

−

Load movement direction

d : Diameter of drilled hole

120 °

h' : Depth of edge

50 µ m Cracks

Ring-shaped crack

Fig. 2: Geometry of drilled hole.

Fig. 3: Cross-section of drilled hole after fatigue test.

d = 0.100 mm

y

h' = 0.100 mm

10 mm

x

Point A

z

Ring-shaped crack around hole-edge

Load

Rigid rolling element

Load movement direction

Elastic-flat body

x

Point A

z

a' = 0.010 mm

20 mm

80 mm

(a) FEM contact model. (b) Ring-shaped crack around the hole-edge. Fig. 4: FEM model of contact between the ball and the flat plate with a small drilled hole.