PSI - Issue 7

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

457

5

Load movement direction

h'

A

y

x

o

d

a''

a'

d

z

Ring-shaped crack

Fig. 5: Ring-shaped crack emanating from the hole-edge under rolling contact.

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

-10 -8 -6 -4 -2 Mode II stress intensity factor K II, drill [MPa ・ m 1/2 ]

-10 -8 -6 -4 -2 Mode II stress intensity factor K II, drill [MPa ・ m 1/2 ] Distance between the center of the rolling element and the center of the drilled hole, x [mm] ∆ K II -0.6 -0.4 -0.2 0 0.2 0.4 0.6

-10 -8 -6 -4 -2 Mode II stress intensity factor K II, drill [MPa ・ m 1/2 ] Distance between the center of the rolling element and the center of the drilled hole, x [mm] ∆ K II -0.6 -0.4 -0.2 0 0.2 0.4 0.6

∆ K II

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 Distance between the center of the rolling element and the center of the drilled hole, x [mm]

(a) q max = 3.0 GPa (c) q max = 2.0 GPa Fig. 6: Change in the stress intensity factor, K II , at Point A in Fig. 5, caused by the movement of the ball under compressive contact. ( d = 0.100 mm, h ′ = 0.100 mm). (b) q max = 2.5 GPa

10 15 20 25 30

10 15 20 25 30

10 15 20 25 30

● Edge of drilled hole under rolling contact stress ( ∆ K II, drill by FEM) Solid line: Penny-shaped crack under uniformly-distributed stress ( ∆ K II0 by Kassir & Sih)

● Edge of drilled hole under rolling contact stress ( ∆ K II, drill by FEM) Solid line: Penny-shaped crack under uniformly-distributed stress ( ∆ K II0 by Kassir & Sih)

● Edge of drilled hole under rolling contact stress ( ∆ K II, drill by FEM) Solid line: Penny-shaped crack under uniformly-distributed stress ( ∆ K II0 by Kassir & Sih)

0 5 Stress intensity factor range ∆ K II, drill , ∆ K II0 [MPa ・ m 1/2 ]

0 5 Stress intensity factor range ∆ K II, drill , ∆ K II0 [MPa ・ m 1/2 ]

0 5 Stress intensity factor range ∆ K II, drill , ∆ K II0 [MPa ・ m 1/2 ]

0.00 0.05 0.10 0.15 0.20

0.00 0.05 0.10 0.15 0.20

0.00 0.05 0.10 0.15 0.20

Radius of crack, d /2+ a' [mm]

Radius of crack, d /2+ a' [mm]

Radius of crack, d /2+ a' [mm]

(a) q max = 3.0 GPa

(b) q max = 2.5 GPa

(c) q max = 2.0 GPa

Fig. 7: Δ K II as a function of crack size under various q max ( h ′ = 0.100 mm).

In the calculation of ∆ K II0 by Eq. (2), ( d /2+ a ′ ) was used as the crack radius, a , and the nominal shear stress range at the depth of hole edge, 2 τ xz was used as ∆ τ . As shown in Fig. 7, ∆ K II,drill is always smaller than that of the penny-shaped cracks under uniform shear. It is assumed that the reason for the difference is the absence of any elastic body inside the hole which does not bear any stress. In addition, it is noted that the discrepancy in two SIFs, ∆ K II, drill and ∆ K II0 , is increased with an augmentation in hole diameter. This tendency proved true, regardless of a q max that ranged from 2.0 to 3.0 GPa and an h ′ from 0.05 to 0.345 mm.