PSI - Issue 7

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

458

6

3. Approximation formula for Mode II stress intensity factor range under rolling contact In this section, ∆ K II, drill is correlated with ∆ K II0 . It was hypothesized that the relationship between ∆ K II, drill and ∆ K II0 could be expressed using an intermediary correlation factor, f drill , as follows:

4

d a

   + 2

  

(3)

π

'

K

f

⋅ ∆ = K II0

f

∆

=

⋅

∆ ⋅ τ

(

)

II, drill

drill

drill

2

π

−

ν

where, ∆ τ = 2 τ xz . The values of f drill were obtained for each q max and h ′ from the results of FEM analysis, all of which are plotted together as a function of the hole diameter, d, as presented in Fig. 8. ∆ K II, drill / ∆ K II0 decreased linearly with an increase in d . The tendencies were similar, regardless of q max and h ′ . Hence, f drill can be expressed as a function of d as follows:

(4)

f A d B = ⋅ + drill

where, A and B are constants. By regressing the results presented in Fig. 8, using the least-square method, A and B were obtained as −1.56 and 0.82, respectively. Thus, ∆ K II, drill is given as follows:

4

d a

   + 2

  

(5)

(

) ( ⋅

1.56

0.82

π

'

∆ = − II, drill K

⋅ + d

∆ ⋅ τ

)

2

π

−

ν

In Fig. 8, f drill , as calculated by Eq. (4), was identified by a solid grey line. The estimation error fell within the range of almost ± 5%, except when the hole depth was much smaller than that of the drilled hole, e.g., ( d , h ′ ) = (0.200, 0.050) mm. Based on the afore-mentioned results, it can be concluded that ∆ K II, drill can be accurately calculated using Eq. (5), within the ranges of 2.0 GPa ≤ q max ≤ 3.0 GPa, d ≤ 0.2 mm, 0.5 ≤ h ′ / d ≤ 6.9, 0.05 ≤ a ′ / d ≤ 0.2 . With respect to the RCF tests conducted during this study, most of the test conditions fell within the previously-mentioned ranges. In the subsequent paper, Eq. (5) is applied to the quantitative evaluation of RCF strength as a crack problem.

1.0

d

f drill = −1.56∙ d + 0.82

h'

0.8

f drill ( = ∆ K II, drill / ∆ K II0 )

0.6

0.4

h' [mm]

0.050 0.100 0.220 0.345

0.2

3.0 2.5 2.0

× × ×

＋ ＋ ＋

■ ●

q max [GPa]

■ ●

■ ●

0.0

0.0

0.1

0.2

0.3

Diameter of drilled hole, d [mm]

Fig. 8: f drill as a function of d for various q max and h ′ .