PSI - Issue 51

Abdelhak Nehila et al. / Procedia Structural Integrity 51 (2023) 152–159 A.Nehila and W. Li / Structural Integrity Procedia 00 (2022) 000–000

157

6

σ

= K

notched unnotched σ

（ 12 ）

f

with σ unnotched is the fatigue strength of smooth specimens and σ notched is the fatigue strength of notched specimens. According the original definition of the fatigue notch factor K f given in Eq. (12), the proposed fatigue limits prediction formula (Eq. (11)) can be used to predict the notch factor K f : 2 t f f f 2 f Δ ' {1 {1 exp[ ( 1)]}} Δ ' K σ d a K α σ a d α = = + − − − （ 13 ） The experimental values of each parameter were substituted into Eq. (13), then the value of the fatigue notch factor K f was calculated, K f = 1.88. It can be assumed that almost K f ≈ K t which corresponds to the case of the full notch sensitivity. Stress ratio effect on S-N curve From literature, Murakami et al. (1999) suggested a formula that can be used to estimate the effect of stress ratio on fatigue strength under the same fatigue life is expressed as: 3.4.2.

σ −

σ

=

1

−

（ 14 ）

1

β R

R

(

)

2

where σ R denotes stress amplitude at the stress ratio R . σ -1 denotes stress amplitude at the stress ratio of ‒1. β is a coefficient with β = 0.226 + HV × 10 -4 . Since the Vickers hardness HV for the 17CrNi steel is 505 kgf/mm 2 , so β = 0.2765. Substituting R = 0 into Eq. (14), herein: 0.2765 0 -1 ) ( σ σ = （ 15 ） By combining Eq. (15) into Eq. (14), Then the relationship between the stress amplitude for the corresponding fatigue life N and the stress amplitude under R = 0 can be given as: 2 1

2 1 ( R −

0.2765

)

σ

0

（ 16 ）

=

σ

1

R

0.2765

(

)

2

In order to improve the life prediction accuracy for the notched specimens, the surface failure data of the smooth specimens were fitted and the corresponding S-N curve for the surface failure is obtained as follows: 17 1 4.42 3.34 10 ( ) a N σ × = （ 17 ） By combining Eq. (16) with Eq. (17), the S-N curve for the smooth specimens of the 17CrNi carburizing high strength steel can be generalized to different stress ratios R is given as: 17 1 0.2765 4.42 R 1 3.34 10 ( ) ( ) 1 R N σ × = ⋅ − （ 18 ） 3.4.2.1. Total fatigue life prediction The Eq. (12) was substituted into the Eq. (17) then, the S-N curve for the 17CrNi steel under different fatigue notch coefficient K f and different stress ratios R can be given according to the formula: 17 1 0.2765 4.42 f 1 1 3.34 10 ( ) ( ) 1 a K R N σ × = ⋅ ⋅ − （ 19 ）