Issue 35

X. Liu et alii, Frattura ed Integrità Strutturale, 35 (2016) 88-97; DOI: 10.3221/IGF-ESIS.35.11 94 10 4 10 5 10 6 10 7 10 8 10 9 10 10 0 10 20 30 40 50 60 70 Surface Interior inclusion inclusion R =-1 R =-0.5 R =0.1 R =0.3 Size of Inclusion (area inc ) s,1/2 , (area inc ) i,1/2 ,µm Number of Cycles to Failure Figure 8: Relationship between inclusion size and fatigue life for four tested stress ratios. Fig. 9 presents the comparison of the fatigue strength obtained by Eq. (3) using different inclusion sizes with the experimental data at different stress ratios. It is seen that the estimated fatigue strength by using the minimum inclusion size of the specimens is generally higher than the experimental results, which is regarded as the upper bound of the fatigue strength obtained by experiments. While the estimated fatigue strength using the maximum inclusion size is generally lower than the experimental ones, which is regarded as the lower bound of the fatigue strength obtained by experiments. The fatigue strength obtained by Eq. (3) using the average inclusion size is moderate, which seems to be the medium S–N curve. This indicates that Eq. (3) is suitable for the description of the effect of inclusion size and stress ratio on fatigue strength. It is noted that the shape of S–N curve for high-strength steels often presents a duplex pattern corresponding to surface- initiated fracture mode and interior-initiated fracture mode. Here, we only consider the interior-initiated fracture mode with an FGA surrounding the inclusion at crack origin. Comparison with Goodman formula and Gerber formula Goodman formula and Gerber formula are classic models for the effect of mean stress on fatigue strength. Here, the present model is compared with Goodman formula and Gerber formula for predicting the effect of stress ratio on the fatigue strength in VHCF regime. The present model, Goodman formula and Gerber formula are written as follows. Present model: 1 1 , , , 1                           m R a R a R (4) Goodman formula: , , b 1 1             a R m R (5) Gerber formula: 1 2 , , b 1 1             a R m R (6)