Issue 35

X. Liu et alii, Frattura ed Integrità Strutturale, 35 (2016) 88-97; DOI: 10.3221/IGF-ESIS.35.11 95 where σ m,R is mean stress with respect to R , σ a,R is stress amplitude with respect to R , σ b is tensile strength, and σ -1 is stress amplitude at R =-1. 10 6 10 7 10 8 10 9 10 10 700 800 900 1000 1100 1200 1300 1400 1500 （ ） a Experimental data Upper bound Lower bound Mean valu e Stress Amplitude, MPa Number of Cycles to Failure a 0,max =15 μm a 0,mean =9.3 μm a 0,min =3.5 μm 10 6 10 7 10 8 10 9 10 10 500 600 700 800 900 1000 （ ） b a 0,max =23.5 μm a 0,mean =16.2 μm a 0,min =8.9 μm Stress Amplitude, MPa Number of Cycles to Failure Experimental data Upper bound Lower bound Mean value 10 6 10 7 10 8 10 9 10 10 200 300 400 500 600 700 800 900 （ ） c a 0,mean =17.2 μm a 0,max =27.6 μm a 0,min =6.8 μm Stress Amplitude, MPa Number of Cycles to Failure Experimental data Upper bound Lower bound Mean value 10 6 10 7 10 8 10 9 10 10 300 350 400 450 500 550 600 650 （ ） d a 0,max =16.3 μm a 0,mean =12.1 μm a 0,min =7.8 μm Stress Amplitude, MPa Number of Cycles to Failure Experimental data Upper bound Lower bound Mean value Figure 9: Comparison of fatigue strength obtained by Eq. (3) using different inclusion sizes with experimental data at different stress ratios. (a) R =-1, (b) R =-0.5, (c) R =0.1, and (d) R =0.3. 0 500 1000 1500 2000 0 200 400 600 800 1000 1200 （ ） a Experimental data Present model Goodman formula Gerber formula Stress Amplitude, MPa Mean Stress , MPa 0 500 1000 1500 2000 0 200 400 600 800 1000 （ ） b Experimental data Present model Goodman formula Gerber formula Stress Amplitude, MPa Mean stress, MPa Figure 10: Comparison of predicted fatigue strength by present model, Goodman formula and Gerber formula with experimental data. (a) Fatigue strength at fatigue life of 10 8 , and (b) Fatigue strength at fatigue life of 10 9 .