Issue 35
X. Liu et alii, Frattura ed Integrità Strutturale, 35 (2016) 88-97; DOI: 10.3221/IGF-ESIS.35.11
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.
Experimental data Upper bound Lower bound Mean value
Experimental data Upper bound Lower bound Mean valu e
1000 1100 1200 1300 1400 1500 （ ） a
（ ） b
1000
=8.9 μm
a
=3.5 μm
a
900
0,min
0,min
=16.2 μm
a
0,mean
800
=9.3 μm
a
0,mean
=23.5 μm
a
0,max
=15 μm
a
700
0,max
700 800 900
600
Stress Amplitude, MPa
Stress Amplitude, MPa
500
10 6
10 7
10 8
10 9
10 10
10 6
10 7
10 8
10 9
10 10
Number of Cycles to Failure
Number of Cycles to Failure
Experimental data Upper bound Lower bound Mean value
Experimental data Upper bound Lower bound Mean value
300 350 400 450 500 550 600 650 （ ） d
200 300 400 500 600 700 800 900 （ ） c
=6.8 μm
a
=7.8 μm
=12.1 μm a 0,min
0,min
a
=17.2 μm
a
0,mean
0,mean
=16.3 μm
a
=27.6 μm
0,max
a
0,max
Stress Amplitude, MPa
Stress Amplitude, MPa
10 6
10 7
10 8
10 9
10 10
10 6
10 7
10 8
10 9
10 10
Number of Cycles to Failure
Number of Cycles to Failure
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.
1000 （ ） b
1000 1200 （ ） a
Experimental data Present model Goodman formula Gerber formula
Experimental data Present model Goodman formula Gerber formula
800
800
600
600
400
400
200
200
Stress Amplitude, MPa
Stress Amplitude, MPa
0
0
0
500
1000
1500
2000
0
500
1000
1500
2000
Mean stress, 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 .
95
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