Prediction of Fatigue Cracks Using Gamma Function

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Experimental loading conditions and equivalents’ initial and final crack lengths for different stress ratios_

R-ratio	a0(mm)	af(mm)	Pmin(KN)	Pmax(KN)	P(KN)	N(cycles)	ΔK0(MP√m)	ΔKf(MP√m)
0.1	3.34	7.875	0.115	1.149	1.034	382.000	5.395	22.696
0.2	3.31	7.14	0.237	1.184	0.947	569.700	4.85	16.88
0.3	3.365	7.365	0.348	1.16	0.812	547.000	4.22	15.90
0.5	2.735	6.28	1.25	2.50	1.25	240.000	5.535	15.82

Coefficient of Paris model_

R-ratio	C	m
0.1	1 · 10−8	3.645
0.2	1 · 10−8	3.7053
0.3	9 · 10−9	3.8712
0.5	5 · 10−8	2.9287

Mechanical properties of Al-Alloy 2024 T351_

σ0.2	σR	A	E	G	ν
363	477	12.5	74	27.82	0.33

Dimension of fatigue specimens_

Lt	L	l	h	B	a0
64	50	14.5	10	10	2

Chemical composition of Al-alloy 2024 T351_

Elements	Si	Fe	Cu	Mn	Mg	Cr	Ti	Zn	Pb	Ni	Al
%	0.105	0.159	3.97	0.449	1.5	0.05	0.018	0.109	0.056	0.02	Rest

Performance of Gamma model

R-ratio	0.1	0.2	0.3	0.5	Mean value
%Dev	4.520	3.892	1.220	5.200	3.708
Prediction ratio	0.961	0.968	0.988	0.951	0.967

The values of the constants of the adjustment curves_

R-ratio	A	B	C	D	E	F
0.1	−44,955 · 104	282,743 · 103	−71,01 · 103	8932.6	−566.95	15.047
0.2	−16,180 · 104	139,644 · 103	−42.59 · 103	6101.5	−424.49	12.113
0.3	−10,975 · 104	603,626 · 103	−132.9 · 103	14.714	−823.39	19.20
0.5	−56,762 · 104	384,000 · 103	−104.6 · 103	14.404	−1008.9	29.449