The exisiting data reported by several investigators for three kinds of structural steels and two kinds of Al-alloys were analyzed by a statistical model based on the Weibull distributions of mixed type. The main conclusions are as follows.
(1) In the case of steel, the following mixed distribution is well fitted to the fatigue life distributions at stress levels around the fatigue limit σ
w.
F(N)=p
1F
1(N)+p
2F
2(N)+p
3F
3(N), p
1+p
2+p
3=1,
where
F1(
N) is a distribution which appears mainly at stress levels well above σ
w,
F2(N) is that appearing around σ
w, and
F3(N) is the distribution around and below σ
w. There are fixed relationships between the parameters of
F1(N),
F2(N) and
F3(N) and the stress, as well as between the probabilities of occurrence of
F1(N),
F2(N) and
F3(N),
p1,
p2 and
p3, and the stress. Namely, the shape parameters
m1 of
F1(N),
m2 of
F2(N) and
m3 of
F3(N) are virtually constant, and the scale and location parameters
a1, γ
1 of
F1(N),
a2, γ
2 of
F2(N) and
a3, γ
3 of
F3(N) show approximately linear relationships on log
a-σ and log γ-σ or log γ-log σ diagrams. Moreover, the probabilities of occurrence
p1 and
p3 change almost linearly with σ on a normal probability paper, while
p2 shows a maximum at certain σ.
(2) In the case of Al-alloy, the following mixed Weibull distribution is well fitted to the fatigue life distributions at stress levels around σ
w, the fatigue strength at about 10
7.
F(N)=p
1F
1(N)+p
2F
2(N), p
1+p
2=1,
where
F1(N) and
F2(N) are single distributions which appear at stress levels above and around σ
w, respectively. There are fixed relationships between the parameters of
F1(N) and
F2(N) and the stress, as well as between the probability of occurrence of
F1(N) and
F2(N),
p1 and
p2 and the stress. Namely, the shape parameters
m1 of
F1(N) and
m2 of
F2(N) are almost constant independent of σ, while the scale and location parameters
a1,
a2 and γ
1, γ
2 of
F1(N),
F2(N) show approximately linear relationships on log
a-σ and log γ-σ or log γ-log σ diagrams. Moreover, the probabilities of occurrence
p1 and
p2 change almost linearly with σ on the normal probability paper.
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