Abstract
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 σw.
F(N)=p1F1(N)+p2F2(N)+p3F3(N), p1+p2+p3=1,
where F1(N) is a distribution which appears mainly at stress levels well above σw, F2(N) is that appearing around σw, and F3(N) is the distribution around and below σw. 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, γ1 of F1(N), a2, γ2 of F2(N) and a3, γ3 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 σw, the fatigue strength at about 107.
F(N)=p1F1(N)+p2F2(N), p1+p2=1,
where F1(N) and F2(N) are single distributions which appear at stress levels above and around σw, 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 γ1, γ2 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.
