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)=p₁F₁(N)+p₂F₂(N)+p₃F₃(N), p₁+p₂+p₃=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, 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 σ_w, 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 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 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.

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The main purpose of the present study was to investigate the fatigue life distribution at stress levels around the endurance limit σ_w. Three multiple-type rotating bending testing machines were manufactured, each of which can test eighteen specimens simultaneously. Approximately twenty specimens were tested at each respective stress level around the endurance limit σ_w with the maximum number of stress cycles of about 5×10⁸. The specimens used were heat treated rimmed steel CH10R bars. The results were analyzed using the Weibull distribution of mixed type.
The major conclusions are as follows;
(1) In the stress range above σ_w, there are fixed relationships between the parameters of Weibull distribution and the stress, that is, the shape parameter m is constant, and the scale and location parameters, a and γ, have linear relationships on log a-σ and log γ-log σ diagrams.
(2) The Weibull distribution of mixed type
F(N)=p₁F₁(N)+p₂F₂(N), p₁+p₂=1,
is well fitted to the fatigue life distributions at the stress levels around σ_w. The parameters m₁, a₁ and γ₁ of F₁(N) are given by extending m-σ, log a-σ and log γ-log σ relations in the stress range well above σ_w to the stress range around σ_w. And F₂(N) appears only at the stress levels around σ_w, whose parameter m₂ is constant and parameters a₂ and γ₂ have different linear relationships on log a₂-σ and log γ₂-logσ diagrams.

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A large-scale database MSDRD on mechanical properties of structural materials such as metals, composites and ceramics was constructed by The Research Group for Statistical Aspects of Materials Strength. In this study, fatigue data of carbon steels and alloy steels for machine structural use are obtained from the present database and distribution characteristics of fatigue properties are analyzed by a statistical procedure developed by the authors. It is found that fatigue lives of the respective steels have a complicated distribution pattern depending on the stress level and that mixed-mode Weibull distribution is preferable to represent the fatigue life distribution in a wide variety of steels and a wide range of stress levels. In fact, statistical fatigue properties thus analyzed are in good agreement with the experimental data filed in MSDRD and analytical results are applicable to the reliability design of mechanical structures.

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In order to examine the percentage of appearance of the typhoons which have the maximum wind speed in their navigable (left) semicircle, typhoons of 2001 through 2005 are statistically analyzed using the Japan Meteorological Agency Best Track and Mesoscale Analysis data. As a result, 31% of all the typhoons are found to have the maximum wind speed in their left semicircle. The percentage tends to be higher with progress of season, reaching up to 44% in October. It is moreover found that the percentage is greater for eastward-moving typhoons and for those with a traveling speed of over 40km/h. These results indicate that the transition process of a typhoon to an extratropical cyclone is one of the main causes for the appearance of the maximum wind speed in the left semicircle. Thus, this paper finally suggests that caution should be exercised for the left semicircle of the typhoon which approaches to Japan in late autumn, moving eastward at a high speed.

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The statistical fatigue tests were carried out on S38C steel specimens in two environments by using two sets of rotating bending machines, each capable of testing ten specimens at the same time. One environment was an uncontrolled room atmosphere and the other was a dry atmosphere where the relative humidity at 21°C was reduced to about one percent. Fifty specimens were equally allocated to each stress level, covering the failure probabilities from zero to 100 percent. From the experimental results, Weibull three parameters were evaluated by maximizing the correlation coefficient, and their stress dependence was investigated. Moreover, the beta distribution was used to approximate the distribution of endurance limit and good agreement was obtained throughout the failure probabilities from zero to unity for both environments. The effect of the reduction of humidity was distinct: the fatigue life as well as the endurance limit were improved in a dry atmosphere.

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Recently the application of the friction welded butt joint to mechanical structures has come into wider use. A further increase in demand for this sort of joint is anticipated because of its utility for some engineering purposes and the technical easiness of this welding method to make the butt joint of dissimilar metallic materials. However, there exist only a few papers concerned with the fatigue strength characteristics of this type of joint, for it has been recognized empirically that the fatigue strength of the friction interface exceeds that of the base material and thus no noticable problem on this type of joint exists from the view point of fatigue strength.
In the preliminary study conducted by the authors on the friction welded butt joint specimens composed of 0.23%C carbon steel, however, it was revealed that the fatigue lives of these specimens showed a considerably wide scattering in comparison with those of the base material specimens.
To clarify such statistical fatigue strength characteristics of the friction welded butt joint specimens, a series of experiments were planned and conducted on the base material specimens of 0.46%C carbon steel and the friction welded butt joint specimens at several stress levels in the overstress range.
Statistical discussions on the results obtained were made by accepting the Weibull distribution as the original distribution for the fatigue life. It was revealed that there existed a distinct difference in S-N relation between the base material specimen and the friction welded butt joint specimen, when the distribution of fatigue life was taken into consideration.

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Although fatigue life distributions are often represented by the Weibull distribution with three parameters, the properties of these parameters have not been clarified. In this study, the fatigue tests were conducted on JIS S 35 C steels with two different grain sizes at stress levels near each fatigue limit by using a Wöhler type fatigue testing machine. The property of each parameter in Weibull type representation was discussed from the viewpoints of its dependency on the grain size and microscopic observations.
The value of the scale parameter was larger for the material with larger grain size. The value of the shape parameter was roughly proportional to the applied stress for the material with larger grain size, while it was almost constant independently of the applied stress for the material with smaller grain size. From the microscopic observations of the crack growth behavior, it was suggested that the value of the location parameter might correspond to the number of stress cycles where the transition from stage I type crack to stage II type takes place.
At stress levels near the fatigue limit of each material, the relationship between the applied stress σ and the fracture probability P_f could be approximated by the following linear equation,
P_f=Aσ+B
where A and B were material constants, and A increased as the grain size became larger. The evaluation of the safety factor was discussed on the basis of the above relation.

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The statistical fatigue tests were carried out on low carbon steel specimens by using a multi-type rotating bending machine developed by the authors, in which fifty specimens were assigned to each of five stress levels. The fatigue life distributions obtained experimentally at these stress levels were well fitted by either the three parameter Weibull distribution or the log-normal distribution, and, hence, equations were derived to transform three parameters of the Weibull distribution into two parameters of the log-normal distribution. Stress dependency of the distribution parameters was discussed and it was suggested that, at lower stress levels near the endurance limit, the distribution parameters are independent of the stress and only probability of survival at ultra long life region is increased with the decrease of stress. Discussions were also made on the dependency of the estimates of distribution parameters on sample size and on the distribution of fatigue strength at a given life.

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The main objective of this study was to clarify the strength degradation and the strain behavior of engineering ceramics at high temperature during long-term range. For this purpose, a high temperature creep testing machine for ceramics was newly developed together with a displacement measuring device. To begin with, alignment of load transmission train of this testing machine was carefully checked and sufficient performance of this testing machine was confirmed. Then, experiments were carried out by using sintered silicon nitride and sintered silicon carbide at several temperature levels up to 1723K and during long-term up to 1000 hours. The results indicated that the creep rupture curves of both ceramics showed a straight line relationship on log-log diagram of applied stress vs. rupture time at respective temperature levels, and furthermore that the scatter of the rupture lives may be negligible when compared with that of cyclic fatigue strength of these ceramics. Discussion on the creep rupture life of sintered silicon nitride from the viewpoint of the creep strain behavior revealed that the Monkman-Grant's law governed the rupture time of this type of ceramics analogous to the case of metallic materials.

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When an external force is applied to spot welded structures, the load assigned to each spot is not uniform. Moreover, the fatigue life of a welded spot can not be set deterministically and thus the life has to be evaluated from the statistical viewpoint.
In this study, the distribution pattern of load imposed to individual spots was first examined experimentally, and, then, fatigue tests to obtain the life distribution were performed by using a number of specimens in single-spot and multi-spots types. By combining the distribution characteristics of load imposed to respective spots and the fatigue life distribution of single-spot joint, theoretical derivation was attempted on the fatigue life distribution of multi-spots joint. Finally, a good agreement was accomplished between the theoretical and experimental fatigue life distributions of this type of welded joints.

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To clarify the understressing effect in the two-steps program load condition involving the transitional impact load at the rise time to higher stress level σ₁, a series of the rotating bending fatigue tests have been planned and conducted.
On this experiment, the maximum stress σ_max introduced by the impact loading and the program period m, which is the sum of the period for the primary stress m₁ and that for the secondary stress m₂, were taken as the experimental variables. On the other hand, the period for the primary stress, m₁, was held constant as m₁=2sec., and the magnitudes of the primary and secondary stress, σ₁ and σ₂, were fixed to the values of 13.4kg/mm² and 11.0kg/mm² respectively to lie below the fatigue limit of the fundamental S-N curve obtained under the constant load condition.
The main results obtained are as follows: It was recongnized that the understressing following the maximum stress acted as the weakening factor as a whole in the range of this experiment, and that the cumulative damage in the meaning of the Miner's rule became larger. In other words, the weakening effect of the understressing gradually decreased when the magnitude of the maximum stress took a higher value especially in the case of the relatively short program period m=4. And then, according to the estimation from the view point of the hysteresis energy calculated with the assumption that the cumulative hysteresis energy needed for failure takes the same value in spite of the difference in load pattern, it was revealed that the weakening effect of the understressing increased in its amount but decreased in its contribution fraction when the program period m became longer.

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