In the deflection formula of a coiled spring δ=η8DPn/Gd, the different values of correcting factor η have been obtained by several authors for the small values of index D/d. Authors made experiments in order to determine a dependable value of η using steel and piano wire helical springs.
In the above formula, d, D and G are the constants determined uniquely if the type and the dimension of the spring are given as to the material. The number of effective coils n is N-2, N being the total number of coils, and δ is the deflection of the helical spring obtained under the action of axial load P.
Two correcting factors were considered as follows:
η_t is the correcting factor for the case where the total deflection of the spring is considered. η₁ is the correcting factor when only one coil in the middle section of the spring is considered in relation to deflection.
We conducted some experiments on helical springs with various materials, types and dimensions.
First, the modulus of rigidity G of the wire was measured. Then the relation between load and deflection were obtained for the whole coils of spring and for the middle one coil with no effect of the ends. The changes of the diameter D of the coil under various loads were also measured.
The results obtained are as follows:
(1) η_t is smaller than unity for small values of D/d, but it become larger than unity for larger values of D/d.
(2) η₁ is smaller than η_t by about 0.02. And they all tend to become constant for large values of D/d.
(3) The manner in which the values of η₁ change matches well with the result given by Göhner.
(4) It is concluded that as the deflection factor for small helical springs, Göhner's one may be properly used.

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There have been published several studies on the relations between mechanical properties and fatigue strength of the polished laboratory specimen of steels and other alloys. The fatigue limits of steels range from about 0.4 to 0.6 of their tensile strength, and it is well known that the fatigue ratios of aluminium alloys show lower values than those of steels.
In this report, authors studied on the relations between mechanical properties and rotating-beam fatigue strength of wrought aluminium alloys at 10⁷ cycles. Those alloys were of 13 kinds and treated by the following conditions respectively; annealed, naturally aged after solution heattreatment, precipitation treatment after solution heat-treatment, and others (cold-drawn, precipitation treatment after manufactured, cold worked after solution treated and precipitation treated).
The relations between the statical strength and the fatigue strength of those alloys seem to be approximately parabolic and so the specimen of higher statical strength shows a higher fatigue strength. When those results were classified in each treatment, a fine correlation between the mechanical properties and fatigue strength is obtained and the correlation coefficient and the regression line of those relations are shown in Table 1. A smaller estimate error in the fatigue strength is obtained in the case of Brinell hardness as compared with other cases.
In the case of alloys identically extruded in smaller sizes and heat-treated, the scattering of the fatigue strength is about 2kg/mm², and the previously obtained result that the specimen of higher statical strength shows higher fatigue strength is not always applicable to the case.
The fatigue ratios of softer alloys tend to show higher values and scattering than those of harder alloys. The values of naturally aged alloys vary from 0.3 to 0.53 and those of precipitation treated alloys vary from 0.26 to 0.46. In those conditions, Al-Mg₂Si alloys show higher values of fatigue ratios compared with other alloys.

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The author proposes in this paper a new device directly analysing the strength of constructions submitted to dynamic loads in service. This is a sort of qualitative dynamic strain counter which permits us, the author expects, to make ovar-all evaluation of these constructions from the point of view of fatigue strength.
The essential features of this device are as follows:
i) the materials, which are sensitive to repeating strain, should be ductile metals; for example copper,
ii) these metals should have a fine wire or ribbon shape and be attached to the surface of construction members with some kind of resin adhesive just as in the case of wire strain gauge,
iii) the variation in some characteristic qualities of the detecting metal should be easily distinguishable and so definitely regular that we could determine the equivalent strain amplitude and cycles of the examined construction with the indication of this device.
As one example of such device the author has described here his first attempt utilizing a notched fine wire and some of his characteristics revealing the feasibility of the proposed device.
Purposes of several reports in U.S.A. and England are a little different from mine. The latter is never any fatigue detector but a load counter of fatigue testing machine (i.e. in service condition) utilizing the actual construction in service as test piece.

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Details of a newly developed dynamic creep testing machine are presented. It has been designed to conduct research into dynamic creep and rupture properties of materials at elevated temperatures under the axial load ranging from the static tensile to the perfectly reversed alternating load.
This machine is of the type that applies the static load to the specimen with a pair of coil springs and the alternating load with rotating eccentric masses. The capacity of the machine is as follows:
Maximum static load 1ton
Maximum alternating load ±1ton
Alternating speed 1800-5600cpm
Maximum test temperature 800°C
The static load is maintained constant automatically with microswitch and relay mechanism so that it is not influenced by the creep of specimen. The load (magnitude and wave form) can be observed in the cource of tests by means of a load measuring apparatus constructed with wire strain gauges. The specimens are heated by electric furnace and the temperature is controlled to be within ±1°C by an automatic temperature controller. As the measuring apparatus of elongation of specimen is used the combination of dial gauge and dash-pot.
Fatigue tests at a room temperature and dynamic creep tests at an elevated temperature (450°C) were made with regard to low carbon steel, using these apparatuses, and some of the results are presented.

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Residual stresses greatly affect the fatigue strength of metallic materials, in such a way that compressive residual stress improves fatigue life and vice versa. However, the existence of residual stress means instability of structure and therefore natural trends of the change of residual stress must be considered when the influence of residual stress on fatigue strength is discussed, since the application of repeated stressing is to give an exitement to the unstable material structure.
Following the study of authors on the change of residual stress caused by cold working due to stress repetition, the behaviour of residual stress initiated by heat treatment was studied in the same view point. The character of residual stress by heat treatment was classified in two categories:
thermal residual stress-embedded in materials by heat treatment without transformation.
transformation residual stress-embedded in materials by heat treatment accompanied by transformation.
A high carbon steel with 0.88per cent carbon content was used for the material of specimens, which were 3.2mm in thickness. Specimens with thermal residual stress were prepared by heating at 500°C and subsequent quenching in water. Those for transformation residual stress were heated at 850°C and then quenched in oil. The distributions of residual stresses were observed by means of the corrosion method with 30 percent solution of nitric acid.
A series of tests were carried out for the study of change of residual stress due to aging effect, and another series of tests were for the study of change due to the repetition of stresses in alternating bending.
The conclusions obtained are as follows;
1) The thermal residual stress changes in monotonous decrease with time. The same trend is observed in greately accelerated feature when alternating bending stresses are applied.
2) The transformation residual stress remarkably decreases in the course of one week after quenching and then tends to increase slightly. The increase ceases around the end of the second week and then decreases monotonously. The character of residual stress variation was interpreted by the transformation process of retained austenite to martensite.
3) The application of alternating bending stress to the structure with transformation residual stress accerelates and magnifies the trends of change described in the foregoing item. The magnitude of residual stress at the occasional increase was almost the same as the initial value.

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