An X-ray observation was made during the fatigue process of 100 mm, 20 mm and 10 mm dia. rotating bending fatigue specimens machined by a lathe. The results obtained from this experiment are as follows : (1) It became clear that there exists a thin surface layer which has been work hardened by machining and is sensitive to repeating stress. This surface layer yields throughout the specimen surface fairly uniformly before crack initiation. (2) When the reduction rate of surface residual stress at the number of cycles N=10⁴ and N=10⁵, Δσ_R/σ_R_0 (where Δσ_R is the changed value of residual stress and Δσ_R is the changed value of residual stress and σ_R_0 is the residual stress of initial state), was plotted as a function of number of cycles to failure, all the points lie close to a single line. Thus, the change in residual stress during the fatigue process depends mainly on fatigue life itself irrespective of specimen size.

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Following the 1st report, the mechanism of crack propagation in the initial stage of fatigue process was studied on copper by two kinds of test; (1) Repetition of stressing (for the equal number of cycles) and polishing, (2) that of stressing, polishing and annealing. The former test showed that the depth of cracks formed during one stress period decreased more or less in the earlier stages of the test as the sequence of operations was repeated, but increased gradually in the later stages. On perfect removals of such cracks, however, the test-pieces did not fatigue-fractured, even though cycled more than 10 times the expected life. And in these specimens, markedly developed fine cells were observed, in which dislocations were relatively diluted. The depth of cracks formed during one stress period increased when the specimen had been annealed in the preceding stage. Dislocation patches formed disappeared in the annealing at a relatively low temperature, but the cell structure did not, and most of cell boundaries composed of tangled dislocations transformed to twist ones. An inference can be drawn from these experiments that dislocations such as dipoles of vacancy type responsible for crack growth become less movable in the structure like patches, but relatively free to move through the cell structure.

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The fatigue lives under the service load are usually determined by the stress amplitude over the fatigue limit, but several experiments performed hitherto have showed that the stress amplitudes below the fatigue limit, which take the greater part of the service load, influence the fatigue life. But there is not any systematic experiment reported on this problem. Therefore authors have performed program fatigue tests by rotating bending with perforated round specimens of normalized 0.35% carbon steel under the load spectra, which include a stress amplitude below fatigue limit. To clearify the effect of these low stress amplitudes, the length of the fatigue crack is measured. As for the program fatigue lives in this experiment, modified Miner's law can be used for the estimation. According to the results of the measurement of fatigue cracks, the effect of the stress amplitude below fatigue limit changes depending on the crack length at the time the stress is applied, the magnitude of the stress amplitude, and the number of stress cycles in a program cycle.

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The Sachs boring-out method is used for determining axially symmetrical residual stresses in circular cylinders. However, when holes bored out in a circular cylinder layer by layer are not exactly concentric, the above method will not be satisfactorily applicable to estimation of the residual stresses in the cylinder on account of the eccentricity of the holes. Since it is usually accepted that dimensional changes caused by any relaxation of stress are purely elastic, the author analyzes the effect of eccentricity on the deformation of a cylinder from purely elastic theory and gives the numerical evaluations.

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There are many studies on the stress at the root of a loaded bolt thread which is screwed in a nut thread, but most of them are being based on the two dimensional analysis. This paper presents a three dimensional analysis of a bolt-nut joint by the finite element method and Okubo's copper-electroplating method. In the 1st report, such two methods of analysis are applied to a V-grooved rod under a tensile load as the first step. Firstly, the numerical solution of the stress concentration factor by the finite element method is computed by an electric digital computer. Secondly, a high accurate measuring method of the stress concentration factor of the V-groove by the copper-electroplating method is presented. These two methods of analysis are applied to V-grooved rods having three kinds of root radius, and the results are compared with each other. They show good agreement, but the value by Neuber's method is smaller than those two values.

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In the previous report authors clarified the existence and the cause of the two main behaviours, the accelerated crack propagation behaviour and the stagnated one under varying load conditions. In this paper, a quantitative estimation of the crack propagation under varying load condition is attempted considering the accelerated crack propagation behaviour. As this behaviour depends upon the crack opening phenomenon, quantification is attempted by the following method. As the area which sustains the compressive stress under lower stress condition in a high-low type varying load fatigue test (the cracked surface does not sustain the compressive stress) is smaller than one under constant stress amplitude fatigue test (the cracked surface sustains the compressive stress), the section modulus for the former is smaller than that for the latter. Now, these section moduluses are calculated by considering the crack depth, then the actual nominal stress under low stress amplitude in the high-low type varying load fatigue test is obtained quantitatively by calculating the ratio of the net nominal stresses at the crack tips which are estimated by using the above section moduluses. The crack propagation curves for the above actual nominal stresses are interpolated among the curves for the constant stress amplitudes, then these become the estimated crack propagation curves. Reasonable estimation is possible for the crack propagation under varying load fatigue test of carbon steel specimens.

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It is generally accepted that the flow stress as well as the strain-to-fracture of brittle materials is increased by superposed hydrostatic pressure. However, the fundamentals underlying the effect of hydrostatic pressure on brittle materials are yet to be explained. Torsion tests were carried out on cast iron under hydrostatic pressure up to 4000 kg/cm² in order to elucidate the effect of hydrostatic pressure on the deformation and fracture of brittle materials. It is shown in this paper that the deformation and fracture properties of cast iron are strongly influenced by the currently acting hydrostatic pressure rather than the strain history of the material. Anisotropy of cast iron usually observed in torsion tests is decreased by hydrostatic pressure.

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Natural frequencies of short cantilevers with different slenderness ratios are calculated using damped Timoshenko beam equation. The existence of extrema is found in the relation between the frequencies and slenderness ratios, and between the frequencies and the damping coefficients belonging to the first spectrum.

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The governing equation of the flexural free vibration of a viscoelastic bar with a viscoelastic coating subjected to a static axial force is developed by utilizing the Bernoulli-Euler beam theory. The general solution is obtained for a simpy supported coated bar where both core and coating materials are described by a four element linear viscoelastic model. As a numerical example, the free vibration of a coated bar, composed of core and coating materials described by the standard linear solid and Max-well models, respectively, has been analysed. In the present example, the results show that the effect of damping increases monotonically with an increase in the ratio of the sectional area of coating to that of core and also the application of an axial compressive force to a viscoelastic coated bar yields high damping.

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The vibrations of a circular plate with uniformly distributed load around the outer periphery are studied. The circular plate has a hole at the center and the profile is of an exponential curve. The frequencies of circular plates with various boundary conditions are also obtained and the deflections, the inclinations, the bending moments and the shearing forces are shown in graphs.

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The secondary jets induced by double laminar steady plane jets of an incompressible fluid in the domain between jets is investigated. A full Navier-Stokes equation is solved numerically for this problem by using the finite difference approximation method. The general features of the secondary flow by jets are as follows. (i) The more the outlet velocity increases, the farther the centers of two vortexes leave the wall. (ii) The change of the velocity profiles is very remarkable between the wall and the centers of the vortexes. (iii) The maximum velocity of an induced flow to the wall is 30% of the outlet velocity. (iv) The profile of the vorticity distribution is hardly influenced by the outlet velocity, but the vorticity is much influenced by it. And the experimental data are in good agreement with the numerical solutions.

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A basic equation of air-lift pump performance is derived from a simple momentum equation. In the analysis, frictional pressure drop in two-phase flow is expressed by means of liquid volume fraction of the mixture, and slug flow is assumed in order to obtain the relationship between liquid volume fraction and flow rates of both phases. The results predicted by the analysis are compared with experimental data of other investigators as well as of the authors. Good agreement with experimental data is shown in the ranges of 25 mm≤D (inner diameter)≤100 mm, 4 m≤L (length of pipe)≤42 m and 0.4<σ (submergence ratio)<0.8. To give a clear explanation for pump characteristics, the efficiency of air-lift pump is subdivided into two components, the pipe efficiency and the ideal discharge efficiency. A procedure of a pump design is proposed.

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Among the noises of an axial-flow fan with stator and rotor, a discrete noise is most troublesome. This discrete noise is chiefly caused by the interaction between stator and rotor. In this paper we dealt with the axial spacing and the tilting angle in the spanwise direction between guide vane and rotor blades as parameters. Some experiments on the effects of those parameters on noise reduction were made, and at the same time measurements of the pressure fluctuation on the blade surface of the guide vane were carried out. To abate the noise caused by the interference of blades with viscous wakes, we tried to make small the non-univormity of the flow from the inlet cascade by inserting a flow-regulator between the stator and the rotor, and we found that this method is effective for the reduction of the noise. Finally we clarified experimentally that the method of increasing the tilting angle is effective for noise reduction, if the axial spacing bertween the rotor and stator vanes is within a certain range.

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The liquid droplet transfer onto the duct wall was studied experimentally in the previous paper, part 1. In the present paper, a method for predicting the droplet transfer rate is proposed. The droplet transfer coefficient is expressed theoretically in terms of the duct height, the eddy diffusivity and scale of turbulent motion of droplet based on an analytical model, in which are introduced a diffusion equation for droplet concentration in the turbulent core region of duct flow and a new boundary condition taking into account the behavior of droplets near the duct wall. The ratios of the eddy diffusivity and scale of turbulent motion of droplets to those respective values of gas phase are estimated from Tchen's theory by substituting empirical data of turbulent energy spectrum of single phase gas flow. The trend of predicted values for the droplet transfer coefficient agrees well with the empirical results described in the previous paper when the effect of droplet concentration on the turbulence of gas phase can be neglected. A general semi-empirical equation for the coefficient including the effect of droplet concentration is also presented.

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The present paper has been carried out for the purpose of calculating the distribution of stress along the fillet curve of a spur gear tooth with a force-fitted shaft in the rim. Using the two-dimensional elastic theory and the transform function proposed by H. Neuber, the authors have introduced equations for the calculation of the stress at the fillet curve of a gear tooth caused by force-fitting. Moreover, the authors have examined the stresses of various factors, that is, dimensions of gear, thickness of gear rim, conditions of fitting etc. Consequently the practical formulas have been introduced for the stress at the weakest section of a gear tooth with a force-fitted shaft in the rim. By the practical equations, the stress along the fillet curve of force-fitted gear can be calculated more easily than by theoretical equations.

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The authors have compared the strength of force-fitted gear with that of no force-fitted gear, and have examined the variation of the residual stress at the loaded and the opposite side of the root fillet in a bending fatigue test, and have observed the occurring conditions of crack. The following conclusions have been obtained (1) The bending fatigue limits of force-fitted gears are low in comparison with those of no force-fitted gear and the strength of bending test shows the same tendency. (2) Variation aspects of residual stress at the loaded or the opposite side of root fillet of tooth in the bending fatigue test correspond with the growth of crack occurring at the root of tooth.

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