This method is proposed to determine or calculate the endurance limit under any combined repeating stress within the elastic range and plastic range. The fundamental theory is based on the effective strain energy concerning the octahedral plane direction. The general formula is described as follows : [Mean stress function]×[Effective repeating shear strain energy]+[Equivalent static energy due to the mean stress]=Limiting value. This formula has experimental constants, as other hypotheses, but these can be easily determined by tension-compression and repeating shear experiments.

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From the repeating shear experiment the constant n is determined for steel, cast iron, and Al-alloy stated in the 1st report. The endurance limit under biaxial repeating stress both alternating and repeating to their direction is calculated and plotted as curved lines in the tension-compression and tensiontension quardrant of the biaxial coodinates, and this forms the envelope of Mohr's circles in σ_n-τ coodinates. This principle will be applied to 3-dimentional problems, for example, a bar subjected to alternating tension and compression in axial direction and static pressure on its outer surface.

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It was shown in the 2nd report how the fundamental formula is applied to the twodimensional stress, and now in this report, we treat the combination of normal and shear stresses and the computed fatigue limits are shown in terms of σ-τ coodinates as curved lines for each material, compared with experimental results of the combined bending and torsion. In the case where either normal on shear stress is static and the other repeating, the endurance limit of ductile materials, decreases or tends to increase (in some range) with the increase of static stress, the characteristics of which agree with experimental results.

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At the fatigue test under actual load, the induced strains become rather stabilized after some number of cycles, and the stress-strain curves show loops according to the stress wave forms. Therefore, plastic strain ε_p is supposed to be caused by the deviatric stress of each stress peak i from the mean stress of the wave. Then, the influence of other stress peaks for the ε_p of a peak is analogized bv the static stress-strain curve in the plastic range. And the stress amplitude of ordinary fatigue test that causes the same plastic strain as the peak i is called as an equivalent stress amplitude σ_{eq, i} and its cumulative distribution curve is drawn. And then, program test or cumulative fatigue damage law according to the distribution curve is adopted the evaluation of fatigue lives under the actual stress wave form.

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In order to investigate the Cumulative fatigue strength under the double repeated stresses, the stress-strain hysteresis loops were measured through all stages of fatigue process. The main results obtained are as follows : (1) The main reason prolonging the fatigue life is caused by the strain aging effect in the case of ascending stressing; and the sums of hysteresis energy accumulating until fatigue failure are increased in the same case. (2) Under the strain aging effect the magnitudes of hysteresis energy are decreased in the case of ascending stressing, but under not the strain aging effect the magnitudes hof one are increased. (3) The sum-totals of hysteresis energy are proportional to the fatigue life. (4) The strain aging effect does not cause the variation of fatigue life in the case of descending stressing.

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The authors have conducted fatigue tests on induction hardened V-notched specimens (ρ=0.25;0.5;1 and 5 mm) of C=0.40%, 0.34% and C=0.29% steel. Induction heating temperature was chosen at 700, 800, 900 and 1000°C, the same as in the 3rd report (experiment on C=0.13% steel). The experimental results may be summarized as follows : (i) There is some difference between σ_w1 and σ_w2 of notched specimen, but the differences in C=0.40%, C=0.34%, and C=0.29% steels are smaller than that in C=0.13% steel. The difference between σ_w1 and σ_w2 becomes larger when a becomes larger, the same as in the 3rd report. (ii) Maximum value of σ_w1 at ρ=0.25mm, d=10mm of specimen is 50kg/mm², under the conditions of C=0.34% in steel, and heating temperature 1000°C. And this value is nearly equal to (2σ_w0/α). As yet the authors cannot understand clearly the reason why σ_w1 becomes (2σ_w0/α). (iii) According to the authors' past experimental data on notched specimen (ρ=0.25 mm, d=10 mm), the values of σ_w1 are almost proportional to the hardness at the notched-bottom, but the values of σ_w2 are almost proportional to the Vicker's hardness in the ranme lower than Hv≅500 and are nearly constant in the range over Hv≅500.

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Specimens of annealed 0.35 % C steel were submitted to rotary bending tests in city water at speeds of 1500, 750 and 50 rpm. It was found that the S-N curve of each cyclic frequency, tends to approach the horizontal, however, under continued testing conditions it begins to descend again. In the range below the horizontal, the time until fracture at low cyclic frequency, was shorter than that at higher frequencies. In this range the intermittent pause test, during which the spechnen are in contact with water, shortened the life of specimen in comparison with the sontinuous test. The author endeavours to explain this phenomenon by considering that at high stress, growth of cracks is mainly attributable to stress, and that at low stress it is related to stress and the corrosive effect of water, however, that it is more difficult for the water to enter into the end of deep cracks.

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In this paper an idea to explain the features of the fatigue strength of strength-anisotropic steels is proposed. The underlying idea is that the incipient fatigue crack, developed near surface of the specimen as a result of an occurrence of extrusions and intrusions due to fatigue stressing, spreads step by step by the cracking of the plastic zone at the root of the crack. The cracking is assumed to follow the Griffith's energy condition. The portion where the incipient crack appears differs in torsional and in bending spcimens, sihce the specimens have strength anisotropy. It is assumed that in twisted specimens a plane crack and in bent specimens a semi-circular crack propagates under the action of normal and shearing stresses. The expressions of fatigue strength obtained represent satisfactorily the experimental results made with carbon steels which are reported elsewhere.

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The photoelastic freezing method is applied to obtain the maximum stress in a plate under tension, having a circular hole reinforced by a stiffening ring. Araldite B is used for the photoelastic material and the stiffening ring is bonded to the hole cut in the plate. The plane of slice in the ring is taken parallel to the plane of plate. The difference method is used to investigate the variation of fringe intensity arising by slicing off the materials in the ring. The maximum stress at the boundary of the reinforced hole is given for the various thicknesses of stiffening rings and the optimum strength condition for the circular hole with a stiffening ring is discussed.

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The term "Polygonal Cross-Section" is given for a non-circular but continuosly curved cross-section. This profile is produced by the lathe tool which is reciprocated laterally, and synchronized with the revolution of main spindle. And the standard type of the profile is produced by the simple harmonic motion of the tool. We can use a pair of polygonal shaft and boss for the power transmission coupling. First of all, in this report, we touch on the theoretical analysis of the torsion of the bars with this profile. The shear stress, twisting moment and twist angle in the torsion of this bar are calculated approximately on the basis of Saint Venant theory. Next, some results of experiment are presented. It is shown that the analytical results agree satisfactorily with the experimental ones and can be used as the design formula.

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The variation of the indications of commercial Shore hardness testers is investigated by replicating the tests on particular specimens periodically. The results show that the observed variation is composed of a long-term variation, a day-to-day variation and a variation within repeats. Then a factorial experiment is made to determine the contributions of such factors as the testing conditions, the operating way of testers, the local variation of hardness in specimens and random errors to the total variation. It is disclosed that hardness values are influenced by the ambient temperature. Finally, a most effective procedure to maintain a constant hardness scale on the basis of a given standard is discussed and a method of obtaining a better accuracy than 0.6 Hs over four years with a commercial tester is developed.

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The object of this study is to estimate the theoretical value of Shore hardness. The value of Shore hardness is determined generally by the height of rebound of a falling indenter which will depend upon the elastic and restitution properties of the specimen. If the equation showing the relation between the static load and the depth of indentation is applicable to the dynamic indentation, the energy which determines the height of rebound of hammer can be deduced theoretically on the basis of that equation. A comparison of the theoretical Shore hardness numbers and experimental ones of some specimens shows a good agreement between them.

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This paper deals with the natural frequencies and modes of a simple supported beam which is equivalent to a leaf spring with an added mass and an added moment of inertia. The results may be summarized as follows : (l) If the added mass is at the center of a uniform beam, there is no coupling between. the vertical and rotary vibrations of the mass. (2) Neglecting the width of the added mass, the higher the vibration order is, the more the natural frequency deviates from the accurate value. (3) According to the calculated example in this paper, the natural modes have a little difference between a uniform beam and three laminated beams, the natural frequencies have, however, little between them.

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The vibration of a U-bar which occurs in its plane is studied. The U-bar is consisted of one circular arc bar and two straight bars or of three straight bars. The ends of U-bar are built in and the material and the sectional dimensions of two legs are homogeneous and uniform respectively. The frequency equations and the boundary values are obtained by minimizing the Lagrangian. The frequencies of U-bar with an arc are calculated and shown with graphs. The experiments are carried out and their results are compared with the theoretical ones.

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The fundamental equations of nonlinear flexural vibration for a rectangular elastic plate are solved approximately by employing a method of successive approximation, and the influences of temperature changes and large amplitudes on the period of free vibrations are established. Some numerical examples are given for a plate with hinged and immovable edges, and it is shown that the above effects are considerably large and cannot be neglected even when the temperature changes are small.

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Formerly, the rubber vibration isolators of fundamental type have been discussed in various ways, but practically, those of compound type are often used, and there various types of the latter isolators. So the authors picked up the typical types which are generally used, and tried to calculate and arrange the formulae to get the stresses induced in rubber parts and their spring constants. In this study a special attention was paid to the shearing stress. Generally, the shearing stress does not distribute uniformly over the cross section, so the influence of this fact should be considered in such short machine parts as rubber vibration isolators. Then, we have to derive some correction in the calculation of shearing stress, Whenupon, putting the coefficient to correct this stress as β, the authors calculated β and found that it is the function of only the inclination of cross section of rubber for the load.

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Positive torque feedback was suggested to eliminate the influence of load variation in servomechanisms, while the requirements imposed on a torque transducer were severe, and the theoretical explanation for this method was not complete as yet. In this paper, the author has introduced the computed torque feedback method, in which the motor torque is computed from both manipulated variable and output speed without using a torque transducer. The servomechanism applying this method is analyzed by the phase plane technique, and it is shown that the servomechanism with torque or computed torque feedback resembles the relay servo with nonlihear velocity feedback. The system can be designed to have the characteristics of an optimum nonlinear control for a fixed load, but the response becomes oscillatory overdamped or as the load inertia increases or decreases. Computed torque feedback is applied to direct current servomechanism, and the satisfactory experimental results are obtained.

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