This is one of the plane stress problems of a semi-infinite body under a load distributed in geometrical figure on its boundary. Starting from the well-known Airy's stress function with α=nπ/a, we have
F=∞Σ1A_n(1+αy)e^-αy·cosαx
for a symmetrically distributed load along the boundary line.
According to Fig. 3, equation for a distributed load in equilateral triangle will be given by
p(x)=p₀(1-x/c)
for a range 0<x<c, where p₀ is the height of the load triangle and 2c is the length of its base line. After expanding p(x) in Fourier's series, we have
p(x)=∞Σ12p₀/ac1/α²(1-cosαc)cosαx
For y=0, the normal stress on the boundary will be given on the other hand by
σ_y=-∞Σ1A_nα²cosαx=-p(x)
After determining constant A_n, we have following stress function in the from of integral instead of series:
F=p₀/πc∫∞02/α⁴(1-cosαc)(1+αy)e^-αycosαx·dα
Stress components are the second derivatives of the stress function F referred to x and y respectively, thus we have
σ_x=p₀/πc[-4r·cosφ·logr+2r·sinφ·φ+2r₁·cosφ₁·logr₁-r₁·sinφ₁·φ₁+2r₂·cosφ₂·logr₂-r₂·sinφ₂·φ₂],
σ_y=p₀/πc[2r·sinφ·φ-r₁·sinφ₁·φ₁-r₂·sinφ₂·φ₂],
τ_xy=-p₀/πc[2r·cosφ·φ+r₁·cosφ₁·φ₁-r₂·cosφ₂·φ₂].
Transformation of coordinates from rectangular to polar is made in the above calculation.

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For the purpose of conveniently expressing the form factor of overlapping notch, the author made some approximation in his consideration and introduced a simplified formula for the form factor. As the case of overlapping notches, the author treated the following examples.
(1) torsion of round bar with a shallow overlapping notch,
(2) uniform tension of semi-infinite plate with an overlapping notch.
Theoretical consideration about the form factor are made by taking the mapping function expressed by the Laplace transformation corresponding to the arbitrary form of notch. As an example of this method, the semi-circular notch overlapped by a semi-ellipse are taken. The results of calculation show that the form factor of overlapping notch are expressed by the formula founded on the equation of ellipse.

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This investigation forms a part of the research on the optimum conditions in the process control. In this paper, using a real process whose scale of plant is the same as actual one, the dynamic characteristics of the comprising elements in the process control system and the cotrolling performance of the whole system are investigated analytically and experimentally.
The results obtained from this research may be summarised as follows:
(1) The dynamic characteristics of air compressor, reduction gearing, VS-motor, etc. are clarified analytically.
(2) The polytropic constant of the air vessel and the coefficient of discharge at the flow-out valve are decided not only analytically but experimentally.
(3) It is shown that, in such a non-linear system as this process control system, it is meaningless to analyse the system quantitatively without confirming the correspondency of several characteristic values in the system.
(4) It is clarified that such cascaded control system as this system, consisting of a VS-motor and a pneumatic controller, gives an excellent control performance for the control of the gas process.

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Fatigue tests with repeated loads of two steps and sequential multiple steps were made on 0.35% carbon steel specimens by means of a rotary bending fatigue tester of Ono's type. The specimens were normalized in blank before machining at the temperature of 870°C in 1 hour, with subsequent air-cooling. The mechanical properties of the material are given as follows: tensile strength σ_B=56.6kg/mm², lower yield point σ_S=32.2kg/mm², elongation φ=27.3% and the fatigue limit σ_wb=28.1kg/mm².
In the test of two steps loading, four kinds of loading, namely σ₁_??_σ₂=30_??_37.7kg/mm² (beyond the yield point) and 28.9_??_31.8kg/mm² (beneath the yield point) were applied in various cycle ratios, to investigate the aspects of fatigue damage. In the test of multiple steps loading, sequentially ascending and descending loadings of equal 2, 4 and 8 steps in equal cycle ratios were applied in the same range of stresses as in the case of the two steps loading, and the variations of the endurance life were measured.
The test results can be briefly summarized as follows. When the sequential loading is an ascending type, the total sum of cycle ratios up to fatigue fracture is larger than unity, ascending up to 1.3 in average, while the sequential loading is a descending type, the total sum of cycle ratios is smaller than unity, descending down to 0.7 in average. The value of the sum of cycle ratios is almost independent of the number of steps in sequential loadings, whether the stress amplitudes exceed the yield point or not. While scattering of the test results was more remarkable in ascending loadings than in descending loadings. The test results were compared to those of the theoretical prediction by D. L. Henry, and the reason for the scattering of the test results in ascending loadings and some other considerations are discussed.

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Rotary bending fatigue tests were carried out with specimens of 0.25% carbon steel, varying stress amplitude in two stages. After receiving any stress cycles at the first stage, the stress amplitude was changed to the second stage and fatigue tests were carried out till the test pieces were fractured. When the stress amplitude of the second stage is higher than that of the first stage, the cumulative cycle ratio exceeded unity, sometimes reaching infinity. When the stress amplitude of the second stage is lower than that of first stage, the cumulative cycle ratio exceeded also unity or was equal to unity.
Now, suppose that a material which received the repeated stress of the first stage by N₁ cycles, was fractured after receiving the same stress amplitude by N₂ cycles, then we are compelled to consider that the material was damaged by the repeated stress of the first stage and the residual life was shortened. In the present experimental results, the material was not only damaged but also strengthened by the repeated stress of the first stage if the repeated stress amplitude of the second stage is higher than that of the first. Therefore, we can not predict whether the repeated stress of the first stage damaged the material or not if the repeated stress amplitude of the second stage to be followed is not known.
Such a phenomena will be explained if we consider the process of fatigue as follows. The material is hardened gradually by the repeated stress, i. e. the material becomes brittle and proceed the way to fracture, reducing the residual life. At the same time, the material which has been hardened by the repeated stress receives artificial strain ageing by the action of the repeated stress and the material is strengthened, prolonging the life before cracks originate. These two actions coexist in the process of fatigue. By the change of the repeated stress from the first stage to the second which is, e.g. higher than the first, both weakening and strengthening actions are increased. If, in this case, the increment of both actions are the same, the cumulative cycle ratio is equal to unity, but if the increment of the strengthening action is larger than that of the weakening action, cumulative cycle ratio will exceed unity.

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As is generally the case, a large number of machine members are subjected to repeated stresses of varying amplitude under the mean stress level which is varying continuously, and some parts are subjected to occasional overstresses (the stresses over the fatigue limit under constant stress amplitude). It is important in both academic and practical sense to estimate the fatigue strength, i.e. the fatigue life and the fatigue limit of metallic members under the stress condition like this.
A number of workers have investigated this problem, but none have established a rational formula which predicts the fatigue life and the fatigue limit of metal under varying repeated stresses. For the accurate determination of the fatigue strength in these cases, the new criterion and formula have been established by employing the idea of the fatigue damage and the stress history.
The functions of fatigue damage and stress history of metallic materials were established in this paper from the experimental investigations, considering the phenomena of work hardening caused by the repetition of the microscopic plastic strains of metals. The formulas which give the analytical S-N curves and the calculating methods to predict the fatigue lives and fatigue limits of metallic members under alternating stresses of varying amplitude, were obtained by employing the functions of fatigue damage.
The fatigue test results under alternating stresses of varying amplitude carried out by Nishihara and Yamada, and those by Dolan and others, were analyzed by applying the calculating methods described.
And it has been made clear that the analytical fatigue lives and fatigue limits under alternating stresses of varying amplitude had a good agreement with the test results. So it is concluded that the fatigue strength of metals subjected to varying repeated stresses like this can be determined by the analysis introduced in this paper.

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It is very important in clarifying the statistical nature of fatigue fracture to know whether carbon content or ferrite path is prevalent factor in scatter characteristics of fatigue life. Hence the scatter characteristics of fatigue life of Swedish steel containing the same carbon content, but with coarser grain size than the steel (0.41% carbon steel) upon which the statistical data has been previously obtained was studied. The ferrite grain size also was determined of all the kinds of steel upon which statistical study has been previously carried out.
The present study showed that, comparing two steels containing the same carbon content but with different grain size, in finer grained steel,
(1) the scatter of fatigue life is greater,
(2) the proportion of the apparent incubation cycle N_c' (repeated cycle to the point at which the frequency distribution curve of fatigue life begins to have a finite value) to the average fatigue life N_t is smaller,
(3) and the frequency distribution curve of fatigue life is more possitively skewed. than in coarse grained steel.
It appears that ferrite path is a prevalent factor instead of carbon content in the statistical behavior of fatigue fracture of steel, and that the finer the grain size, the larger the scatter of fatigue life and the smaller the ratio of N_c' to N_t, and the more positively skewed the frequency distribution curve of fatigue life.
The another possible factor, however, appears to be inclusions contained in steel, and the determining of the inclusion rating of these steel investigated is now undertaken.

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The fact that the inclusion has detrimental effect to the fatigue strength of metals is well known from many experimental results, but we cannot presume the general tendency that how much decrease in the fatigue limit should be counted according to the kind and the magnitude of inclusion. It is due to not consider the characteristics of inclusion. The author, therefore, discussed the effect of inclusion in conformity with the stress state around ellipsoidal inclusions, calculated by R. H. Edwards, and stated the effect of magnitude of inclusion upon the lowering of fatigue limit. As a conclusion, it is most important to find out the contact state between the inclusion and surrounding material exactly, and if there exists the cohesion force between them, the elastic properties must be considered.

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The effect of low-temperature annealing upon the properties of cold-drawn steel wires has been studied by many investigators, and it has been found that annealing at temperatures up to 400°C after cold-drawing improves their properties to a considerable degree, and the advantage is taken in the steel wire industry. The representative investigation on the effect of low-temperature annealing upon the fatigue properties of carbon steel wire was reported by E.T. Gill and R. Goodacre, and even up to the present, their result has been quoted in many reports and books. They reported that for all the carbon steel wire they examined, there was a critical reduction, at which the fatigue limit of high carbon steel wire under certain annealed state fell considerably below that of the wire as-drawn.
Present investigation was planned for researching the existence of this critical reduction, for 0.65% carbon steel wire, drawn at various reduction, from 60% to 90%, with subsequent annealing in the range 150°C to 400°C, it was investigated that the effect of low-temperature annealing upon the fatigue properties and its tensile properties. The diameter of the specimen was 1.3mm.
The fatigue test was made on the polished specimen using the Hunter fatigue testing machine. As the result of the fatigue test, it was clarified that the fatigue limit of 0.65% carbon steel wire increased as the reduction increased for wires both as-drawn and annealed and so there was not any critical reduction, and that the maximum fatigue limit was found at the annealing temperature 200°-300°C.
From the results obtained by this investigation, it was made clear that the presence of the critical reduction reported by Gill and Goodacre was due to their unpolished specimen.

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The mechanical properties, especially the fatigue strength of carbon steel are improved by the low-temperature quenching and the spheroidizing treatments, because of the diffusion of carbon and nitrogen atoms occurring in such a ferrite structure.
In the present paper, the investigation has been done to understand the effects of quench aging and that of strain aging on the fatigue strength of 0.04% and 0.59% carbon steels which were quenched at low temperature and spheroidized at 700°C. When the specimens were aged at 100°C, their hardness increased with aging time, and reached the maximum at about 40min, regardless of their carbon contents and structures. In this case the maximum difference of hardness, named “Age-hardening-power”, would be a measure of the ability of age-hardening of the material.
In the material with high age-hardening-power, the strength at the notch root region will be increased during repeated loading. This is explained from the fact that a fairly good agreement between the hardness distribution and the stress distribution on the section across the notch root is obtained in the spheroidized specimen with a high age-hardening-power, while the hardness of annealed steel remains unchanged.
The region resisting against the fatigue failure of notched specimen develops inward more and more during repeated loading in the structure which has high age-hardening-power, therefore the resistance to fatigue failure is raised. In the other hand, the fatigue notch coefficient β must be decreased with increasing age-hardening-power, ΔH_max, and the result obtained would be represented by the following equation for the stress concentration factor α=3.3, β=k₁e^-k₂ΔH_max where k₁ and k₂ are constants depending on materials.
From the above, it may be concluded that if a material is capable of strain-aging, it has good fatigue strength, because in such a material, dislocation movements are impeded both by fine precipitates and by solute atoms anchored to them.

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The effects of speed of cyclic stressing on the fatigue strength of pure Al, duralumin (D), super-duralumin (SD), extra-super-duralumin (ESD) and pure copper sheets were studied on Schenck's vibrating sheet bending machine. Tests carried out using completely reversed stress at 2, 60 and 3600 cycles per minute and the number of cycles to failure varied from 5×10² to over 10⁵. The reduction of fatigue strength increased as speed of cyclic stressing decreased and those phenomenon markedly observed with repeated cycles. ESD showed the max. reduction of fatigue strength at the slowly speed of cyclic stressing and SD and D were next. The relations between the reduction of fatigue strength and the speed of cyclic stressing were shown in Fig. 8.

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Rotary bending test is the easiest to carry out among various sorts of testing method of fatigue, and is often practised for determining fatigue characteristics of metallic materials. For fatigue tests at elevated temperatures, rotating load type machine is more preferable to rotating specimen type in order to achieve accurate measurement of specimen temperature. A rotary bending fatigue testing machine of rotating load type for tests at elevated temperatures was designed and manufactured. A brief description on the machine is rendered in this paper.
The original intention of the present study is to discuss the influence of frequency of stress cycles on fatigue life of heat resistant alloys at elevated temperatures. As a preliminary study for it, fatigue of low carbon steel at elevated temperature of 450°C was investigated by applying three sorts of stress cycles, 170, 750 and 3000per min., using the new testing machine. Each test was carried out under the condition of constant strain amplitude.
The results of the tests are summerized as follows; as far as the strain amplitude applied is large, the number of stress cycles till fracture is not affected by the frequency of applied cyclic stress and so, under the action of the definite magnitude of strain amplitude, specimens fracture at definite number of stress cycles. When the strain amplitude is small, however, specimens are likely to fracture at definite time notwithstanding different frequency of stress cycles imposed. The intermediate feature of fracture is apparent in the test under strain amplitude between both extremes which lead to the results contradictory to each other.
The mechanism of fatigue at elevated temperatures is discussed by taking inelastic deformation in every stress cycles, which depends on frequency of stress cycles, as operative factor on fatigue. The qualitative interpretation of the experimental results is given.

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The results of fatigue test concerning metals with various flaws usually scatter to such a extent, that they must be represented by means of a scatter band of considerable wide range, in cases when they are simply classified in groups from the view point of superficial flaws. On the contrary, the internal friction is supposed to have much closer connection with internal flaws of material, thus investigations were made on the relationship between the internal friction and the fatigue strength.
The internal friction is measured by means of period in which the amplitude of free damping vibration diminishes to one fourth of its original magnitude (quarter-value period). Test pieces are cut out along a radius of a forged block of about 600mm in diameter which has been previously inspected by supersonic wave to ascertain the inclusion of much flaws. Referring to the supersonic inspection, they are devided in three groups of layers, the first layer being near the cuticle and the third near the core. The superficial flaws of each specimen are investigated by means of magna-flux method. The test is carried on in such a way that each test piece is hung down in the air by thin threads at the nodes of transverse vibration of both ends free, so that the quarter-value period is measured.
The rotating bending tests are carried cut. The results obtained from specimens belonging to the second and third layers show scattering, as expected, to a great extent, which can not be explained by the number of superficial flaws. It is found, however, that the scattered results can be arranged in fairly good order, if they are classified by the quarter-value period.

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It is one of the most important problems to know the distribution of longitudinal residual stress over the cross section of drawn wire and many investigations have been made for this purpose. It is very difficult to measure the residual stress by simple method with accuracy, because of the small diameter of the specimen used.
This paper deals with design and manufacture of a simple apparatus for measuring longitudinal residual stress with sufficient accuracy.
Electrolytic dissolving method was used in order to remove outer layer of the specimen without any effects of work-hardening, and optical lever method, with which the error due to the temperature difference was automatically eliminated, was used to measure the dilatation of the specimen resulted from removal of outer layer.
For computing the longitudinal residual stress σ, Heyn's formula, equ. (1), was used.
σ=Er_n²Δl_n-r_n-1²Δl_n-1/(r_n-1²-r_n²)l₀ (1) where E is Young's modulus of the specimen, l₀ and r₀ are original length and radius of the specimen Δl_n and r_n values of the dilatation and the radius of the specimen under dissolving. It is very difficult to measure the diameter of the specimen under dissolving directly and so the value of r_n was determined by means of the calibrated chart showing the dissolving depth and the time for the specimen.
From the results of some experiments obtained by using this apparatus, it was found that this apparatus was very suitable for measuring longitudinal residual stress over cross section of drawn wire.

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Ordinary creep tests are usually performed at constant temperatures. A creep test under varying temperatures has not been studied in details. It is well-known that there are many cases where creep in the machine parts is caused under varying temperatures.
Thus employing 0.14% carbon steel, the authors investigated the creep behaviour under varying temperatures. It is found that the creep behaviour in such a condition can be predicted from the results obtained at constant temperatures, using the assumption that the idea of mechanical equation of state is applicable in this case, that is, the creep strain ε is determined by the strain rate dε/dt and the temperature T shown as
f(ε, dε/dt, T)=0.

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This paper describes on the failure process of carbide tool, and the effect of chip breaker on it; that is, how the failure of carbide tool progresses as the cutting proceeds, what kind of appearance of failure the tool shows at the end of its life, how the failure process of carbide tool with chip breaker differs from that without chip breaker, and so on.
The kind of carbide tool used in the experiment is S 1 and the cutting material is 0.4% carbon steel (Rockwell hardness B 64). Cutting conditions are as follows: cutting velocity 100 and 150m/min, depth of cut 2mm, and feed 0.3mm/rev.
From the results obtained from the observation by using microphotographs, universal measuring machine, and so on, the following facts were recognized:
(1) The kinds and processes of failure of carbide tool at cutting of steel were clarified.
(2) It was ascertained how the final damage of tool occurs.
(3) The effect of grooved flank wear on tool life should not be neglected.
(4) The distance between the centre of crater and the cutting edge is not constant contrary to the conclusion by Opitz.
(5) The chipping of end cutting edge induced by the development of cratering on tool face often determines the life of tool.
(6) The existence of chip breaker gives a slight change of the development of cratering, especially in the early stage of cutting.
(7) Generally speaking, chip breaker does not affect on tool life.
(8) The values of the radius of chip-curl calculated by Henriksen's formula fairly disagree with those obtained in the experiment.

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The specimens of polyethylene were deformed by tensile force at the various temperatures between 8°C and 80°C. The cross sectional area of the specimens is 6.8×3.3mm² and the length of their parallel portions is 50mm. The tensile stress-strain curves are shown in Fig. 2, where the logarithmic strain is taken along the abscissa. The characteristic feature of these curves is rendered by three straight lines and a curve, the former consisting of three portions of the strain ranges of 0% to 5%, 15% to 65% and over 65%, and the latter being the portion of the strain range of 5% to 15%. These strain ranges are independent on the test temperatures, but the flow stress corresponding to a certain strain decreases with the increment in the temperatures. The orientation of the chain axes of the molecules in the plastically deformed specimens was also observed from the X-ray diffraction photographs in Fig. 4. The chain axis direction of most molecules in the crystalline region can be calculated from the angle ∅ (in Fig. 4) between the equatorial direction and the radius to the point of maximum intensity on the (110) ring, with the result that the chain axis direction approaches more and more to the tensile direction. As shown in Fig. 5, the angle ε between the tensile direction and the chain axis decreases in proportion to the logarithmic tensile strain. It is evident from the X-ray diffraction patterns in Fig. 4 that the chain axes of the molecules in the amorphous region are made also oriented towards the tensile direction, because the intensity is not uniform on the halo, but stronger near the equatorial direction.

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Tensile creep-rupture tests of unplasticized polyvinylchloride were made on test pieces taken from pipes, up to 100 hours, under several temperatures below the second order transition temperature.
It was found that the Larson-Miller method developed in the research of metals could be applied to that of this material. With the rupture time-temperature as parameter, T (50+logt), we obtained a considerably fair line, i.e., so called master rupture curve.
A discussion was given on the fracture mechanism, especially on the deformation and fracture processes. We presented a significant temperature-stress diagram, having four characteristic regions divided by three straight lines started from 80°C. Each region indicates a different fracture mechanism. This diagram stands also for use in selecting the materials in design. It may be suggested that the similar relationship will be applied for other polymers.
So far as the deformation process is concerned, this material flows perfectly in the shoulder of a neck, within certain stress-temperature regions. This region corresponds to a characteristic creep curve-at the end of the 3rd stage, the creep rate apts to decrease-and a fracture marking.
The necking mechanism was studied by using X-ray diffraction pattern, electron microscope, density measurement and hardness test. Above all, electron micrographic studies by replica method revealed the fine direct evidence of a marked orientation of the material.
The effect of residual stresses before and after a heat treatment, was also discussed.

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In connection with our research on oiliness we measured the thickness of oilfilm and the breaking load of the film. The measuring method is as follows.
We measured the capacity of the condenser which is composed of lubricating oil and two metal plates with the oil in between. By elementary formula we calculated the thickness of the oil from the capacity. So we came to know the relation between the load on the metals and the thickness of oil and also the load which will break the oil film.
At the appendix we show how to make relate this result to our research on oiliness. It is as follows.
Lubricating oil has two different natures which serve to lubrication: -viscosity and oiliness. The relation between lubricating ability and viscosity is almost clarified by many previous reserches, but the relation between lubricating ability and oiliness still remains unexplained. Generally, the following definition on oiliness described in many books is believed to be correct: -“Oiliness is the nature gives the difference to frictional coefficient which does not arise from viscosity under the same condition.”
Lubricating ability at the condition of boundary friction should be measured by the ability of oil covering metal against tearing force to it, not the matter of friction. So this definition does not touch the essential nature of it, we need essential one.
We give a new definition on it from this viewpoint as follows:-“Oiliness is the nature of covering metal by physical and chemical binding force of oil and the metal.”We give the idea how to show the tendency of the magnitude of oiliness and how to measure the magnitude. By measuring the breaking load for given metals and oils at every temperature, we can plot the temperature-breaking load diagram.
This shows the tendency of the magnitude of oiliness, because the breaking of oil film by frictional force is similar to the breaking by dead load. We can choose the best lubricating oil from the diagram for given metals. This is the relation.

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