In the present paper, some problems of temperature history on transient stage creep are discussed, and the experimental and analytical results on 0.15 per cent carbon steel are presented. From these results the following are concluded : (1) In the case of single temperature cycle as shown in Fig.5 (a) under fixed tensile stress, the "incubation period" is observed immediately after the lowering of temperature and it is found that the period depends on the time interval t' elapsed under a higher temperature level, being larger for the larger t'. (2) In the case of Fig.5 (b), it is found that the amount of strain increment just after the raise of temperature is likely to depend on both the time interval t' elapsed under a lower temperature level, being slightly larger for the larger t', and the strain at which the temperature is lowered from the reference temperature T₀, being larger for the small strain. (3) The effect of temperature history on creep is composed of transitional change in internal yield stress, that is, recovery or aging, where the internal yield stress is defined as the local stress at which deformation beings without the aid of thermal fluctuation. (4) From a practical point of view, however, these effects are negligibly small and the concept of "mechanical equation of state in solid" is applicable to the prediction of creep under such temperature variation, within an error of 5 per cent in terms of strain.

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In the present paper, the analytical relation of creep under temperature cycling to static creep under steady temperature is presented and is examined by the creep tests under step-wise temperature cycling on low carbon steel, 13 chrominum steel and 18-8 stainless steel. The following are the conclusions from the present study : (1) The experimental creep curves of multiple cycle of step-wise temperature variation under fixed tensile stress are fairly close to the analytical ones based on the concept of "mechanical equation of state in solid" for the case of small value of τ/p, where τ/p denotes the ratio of τ, the time exposed to the reference temperature, to the period p of every cycle. The creep curves under such cyclic temperatures can be predicted from the results of test at constant temperature within an error of 5 per cent in term of strain. (2) The creep strain under cyclic temperatures can be predicted easily form the static creep test data by introducing the equivalent steady temperature T_e as defined by Eqs. (9) and (10). The analytical results are in good agreement with the experimental ones.

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In the present paper, the influence of temperature cycling on accelerated stage creep and the rupture life is discussed by employing AISI 318 type stainless steel. In this discussion, the comparison of both strengths in temperature cycling and steady temperature is made by taking the equivalent steady temperature for rupture life of temperature cycling test same as the test temperature of constant temperature test. From the creep rupture tests under saw-type cycling of temperature the following are concluded : (1) Embrittlement of crept material subjected to temperature cycling is significantly larger than the case of steady temperature. The rupture life under such temperature cycling is nearly twice as much as that under steady temperature and the elongation is approximately half of that under constant temperature. It would probably be because of a difference in metallographic structure change occurred during tertiary stage of creep, for both series of tests. (2) In the case of transient and steady stages of creep, the influence of temperature cycling is negligibly small. It would probably be due to the absence of difference in structure change during such stages of creep for both temperature cycling test and steady temperature test.

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Dynamic creep and fatigue tests were conducted on a 18-8 Mo-Cb steel at a temperature of 650°C. The results were discussed from the standpoint of the analysis which had been proposed by the authors previously to predict the dynamic creep and the fatigue strength from the static creep and rupture data together with reversed stress fatigue data. The prediction by the analysis showed a quite satisfactory agreement with the experimental results for the practical purpose, although a little discrepancy was observed due to the acceleration of the precipitation hardening by alternating stress. As a contribution to make clear the relation of the precipitation hardening characteristics of the material to its strength characteristics, especially the discrepancy between the analytical and experimental strengths, the following tests were also carried out, (1) the hardeness test of the material before and after the dynamic creep, (2) the observation of structure before and after the dynamic creep by an electron microscope, (3) the creep rupture test after the dynamic creep. According to the results of these tests, the variations of structure and of hardness during the dynamic creep process seemed not to be related directly with the discrepancy, but the results of the creep rupture test after the dynamic creep showed appreciably greater life than in the case of static creep rupture, and it was believed certain that the cause of the discrepancy consisted in strengthening of the material by the alternating stress related to the precipitation hardening.

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The rotating bending fatigue tests were performed on the specimens of 0.21% carbon steel with various circumferential notches at elevated temperature. The effects of the test temperature, the test speed and the notch sharpness on the fatigue strength and the notch factor were studied from various angles. The data indicate that the fatigue strength of the smooth specimen takes the highest value at a temperature of about 300°C based on the bluebrittleness. As the notch becomes sharper, such an increase of strength at 300°C is gradually eliminated, and for the sharpest notch the highest fatigue strength is obtained at a temperature of 500°C. The notch factor also takes the highest value at 300°C, and at 500°C it reduces considerably. The effect of the test speed is more pronounced for the sharper notch. The notch factor is decreased considerably by lowering the test speed at 500°C.

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A Thermal Fatigue Apparatus has been newly designed and made. With this apparatus, the effect of variations of the temperature cycle on the thermal fatigue of 18-8 Cb steel are studied. In this experiment, the temperature-range and the hold time are varied, maintaining the mean temperature 350°C constant. The following results are obtained. (1) The number of cycles for failure is the function of four tightly correlating factors : the temperature range, the hold time, the stress amplitude Δσ and the cyclic plastic strain Δεp. (2) The relation between the plastic strain energy ΔU (=Δσ·Δεp) and the number of cycles for failure N, ΔU·N^α=K, is obtained, and the value of α is constant independently of the change of the hold time, then the effect is negligible. (3) Very small deviations in the amount of chemical component of the steel affect seriously its thermal fatigue strength, and it is seen that one of the most important factors is the hot ductility.

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In the "Testing method of Rockwell hardness", JIS Z 2245 (1955), it is prescribed that the difference of diameter of a steel ball between two directions, the direction of loading and perpendicular to it, should not exceed 0.01mm. Permanent deformations were made in normal steel ball by indenting on materials hardness of which is over H_RB 100. The author made an experiment about the effect of this deformed steel ball on the hardness value of H_RB. The author have obtained the following results : Even with the same amount of permanent deformation, the effect differs according to the deformed form, in one case the errors ΔH_RB increase proportionally to H_RB of specimens, in other case ΔH_RB decrease, and in the third case ΔH_RB have little relation with H_RB. The author tried simple but reasonable consideration about the classification of these cases, applying the enlarged Meyer's law, and reached almost the same conclusion with the experiment. The author now conclude that the permissible limit of 0.01mm of amount of permanent deformation prescribed in JIS is too larger, and the permissible limit should be 0.02mm.

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This paper reports on the theoretical conversions between Rockwell, Brinell and Vickers hardnesses. Theoretical hardness conversions based on the principle of geometric similarity and Meyer's law agree well with experimental conversions now used in general. Furthermore, the authors show that variation of conversion relationship for various metals can be explainable with Meyer's index almost clearly.

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Dependence of conversion values between Vickers and Rockwell hardnesses upon materials must be illustrated by the difference of elastic recovery which is seen in the measurement of Rockwell hardness. At first, the recovery of indentation and the changes of indented profiles were determined on the basis of the theories of plastic indentation and elastic contact. These theoretical results coincided well with those of experiments. By introducing the values of elastic recovery of indentation into the conversion formulae, the changes of conversion value by materials were explained reasonably. Thus, we can conclude the hardnesses for such materials whose conversion charts have not yet been given.

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In this report, the compression of a wedge by a rigid flat die when the initial condition is symmetrical has been investigated. Ten modes of deformation of the wedge are expected depending on the friction at the die surface and the thickness of the wedge but the complete solutions have been obtained for seven modes of them. Some considerations have been made on the extremum principle taking into account the energy dissipation at the frictional surface and applied to the kinematically admissible field to estimate the load in the modes for which the complete solution is unknown as yet. It seems that the kinematically admissible field which satisfies the stress boundary condition on the frictional surface gives the estimation of the load nearly that of the exact solution. It has been shown that the method to estimate a mean value of strain from the work of deformation is convenient.

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The load on and deformation of a wedge compressed by a smooth rigid flat die were investigated. Seven types of slip line field have been shown for the wedge which has any inclination to the die face. These fields are classified into three modes of deformation where (a) the material flows separately on the contact face, (b) dead metal zone is in contact with the die and (c) the material flows only on one side of the wedge. Four of the seven fields are complete solution. The width of the contact face, load or its upper and lower limits and the mean strain of the wedge were compared with these modes of deformation, and it has been revealed that the mode (a) exists in a very narrow range of the inclination and thickness of the wedge and is hardly realized and that the load of the mode (b) is larger than that of mode (c) but as the mean strain is small, mode (b) will be realized rather than mode (c) when the inclination of wedge is small and thickness of wedgeis moderately large and when the material is in the state of strain hardening.

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Slip line fields in a wedge compressed by a rough rigid flat die and the load or its upper and lower limits were obtained. The wedge has any inclination to the die face and the motion of die is arbitrary. The slip line fields are distinguished into three cases according to the direction of the motion. Although the upper and lower limits of the load were calculated by means of the extremum principle described in the first report, the application of this principle is not rigorous and must be justified from the numerical results. The partial solution where all conditions are satisfied in the assumed plastic region differs from the kinematically admissible field where the condition of equilibrium is not satisfied in view of the fact that the latter cannot determine the definite relation between the shape of the field and frictional coefficient at the contact face.

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In this paper, the strict solutions are obtained for the L-bar, of which one end is built in and the other free, for the various angles and ratios between the two legs of L-bar. The vibrations are considered in two cases, one of which is the case where the vibration occurs perpendicularly to the plane of L-bar and the other where it occurs in that plane. The method used is that, at first, from the variation calculus and the boundary values which are unknown and assumed some constants, the vibration functions are determined, then, the unknown boundary values are determined to make the Lagrangian minimum, and the frequency equations are obtained. The results are given by the nondimensional frequencies and the comparisons of the experimental data and Rayleigh method are made. Sometimes, the combined vibrations are caused and the reason for it is explained also.

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Fundamental vibration of a bent beam, which has one bend and is clamped at both ends, is studied in this paper by means of the energy metheod. The frequency equation is obtained in a form of the determinant of five orders, and numerical calculations are carried out for the bent angle of 0°, 45°, 90 °, 135°, 180°and for the length ratio of 1, 3/5, 1/2, 1/3, 1/7.

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In this paper, the fundamental differential equation of vibration of cylindrical shell in a single displacement is discussed on utilization of the fundamental differential equation of thin cylindrical shell for statical problem introduced by the present author. This fundamental equation may be utilized to discuss the problems of general forced vibrations, of pressurized cylinders, or of vibrations of short wave length, etc.

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As the first step of studies on dynamic stress problems in variable section bar used as structual elements, a theoretical investigation of longitudinal motion of variable section bar was carried out. Choosing suitable forms of variable section, fundamental equation of motion can be reduced to the linear binomial differential equation and it's solution is expressed in the form of Hyper-geometric Function or Bessel Function. Variable section form obtained above has two parameters, so the solution can be adaptable over the very wide range of variable section forms. As an example, wave propagation in variable section bar of linear profile in case of impact is discussed and experimental results on linear profile bar of steel showed good agreement with the variation of stress amplitude computed from the theoretical stress wave propagation formula.

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It is known that the frequency transfer function of pneumatic transmission line on pressure signal is expressed approximately by e^-Lejω/(T_ejω+1). So that if a transmission line is connected with a proportional derivative element, the characteristics of the time lag is compensated, but that of the dead time is not. The authors paid their attentions to this simple principle and designed a new dead time element which acts pneumatically. This element is constructed by a transmission pipe and a phase compensator only. As a result of the experiments, the value of the dead time longer than one second was obtained by the transmission pipe of variable length and diameter of this element, although the frequency characteristics of this element are different from the ideal one of the dead time in higher frequency region.

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Previously, the authors obtained the exact periodic solutions, harmonic and subharmonic, for the forced oscillation of a symmetric nonlinear system with so-called "set-up" springs, except for the solutions having three or more zeros in a period. In this paper, the stability of these periodic solutions is investigated rigorously with the aid of the Tsypkin's method used for the stability problems of relay control systems and some interesting results are reported.

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When the load of an actuator consists of mass and Coulomb friction for a valve-controlled hydraulic device, the correct responses are obtained analytically for rectilinear inputs. As any type of inputs can be approximated by a connection of straight lines, the responses to various types of inputs are analyzed. As an application of the analysis, the responses respectively for either a step, or ramp or sinusoidal input are obtained and are approximated by the equivalent transfer functions. The effects of the dither applied to the spool are also clarified by this approach. The validity of the analysis is verified by experiments. The equivalent transfer function is considered very useful to design more complicated servomechanism.

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In order to maintain the output (ex. efficiency) of any engineering system at a desired extreme value, in spite of natural changes in the environment of the system, it is necessary to apply optimalizing control. Various methods for optimalizing control have been contrived by several investigators. The author proposes "a cut-and-try method" with an input move proportionate to the difference of output values before and affect the preceding move. In the present paper, the problems of stability and offset depending on the initial condition and parameters for the system with one input are analized in detail. Moreover, the author presents a method of designing the optimalizing controller which makes the output, starting with any intial condition, arrive near a desired extreme value in a shortest time with the least offset possible.

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