The analysis by the author, which aims to predict the dynamic creep and fatigue strength from the information of static creep tests, is presented in a summarized form and discussed in comparison with the experimental results for various metallic meterials. The analysis is classified into the following four categories:
(a) Dynamic creep rupture: In the case of the dynamic stress with small stress ratio (ratio of alternating stress to mean stress), rupture strength can be estimated from static creep rupture data by analysing on the basis of the idea of cummulative creep damage. In conducting the analysis, the equivalent static stress, which yield the same rupture life as the dynamic stress, has been determined as
σ'_e=σ_m[1/2π∫^2π₀(|1+Asinωt|)^αsd(ωt)]^1/αs,
where σ_m, A, t and ω are mean stress, stress ratio, time and frequency of alternating stress, respectively, and α_s is a constant which is obtained as the inclination of log-log plots of stress vs. rupture time diagram of the static creep rupture test.
(b) Dynamic creep: In the range of small stress ratio, the creep deformation also can be predicted from test results under static stress. The analysis was carried out on the basis of the strain hardening theory, and the equivalent static stress, which causes the same creep as the dynamic case, had been defined as
σ_e=σ_m[1/2π∫^2π₀(1+Asinωt)^α/βd(ωt)]^β/α,
where α and β are the stress index and the time index, respectively, in the case that the creep strain in the transient stage is expressed as a power function of stress and time.
(c) Fatigue: In the case of large stress ratio, the material is likely to fracture due to the accumulation of fatigue damage, and the strength can be estimated from reversed stress fatigue data by assuming that the alternating stress determines the life independent of the mean stress.
(d) Fatigue deformation: In the range of stress ratio, in which the fatigue fracture occurred, the deformation was sometimes larger than that predicted on the basis of strain hardening theory. The deformation in such case was called as fatigue deformation.
The analysis stated above could be applied to materials of relatively stable structure, that is, a carbon steel, some ferritic and austenitic stainless steels and a commercially pure titanium.
In the case of super alloys of precipitation hardening type, however, considerable descrepancy was observed between theory and experiments, and this descrepancy seemed to result from acceleration of precipitation hardening or other strengthening effect by alternating stress. As an attempt to overcome this difficulty, a correction factor, called as degree of strengthening, was introduced into the analysis, such as
χ=[(σ_m/σ_e)_exp-(σ_m/σ_e)_th]/(σ_m/σ_e)_th,
where subscript exp and th denote experimental and theoretical values, respectively. This factor could be expressed as a function of stress ratio and time, that is,
χ=χ₀θ^μt^ν,
where θ=tanA; χ₀, μ and ν are constans, and μ≅1.5, ordinarily. By using this formulae, the strength of such materials under dynamic stress condition also could be estimated from static creep and reversed stress fatigue data.

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A comprehensive study was carried out to investigate the effects of the chemical compositions, heat treatments and grain size on the creep rupture properties of the 18-8 Ti stainless steels, in wide use for superheater tubes and reheat tubes of power boilers. The conclusions are as follows:
(1) Effect of chemical compositions
It was found that the ferrite-free austenitic steels had the creep rupture strength superior to that with 14% ferrite at 550°C and 650°C, both of which had different compositions even though within the range of the specification (AISI 321 or JIS STB 42 D) and were obtainable to single or duplex structure by selection of proper composition also within the range of the specification.
That is speculated to be attributable to occurrence of the precipitation of enormous chromium carbide around the ferrite in duplex austenite-ferrite structure at testing temperature.
From these results, it is desirable as for the chemical compositions to offer fully austenitic structure, if possible, for elevated temperature applications. The results of measuring of the creep rupture strength of the 18-8 Ti steels within the range of 3 to 19 of Ti/C ratio, keeping the constant contents of carbon and other alloying elements, revealed that it increased with decrease of Ti/C ratio. It is assumed that increase of Ti/C ratio follows additional insoluble TiC at the prevalent solution treatment temperature (1100°C) and consequently decrease of TiC effective to creep rupture on the contrary, which precipitates finely and dispersedly into the austenite structure at service temperature. Thus it is recommendable to adopt low Ti/C ratio within the range of 3 to 7, to obtain high strength at elevated temperature.
(2) Effect of heat treatments
Arising of the solution treatment temperature in the range of 1000°C to 1300°C brought about increase of the creep rupture strength of the steels. We might conclude, however, that to the temperature range of 1100°C to 1150°C is practically preferable, because too high temperature heat treatment bears low toughness.
(3) Effects of grain size
It has generally been said that the coarsely grained steel has good creep rupture strengtth in comparison with that of the finely grained. However, in case of austenitic stainless steels, as creep rupture strength markedly depends on the condition of the precipitation of carbide along the grain boundaries at the service temperature range of 550°C to 650°C, it was found that the coarsely grained steel does not always show good creep rupture strength. Thus we may consider that the fact described in (2) is due not to the coarse grain but to the fine and uniform distribution of the precipitated carbide at service temperature, which shows the higher solubility to the matrix at higher solution treatment temperature.
(4) Long-time creep rupture strength
Creep rupture tests up to 13000 hours are practised for advantageously heat-treated 18-8 Ti stainless steel with desirable chemical compositions. The extraporated 100000 hours rupture strength was 9.3kg/mm². That is superior to the average value, 5.5kg/mm², of ASTM STP No. 124. We may probably attribute that to underestimation of 18-8 Ti stainless steel, because the data of ASTM had been obtained before the relations between metallographic behaviors and creep rupture strength in this steel were satisfactorily clarified.

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It has been established that there is a certain relation between the notch sensitivity and the elongation or ductility in the creep rupture test on austenitic steel, and that the notch sensitivity increases, in general, as ductilities decreases. This relation, however, is not simple, for the carbide precipitation phenomenon does not simply affect the notch sensitivity.
Kanamori and Oda showed that the creep rupture elongation of the solution-treated or insufficiently aged austenitic steel decreased under a certain range of stress, and that marked intergranular corrosion occurred by etching in such a specimen ruptured with low elongation.
The elongation, however, does not always decreases even if marked intergranular corrosion occurs.
In this investigation we intend to throw light on the mechanism in which a decrease in elongation is inevitably attended with marked intergranular carrosion.
The main points of this paper are as follows:
(1) Marked intergranular corrosion was due to the existence of the chromium depleted zone which was caused by the diffusion of chromium to the grain boundary during creep. The concentration distribution in the depleted zone was determined by measuring the distribution of anodic equilibrium potential, and it was found the minimum concentration was less than 1 pct. approximately.
(2) The Kirkendall effect that could be expected from the diffusion of chromium atoms was verified by the calculation based upon the measured distribution of chromium concentration.
(3) The excess vacancy concentration ratio was calculated and the value of more than 10² was obtained for LCN 155 aged for 5h at 700°C, and it was shown that the value of about 10² was to be sustained for a longer period of time.
(4) The above excess vacancies may promote the formation and growth of voids in the vicinity of grain boundary under a certain stress or above. These voids will, then, lead to cracks and finally to rupture. Therefore, one may expect this mechanism causes the decrease in elongation of solution-treated or insufficiently aged austenitic steels. This paper will show that various creep rupture phenomena on the austentic steel can be accounted for by this theory.

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The creep-behavior of commercial steels during the process of metallurgical changes were studied by the anisothermal bend-test. As the specimens, SUP-3, SUJ-2, SEH-3, SCM-5, SKH-2, SKD-4, 0.02%C and high carbon rail-steels which had been variously heat-treated or cold-worked were used. The results were as follows:
(1) The hardened steel showed an abnormally large creep during the process of tempering. The higher the temperature of testing, the larger the creep.
(2) The magnitude of such creep was proportional to the applied stress and had a closer relation with the hardness variation during the process than with the hardness itself.
(3) Except for steels which contained special elements such as W, the higher the carbon content, the larger the creep.
(4) The magnitude of such creep was affected by the austenitizing treatment before hardening. The lower the austenitizing temperature and the shorter the holding time, the larger the creep at the temperature above about 500°C.
(5) In the hardened-tempered steel, such creep appeared during heating at the temperature which was higher than that at which it had been tempered.
(6) In the slack-quenched steel, such creep appeared during heating at the temperature which was near and above Ar' temperature.
(7) In the steel which had been quenched from the temperature lower than Ac₁, for example 700°C, such creep was recognized to a certain extent as well.
(8) The annealed steel did not show such abnormally large creep.
(9) The thermal recovery of such creep was recognized during re-heating in the unloaded condition.
(10) The cold-worked steel showed such creep during the process of recovery and recrystallization.
(11) The creep of steel increased sharply during the process of A₁ and A₃ transformations. The creep of austenite immediately after A₁ transformation was larger than that of austenite at the same temperature during the process of cooling after heating to a higher temperature.
(12) The relation between such abnormally large creep and the frequent climbing of dislocations during the process of metallurgical changes was considered.

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Cr-Mo-V steel is widely used for h-p and i-p steam turbine shafts among many high temperature low alloy steels. And it has been recognized by our creep rupture test results of a number of steam turbine shafts that the creep rupture properties of large-sized Cr-Mo-V steam turbine shafts cover a considerably wide range. It is considered that this variance of the creep rupture properties is caused by the variance of the steel making procedures in a limited sense, that is the imperceptible differences of the melting practice, chemical composition, and heat treatment. To make clear the roles of these variables, a test program has been putting forword. The effects of tempering temperature on the creep rupture strength of a Cr-Mo-V steel is presented here.
A Cr-Mo-V steel was austenitized at 950°C for 2h and cooled in a furnace at a rate of 100°C/h, followed by the tempering at 650°C, 675°C and 700°C for 3h. The micro structures were tempered bainite containing a little fraction of ferrite precipitates instead of the fully bainitic structure of actual shafts. The experiments were consisted of the creep rupture test, tensile test and V-notch Charpy impact test for the estimation of the fracture transition temperature. The creep rupture test was conducted with plain and notched bar specimen and the test results were arranged with Larson-Miller's parameter. The tensile test was conducted at room temperature and 538°C.
The experimental results may be summarized as follows:
(1) As the tempering temperature raised, the creep rupture strength of the plain bar specimen decreased, and the difference between 675°C and 700°C tempering was larger as was expected from the tensile test results and the microstructures of the steels.
(2) The creep rupture strength of the notched bar specimens were little changed with tempering temperature.
(3) In this range of tempering temperature and rupture time, notch rupture strength ratios at 538°C were more than unity, but the more the tempering temperature decrease, the more the notch rupture strength ratio tends to decrease. This means that there is every indication which shows the marked notch sensitivity of the Cr-Mo-V steel when the tempering was conducted at the comparatively low temperature.
(4) The ratio of the creep rupture strength of plain bar specimen to the room temperature ultimate tensile strength was nearly constant irrespective of the tempering temperature. The ratio to the 538°C ultimate tensile strength slightly increased as the tempering temperature lowered, and this may be attribute to the stability of structure during the comparatively shorter rupture time. The ratios of the notched bar strength to the ultimate tensile strength at room temperature and 538°C were both gradually decreased with the lowering of the tempering temperature, according to its tendency to notch sensitivity.

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Influence of notch on the rupture strength in Creep Rupture Test (conducted so as to finish in around 1000 hours) of three heat resisting alloys with varying degrees of precipitation hardenability, 17 Cr-13 Ni-3W, LCN-155, A-286, either currently in use or expected to be used for parts of turbines or jet engines, was investigated.
Three different kinds of heat treatments were selected, which were: normal solution treatment, normal aging subseqent to the normal solution treatment, and aging at a temperature 100°C above the normal aging temperature subseqent to the normal solution treatment. In the meantime, three different shapes were chosen for specimen, which were: plain, or unnotched, V-notched (60°) with a tip radius of 1.25mm, and V-notched (60°) with a tip radius of 0.06mm.
The results show that the notch sensitivity is highly influenced by the mode of age hardenability of the material which, in turn, is greatly influenced by the stress concentration, and that it is important to stabilize the structure prior to actual service.

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Many high temperature alloys are used in tubular forms, but most of creep strength or creep-rupture strength data for these materials are based on simple tension bar specimens. The high-temperature strength data based on bar specimens can't eliminate many of discrepancies between test of specimens and actual service. Many of investigators have developed the method closely simulated actual service condition. This method is the creep-rupture test adopted for a tubular specimen under internal steam pressure and at a controlled temperature. The author compared the creep-rupture characteristics of tubular and bar specimens for rolled material and welded joint. The following results were obtained:
(1) Agreement between the data of tubular and bar specimens of 18 Cr-8 Ni·Ti steel is good when the equivalent stress in tube wall is calculated on the formula which developed in ASME.
(2) In case that the strength of weld metal is stronger or indicates a similar degree of strength as compared with base metal, the creep-rupture strength of 18Cr-8Ni·Ti welded joint indicates the similar strength in comparison with base metal.
(3) In case that the strength is weaker than base metal, this 18Cr-8Ni·Ti welded joint decreases in high-temperature strength. But the degree of strength-lowering in the test applied to the bar specimen is more remarkable than that in the case applied to the tubular specimen.
(4) The creep-rupture strength of dissimilar joint between 18 Cr-8Ni·Ti steel and 21/4 Cr-1 Mo steel is lower than the strength of 21/4 Cr-1 Mo steel. But, the degree of strength-lowering is more remarkable in the case of the bar specimen than in the case of the tubular specimen.

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It is said that there exists an intimate relation between relaxation and creep although loading conditions of both tests are quite different. It is practically desirable to estimate relaxation properties of materials from creep data. In this paper, the relationship between relaxation and creep which is a basis for doing this estimation is described.
In relaxation, rate of plastic strain is an important factor for knowing it's characteristics as well as for calculating residual stress based on the stress dependency of strain rate. Previous studies have revealed that rate of plastic strain holds a linear relation with stress in log scale.However, the results of test in the present study illustrate the relation of strain rate to stress as consisting of a break line in the same diagram. The primary region (the 1st stage of relaxation), earlier stage after loading, shows that the rate of plastic strain depends on stress and total strain, consequently on plastic strain. The secondary region (the 2nd stage of relaxation), which dominates in latter stage, shows that the rate of plastic strain depends on stress, and the effect of total strain on it is considerably small. The 1st stage seems to correspond to the transient creep and the 2nd stage to the steady creep.
The residual stress-time relation is also divided into two regions similarly to the case of strain rate-stress relation. Up to the present, the interests have been placed mainly on the latter region of the second stage and consequently the stress-time relation has been presented by a straight line on log-log coordinates.
Analysis was made to predict the residual stress and the rate of strain for 1st stage from transient creep data, based on strain hardening theory, and also to predict the residual stress in 2nd stage from the data of steady creep rate in creep test. The calcurated results were not coincide satisfactorily with the experimental values. It is considered as the reason for this incoincidence that in the analysis the effects of stress history and creep recovery phenomenon which would presumably influence to relaxation process are not taken into account.
Relaxation process is taken as the creep under successively decreasing stress. Stress decrease would inevitably accompany the creep recovery. Although creep recovery that is considered to occur in relaxation has not been fully understood in the present stage of study in this field, the analysis was corrected by taking this phenomenon into account. The corrected value became nearly equal to the experimental result.

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In order to clarify the basic characteristics on the thermal fatigue strength of metals, the authors have investigated on the changes in dimension, deformation, hardness, specific gravity, microstructure, temperature distribution and yield strength at elevated temperatures during simple thermal cycling of the various metals and alloys for reactor use, and the following results were obtained:
(1) Armco iron and 304L stainless steel elongated in longitudinal direciton, but carbon steel having various carbon contents, 21/4Cr-1 Mo steel and four kinds of Fe-Al-Cr alloy contracted after the thermal cycling.
(2) The grain growth due to thermal cycling of both 304L stainless steel and Fe-7.5 Al-6 Cr alloy containing 0.5% Ti and 1% Nb which suppressed the contraction was faily small. But in both alloys, surface crack occurred in the early stage of thermal cycling and propagated to the interior of samples. In the other Fe-Al-Cr alloys which displayed contraction by thermal cycling remarkable grain growth occurred and, in these cases, crack initiated only on the surface layer of sample at later stages than in 304L stainless steel, where that did not propagated. Therefore the grain growth itself could not be seemed as the essential cause of dimensional changes, because thermal stresses due to thermal cycling are relieved during the grain growth and not to promote but to retard the dimensional changes.
(3) The temperature and yield strength distributions in sample during thermal cycling of 304L stainless steel and two kinds of Fe-Al-Cr alloy (8% Al and 12% Al) were measured. For latter alloys the intense decrease of the yield strength was observed at higher temperature than 500-550°C but for former alloy such marked change of yield strength was not observed through a temperature range up to 750°C. From these results, the authors concluded that the essential cause of the dimensional changes in such metals and alloys having simple phase as armco iron, 304L stainless steel and Fe-Al-Cr alloys depends generally upon the amount of thermal strain due to temperature gradient and the change in yield strength.
Besides, the authors suggested that whether elongation or contraction was dependent apparently upon the existence of the marked decrease of yield strength within the cycling temperature range. However, the critical values could not be decided quantitatively because of lack in data. The authors will study further quantitatively to clarify the mechanism of the above mentioned phenomena.

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In recent years the problem of thermal fatigue of heat-resisting metallic materials has received attention and several reseachers have performed fundamental works in this line. There are, however, several open questions as to the fundamental method of testing with which thermal fatigue strength is evaluated. One of the questions is the problem on the shape of test specimen. In conventional thermal fatigue tests thin walled hollow specimen is adopted, but in a few cases solid cylindrical specimen is employed because in case of the former specimen there is difficulty in machining of test specimen from tool steel or roller steel. However, the adoption of solid cylindrical test specimen is not fully developed because of unstable deformation of test specimen during thermal fatigue test, although preparation of solid specimen is much easier than hollow specimen. In this connection it is necessary to verify the adoption of solid cylindrical specimen.
The authors, as well, have been interested in the problem concerned with this unstable deformation of solid test specimen for thermal fatigue test. In the present paper, results of thermal fatigue test with two sorts of solid cylindrical specimens are presented and these are compared with the results of thin walled hollow specimen. Materials tested are AISI 347 type stainless steel and 2.25Cr-1Mo steel.
The test results are arranged in two sorts of presentation, i.e. the thermal strain amplitude-number of cycles and the thermal stress amplitude-number of cycles relations, in order to compare the strength of solid specimen and hollow specimen in thermal fatigue. It is found that the two sorts of solid cylindrical specimen have different lifetimes. In the solid specimen with shorter length the distribution of temperature along the length was farely uniform, while in the cases of solid specimen with longer length and hollow specimen the temperature was considerably high in and around the central part as compared with that at the end portion of parallel length. However, during the thermal fatigue process of the solid specimen of longer length, unstable deformation, i.e. bulge of specimen near mid length, was observed, while the solid specimen with shorter length did not show such a feature. This is considered to have brought about the difference of lifetime.
The results of the present study are summerized as follows: The solid cylindrical test specimen is available as the specimen for thermal fatigue test, where electric current is passed through the specimen as heating source, provided that attention were laid on minimizing the temperature variation along length. The test results of solid cylindrical specimen give a good agreement with those of thin walled hollow specimen on both base of thermal strain amplitude and thermal stress amplitude.

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One of the problems most vital to the strength of the rotor disc of gas turbine for naval ships is its thermal fatigue fracture due to the plastic strain which occurs each time the engine is started and stopped. For the estimation of how often the turbine can be started and stopped without causing the thermal fatigue fracture, it is necessary to know the magnitude of plastic strain which repeatedly occurs at every part of the rotor disc. Therefore, first we worked out, by solving a partial differential equation concerning the heat transfer, the transient temperature distribution taking place in the disc before the status of its interior becomes almost steady after the turbine has been started, and in order further to know the change with time in the status of stress and plastic strain in the disc, we, on the basis of the transient temperature distribution, worked out the elasto-plastic solution of the fundamental equation on the rotor disc, using the finite strain theory and the trial and error method (so-called S.S. Manson's method). Thus we could calculate the magnitude of the plastic strain. At the same time, we made a constant strain fatigue test of the material of rotor, and from the results obtained it was presumed that the rotor disc would stand 400-1700 times of starting and stopping of the turbine at the lowest estimate, thus proving that this gas turbine is fully serviceable as a buster.

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