In the present study, the temperature dependence of elastic moduli of aluminum alloy, nickel-steel, and stainless steel has been determined by use of the resonant frequency method. The classical static method of determining elastic modulus has drawbacks at high temperature, owing to the presence of creep and relaxation effects. The dynamic methods are much more prevalent. This determination is obtained nondestructively with minimum number of specimens.
An attempt has been made by the authors to construct the equation of the state for the tensile deformation in order to clarify the influence of strain-rate and temperature on the flow stress of mild steel. In the present investigation an equation giving the relation among strain, strain-rate, temperature and dislocation density has been set up, taking both the strain-aging and recovery processes into consideration. The equation has been materialized in predicting the dislocation densities of low carbon steel deformed in tension under various test conditions(i.e.ε=0.1, 100%/min, temp.=R.T. 600°C). Validity of the equation was examined experimentally by X-ray profile analysis.
In order to clarify the behaviors of low carbon steels, the annealed and the surface-rolled, in their propagation of fatigue crack, the microfractographic observation of the specimens both of these descriptions of materials, has been performed by the electron microscopic replica method, with particular respect to their fatigue fractured surfaces. The results of the observation have been fully discussed, and the macroscopic investigation has been made of the specimens concerning their behaviors in propagation of fatigue crack. The results are summarized as follows: (1) The fatigue crack propagation rate in the surface-rolled specimen is undoubtedly slower than in the annealed specimen. (2) The spacing in striation on the fatigue fractured surface in both the sorts of specimens is larger than what was first estimated from the fatigue crack propagation rate, dl/dN. This fact shows that there is the latent period in the fatigue crack propogation process in both the sorts of specimens. (3) The various patterns observed on the fatigue fractured surfaces are similar in both the sorts of specimens, therefore the fatigue fracture mechanism in both the sorts of specimens is considered to be essentially the same. (4) The platy on the fatigue fractured surface in the surface-rolled specimen is smaller in size than that in the annealed sort, and the striation on the platy in the surface-rolled specimen runs in locally different direction from the main crack propagation line. It can be considered from these facts that in the surface-rolled specimen there have been formed, in consequence of micro internal stress in the work hardened surface layer, branched microcracks at the tip of the main fatigue crack. (5) The slower fatigue crack propagation rate in the surface-rolled specimen is due to the longer latent period that has come, so it is considerd, from the structural difference between the annealed specimen and the surface-rolled specimen, and also from the stress relaxation at the branched crack tip in the surface-rolled specimen.
It is known that fatigue induced dislocations structures in iron and low carbon steel are cell structure at high stress amplitude, and band structure at low stress amplitude. The authors made fatigue testing of low carbon steel specimens, which had been rolled beforehand to give cell structures, at low stress amplitude, and examined the dislocation structures of these specimens, comparing with those of the annealed specimen by the transmission electron microscope. The results obtained are as follows: (1) Two types of subboundaries have been recognized in the fatigue process of the rolled specimen at low stress amplitude. The one has larger misorientation between the neighboring subgrains, and the other has almost no misorientation. The former is characteristic of the rolled specimen, and can be imagined to be made well defined by the recovery during the fatigue deformation. The latter is similar to the subboundary recognized in the annealed specimen for the low amplitude fatigue. (2) The cell size and dislocation density both in the annealed and rolled specimens become similar just before the fatigue failure. These results are similar to those observed in high stress fatigue. (3) The annihilation of dislocations occurs in the rolled specimens, perhaps by abnormally high vacancy concentration produced during the fatigue process. (4) The consumption of vacancy by the climb motion of the edge dislocation, or the annihilation of edge dislocation, seems to delay the generation of pores on the surface in the rolled specimen, and thus the fatigue strength of the rolled specimen seems to increase.
The machine parts or the members of structures are generally subjected to complex stress waves in the service. It is considered that this service stress which varies usually at random consists of continuously varying stress amplitude and continuously varying mean stress. In this study a statement is made of the tests that were carried out of varying stress amplitude fatigue under constant mean stresses and varying mean stress fatigue under constant stress amplitudes on coiled springs because they are among the most important mechanical elements. We not only counted the number of stress cycles to failure under the pulsating compression stress, but also investigated the change in residual deflection due to fatigue stressing, and obtained the relation of the residual deflection to the fatigue life. From these results, it is found that the fatigue life is more dependent upon the stress amplitude than upon the mean stress, and also that the residual deflection is more influenced by the mean stress than by the stress amplitude. On the basis of these experimental results the fatigue life under repeated varying stress has been estimated by application of Miner's linear damage law. The authors have succeeded in estimating the fatigue life with considerable accuracy for a certain region of the number of stress cycles by introducing the correction factor e-α.
Much work has so far been made on the problem of the strength and rupture of materials under non-uniformal stress distribution in such cases as bending, torsion and tension of notched bars. It is well known that the beams of gray cast iron can support 15-25% larger bending moment than the theoretical rupture moment calculated upon the maximum tensile stress hypothesis. This is attributed to the existence of non-uniformal stress distribution by bending, though the relation between the rupture strength and stress distribution is not clear. The author carried out some experiments about the influence of non-uniformal stress distribution on the rupture strength of cast iron by the bending test. Using rectangular specimens of different depths each specimen was measured regarding its rupture moment and strain on the surface. The results obtained are summarized as follows; (1) In static bending of gray cast iron, the ratio of the measured rupture moment Mb and the theoretical moment Mth, of which the latter was calculated upon the maximum tensile stress hypothesis, changes with increase of its depth h. Mb/Mth increases with decrease in h, and the rupture moment decreases to the theoretical value by increasing h. (2) The author defined the strain gradient. xε by xε=1/ε1(dε/dx)1, and found that there was relation between xε and Mb/Mth, where Mb/Mth=1+√δxε. The type of the relation as mentioned above was similar to that which was proposed by Siebel and Petersen on the fatigue strength of notched bars. (3) In the relation, δ is regarded as material constant. For the gray cast iron used in the present experiment, δ was about 0.25mm. This value was almost the same as that obtained by Stieler on the fatigue strength of notched cast iron. (4) The rupture moment of cast iron beams can not be calculated by the bending strength which is determined as material constant. The bending strength varies according to the stress or strain gradient in the beam.
Hereunder is given a report of the stress relaxation tests of mild steel that were made by Oding's eccentric ring method for a short time (1∼1200min) at 300∼600°C. In this method, the stress relieved is known by measuring the initial spacing of the gap (d0) of the ring specimen, the spacing of the gap (d) which is broadened before heating the specimen, and the gap spacing (d') retained after removing the wedge after heating at test temperature. From these tests, the following results have been obtained. (1) In Oding's ring test, “shape constant”A(δ=Aε, where δ=(d-d0)/d0, and ε is the average fiber strain defined in Fig. 1) should be kept as much in uniform as possible with each specimen, in order to apply the desired initial stress, and to know the stress being precisely relaxed. As a unique relation is found experimentally between A and the initial gap-spacing d0, the specimens with uniform A must be prepared by making their gap-spacing d0 as much in uniform as possible. (2)In the case of mild steel, the relation between the remnant stress σ and time t in the earlier stage of the relaxation process at 400∼600°C, is well expressed by σ=σ0-m'(logt-C'), where m' and C' are constants which vary exponentially with temperature, and m' increases with σ0. (3) The relaxation data of mild steel at 500∼600°C, around σ0 of 18kg/mm2, seem to be well rearranged into a single master curve using the relationship T(logt+6.5)/(1-8.5×10-4T)=F(σ/σ0) where t is testing time (hr), and T temperatnre (°K).
In recent years much attention has been paid to the application of the finite element method to the continum mechanics, partly due to the rapid development of digital computers. In the present work, report is made of the method that was adopted to analyze the creep due to stress and that to strain in double edge V notched plates and circumference V notched round bars. The time dependent variation of stresses and strains in the transient stage of creep was calculated on the basis of a time-hardening hypothesis. The following results have been obtained: (1) The Neuber's stress concentration factor Kt(Neuber) is smaller than the stress concentration factor Kt(FEM) obtained by the finite element analysis. Between the two the following relation is found both for the notched plates and for the notched round bars. [Kt(FEM)-1]/[Kt(Neuber)-1]=1.3 (2) The maximum elastic stress at the notch root relaxes by creep, reaching its steady state after a certain lapse of time. The stress redistribution occurs more rapidly in the notched plates than in the notched bars having the same stress concentration factor and subject to the same magnitude of nominal stress. (3) Steady stresses in the axial and tangential direction on the minimum cross section of the notched bars have their maximum values at a point below the notch root unlike those of the notched plates. The position of the maximum values of stress moves away from the notch root as the stress concentration factor decreases and the applied nominal stress increases. The results are closely related to the sharpness of strain concentration near the notch root and the extent of restraint of creep peformation on the specimen axis. (4) The stress concentration factor Kσ for the steady stress is under a half of the elastic stress concentration factor Kt. The strain concentration factor Kε at the time when the stresses reach their steady state is larger than Kσ, and Kε is smaller than Kt, showing that the Neuber's rule does not hold in this case. (5) The von Mises effective stress σ* on the minimum cross section is maximum at the notch root both for the notched plates and for the notched bars. The mean value of the effective stress across the minimum cross section is smaller than the nominal stress. (6) In the creep condition, the hydrostatic component of stress σm on the minimum cross section has its maximum value at a point below the notch root. This may be one of the factors which explain the experimental results on the origin of cracks lying just below the notch surface.
In this paper is presented analysis of stress relaxation at elevated temperature by using assumptions, (1) that the relaxation of the applied stress (σ) consists of two relaxation processes of internal stress (σi) and effective stress (σe), (2) that the decrement of σi is defined by the Bailey-Orowan equation, and (3) that the plastic strain rate εp at stress relaxation is expressed by the relation εp=A exp (ασe), where A and α are constants. From this analysis, the following conclusions have been given. (1) Relaxation mainly depends on the decrement of σe in the earlier stage and in the later stage on the decrement of σi. (2) The relaxation properties after re-loading are determined by the magnitude of instantaneous internal stress. If re-loading is carried out in the period where σi is larger than the initial internal stress, relaxation resistance is increased, and if re-loading in the period where σi is smaller, relaxation resistance decreases. (3) Relaxation rate in the later stage is approximately represented in the following equation, σ≅-r/(1+h/E) where r is the rate of recovery, h the coefficient of work hardening, and E is Young's modulus. (4) If r and h for creep can be substituted with those for relaxation, the following relation between the minimum creep rate εc(=r/h) and relaxation rate εr(=-σ/E) is obtained. εc>εr Putting the stress exponents of these strain rate as nc for creep and as nr for relaxation, the inequality nc>nr is also obtained. However there are such cases where these relations fail for the certain kind of steel accompanied by such structural changes as strain aging.
Hereunder is presented the report of studies, both theoretical and experimental, made of the criterion for the yield and fracture of angle ply laminates wound with filament, in their biaxial tension. Cylinders wound with filament at the angle of 54.75° have been tested in their biaxial tension (σx: axial stress, σy: hoop stress), and interesting facts have been found. (1) In axial tension (σy/σx=0) the yield strength coincides with the breaking strength, but (2) In internal pressure (σy/σx=2) (3) In pure hoop loading (σy/σx=∞) (4) In stress ratio σy/σx=4}the breaking strength is remarkably larger than the corresponding yield strength. To explain these experimental facts a new idea of volume effect has been introduced. In the calculation of the stresses of each layer after the fracture of matrix, variations of elastic moduli have been introduced for the open crack case and the close crack case. The theoretical conclusion thus obtained coincides well with the complex experimental results.
Hereunder is presented the report concerning the experimental studies made of the effect of ultraviolet rays on the electric properties of epoxy resin, and discussion is made on how such an effect has been brought about. Exposure of specimens to radiation of ultraviolet rays consists of two processes, their exposure in the fademeter and their natural aging. Natural aging of epoxy resin is carried out outdoors by fixing its specimens on the exposure stand at the angle of 45°facing south under glass cover. Three types of epoxy resin specimens have been used, the bisphenol type, the novolac type and the cycloaliphatic type. The specimens have also been tested with respect to their electric properties, such as insulation resistance and arc resistance, and with respect also to their mechanical properties from the practical point of view as electric insulation materials. The results of these experiments are as follows. (1) Exposure of the specimens to the radiation of ultraviolet rays in the fademeter has had an effect of reducing their insulation resistance, as shown in the declining curves, whether gradually or abruptly depending on the lapse of exposure time. The decrease in insuration resistance is comparatively smaller with specimens of the cyclialiphatic type epoxy resin. (2) Exposure of the specimens to the radiation of ultraviolet rays in the fademeter has had an effect of reducing their arc resistance. With specimens of the bisphenol type epoxy resin, arc resistance either drops rapidly for the initial 1000 hours or less, and then remains nearly constant, or it gradually falls all through. With specimens of the cyclialiphatic type epoxy resin, arc resistance is higher than it is the case with specimens of the bisphenol type epoxy resin. and there is but little drop of arc resistance all through in spite of the longer lapse of exposure time. It is considered, as the result of comparative experimental studies, that the discoloring effect on specimens by natural aging outdoors for 8 months is nearly equal to that by their exposure to radiation of ultraviolet rays in the fademeter for beween 700 and 1000 hours. It appears that arc resistance has little to do with discoloration of specimens. (3) So far as practical industry is concerned the cyclialiphatic type epoxy resin is considered to be the most efficient electric insulation material. If the bisphenol type epoxy is preferred for the purpose, the use of DAT, HHPA or DDSA is recommended as efficientresistor to ultraviolet rays.
It is intended in the present study to investigate direct application of the Griffith fracture criterion to the fracture of viscoelastic materials. In the experiment, a strip specimen of polybutadiene rubber with artificial flaw of razor cut was stretched up to rupture limit of elasticity under various temperatures and at various strain rates. The results obtained are as follows; (1) A simple relation similar to Griffith's criterion was obtained between the fracture strength σba and artificial cut length Ci even in viscoelastic materials, and this relationship depends remarkably upon temperature, that is σba_??_Ci-α(α=1/2∼1) (2) The authors attempted to apply Griffith's criterion to the fracture of viscoelastic materials by using modulus Eba at rupture point instead of Young's modulus E. Hence the fracture energy Γart.c which includes the configuration factor and surface free energy, strongly depends on temperature and strain rate (time).