Previously, the authors studied the fatigue lives under the reversed stress with periodical two stress amplitudes. The equation predicting fatigue lives was modified by introducing the stress correction factors. Three kinds of carbon steel were tested under such load conditions and the values of stress correction factors were obtained. At that time, however, no physical or mathematical meaning was given for these factors. In this paper, the authors have investigated the significance of this stress correction factors by the analysis starting from the modified linear damage criterion. The conclusions obtained are as follows (1) The fatigue damage should be considered as the function of the practical strain amplitude (instead of the nominal strain amplitude). In this study, we introduced the damage function as D=CΣpj=1(εj1/mnj). (2) This strain εj should not be the strain of the virgin material but the practical strain after various stress histories. (3) The stress correction factors should be defined as the ratio of the 1/m-th power average of this practical strain to the nominal strain. Accordingly, these factors are not only experimental constants but the factors with sufficient physical significance.
In many cases, the life of machine members under fatigue tests with random loadings is usually estimated on the basis of the so-called“linear damage criterion”. In most cases of the experimental results already reported, however, the linear damage criterion does not necessarily agree with the experimental results. It seems that this fact does not depend upon the scatter of the strength of its material, but upon the mutual interaction between the stress levels. As a method of discussing this interaction of stresses, the authors noted the change of stress and strain-amplitudes during the fatigue stressing under the multiple repeated load of multi-step, and tried to lead the method of calculating the fatigue life.
A new fatigue testing machine was developed for the purpose of reproducing the same load conditions as those generally experienced by the rotating shafts of the machine under service conditions. In this machine used for the experiment the rotating specimen was primarily loaded by the constant weight as in the machine of cantilever beam type, and was secondarily loaded by the vibrator, which was driven by the out-put current of the generator or by another A. C. power, and generated the vibration of constant amplitude with certain frequency. The results were that each point of the circumference of the specimen received in general different multi-harmonic stress. But for certain combination of the frequency of the vibrator and the rotating speed of the specimen, it was possible for every point on the circumference to receive approximately the same multi-harmonic stress. The performance of the machine was found to be quite satisfactory through the tests.
The tensile properties of metals under dynamic loading have hitherto been studied by many investigators with it in view either to determine stress-strain curves or to measure the yield stress, the tensile strength, and the change in length of the specimen at failure, under the action of strain rates higher than encountered in the usual static test. Little or nothing has so far been made, however, to clarify the effect of strain rates on the internal structure and the mechanical properties of rapidly stretched materials. This investigation has been conducted to make a thorough examination of the problems given above. An explosive-rapid tension tester used in the present experiment has provisions for measurement of instantaneous changes of load and elongation as a function of time or load-elongation diagram. The 0.12% and 0.37% carbon steel specimens have been used in this study. The test has been carried out by the following procedure. (a) static and rapid tension test for annealed specimens (b) static tension test for statically and rapidly stretched specimens (c) rapid tension test for statically and rapidly stretched specimens (d) hardness test and microscopic observation for statically and rapidly stretched specimens The main results obtained are as follows: (1) The strain rate gives a remarkable effect on the resistance in deformation of carbon steel in spite of its having been annealed and pre-stretched. The large increase in yield stress indicates that the friction stress increases greatly at high strain rates. (2) It is recognized that the behavior of propagation of Lüder's band by rapid loading differs from that by static loading. (3) It seems from the tension and the hardness test and the microscopic observation of the slip band that the change of internal structure caused by high strain rate gives some effect on the resistance in deformation.
Following the line of the previous reports, we have investigated the effects of notch sharpness and annealing on the notched tube impact bending strength of small-diametral, cold drawn and seamless steel tubes (the dimensions of the tube: 25φ×1.5t, the reduction percentage in the tube drawing: 10 and 300). The results obtained are outlined as follows. (1) With larger reduction percentage in the tube drawing, the notched tube impact bending strength decreases. And its decrease is noticed most clearly in the impact test at low temperature, say at about -100°C. But when the cold drawn tubes are soft-annealed at 700°C, the above effect disappears. (2) When the cold drawn tube is annealed at low temperature, say at 200∼400°C, its hardness increases to some extent and its impact strength does not change. But when it is annealed at above 400°C, its hardness does not decrease, but its impact strength increases gradually. And when it is annealed at above recrystallization-temperature (600 and 700°C), its hardness decreases largely and its impact value increases rapidly. (3) With the reduction of notch radius of impact test-specimen, its impact value decreases. And this effect is more clearly noticed in the impact test at lower temperature. But in the soft-annealed steel tubes, such notch effect is not clearly seen. (4) The impact strength of the cold drawn steel tubes reaches its maximum value near the room temperature, but rapidly decreases at below -100°C, and drops almost to zero in value at -190°C. (5) When the cold drawn tube is annealed at 400∼450°C, its hardness scarcely decreases, and its impact strength increases to some extent. Moreover, this heat treatment removes its internal stress by the cold drawing. Therefore, in order to make the cold drawn steel tubes tough, it is advisable to anneal them at 400∼450°C. (6) In the impact test of cold drawn steel tubes, we recommend the low temperature test at about -100°C, because this test shows the difference in these tubes most clearly.
The creep properties were studied for high-density polyethylene by the use of the test machine specially designed to work under the constant stress condition. The tests were carried out at constant temperatures from 20°C to 90°C on several stress levels. The instantaneous strains occurring just after the weighting were evaluated based on the applied stress and Young's moduli measured by the vibrating reed method. The creep curves, exclusive of ultimate stage to failure, consist generally of two stages, both being expressed by Nutting's equation. The first stage can be approximately expressed by Andrade's equation, but the period of this stage becomes shorter with increasing temperature and is hardly measured at temperatures above about 80°C. For the second stage, the creep strain εc2 can be denoted by the equation, εc2=a20 sinh (ασ)tn2, similar to Findley's equation, as a function of stress σ and time t. The a20, α and n2 are respectively the material constants dependent on the temperature. In the range of the test temperature, a20 decreases, α increases and n2 slightly decreases with increasing temperature. Creep tests were also made with the samples irradiated from Co60 (dose rate, 105r/h). The creep character depended markedly on both the radiation dose and the atmosphere of irradiation. The samples irradiated in the vacuum showed higher creep resistance, and the creep strain decreased with increasing crosslinking as εr=εoe-αx, where εr is the creep strain of the irradiated sample, εo the creep strain of the nonirradiated sample. x the degree of crosslinking and α a constant independent of stress and temperature. On the other hand, the irradiation in air did not change the creep properties in a monotone, and the sample irradiated by some constant dose showed the minimum creep resistance. These phenomena, however, can be explained from two inverse effects of radiation, the crosslinking and the degradation, in which the former increases with increasing dose and raises the creep resistance, but the latter occurs in the surface layer predominantly when the thinner sample is irradiated with low dose rate, and decreases the creep resistance.
The present study has been pursued for two purposes, to clear experimentally the method of measuring the scratch hardness of plastics by using Martens hardness tester on one hand, and on the other to find theoretically and also experimentally the relation between scratch hardness and Vickers hardness for plastics. The results obtained are as follows; 1) The sectional form of the scratched groove on plastics has wider variety than that on metals. 2) The width of the scratched groove slightly decreases with the increase of scratching speed. 3) The time to measure the width of the groove has to be limited within about 5 minutes after scratching, because the width of the groove decreases with time according to the retarded elasticity. 4) The ratio of the vertical load P on the scratcher to square of the groove width b2 is almost constant at any vertical load for each plastics, so the scratch hardness Hc has been represented by the following formula; Hc=P/b2 5) The relation between the scratch hardness Hc and Vickers hardness Hv is shown by the following equation; Hv=4/π·α2·β·sinθ0/2·Hc where α and β are the constants which are nearly the same in every plastics, that is, 0.815 and 2 respectively, and θ0 is the vertical angle of conical scratcher.
The formula on the abrasion of plastics has been derived from the scratch hardness test as follows; V=β.P.l.η……(1) where V is the total abrasion volume, β abrasion coefficient and represented by the term, (α/4Hccotθ/2·n2), P vertical load on the abrasion surface, l abrasion distance, and η abrasion efficiency. And Hc is the scratch hardness number, α, cotθ/2 and n2 are the constants peculiar to each material and determined by the figure of scratched groove. It has been proved that the formula (1) nearly corresponds to the results of the actual abrasion test which was carried out by using ASTM type's abrasion tester for several plastics, such as phenolic, polyester, acrylic, polystyrene, polycarbonate and nylon. Generally, hardness number Hc of thermosetting plastics is greater than that of thermoplastic material, but the values of the above constants, such as α, cot θ/2 and n2, for the thermosetting plastics are so greater than those for thermoplastic material, that the value of abrasion coefficient β for thermosetting plastic becomes greater than that for thermoplastic material. The effect of the grain size of abrasive Al2O3 on the abrasion efficiency, and of the relative speed between the surface of test piece and abrasive on the abrasion efficiency are also experimentally discussed respectively.
In the present experiment the densities of melts in the system Li2O-B2O3, Na2O-B2O3, K2O-B2O3, BaO-B2O3, SrO-B2O3, Li2O-K2O-B2O3, Li2O-Na2O-B2O3, and K2O-BaO-B2O3 were measured by a counterbalanced-sphere method at temperatures ranging approximately from 800° to 1250°C. The results of the measurement are shown in Table 1, Fig. 1, Fig. 2 and Fig. 3. The more direct way of showing the effect of addition of alkali oxide upon B-O network in alkali borate glass is to study the apparent molar volume (V) calculated from the density data as a function of composition. Fig. 4 illustrates the effect of alkali oxide addition upon the molar volume of the melts. The comparison of the data of the three systems shows that the apparent molar volume of the lithiumborates is definitely lower than that of the two other alkali borates. On a mole basis the order of the contracting effect of the B-O network is Li>Na<K. A similar observation can be made for the data of BaO-B2O3 and SrO-B2O3 glass melts as shown in Fig. 5. The relationships between the apparent molar volume of binary alkali-borate glasses and alkali oxide content are shown in Fig. 7 and Fig. 9. If one alkali oxide is progressively substituted for another it is found that the molar volume varies linearly with the molar fraction of alkali oxide substituted when the molar fraction of B2O3 is constant.