It is well-known that the enormous increase in fatigue strength of case hardened steel is due to the high compressive residual stress in the material and to the doubled hardness caused by heat treatment, and that the effect of the residual stress on the endurance limit can be accounted for by taking it as the mean stress. In this paper the fatigue test results which were obtained of the carburized and induction hardened steel, have been re-examined from the viewpoint of crack propagation process. It appears that the fatigue strength of case hardened steel can be regarded as resistance against fatigue crack propagation in the specimen having minute flaw, because, in highly hardened material, the micro inclusions and metallurgical discontinuity can be taken as the origins of fatigue cracks.
In order to find the mechanism of fatigue, it is very important to investigate the change of stress-strain relation during the fatigue process. During the past several years, the author performed a series of studies on the fatigue under the low-cycle rotating-beam bending and summarized their results. In the present report, the results of the studies are given in outlines concerning the effects of various tests conditions on the stress-strain relation and the criterion of fatigue failure. From the measurements of strain amplitude in their change in several kinds of metallic materials during the fatigue tests of the constant stress amplitude, the difference is indicated in fatigue hardening (or fatigue softening) among the materials, and the dependency of fatigue hardening (or fatigue softening) on the time rate is evaluated. Its relation to strain hardening is also discussed.
Hereunder is presented the report of the studies that the authors have made about the effect of mean stress on fatigue crack propagation rate at room temperature and at various other low temperatures. Some of authors' conclusions have appeared to be different from those of other investigators. To make clear these apparent inconsistencies the experimental data of others have been rearranged, assuming that the propagation of fatigue crack is devided into four stages, the initial, the tensile mode, the shear mode and the final propagation stage. As the result, it has been proved that there is no inconsistency after all between authors' conclusions and others'. Besides there has been new information that has been obtained in this connection.
It is well known that the stress amplitudes below the fatigue limit can damage the materials under the programmed fatigue tests or in service loadings. But its proper estimation has not yet so far been established. The authors have found that the linear cumulative fatigue damage law in terms of the plastic strain range-pair gave good estimation of the fatigue lives in low and high cycle fatigue nearly up to the fatigue limit with the low or medium carbon steels. From such a view point, the push-pull type programmed fatigue tests having the stress amplitude below the fatigue limit with intermittent high level stress were carried out with unnotched specimens of the normalized medium carbon steel S35C, and the behavior of the plastic strain was investigated. In the constant stress amplitude test, it is observed that there is fatigue limit to the plastic strain as there is to the stress. In the programmed tests the plastic strain range corresponding to the stress below the fatigue limit is found to be larger than that of the constant stress amplitude, due to the influence of intermittent high level stress. Moreover, it is found that the fatigue limit in terms of the plastic strain has disappeared, and that the fatigue damage caused by the plastic strain range below it is linearly accumulated.
The varying mean stress can occasionally be observed in service load acting on some structures or machine parts. It is important to estimate the effect of this varying mean stress on the fatigue strength of material. Hereunder is presented the report of experimental studies that were conducted according to a series of program of fatigue tests in which the mean stress changed periodically with long and short term. The results obtained are as follows. The large stress range as the result of the mean stress change accelerates the fatigue damage to be caused by the repetition of small stress that succeeds it. The greater the change in the mean stress, the greater this effect becomes, and this influence gradually fades cycle by cycle. This phenomenon has been proved by measurement of the plastic strain at the notch root and of the fatigue crack growth rate. Though the mean stress changes in short term, the fatigue damage generated by the small stress cycles superposed is accelerated uniformly, but the transient aspect is not remarkable. The methods to predict the fatigue lives according to the change in the mean stress are proposed. These are based on the fatigue damage effectively accelerated by the large stress range, and on the transient effect in the plastic strain behavior under the mean stress varying in amplitude.
The random and program loading tests and the tests with constant amplitudes were carried out of U-notched specimens of S50C carbon steel under plane bending stress condition with the mean stress zero. The load programs were so designed that the relative frequency distribution of stresses would be coincident with that of the random load excepting the truncation of higher stresses than 1.5σp, 2.0σp and 2.5σp, where σp was the median of stress peaks. The major conclusions derived from the experiments are as follows; (1) Even if the higher stress levels appeared in the random loads were incorporated in the load programs, it is difficult to estimate the fatigue strength under the random loads from the results of program loading tests, when the comparison was made on the basis of total number of cycles to fracture. One of the main reasons for this difficulty seems to be caused by the difference of crack propagation rates under respective loads. (2) The difference in the load sequence such as Lo-Hi-Lo, Lo-Hi and Hi-Lo sequences had no effect on the results of the program loading tests. (3) Discussions were made on the modified S-N curves which would be laid as the base of life estimations under random and program loads with the assumption of the linear damage rule.
A push-pull fatigue testing machine under high pressure up to 6000kg/cm2 was developed. Using this machine, the preliminary fatigue tests in the low-cycle fatigue range were conducted under the load-cycling conditions with OFHC copper, 5005 Al alloy and S35C carbon steel under hydrostatic pressures up to 4000kg/cm2. The unnotched fatigue strength showed a slight but definite increase with increasing ambient pressure. No discernible difference was observed in the notched fatigue strength of OFHC copper between 0 and 3000kg/cm2 ambient pressure. The scanning electron fractograph of unnotched OFHC copper specimens revealed no apparent difference in the striated regions of fatigue-fractured specimens under 3000kg/cm2 and zero ambient pressure.
It has been confirmed by the present authors, as the result of the experimental studies they performed of the creep of pure aluminum and pure iron in the normal temperature range below 0, 5Tm, 1Tm being the absolute melting temperature, that the creep rate of polycrystalline metals tends to decrease with the increase in hydrostatic pressure regardless of such a normal temperature range in which its diffusion mechanism is not to be expected theoretically3)13). It has also been confirmed that the effect of hydrostatic pressure on the flow stress of metals can be described satisfactorily by assuming the formulation of yield condition including the first invariant of stress J1=σkk, (a) J2'=k(k2+CkJ1+DJ12)1/2, and further that the qualitative explanation of creep rate decreasing with hydrostatic pressure of metals subjected to constant load is given uniformly by this yield condition from a side view of continuum mechanics. Secondly, however, in order to understand better the relationship of hydrostatic pressure to the deformation mechanism in plasticity and creep of metals it is necessary to evaluate quantitatively the difference in the intensity of the influence of hydrostatic pressure between these deformations. In the present study, therefore, it has been aimed at to evaluate numerically the change in the structure of metallic materials, i.e. the effects of hydrostatic pressure on the magnitude both of their plastic and of their creep deformation, and with these ends in view, various hydrostatic tests, creep tests and simple torsion tests, of polycrystalline materials, e.g. pure aluminum, pure iron and pure zinc, have been carried out under several levels of hydrostatic pressure at room temperature. It is to be noticed that the torsion test is found effective in the investigation because its stress condition does not cause the change in the form of the test specimens, nor does it enter into the hydrostatic stress component. The results are summarized as follows: (1) There has been little influence of hydrostatic pressure on the plastic flow stress of pure aluminum but on pure iron there has been effect to some extent after leaving plastic defomation, while remarkable influence appears on pure zinc in an early stage of deformtion. On the whole, such effects grows gradually with advanced deformation. (2) The shape of the yield surface that varies with plastic deformation is determined by replacing the parameters both C and D in the Eq. (a) with numerical values. The calculated values of C and D, without regard to the kind of metal, are nearly zero during the shearing strain between zero and 30% but increases rapidly with the advanced shearing strain. (3) On the creep of metals at room temperature, the confining pressure has a distinctive effect of decreasing the creep rate. The numerical values of C and D in the creep process of pure zinc agree with those in their static plastic flow respectively. Therefore, it is clear that the intensity of the influence of hydrostatic pressure on the creep rate is of the same magnitude as that on the static plastic deformation.
The specimens of 0.01%C annealed and 15% cold-rolled steels were fatigued under completely reversed plane bending. The effect of stress amplitude on fatigue process of these materials was investigated by using the X-ray microbeam diffraction technique, optical microscopy and electron microscopy. The results are summarized as follows: (1) The stress cycles at slip band formation Ns and the crack initiation Nc were measured of both the materials by means of an optical microscope. The ratios of Ns and of Nc to the number of stress cycles at fracture Nf were obtained of the annealed material as Ns:Nc:Nf=0.02∼0.04:0.40:1, and of the cold-rolled material they are expressed as Ns:Nc:Nf=0.002∼0.003:0.26:1. The critical stress amplitude of slip band formation during fatigue in annealed materials is nearly equal to the frictional stress. (2) The amount of crystal deformation during fatigue was dependent on the applied stress amplitude. In the case of the annealed material, the micro-lattice-strain Δd/d at the half of the total fatigue life was related to the stress amplitude σn in the following equation, α·σn=9.3+2.0×104(Δd/d), where α is the stress concentration factor of the specimens 1.03. The excess dislocation density D is also a function of stress amplitude. The function is approximated as follows: α·σn=11.0+5.8×10-4√D, when σn is less than 22kg/mm2. (3) For the cold-rolled material, total misoriention β at the half of the total fatigue life increased when stress amplitude was higher than the yield stress. Subgrain size decreased during fatigue and the amount of its decrease was larger when σn was higher. (4) Fatigue cracks were nucleated through the linking of pores formed along the subboundaries in the annealed material. A similar mechanism of fatigue crack initiation by pore linking was verified for low stress amplitude fatigue in the case of the cold-rolled material. On the other hand, the formation of pores was not observed in high stress amplitude fatigue.
Fatigue failure mechanism in polymers was examined by using a fatigue testing machine of constant deflection type. The fatigue tests were carried out both on polycarbonate and polyamid, and the effect of the difference of their structure on fatigue behaviors was investigated. Moreover, the effect of temperature on a fatigue crack propagation was also investigated. The state of stress in the specimen during crack propagation was theoretically analyzed and compared with the experimental value. From the relation between the rate of fatigue crack propagation and the applied stress the fatigue life of polymers was discussed. The following results have been obtained: (1) The results obtained from the stress analysis are qualitatively consistent with the experimental value. The rate of fatigue crack propagation is found to be proportional to 2-3 power of applied stress in polycarbonate, and it has decreased with an increase of the testing temperature. (2) It has been found from fractographic examination that: (a) the fatigue crack in polycarbonate has initially propagated, forming striation markings on the fracture surface, but this marking of striation has not necessarily corresponded to each cycle, (b) the spherulite structure in polyamid seems to have had great influence on the failure mechanism.