The constitutive equations of a plastic material with general work-hardening are proposed. Two internal state variables, scalar and tensor, are introduced. The plastic potential is assumed to be a scalar function of the translated stress and the scalar internal state variable. Four constitutive assumptions are taken into cosideration. A mechanical constitutive equation and two evolutional equations are derived, where the former relates the translated stress rate to the stretching, and the latter govern the temporal variation of the internal state variables. These constitutive relations may show the kinematic work-hardening as well as the isotropic work-hardening. A fracture rule is also proposed. It is supposed that the fracture occurs when a scalar function of two internal state variables, called the fracture function, has a critical value.
The stress amplitude of most of service loads is below the fatigue limit. In the previous paper, we examined the effect of such stress amplitude on the fatigue life by the program fatigue tests, and found that the fatigue life can be shorter or longer than that estimated by Miner's law. In the present paper, two step and two fold program fatigue tests were carried out and the crack propagation behavior was observed to clarify the effect of fatigue crack propagation by stress amplitudes below the fatigue limit on the fatigue life. The results reveal that the fatigue crack is propagated by the stress amplitude below the fatigue limit, and that the crack propagation rate in the first period of the repetition of the stress amplitude below the fatigue limit is higher than the estimated value obtained by extrapolating the result in the range of stress amplitudes above the fatigue limit to the range of stress amplitudes below the fatigue limit. It seems that this acceleration effect of the crack propagation is caused by the preloading due to the stress amplitude above the fatigue limit. On the other hand, the crack propagation by the stress amplitude above the fatigue limit in the first period of that repetition is retarded by the preloading due to the stress amplitude below the fatigue limit. As a crack propagates, this retardation effect disappears and the crack propagation rate gradually recovers to that of the constant stress. Therefore, the fatigue life under service loads should be estimated by considering both the acceleration and retardation behaviors in crack propagation by the stress amplitudes below the fatigue limit.
Fatigue tests were carried out on smooth specimens of 0.33% carbon steel by applying one high tensile load or periodic high tensile loads during stress cycling, and the results were discussed on the basis of variations of plastic strain range at cyclic stress and high tensile load, and surface observations during stress cycling. The main conclusions obtained are summarized as follows: (1) In the fatigue tests with one high tensile load during stress cycling, the high tensile load corresponding either to the lower yield point (σH=36.5kg/mm2) or to 9.1% strain (σH=57.0kg/mm2) of the virgin specimen does not influence the fatigue life. (2) In the fatigue tests with periodic high tensile loads (σH=36.5kg/mm2) during stress cycling, the fatigue lives are almost the same as those of the virgin specimen in the range of overstress levels, but the fatigue failure occurs by understress levels and the S-N curve bends slightly to the side of shorter life. (3) In the fatigue tests with periodic high tensile loads (σH=57.0kg/mm2) during stress cycling, the fatigue lives are almost the same as those of the preloaded specimen in the range of overstress levels and the S-N curve bends abruptly to the side of shorter life in the range of understress levels. The fatigue lives are shorter than those in the case of σH=36.5kg/mm2. (4) In the two fatigue tests with one high tensile load and periodic high tensile loads during stress cycling, the plastic strain range at cyclic stress after high tensile loads tends to reduce in comparison with the virgin specimen. This is due to work hardening by high tensile loads. (5) As mentioned above, the plastic strain range is smaller than that of the virgin specimen, but the correlation between plastic strain range and fatigue life does not exist. This results from that the fatigue failure of specimens subjected to high tensile loads occurs by local causes such as the stress concentration due to non-uniformity of strain distribution and the opening of slip bands or micro-cracks by high tensile loads. (6) When the fatigue tests with periodic high tensile loads are regarded as the two steps repeated multiple loads fatigue tests, the values of cumulative cycle ratio are very small. Especially, it is interesting and important that, in the case of σH=36.5kg/mm2, the fatigue failure occurs by the combination of stresses that do not cause failure individually.
Fatigue tests of two-level multiple-step wave stress were carried out on austenitic stainless steel SUS 316 by use of a varying loading apparatus combined with a rotating fatigue testing machine. Discussions of the test results and the analysis of equivalent alternating stress were presented. The following results were obtained. (1) In comparably small strain hardening materials such as carbon steel or Mg-alloy, the equivalent alternating stress could be obtained from the fatigue data under alternating stress σa combined with the mean stress σm by using the rectificating coefficient η of 0.50. On the other hand, remarkable strain hardening was observed in the test specimens of SUS 316 fractured under the condition of ∞>A≥1.0 (A=σa/σm), and little effect of σm on the fracture life was detected. However, from the test specimens fractured under the condition of two-level multiple-step wave or two-level two-step wave stress, little strain hardening was observed because both stress ranges of σa1 and σa2 (σa1>σa2) were alternating stresses. Therefore, η of 0.50 was found to be usable, if the stress shape of two-level multiple-step wave was assumed to be changed partially to alternating stress of pulsating stress. (2) The stress shape of two-level multiple-step wave could be translated to the shape of partial alternating stress. However, the equation of Σn1/Neq=Σn2/Neq=1/2 was hardly applicable in two-level multiple-step wave stress except for the case of partial alternating stress. Then, by using the linear damage rule and the medium of partial alternating stress, the equivalent alternating stress σ'aoe and the equivalent number of cycles to fracture N'eq were obtained analytically from the basic data of alternating fatigue tests.
Although two kinds of stresses σa1 and σa2 are applied in two-level multiple-step wave or two-level two-step wave fatigue tests, those stresses must be translated into one stress such as alternating stress σa0 when they are shown on σa-N curves. In this study, a way to calculate the equivalent alternating stress from the data of partial alternating wave tests is examined. The results obtained are as follows: (1) In small strain hardening materials, the equivalent alternating stress σaoe may be calculated from the data of fatigue tests of repeated stress σa with the mean stress σm. In this case, the values of η were about 0.60 at 3600cpm and 0.50 at 40cpm in the range of ∞>A>0.5∼0.7 (A=σa/σm). The stress range diagram calculated from η=0.50 is very close to the linear range diagram or that obtained by the modified Goodman method. (2) When one of the lives Σn1 under σa1 and Σn2 under σa2 is given in two-level multiple-step wave tests under σa1 and σa2 (σa1>σa2), the other can be estimated very close to the experimental data by using the analyzed result. (3) The analyzed result of two-level multiple-step or two-level two-step wave can be extended to the case of multiple-level multiple-step wave. Hence, it seems possible to calculate the equivalent alternating stress σ'aoe and the number of cycles to fracture N'eq in the multiple-level multiple-step wave.
Although a number of studies have been carried out on the influence of various factors on the stress corrosion cracking of austenitic stainless steels, only few have been dealt with the influence of applied stress which is one of these factors. The purpose of this paper is to explore the influence of applied stress on the fracture time, the process of stress corrosion and the fracture surface of stress corrosion cracking of austenitic stainless steel in the boiling magnesium chloride solution. The results indicate that the applied stress influences remarkably on the fracture time and fracture surface as follows: On the plots of the applied stress versus the fracture time, the threshold stress was observed, above which the logarithm of the fracture time decreased linearly with increasing level of stress and below which it increased remarkably with decreasing level of stress. It was thought that this result was highly connected with the degree of the plastic deformation on the specimen surface. On the fracture surface under the applied stress of 15kg/mm2, the transgranular fractures were observed chiefly and the intergranular fractures only partly in the regions near the center of the specimen cross section, while under the stress of 30kg/mm2, the intergranular fractures were observed chiefly and the transgranular ones only partly in the regions near the specimen surface. From these results, the applied stress was considered one of the important factors by which the transgranular fracture was transformed into the intergranular one.
Stress corrosion tests were conducted on the notched plates of SNCM 8 steel tempered at low temperatures in 3.5% NaCl solution environment. The effects of notch radius and plate thickness on nucleation and growth of cracks were analysed from a viewpoint of fracture mechanics. The results obtained are summarized as follows: (1)The time to crack nucleation at the notch root tn was correlated to the notch radius ρ and the stress intensity factor K0 by the following equation: tn=5.8×1027(K0/√ρ)-12.5 (2) The relation between crack growth rate and stress intensity factor was divided into three regions I, II and III. In regions II and III, the growth rate was found to be higher in thicker specimens than in thinner ones, while there was no thickness effect on growth rate in region I including KISCC. (3) Scanning electron microscopic observations of fracture surfaces indicated that intergranular fracture along prior austenite grain boundaries was predominant in the region of low stress intensity factors and that the fraction of grain boundary fracture area in the total fracture surface decreased with increasing stress intensity factor.
A new statistical theory for brittle solids under multiaxial stresses is presented with a particular emphasis to Mode I and Mode II fracture. The advantages of the present theory are: (1) it is based on the same assumption as that of the well-known Weibull's theory of uniaxial stress, which can explain the effects of size and stress distribution on the variation of strength observed in strength tests quite nicely, and (2) it is applicable to the farcture of anisotropic materials as well as isotropic ones. The applicability of the theory to the existing fracture data under biaxial stress state are shown.
The behaviors of glass fiber reinforced plastics (GRP) under compressive load were investigated by using unsaturated polyester resins reinforced with roving cloths or chopped strand mat. The influence of fiber content on the behaviors was also investigated. The results obtained were as follows. (1) There was no microcrack in the specimens under low compressive stress, while many microcracks appeared under low tensile stress. (2) The elastic modulus in compression increased in proportion to the volumetric content of glass fiber β. However, this effect was not large in M-GRP (reinforced by chopped strand mat). (3) R-GRP (reinforced by roving cloths) showed complicated strain behavior due to their cloth structure, but M-GRP showed semi-homogeneitic behavior. (4) The compressive strength of M-GRP was better than that of R-GRP at the same glass content. (5) The limit value of β at which the compressive strength did not increase proportionally with β any more was lower than that for the tensile strength.
Epoxy resins are widely used as the constitution materials of various electrical apparatus because of their good physical properties. Arc resistance of epoxy resin is an important factor for their use in electrical apparatus subjected to arcing condition. Although arc resistance of epoxy resins cured with sole curing agent has hitherto been investigated fairly well, few studies have been made on the effect of composite curing agents. Such studies are considered desirable because epoxy resins with good arc resistance may be obtained by using two or more composite curing agents and the results will help to establish the mechanism of improving the arc resistance from the standpoint of composite dielectrics. In this paper, the ASTM D495-71 arc resistance test was carried out by using epoxy resins with various composite curing agents, and the effects of composition, especially those of species of curing agents, ratio of mixture, etc. were investigated. The results showed that three cases appeared when two or three composite curing agents were used: the case with higher arc resistance than that with sole curing agent, the case with lower arc resistance and the case with the average arc resistance of those with sole curing agents. The difference in change of arc resistance was also observed depending upon the species of epoxy resins used. The thermal, mechanical and other properties were taken into account to evaluate those with improved arc resistance, and it was found that the epoxy resins cured with the composite curing agents are good enough for practical use.
Microfractographic aspects of fatigue fracture were quantitatively studied in relation to the strength level of materials and stress ratio. The specimens used were heat-treated low carbon and low alloy steels with 4 levels of Vickers hardness (HV 140, 330, 430, and 480). Fatigue tests were conducted in the low- and high-cycle regions under axial load conditions (stress ratio R=-1 and 0). The striation pattern was observed for all the materials and its area fraction tended to become maximum at a certain value of stress intensity factor, ΔK. The upper limit ofΔK at which the striation disappeared increased with an increase of the Vickers hardness of materials. The dimple was found simultaneously with the striation and its area fraction increased with an increase of ΔK. It was shown that the average dimple size for different materials fell on a single linear line when plotted as a function of the cyclic plastic zone size at the crack tip on a log scale. The intergranular fracture was also observed among striation patterns except for the material of HV 330. The area fraction was decreased with increasing ΔK for the materials of HV 140 and HV 430. The applicability of these quantitative microfractographic data for failure analysis was pointed out.