To investigate the effect of cyclic strain aging on the fatigue life distribution of an annealed low carbon steel, rotating beam fatigue tests were made in the temperature range from room temperature to 450°C. The results obtained were analyzed by means of the Weibull distribution with three parameters. It was found that the following Weibull distribution of mixed type was well fitted to the fatigue life distribution, as the cyclic strain aging plays an important role on fatigue behavior of the carbon steel. F(N)=P1F1(N)+P2F2(N), P1+P2=1, where F1(N) is the distribution which is independent of the cyclic strain aging and has an increasing failure rate. F2(N) is the distribution which is concerned with the cyclic strain aging and has a decreasing failure rate. P1 and P2 are the probabilities of occurrence of F1(N) and F2(N), respectively. The shape parameters of F1(N) and F2(N) were about 2.63 and 0. 86, respectively. At room temperature, the distribution at higher stress levels (i.e. in the finite life region) is expressed by only F1(N), because the strain aging cannot be expected, while the distribution at lower stress level (i.e. around the endurance limit) must be expressed by the mixed type, because the cyclic strain aging becomes effective during the cyclic stressing over a long period. At 375°C, since the cyclic strain aging occurs so rapidly that the multiplicated dislocations are relocked at each cycle, the distribution in all the stress levels is expressed by only F2(N), and P1 is negligible.
Fatigue tests were conducted on smoothed specimens of a carbon steel, S35C, under repeated two-step loadings as well as constant amplitude stresses, and the probabilistic characteristics of fatigue lives under varying loading conditions were examined by considering the both relations of stress-plastic strain and of plastic strain-fatigue life. The main results obtained are as follows; (1) The distribution of fatigue lives was found to be represented by log-normal distributions for both constant stress amplitude and repeated two-step loading tests. (2) Although fatigue lives under the constant stress amplitude tests showed a fairly large scatter at a stress level near the fatigue limit, those under the varying loading tests did not show such a large scatter at that level and a slightly increasing tendency of the standard deviation of fatigue life with the increase of fatigue life was found in the region below the fatigue limit. (3) Little correlation was found between the variances of the stress-plastic strain relation and of the plastic strain-fatigue life relation for the varying loading tests, and it was found that the variance of the former relation was very much smaller than that of the latter one. Therefore, the variance of the stress-fatigue life relation for the varying loading tests of a particular load pattern was concluded to be determined by the variance of the plastic strain-fatigue life relation.
Fatigue tests were conducted on smooth specimens of low carbon steel under rotating bending and torsion in air, in distilled water and in 3% salt water, and the crack length distributions for the fixed cycle ratios were examined. The crack length was found to be arranged by the Weibull distribution under both loading conditions and three environments. Moreover, the dependence of shape parameter of the weibull distribution on stress levels and cycle ratios showed different behaviours in each environment. This seemed to be caused by the difference in crack propagation behaviours.
In the previous paper, the parameter estimation was performed by several methods and the distribution characteristics of the estimated Weibull parameters were discussed in order to clarify the pattern of fatigue life distribution of machines or structural members. From the comparison of the statistical properties of the estimates, the most preferable method to estimate Weibull parameters was selected for perfect samples. In the long life region around the fatigue limit, however, it is usually difficult to obtain the perfect samples, and non-fracture specimens often appear in the fatigue tests at these low stress levels. From this view point, formulation of fatigue life distribution was made in the present study for the population with the probability of non-fracture events, and the most preferable estimation procedure proposed in the previous study was modified to apply on the Type I censored samples. By examining the distribution characteristics of the parameter estimates obtained here, it was shown that the present method is acceptable to estimate the Weibull parameters of fatigue life distribution from the Type I censored samples at low stress levels around the fatigue limit.
Properties of the scatter distribution of impact fatigue strength were experimentally investigated on smoothed and circumferentially notched specimens of four structural carbon steels. Based on the probability relations between parameters of impact fatigue strength and static tensile properties, the impact fatigue strength was estimated analytically from static tensile properties. The results obtained were summarized as follows; (1) The impact fatigue strength σ shows the scatter of a logarithmic normal distribution and can be evaluated as the probability value by the following formula. σNfm0αaTm0=αcD0μsu where Nf is the life to failure, T is the duration time of an impact load, D0 and m0 are the parameters of impact fatigue strength, a and c are the experimental constants, α is the stress concentration factor and μ and s are the parameters of scatter properties. (2) The parameters of scatter properties for the impact fatigue strength, μ and s, can be estimated from those of the static tensile properties (σB, φ) with a logarithmic normal distribution. (3) The scatter of impact fatigue strength for the notched specimens must be estimated about 1.03 times as large as that for the smoothed ones. (4) The scatter of impact fatigue strength for the smoothed specimens needs to be estimated 1.032 times as large as that of static tensile strength.
The change in strength distribution of glass fibers with varying specimen length was investigated. When the fiber length decreased, the mean value of fracture stress increased remarkably, but the coefficient of variation decreased. The effect of specimen length on the strength distribution was analysed by using the weakest link model. The strength distribution of links was assumed to be exppressible by Weibull distribution function. In this case, the shape parameter (corresponding to the coefficient of variation) was found to include the variation in sectional area of glass fibers when obtained from the fracture load data. The correlation coefficient for the fracture load and the sectional area was about unity and the coefficient of variation in fracture stress of glass fibers was 15-20%, which is lower than those estimated previously by several researchers.
The definition of the fleet reliability R' has been recently introduced by A. M. Freudenthal on the basis of the scatter factor defined as the ratio of the maximum likelihood estimator of the scale parameter of two-parameter Weibull distribution with a known shape parameter, assumedly describing the life distribution of structural elements or components, to the“time to first failure T1” among a fleet of nominally identical elements or components subjected to nominally identical operating conditions. Unfortunately, however, R' thus introduced does not represent rigorously the true fleet reliability R to be defined theoretically as R=P[T1≥t1*], where t1* is the service life (minimum life) specified for the fleet. Further, R' in itself is of statistical nature and therefore needs to be dealt with as an estimator of R. In this respect, a new estimator of R, termed as R in the case of known shape parameter, has been proposed in the present study. Statistical natures of R' and R have heen carefully examined and compared with the aid of Monte Carlo techniques, thus leading to the conclusion that R is much better than R'. The mathematical difficulty multiplies when the Weibull shape and scale parameters are both assumed to be unknown. However, this case is undoubtedly consistent with engineering reality. For these conditions, therefore, the reliability estimators R and R" have also been introduced as a natural extension of aforementioned R and R', respectively. Procedures involving Monte Carlo techniques have been established to evaluate the statistical properties of these estimators. Simulated results show that R is again much better than R". The effect of the size to be used in the fatigue test, of the fleet size and of the reliability level on the accuracy of such estimation has also been discussed. The fleet reliability can then be estimated based on either R in the case of known shape parameter or R unknown shape. This is believed to satisfy the essential part of the requirement in the reliability-based safety design of machines and structures.
The mechanical properties and deformation behaviors of type 329J1 two-phase stainless steel have been examined by various methods of tensile, fatigue and creep rupture tests in the temperature range of room temperature to 1073K. The results obtained are summarized as follows: (1) The short time tensile strength of 329J1 two-phase stainless steel was higher than that of type 304 stainless steel at temperatures below about 850K. The serration appeared in the stress-strain curves obtained in the temperature range of 500 to 750K, accompanied with an increase in tensile strength. The appearance of such a serration is considered to be due to the dynamic strain aging caused by nitrogen. (2) The flow stress of the α-phase was much higher than of the γ-phase at low temperatures, but at higher temperatures about 823K, it became lower than of the γ-phase. This result indicates that the strength of the two-phase stainless steel is influenced mainly by the α-phase at lower temperatures below about 823K and by the γ-phase at higher temperatures. (3) The rotating bending fatigue strength and the fatigue ratio of type 329J1 steel were much higher than those of type 304 steel at all the testing temperatures. These high strength seem to be due to the phase separation of α-phase and α'or the precipitation of σ-phase. (4) The appearance of“knee”in the S-N curve which is related with the coaxing effect, was recognized in the two-phase stainless steel. The reason for the appearance of such an effect is considered to be mainly due to nitrogen. (5) The two-phase stainless steel exhibited a high creep rupture strength in spite of the existance of the α-phase which possesses a low strength at higher temperature. On the other hand, the creep rupture elongation was extremely large, for example, more than 150% at 1003K and the remarkable structural change was observed in the ruptured steel.
In the previous report, the fatigue problem in friction welded specimens caused by cyclic stressing was investigated in connection with the microscopic-strain distribution or the strain concentration factor and the occurrence of slip-lines. It was found that the slip-lines in the specimen appear more densely at the parent material where the strain concentration factor is maximum, and the fracture occurs at this location. In the present paper it is intended to find out the influence of the tufftride treatment on the strain distribution and fatigue damage of the friction welded specimen subjected to rotary bending. The results obtained are summarized as follows; (1) The strain distribution or the strain concentration factor in the friction welded specimen is not influenced strongly by the tufftride treatment. (2) The occurrence of slip-lines in the tufftrided specimen are remarkably restrained and the fatigue limit is improved, but the fatigue fracture is influenced by the microscopic-structure of the specimen, and occurs at the parent material. (3) The depth of diffusion layer by the tufftride treatment is not uniform and depends on the microscopic-structure of the specimen.
The bending behavior under impact load was studied for the sandwich beam consisting of FRC (fiber reinforced cement) to give a guide for its effective use. As representative examples of FRC signifying different characteristics, GFRC (glass fiber reinforced cement) and NFRC (nylon fiber reinforced cement) were selected. In the experiments, the impact test was carried out with a three-point bending method by using a falling elastic bar. And the strain caused by the transient phenomenon in the loading elastic bar and the location where the crack occurred in the FRC were measured. Then the impact resistance of FRC was considered. Moreover, in order to interpret the behavior of the sandwich beam under impact load, a simple sandwich model with a homogeneous reinforcement was constructed for analyzing the impact test and for facilitating numerical calculation. And the effect of the span length on the dynamic flexural strain of the sandwich beam was considered. From the results obtained experimentally and numerically, it was shown that the crack occurred at the same position of the specimens, independent of the span length, and that the impact resistance of FRC improved by using it as a sandwich construction.
Fractographic study was conducted for austenitic stainless steels fractured in the five basic creep-fatigue tests, named PP, PC, CP, CC and DC tests. Fracture surface was observed with an SEM and the crack growth behavior was examined in the longitudinal cross section of the specimen with an optical microscope. Fracture morphologies were found to be closely related to the type of test, that, is, the type of inelastic strain cycled to the specimen. When Δεpp-type of strain was cycled, transgranular crack initiation and its growth at the specimen surface were typical. When Δεpc-type of strain was cycled, dimple formation occured inside the specimen and led to a tensile-like fracture. When Δεcp-type of strain was cycled, the initiation of many cracks in the grain boundaries and their intergranular or transgranular coalescence were typical. When Δεcc-type of strain or δc-type of strain was cycled, intergranular crack initiation and its growth at the specimen were fundamental features of the fracture surface. The effects of environment, temperature and stress or strain condition on each fracture morphology were discussed. The fundamental mechanism of nucleation of voids in the grainboundary can be used to explain the difference among the fracture morphologies.
The fracture behavior of alumina ceramics subjected to triaxial stresses, which were produced in the lower surface (tension side) of a bar with rectangular cross-section by applying uniform bending, was examined. The results obtained are summarized as follows. (1) Under hydrostatic pressures up to 28kg/mm2, all specimens fractured in a brittle manner without any plastic deformation. (2) The mode of fracture face around the origin of fracture was not influenced by hydrostatic pressure, and showed almost totally intergranular fracture. (3) The influence of hydrostatic stress σm on the maximum tensile stress of three principal stresses occurred in the lower surface of the bar at fracture was examined. The maximum tensile stress was almost constant from the value of σm obtained by the expriments at atmospheric pressure to σm of about 4.5kg/mm2 but decreased with an increase of σm to the compression side. (4) When the fracture stresses were expressed in the principal stress space, it was found that none of the stress components of the maximum tensile stress, the maximum shear stress and the octahedral shear stress could be regarded as critical value for fracture. (5) Two kinds of models for fracture were assumed by considering small cracks or cavities in the interior and the surface of a material and the fracture criterion for ceramics was examined. The fracture criterion obtained by assuming small cracks as the most affective factor for fracture agreed approximately with the experimental results.
Powdered polystyrene which was prepared by grinding at a temperature of liquid nitrogen was compacted into a cylindrical shape for a triaxial compression test. These specimens having various void fractions n0 were compressed at various confining pressures σ3. The mode of fracture of the specimens changed with an increase in σ3 or n0 from axial cleavage fracture to typical shear fracture, and then to shear fracture accompanied by consolidation. Yield loci were obtained from Mohr's stress circles using σ3 and the axial stress σ1 corrected by Taylor-Bishop's method. The yield criterion was expressed by τ2=μt2σ2+4σt(1+μt2)(σ+σt), where τ is shear stress, σ is the normal stress, μt is a constant, which is related to the sliding friction between particles and is close to the coefficient of effective internal friction, and σt is a constant corresponding to the tensile strength of the powder compact. The criterion can be related to the mechanisms of fracture of powder compacts. The second term of the criterion is larger than the first one under the condition where n0 and σ3 are small; in this case the specimens showed axial cleavage fracture which is characteristic of brittle materials. For larger values of n0 and σ3, on the other hand, the first term is larger than the second, and the specimens showed shear fracture.
Rheological properties under steady shear were studied with a rotational viscometer for the 30vol% aqueous suspensions of titanium dioxide stabilized with different amounts of sodium pyrophosphate. The apparent viscosity at any given shear rate showed a minimum at 2mg/gTiO2 of Na4 P2O7·10H2O. By a shifting procedure, a composite flow curve was obtained from the shear-rate dependence of the apparent viscosity for suspensions stabilized with different amounts of Na4P2O7·10H2O. The characteristic shear rate at which the pseudoplastic flow appeared was also found to show a minimum at 2mg/gTiO2 of Na4P2O7·10H2O. From the sedimentation tests, the rheological properties of suspensions were revealed to be closely associated with the flocculation of suspended particles. The effects of the amount of Na4P2O7·10H2O on both the sedimentation and the rheological properties were discussed on the basis of the theory of the stability of lyophobic colloids (DLVO theory). It has been concluded that the dependence of apparent viscosity at a fixed shear rate on the amount of Na4P2O7·10H2O can be attributed to the difference in the degree of dispersion in suspensions resulted from the changes in the colloidal forces between the suspended particles. On the other hand, the characteristic shear rate can be elucidated to be closely correlated with the hydrodynamic forces required to attain the same degree of dispersion for the suspensions with different colloidal stabilities.
This paper reports in detail a fundamental concept of a P/V difference method which is one of rainflow algorithms. The method is one of cycle count procedures which are useful for analyzing a complex strain time history. A strain time history should be analyzed keeping in mind the stress-strain behaviour in the background. Based on this concept, the rainflow algorithm subtracts from a strain time history the parts which correspond to closed hysteresis loops in the stress-strain relation. The subtracted parts and the residual parts are successively processed for fatigue damage evaluation. The algorithm given in this paper is simpler than the ones already presented, by the use of successive absolute differences between neighbouring peaks and valleys called P/V differences. The simplicity enabled us to make a real-time on-site fatigue damage indicator.