The objective of this study was to investigate the relationship between the scatter of fatigue crack growth rate and the scatter of fatigue life. Fatigue crack propagations were obtained in a wide range of stress amplitude under carefully designed four point out-of-plane bending fatigue tests in a constant temperature and humidity condition. The median S-N relations and the scatter of fatigue life presented in the authors' previous paper were used in this study. An empirical law of crack growth rate as a function of the bending stress intensity factor range was determined. An S-N equation was derived from this crack growth law and compared with the data of the median S-N relations. Using this S-N equation the relationship between the scatter of crack growth rate and the scatter of fatigue life was discussed and compared with the test results. It is concluded that the scatter of crack growth rate provides a reasonable estimate of the scatter of fatigue life.
When an external force is applied to spot welded structures, the load assigned to each spot is not uniform. Moreover, the fatigue life of a welded spot can not be set deterministically and thus the life has to be evaluated from the statistical viewpoint. In this study, the distribution pattern of load imposed to individual spots was first examined experimentally, and, then, fatigue tests to obtain the life distribution were performed by using a number of specimens in single-spot and multi-spots types. By combining the distribution characteristics of load imposed to respective spots and the fatigue life distribution of single-spot joint, theoretical derivation was attempted on the fatigue life distribution of multi-spots joint. Finally, a good agreement was accomplished between the theoretical and experimental fatigue life distributions of this type of welded joints.
In the practical structures we can hardly disregard the effects of size and shape of their components as well as possible cracks on the fatigue crack propagation behaviors. Without assessing these effects properly, we can hardly attain the desired level of reliability imposed on those structures. In this respect, we have constructed a stochastic crack growth model to reflect the engineering reality, and have successfully derived, in a closed form, the fatigue crack propagation life distribution under random loading of the material with random propagation resistance. Further, as a numerical example, we have computed and discussed the residual life distribution of the material with center and single edge cracks subjected to constant amplitude stressing. Finally, we have proved the wide applicability of the proposed model.
Although fatigue itself is considered to be a phenomenon in which the failure rate increases with time, it might be possible to have a case that the failure rate of a mixed population decreases monotonously with time even if failure is caused by fatigue. In order to make clear whether this is truely possible and thus to help proper understanding of field data, the time dependence of the failure rate of a mixed population has been investigated theoretically. This mixed population is composed of members each of which has been extracted from each own original (native) population, and each original population has the failure rate of h(t)*=w·h(t), where the function h(t) is common to all the populations and the coefficient w takes different values in different populations. From the study of time dependence of the failure rate of this mixed population, the following conclusions were obtained. (1) When the failure rate of each original population h*(t) has the property of dh*/dt≤0 for all t, the failure rate of the mixed population decreases monotonously with time. (2) When each original population has the Weibull-type failure rate h*(t)∝tα-1 with α>1, the failure rate of the mixed population does not decrease monotonously with time. This implies that, if fatigue is characterized by the Weibull-type failure rate with α>1, the failure rate of the mixed population subjected to fatigue does not decrease monotonously with time. (3) However, if each original population has the failure rate of the form h*(t)∝(tα-1+constant) with α>1, the failure rate of the mixed population λ(t) can decrease monotonously with time. This implies that there is a case in which λ(t) can decrease monotonously with time even if dh*/dt≤0 for all t (the condition mentioned in (1) above) is not satisfied.
It is an urgent problem to establish a design format for unpainted structures of weathering-proof steel and for painted steel structures exposed to a sea wind, especially for the friction type joint with high strength bolts used in these structures. One of the difficulties involved in this problem is due to the time-dependent properties of the structural joint caused by corrosion. In the present study, to obtain the basic data for design of corroded bolted joints, the static and fatigue tests were performed on the corroded specimens of three types of steel SS41, SM50 and SMA50. The results obtained show that the mean value of the slip coefficients of the joints for each type of steel descended slightly with a trend of increasing scattering for longer corrosion period. As for the S-N curve of the specimen composed of steel plate SS41 in which fatigue crack started through the net section, the slope increased after corrosion, and the fatigue strength for 2×106 stress cycles decreased apparently. Based on these results, the variation of the probability of occurrence of slip of the friction type joints were analysed for the cases for which the bolts were clamped by different methods and the joints were corroded acceleratively at various rates.
This paper presents the optimal reliability-based design of the skeletal structures under the both probabilistic constraints of stress at service load level and plastic collapse at ultimate load level. The upper and lower bounds of the effective region satisfying the both constraints were determined by the proposed method. Then, a new probabilistic displacement constraint at the service load level was added to the above constraints. Herein, a minimum structural weight is regarded as an optimal criterion, and it was assumed that the strength of members and the static external loads were normally distributed. Finally, two design examples are presented to demonstrate the availability of the proposed method. The results show that the proposed method can be used to optimize the structure under the both probabilistic constraints of stress at service load level and plastic collapse at ultimate load level, and the upper and lower bounds of effective region obtained by the proposed method agree with the results of numerical experiments.
Low temperature tensile properties of microduplex stainless steel having different hardness of ferrite phase were investigated by means of transmission electron microscopy and X-ray diffraction. The hardness of ferrite in duplex stainless steel was changed by heat treatment. The main results obtained were as follows; (1) The austenite phase in the microduplex stainless steel was metastable. Therefore, martensite transformation was induced during tensile tests below room temperature. (2) The elongation to fracture showed a peak at 201K in the elongation-test temperature curves. This phenomenon is closely related to the amount of strain necessary to induce α' martensite, the amout of α' martensite and the ductility of the ferrite phase. (3) A discontinuity in flow stress-strain curves, namely the quasi-yield point phenomenon, was found buring tensile tests at 77K. This phenomenon seems to be associated with both necking arising from the formation of ε martensite and strengthening of that portion due to the formation of α' martensite. (4) Md temperature was unchanged in spite of the variation of ferrite hardness in the duplex stainless steel. This fact may suggest that the deformation of ferrite and austenite phases follows the rule of mixture.
The plate specimens of two-phase stainless steel were fatigued by a cyclic bending fatigue test machine. The surface morphology and the dislocation structure just beneath the specimen surface were examined through a transmission electron microscope operated at 200kV. Tensile tests were also performed to understand the basal deformation behavior of two-phase stainless steel. Based on these experimental results, the behavior of fatigue crack initiation was discussed. The main results obtained are as follows; (1) When the specimens were stretched, sharp slip bands were observed in austenite phase, whereas in ferrite phase they were not clearly detected because of the occurrence of fine wavy slips. (2) When the specimens were fatigued, persistent slip bands were observed in both phases. The fatigue cracks leading to failure, which were expected to be formed preferentially in austenite phase from the above experimental results, however, were observed only in ferrite phase of both solution treated and aged specimens. (3) The reason why persistent slip bands in austenite phase could not be developed into fatigue cracks may be due to the finer grain diameter of austenite phase than that of ferrite phase and the high strength of austenite phase containing a significant amount of nitrogen.
Pulsating tension fatigue tests (R=0.1) and statical tension tests at room temperature to 500°C were performed on the as-cast and heat-treated materials of spheroidal graphite cast iron. The macro and microscopic observations of the fatigue-fracture surface of the specimens were carried out by SEM to interpret fatigue strength data. The results obtained are summarized as follows: (1) The tensile strength at elevated-temperatures decreased with the elevation of testing temperature. However, the effect of normalizing and austempering heat-treatment was remarkably noticed. (2) The fatigue strength decreased with the elevation of testing temperature, which is the same as the tensile strength, but the effect of heat-treatment was noticed very slightly. The fatigue limit at 500°C for the bainitized material was σu=92MPa and for the annealed material σu=77MPa. (3) Fatigue cracks appeared from internal defects such as small pinholes. Therefore, it is considered that the heat-treatment does not affect the fatigue strength so much.
Adhesive bonding has attracted special interest recently as a joining technique of mechanical structure. Hence, a research on estimation of fatigue strength is important to establish the design criteria for the adhesive joint. In this study, the estimation of fatigue strength was conducted for a lap joint bounded by an epoxy-polyamide adhesive. The results of numerical analysis by FEM show that, in the case of a lap joint, the maximum tensile stress generated at the lap end well exceeds the maximum shear stress at the same location. Then, based on the assumption that the fatigue strength of the lap joint is dominated by the maximum tensile stress, the fatigue strength of the lap joint was estimated from the S-N curve of the adhesive bonded butt joint of the thin wall tube which has a uniform stress distribution. It is confirmed that the estimated fatigue strength of the lap joint agrees well with the experimental results and, furthermore, it gives a conservative estimation.
Fatigue tests of notched and smooth specimens of alumina particulate filled epoxide composites were conducted and the effects of alumina dispersion on the fatigue strength, the fatigue limit, the fatigue fracture process, the final fracture condition in fatigue and the inherent flaw size were studied. The alumina volume fractions Vf used in this experiment were 13% and 37%. As a basis of comparison epoxy resin with no filler was also tested. The results obtained are summarized as follows. (1) Alumina dispersion had both (a) reinforcement effect and (b) flaw dispersion effect from the viewpoint of fatigue strength. The fatigue strength of the smooth specimens with 13% Vf reduced from the level of epoxy resin, and the strength recovered when Vf increased to 37%. (2) The fatigue strength of the notched specimens was improved as alumina Vf was increased. (3) The inherent flaw size became longer by the alumina dispersion and the composite became less sensitive to surface flaws than the epoxy resin. (4) The fatigue limit of the composites seems to be determined by the condition that microdebond of particle/matrix interface in surface layer does not propagate. A model of fatigue limit was proposed based on the observation and the fatigue limit stress level vs. Vf relation was satisfactory explained.
This paper deals with the fatigue behavior of FRP laminates with a U-type notch. The material used in this experiment was plain-woven glassfiber cloth reinforced unsaturated polyester resin. The fatigue tests of the notched specimens were carried out in such a wide range that the number of cycles to failure varied from 5 to 8000000. The fatigue tests of the unnotched specimens were also conducted. The fatigue damages at various cycle ratios were observed, and the fatigue lives for various stress levels were measured. A simple residual strength degradation model was proposed in order to predict the fatigue life under pulsating tensile loadings. The prediction of fatigue life computed by the proposed fatigue damage cumulative model agreed well with the experimental data.
The influences of anisotropy of material on static and dynamic SCC crack growth rates including the case of part-through one have been investigated using high-strength aluminum alloy ZK 141 (JIS 7N01) sensitive to active path corrosion type SCC. As for through crack growth, the crack plane orientation had a great influence not only on the crack growth rate but also on the threshold value; when the crack growth direction was longitudinal, i.e., in S-L and T-L specimens, anodic dissolution at grain boundaries was easily brought about, resulting in an enhancement of crack growth rate and a decrease in threshold value with respect to L-T specimens, where the crack growth direction was long transverse. This crack growth enhancement and the decrease in threshold value were especially marked on S-L specimens. Moreover, superimposed vibratory stresses had a great influence on the crack growth rate for T-L and L-T specimens. However, the dynamic SCC crack growth rate was smaller than that of static SCC for S-L specimens, with a slightly higher KDSCC value than that of KISCC, which results from crack branching. In a corrosive environment, part-through static and dynamic SCC cracks grew in the longitudinal direction as well as in the surface and the depth directions. The longitudinal cracks grew under a mixed loading of Mode I and Mode II.
Stress corrosion cracking (SCC) and corrosion fatigue (CF) experiments were performed on the test specimens in three directions (L, LT, ST) of rolled 7075 aluminum alloy. The results obtained are as follows. (1) The SCC life time of the test specimen in ST direction could be estimated from the applied stress, the tensile strength, and the activation energy which is determined by changing the temperature of corrosive solution and immersing the test specimen in LT direction. (2) There was a combined effect of SCC and CF in CF experiments for the test specimen in LT direction, because the total accumulated damage factor was smaller than one when the linear damage summation method was applied to the experimental result of CF at 5min. stress hold time. This effect was confirmed on the fracture surface of the test specimen. (3) However, the effect was not observed either in the CF experimental result or on the fractograph for the specimen in L direction tested at room temperature and 30min. stress hold time, nor for the specimen in ST direction tested at 70°C and 5min. stress hold time.
Fracture toughness tests were performed on the specimens with neighbouring embedded cracks produced by using the diffusion welding method in order to investigate the method of assessment for neighbouring embedded defects. It was found that for s/re2>0.7 (where s/re2 is the ratio of the spacing of adjacent cracks and the radius of a reduced circular crack with an area equivalent to that of a larger crack), the K-value can be estimated by supposing isolated cracks, and for s/re2≤0.7, it can be estimated by using a reduced circular crack with an area equivalent to an added area of adjacent cracks. The proposed method of combining two adjacent cracks does not contradict with the one proposed in the previous paper, in which an embedded crack near surface is substituted with a surface crack.
The effect of loading rate on fracture toughness of ice has been investigated using sharply edge-notched specimens by bending at -10°C. The loading rate KI ranged from 1 to about 103kPam1/2/s. The notch was made by molding a razor blade in the specimen in the ice growing process and removing it before the bending test. Two sizes of specimens, section sized 25×25mm (small size specimen) and 50×50mm (medium size specimen) respectively, were used. About thirty small size specimens or about ten medium size specimens were tested at each loading rate. The experimental results were as follows. (1) The values of KIc were lower in the higher KI range, and there was a transition in the range of KI=10-100kPam1/2/s. (2) The effect of KI was found to be very small in the range of KI larger than 100kPam1/2/s. (3) The effect of loading rate on the minimum value of fracture toughness KIc was small in the whole range of KI tested for both small and medium size specimens. (4) The minimum KIc values of small and medium size specimens seem to coinside each other approximately. The maximum and the median KIc values of medium size specimens were smaller than those of small size specimens. (5) It was found that a vinyl silicone impression material being used for dentistry was suitable to make replica of the fracture surface for macrofractography.
A plasma-assisted fine particle classification and identification method has been developed by using a Geisler tube with a coneshape electrode. A particle is charged in plasma, in which its surface is covered with the sheath made of double layer of negative and positive ions. The charged particle flies to the positive electrode under high voltage. The flying mode, however, is influenced by the gravity, the collision of plasma ions with the flying particles and the viscosity of the constituent non-charged gas molecules. The newly-developed classification setup is made with three main parts; the Geisler tube, a powder supplier and an evacuation system. The fine powders such as alumina, silica, silicon carbide were classified under the condition of DC voltage of 500V and the tube current of 30mA at 2.0Torr (2.7×102Pa). It is found from the experiments that the finer particles fall down near the upper side of cone electrode, but the coarser ones fly apart from it and that the grains with different mechanical and physical properties can be identified.