This paper describes the bending stress-strain relation of laminated inhomogeneous plates. The relation was calculated so as to satisfy the equilibrium equations for bending deformation, in which the plate was divided into thin layers where the initial residual stress and the uniaxial stress-strain relation were given. On the other hand, the tempered and the quenched clad plates composed of low and medium carbon steels were used in the experiments in order to separate residual stress from laminated inhomogeneity. The experimental bending stress-surface strain curves differed little from the calculated values for the laminated inhomogeneous plates both with and without residual stress. It was found that the initial residual stress made the neutral line change in bending deformation, and that the calculated bending transverse strain change showed a close agreement with the experimental values. Consequently, this analysis is found effective to calculate the unmeasurable bending stress-strain relation of the inner layers in the plate.
Analysis of the J-integral was made by using the finite element method for cracks emanated symmetrically from transverse ends of an elliptical hole in a plate which was subjected to uniaxial tension, biaxial load or hydrostatic pressure. The power-law stress and strain relation was assumed in the analysis. The main conclusions obtained are as follows: (1) Under uniaxial tension, the J value for the present problem increases rapidly with an increase in the emanated crack length and approaches to that for a center-cracked plate (CCP) with the same gross crack length, when the elliptical hole is long in the transverse direction. For elliptical holes long in the axial direction, however, the J values increase rather slowly with increasing crack length and tend to give much higher values than that for the CCP at large crack lengths. (2) Under biaxial load, the J values of axially long elliptical holes become smaller when the transverse tensile load is applied, and larger when the transverse load is in compression. For transversely long elliptical holes, the J values show minimum values at certain tensile loads close to the equi-biaxial tensile load. (3) When hydrostatic pressure is applied on the surface of both the hole and the crack, the J values increase slowly with an increase in the emanated crack length because of the mechanical effect similar to that under the biaxial tension. (4) A simple formula for J-estimation, which uses the load and the load point displacement, was found useful if the crack was“deep”. When a notch opening displacement was utilized in place of the load point displacement, the effective range of the formula was very much extended to a shorter crack length.
The crack closure model proposed by Budiansky and Hutchinson for long fatigue cracks was extend to analyze the closure of small fatigue cracks formed in a smooth specimen or near the notch tip. The following results were obtained. (1) The effective fraction U for small cracks initiated in a smooth specimen increases as the crack length becomes smaller, and approaches to unity as the crack length approaches zero. The variation of U with crack length calculated through the present model was found to agree with the experimental data. (2) The influence of crack length on the fatigue growth threshold of small cracks results from the following two causes: the effective stress intensity range and the effective fraction. The dependence of the effective fraction on crack length is more predominant in determining the growth threshold of small cracks. (3) The effective fraction for cracks emanating from the notch tip also depends on crack length. For the cracks larger than the reverse plastic zone size at the crack tip, the value of U is the same as that for small cracks having the same length but without notch.
It is often observed that the data of the time to failure of Zircaloy tubes obtained in the internal pressurization SCC tests vary widely even though the same testing condition, such as the applied hoop stress, iodine concentration, test temperature and texture, is used. In order to keep the failure probability of Zircaloy tubes very small, it seems important to determine the distribution of the time to failure, or the failure probability, of Zircaloy tubes for the SCC test results. A study has been performed to establish the functional form of the distribution of the time to failure by using the statistical approach adopted in the study of strength and fracture of solids. The results revealed that the distribution of the failure probability could be described by the Weibull distribution. An attempt was also made to apply the present method to evaluate the failure probability of the Zircaloy cladding tubes with stress distribution by combining the data of SCC tests with the behavior of fuel rods analyzed by FEM code.
The effect of interaction between fatigue and creep damage on rupture life and crack growth has been investigated in SUS304 austenitic stainless steel at 500°C. The experimental results were compared with a linear superposition model or a competition model (a crack grows by following the process that provides faster growth) and examined by observation of fracture surface. The sum of fatigue and creep damage fraction for rupture life was less than one at low frequencies and more than one at high frequencies. At high frequencies the crack growth rate was in agreement with that predicted from both models in the early stage of crack growth, but the models overestimated the crack growth rate in the late stage. At low frequencies the crack growth rate coincided with that estimated from the models in the late stage of crack growth, but the models underestimated the crack growth rate in the early stage. It was revealed from observation of fractograph that there is a transition in fracture mode from transgranular to intergranular corresponding to a transition in crack growth rate. But the transition point in fracture mode or crack growth rate from transgranular fatigue failure to intergranular creep did not coincide with that estimated from the models. The disagreement between these models and the experimental data for rupture life, crack growth rate and fracture mode transition point at high frequencies may be explained by the decrease of crack growth rate due to creep strain recovery during unloading, but the reason for the disagreement at low frequencies is not clear at present.
In order to study the behavior of lattice defects during low-cycle fatigue tests with strain-amplitude change, electrical resistivity was measured on wire (0.55mm in dia.) of polycrystalline aluminium (99.999%) which had been torsionally fatigued at 77K. Two different total surface-strain amplitudes, 1.8 and 4.4%, were used. The dislocation density in metal during cyclic straining after changing the strain amplitude was given by ρ1/2=ρs1/2[1-[1-ρi1/2β/α]e]-(β/2)γ ρs=(α/β)2 where α is a constant, β is a constant depending on strain-amplitude, γ is the cumulative plastic strain, and ρi is the dislocation density prior to the strain-amplitude change. In this study, the constant β was estimated from the peak torque versus cumulative plastic strain curve for fatigued metal. The concentration of point defects in metal during cyclic straining at 77K was represented as follows: C=Cs[1-1-P/K2-β/2[K2e-(β/2)γ-β/2-K2P/1-Pe-K2γ]]+Cie-K2γ Cs=K1α2/K2β, P=ρi1/2β/α where K1 and K2 are constants, Cs is the concentration of saturated point defects, and Ci is the concentration of point defects prior to the strain-amplitude change. The experimental data was analysed on the assumption that the increment in resistivity in fatigued metal is related to the number of dislocations and point defects as ΔR/ΔRs=mρ/ρs+mC/Cs, m+n=1 where ΔRs is the saturation value in resistivity, ΔR is the increment in resistivity, and m and n are constants.
The fatigue tests of a low carbon steel were made in rotatory bending at room temperature. Both annealed and strain-aged specimens were prepared to vary the effectiveness of initial dislocation locking and of strain aging for fatigue limit. The latter specimen, subjected to a cyclic stress at 375°C prior to the test at room temperature, showed an increase in initial dislocation locking and a decrease in strain aging potential in the preliminary tensile tests. The relationship between the fatigue limit σw0 and grain size d, σw0=Cw+kwd-1/2, was applied to evaluate the characteristic values Cw and kw. The following results were obtained from the fatigue tests. (1) Both the characteristic values Cw and kw increased with cyclic prestress at 375°C. The increases in Cw and kw were about 7% and 65%, respectively. (2) The increase in Cw may be interpreted as a result of the increased frictional stress due to cyclic strain hardening by prestress and precipitation hardening by precipitates formed during cyclic strain aging at 375°C. (3) When kw is regarded as a measure of barrier at grain boundary against crack-propagation of a micro-crack initiated in a grain, the increase in kw may be attributed to the increase in initial dislocation locking rather than the effect of relocking of dislocation by cyclic strain aging. It is concluded that the initial locking of dislocations by solute atoms makes an important contribution to the existence of a fatigue limit at room temperature.
It has been clarified in the previous investigation that the intensity of initial dislocation locking makes an important contribution to the fatigue limit at room temperature, through an increase in kw in the relationship, σw0=Cw+kwd-1/2. In this paper, the nonpropagating crack length lnpc, the grain size d and the ratio r=lnpc/d were observed. The results were analyzed by Weibull's distribution function and thereafter the role of cyclic strain aging on the fatigue limit at room temperature was discussed. The following results were obtained. (1) Most of microcracks remained within a grain (one grain type). A small number of cracks (about 24%), however, grew over several grains, beyond grain boundaries and then arrested (several grains type). When the nonpropagating cracks were separated into these two types, the shape parameter of lnpc was nearly equal to that of the grain size. When they were treated as one group, the distribution of lnpc was expressed well by using the Weibull distribution of mixed type. For a small number of cracks, the crack tips nearly reached grain boundaries, that is, r=1, but the crack tip of most cracks (about 84%) stayed within a grain. (2) The cyclic strain aging may contribute to crack arrest in the course of crack growth until a crack reaches grain boundaries. The effect of crack arrest results in an increase in other characteristic value Cw.
Most rails in the track cannot avoid suffering defects and notches due to the contact rolling load of the wheels. These rails are often found to be broken by fatigue cracks originating from these defects. The most part of the fatigue lives of the members having sharp defects or notches are occupied by the propagating stage of fatigue cracks. Then, by using the specimens cut out from the experimentally melted rail steels (thick plates) and many kinds of rails, the characteristics of the fatigue crack propagation rate and the effect of the metallurgical structures on them were studied. Especially, the effect of residual stress on the crack propagation rate was investigated, because residual stress is inevitably produced in such a shapes as rails. The main results obtained are as follows; (1) The fatigue crack propagation rate is little affected by the chemical composition, pearlite block size and mechanical properties if the stress ratio is held constant. (2) If the fatigue crack propagation rate is expressed by the equation of dl/dN=C(ΔKeq)m, where ΔKeq=√ΔK·Kmax, it can be well represented by one linear relation. irrespective of the stress ratio. In addition, the values of C and m can be evaluated immediately from the case of the zero stress ratio. (3) The variation of the crack propagation rate at the constant stress ratio disappears by the annealing (520°C×30min, furnace cooling). This reason is considered due mainly to the relief of residual stress in the specimens.
The characteristics of fatigue crack growth at stage II in Cr-Mo steel (SCM 435) have been investigated synthetically from both sides of crack closure and fracture mechanisms by varying the tempering temperature (150°C-600°C) and stress ratio (R=0.06, 0.4). The following results were obtained; (1) The crack growth resistance decreased as the tempering temperature became low or the stress ratio became high. Such crack growth behaviors depended not only on the crack closure mechanism, but also on the fracture mechanism. (2) The crack closure and fracture mechanisms in stage II fatigue crack growth played different roles at each of three general fracture regimes, namely stage IIa, stage IIb and stage IIc. (3) At stage IIa and stage IIb, the crack closure was observed and the crack growth rate, da/ dN, could be correlated with the effective stress intensity factor ranges, ΔKeff, regardless of the tempering temperature and stress ratio. (4) At stage IIc, the crack closure was not observed, and the area percentage of dimple fracture due to the pseudo-monotonic fracture mechanism was more than 50%. In this region, da/dN was controlled by the maximum stress intensity factor, Kmax, because the percentage increased with increasing Kmax.
The effect of prestressing, such as partial unloading and perfect unloading, on the fatigue crack initiation life was investigated on the notched or precracked specimens of JIS SNCM 439 steel quenched and tempered at 473K. The crack initiation life and the lower limit mean stress, under which the crack initiation does not occur within 107 cycles at a given stress range, was markedly increased by these two prestress methods, especially by the partial unloading method. The increase in lower limit mean stress by the partial unloading method was large when the range of cyclic stress was middle. The reason why the fatigue crack initiation life was increased by both of the prestress methods could be explained by the decrease of surface tensile stress at the notch root.
Fatigue failure mode of aluminum was inspected by using the X-ray diffraction technique. The specimens of aluminum single crystal were cycled under the reverse plane bending in air and vacuum. The diffraction profiles show that the Laue spots are segmented into several subspots as the stress cycling proceeds and extended gradually to the radial direction in air and to the circumferential direction in vacuum. The pseudo-Kossel patterns indicate that the diffraciion profiles disappear little by little as the fatigue proceeds, and that a few lines in the air-tested specimen remain clearly to the final stage of failure, while all of them in the vacuum-tested one disappear. It is found that the pseudo-Kossel lines disappear gradually in following order of (333), (511), (422), (420)…, This phenomena are believed to be closely related to the slip characteristics of crystal. The difference of slipping modes in air and vacuum may suggest that the oxide layer grown on the surface during fatigue acts as the barrier to the slip motion of crystal in air.
A study of fatigue crack growth in glass mat reinforced polyester laminate was conducted by means of a compliance method using TDCB specimens for ΔK-controlled tests. The relationship between the fatigue crack growth rate and the stress intensity factor range for the specimens without moisture was shown by a straight line in logarithmic representation. The slope of the line was smaller than for the specimens with a little moisture and very much larger than those for metals or polymeric materials. The effect of moisture on the relationship was discussed based on the macroscopic observation of the whitening process due to debonding between fibers and resin at fatigue crack tips.
To examine the acoustic emission in glassy polymers, the tensile tests were carried out on SEN specimens of PMMA in various alcohols. The acoustic emission behavior and the growth manner of crazes in polymer were observed. The results obtained are summarized as follows. (1) With alcohols acting as mild environmental agents, the crazes grew smoothly and AE was not detected. (2) With alcohols acting as more severe environmental agents, the crazes grew stepwise and AE was detected. (3) The fracture surfaces ruptured in alcohols acting as more severe environmental agents have a characteristic shell pattern. (4) The stepwise craze growth, the formation of shell pattern, and AE behavior seem to be correlated with each other.
The elastic stiffnesses of Al-Cu alloys containing columnar crystals were determined from the ultrasonic wave velocities. Ultrasonic testing was done on the alloys subjected to different conditions of casting, solution treatment, and aging preceded by solution treatment. The stiffnesses (A, C and F) relating to normal strain were more influenced by the solute content and the heat treatment than the stiffnesses (L and N) relating to shear strain. The decrease of the stiffnesses A and C after the solution treatment was explained by the dissolution of the eutectic phase occurred in the cast structure. The influence of the solute segregation on the stiffnesses was analyzed to be negligible for a simple model.
In the previous papers, the authors investigated the electrochemical phenomena of some electric conductive materials such as Pt, Ni, Co, graphite etc. in molten sodium diborate glass. In this paper, molybdenum was chosen as the object of study since molybdenum is a particularly interesting electrode material used in electric melting of glass. Anodic dissolution, passivation and catholic deposition of molybdenum were investigated by linear potential sweep voltammetry in Na2O·2B2O3 at 900°C in N2 gas atmosphere. Moreover, the metal-glass interface after polarization was analyzed by EPMA. On cathodic polarization of Mo electrode, a relatively narrow residual current region appeared first and then a steep current increase followed at higher cathodic potential than ca. -0.7V (vs. Pt reference). Borate anions were easily reduced to boron element and the molybdenum boride layer having close texture covered the electrode surface. Sodium oxide layer was formed outside the boride layer at ca. -2.5V, and this layer moved toward molybdenum metal at higher cathodic polarization. Sodium ions were not seemed to be reduced readily till -5V. Ni electrode also formed nickel boride before sodium deposition like in the case of Mo. The anodic voltammogram of Mo electrode showed three current peaks due to the formation of passive films made of molybdenum oxides. At a lower anodic potential than ca. 1V, MoO2 and Mo2O5 films were likely to be formed, but both films re-dissolved at higher anodic polarization. Anodic current increased up to ca. 4V due to dissolution of Mo oxides and Mo metal. Passivation phenomenon at ca. 4V could be attributed to the formation of MoO3 layer. The MoO3 layer looked remarkably porous and was readily sublimed at 900°C, so that Mo electrode was consumed acceleratedly. Ni electrode was revealed to form passive NiO layer.
The study on the anisotropy of the dynamic mechanical properties of wood is an important subject. Among various problems, the effect of grain angle on the modulus of elasticity has been clarified pretty well, but the effect of grain angle on the internal friction has been studied rarely. The only equation treating this effect is the one proposed by R.E. Pentoney3), and so it still remains unsolved. In order to treat the problem, the grain angle was taken to be the angle between the longitudinal direction and the radial one made by rotating the grain around the fixed tangential-axis, and the effects of grain angle on the dynamic modulus of elasticity and the internal friction of wood were investigated by using a flexural vibration method. From the examination of the relationship between the internal friction and the grain angle based on Keylwelth's equation, it was found that the relationship between the variations of specific dynamic modulus of elasticity and internal friction for wood with grain angle was expressible by an exponential equation with two constants which depend upon species of wood. From this result, the equation to evaluate the internal friction of wood having grain angle was obtained. The present result disagrees with Pentoney's result which gives a linear relationship between modulus of elasticity and internal friction.
Boronizing is one of the chemical methods to achieve case hardening of steels. The boronized layer has above 1400 Vickers hardness and a high resistance especially against wear. In the present study, the X-ray method was successfully applied to measure the residual stress distribution in a boronized steel. The X-ray elastic constants were determined separately for FeB and Fe2B phases of the boronized layer, and compared with the mechanically measured values. The results obtained are summarized as follows; (1) The X-ray elastic constants determined were S1=9.10×10-7(MPa-1), S2/2=2.93×10-6(MPa-1) for FeB (212) phase, and S1=4.95×10-7(MPa-1), S2/2=2.13×10-6(MPa-1) for Fe2B (330) phase. The Young's modulus of FeB and Fe2B phases were 494(GPa) and 611(GPa) which were higher than the mechanically determined values of 370(GPa) and 260(GPa), respectively. (2) The residual stress distribution determined by X-rays indicated high compressive stress above 2000(MPa) in the boronized layer. The effect of the boronizing process on the residual stress distribution was examined.