This paper describes the effect of machining textures on lattice strain ε'33vs. sin2ψ relation. A general relation between X-ray lattice strain and applied stress was formalized for an anisotropic single crystal. The calculations under the Reuß model assumption revealed that the ε'33vs. sin2ψ relation for a textured material had a systematic deviation from a linear or an elliptic distribution, which is, respectively, a typical feature in the uniaxial or the shear stress state of an isotropic and homogeneous material. The non-symmetric machining textures were found to disturb the strain distribution and also cause ψ-splitting even if the stress state was uniaxial. The experimental measurements showed that an orthogonally planed pure iron had an extreme texture which could be approximately given by rotation of the cold-rolling texture about its transverse axis. The results of the measurements for 200 diffraction showed no residual shear stress and those for 211 diffraction showed ψ-splitting due only to the machining texture. The distribution of lattice spacing measured for 211 diffraction in the sin2ψ diagram coincided qualitatively with the values calculated under the Reuß model assumption for each pole of the ideal machining textures.
In the present paper, the elastic deformation of polycrystalline metals under uniaxial stress was studied microscopically using a plane model of polycrystals. The stress and strain in a round crystal embedded in a homogeneous medium were analyzed by the finite element method, and the elastic constants of the bulk specimen and the lattice strains in grains reflecting X-rays were calculated. The results obtained are summarized as follows. (1) The stress in a grain calculated with the present model changes from that of a uniform local stress model to that of a uniform local strain model according to the change of crystal orientation in regard to the direction of applied stress. (2) The elastic constants of polycrystalline metals are affected by the condition of restriction of grains, and it is closely related to the extent of elastic anisotropy of crystal whether the influence is large or not. (3) The influence of restriction of grains on the mean value εψ of lattice strain for the grains reflecting X-rays is relatively small and the εψ/σ-sin2ψ relation and X-ray elastic constant (-ν/E)X-ray based on the present model are comparatively close to those of a uniform local stress model.
This paper describes an X-ray study of low-cycle fatigue damage of SUS 304 stainless steel at 873K under a total strain range controlled condition. The micro Laue method of back reflection was used as an X-ray diffraction technique and the damages at two parts of the specimen were measured by intermitting the low-cycle fatigue tests. One was the notched or cracked part and the other was the non-cracked part. From these tests, the following conclusions were obtained. (1) Misorientation at the non-cracked zone increased monotonously with an increase in number of cycles and it correlated well with the cumulative plastic strain range of the material. Dislocation and imperfection densities, calculated from misorientation, increased rapidly in the initial stage of low-cycle fatigue, and after becoming almost constant in the middle stage, they increased rapidly again in the final stage of low-cycle fatigue, which agrees well with the observation by TEM. (2) Misorientation at the crack tip correlated well with COD and the crack propagation rate, but the correlation between misorientation and cyclic J-integral was not so good.
The fatigue crack growth and crack closure behaviors of an explosively bonded stainless clad pressure vessel steel plate (SUS-SPV plate) were studied by using the through thickness crack specimens and the surface crack specimens. The observed behaviors of the fatigue crack growth and crack closure were complicated, mainly due to the influence of the residual stresses which had been introduced in the clad plate through the production process. The shape of the crack was also influenced strongly by the residual stress in the surface crack specimens. The crack was elongated in the thickness direction when the crack was propagated from SUS to SPV, while it was elongated in the surface direction when the crack was propagated from SPV to SUS. The exceptionally high and low values of the aspect ratio, a/c, of the surface crack, the maximum value of 2.2 and the minimum value of 0.35, were observed. The stress intensity factor range, ΔK, was not in good correlation with the crack growth rate for both types of specimens. The effective stress intensity factor range, ΔKeff, was successfully correlated with the crack growth rate for all the specimens tested in this study, including those of the parent materials of the clad plate.
An X-ray fractographic study was made on the fatigue fracture surface of SM50A and HT80 steels. The residual stress and the half-value breadth of X-ray diffraction profile were measured at and beneath the fracture surface. The correlation was examined between the parameters obtained from the X-ray measurements and the fracture mechanics parameter of Kmax or ΔK at which the fracture surface had formed. The residual stress on the fracture surface was found to increase at first, reach to a maximum value at a certain value of Kmax or ΔK and then decrease. It was also found that the residual stress was controlled by Kmax in a low Kmax or ΔK region, while it was governed by ΔK in a high Kmax or ΔK region. The reasons of this behavior were discussed by using the data from constant Kmax and constant ΔK tests which were additionally planned and made in this study. The half-value breadth, B, on the fracture surface was found to increase with Kmax in the two steels used in this study. The value of B was influenced by stress ratio in HT80, although it was not influenced in SM50A. Both of the distributions of residual stress and half-value breadth beneath the fracture surface were found to be useful for the prediction of monotonic plastic zone size or Kmax.
A new polynomial approximation method was proposed for the X-ray multiaxial stress analysis, in which the effect of stress gradient along the penetration depth of X-rays was taken into account. Three basic assumptions were made; (1) the stress gradient is linear in respect to the depth from the specimen surface, (2) the ponetration depth of X-rays is a function of Sin2ψ and (3) the strain measured by X-rays corresponds to the weighted average strain on the intensity of the diffracted X-rays. Consequently, the stress state within the thin layer near the surface was expressed by making use of three surface stresses and six stress gradients in the present method. The average strains by X-rays were approximated by the third order polynomial equations of sin2ψ using a least square method at several φ angles on the coordinate system of specimen. Since the coefficients of these polynomials include these nine stress components mentioned above, it is possible to solve them as simultaneous equations. The calculating process of this method is simpler than that of the integral method. An X-ray plane stress problem was analyzed as an application of the present method, and the residual stress distribution on a shot-peened steel plate was actually measured by use of Cr-Kα X-rays to verify the analysis. The result showed that the compressive residual stress near the surface determined by the present method was smaller than the weighted average stress by the Sin2ψ method because of the steep stress gradient. The present method is useful to obtain a reasonable value of stress for such a specimen with steep stress gradients near the surface.
For the improvement of wear-resistance of high manganese austenitic cast steel, explosion hardening treatment has been tried recently. From the previous study, it became clear that high tensile residual stress was generated in the hardened surface layer by explosion and microcracks were observed. In this study, therefore, the distributions of biaxial residual stresses in the explosion hardened steel were examined and compared with those of the original and the shot peened steels. The results obtained are as follows: (1) In the longitudinal direction of the test specimen of explosion hardened steel, tensile residual stress was generated in the hardened layer from the surface to the depth of about 0.5mm, and the maximum value was about 80kgf/mm2 at the depth of about 0.005mm. In the transverse direction, compressive stress appeared with the maximum value of about 27kgf/mm2. On the other hand, in the shot peened steel both of these biaxial stresses were compressive. (2) In the surface layer hardened by explosion, a good many microcracks perpendicularly intersecting to tensile residual stress were observed. The microcracks had a tendency to grow in the range of high tensile stress by 5% nital etching, and as the stress decreased the cracks disappeared by removing off thin layers successively by electrolytic polishing. (3) It is supposed that the characteristics of residual stress in the explosion hardened steel mentioned above depend mainly on the configuration of test specimen, the setting method of an explosive and explosive heat.
In order to develop an estimating method of fatigue damage caused by stress amplitude below fatigue limit, the present authors carried out several types of varying stress amplitude tests in the past. However, many of them were done at room temperature and only few investigations at elevated temperatures have been reported. In the present study, repeated two-step varying stress amplitude tests which composed of a stress higher than the fatigue limit(overstress) and a stress lower than the fatigue limit(understress), were carried out on the smooth specimens of SUS 316, SCMV 4 and SCM 435 steels under rotating bending stress at temperatures up to 600°C. The fatigue data were analyzed by the Miner's and the modified Miner's laws, and the cumulative fatigue damage was discussed. The main results obtained are as follows: (1) Under varying stress amplitudes, the understress gave a fatigue damage to the specimens and the cumulative fatigue damage calculated by Miner's law was less than unity. (2) The modified Miner's law gave a conservative damage value for SUS 316 stainless steel at 600°C, although it gave poor damage values for SCMV 4 steel at 300°C and 500°C, and SCM 435 steel at 300°C.
Experimental and analytical investigations of simplified models of concrete were carried out to study the stress around a lightweight-aggregate located in the concrete subjected to uniaxial short-term compressive stress. The concrete was idealized by a model consisting of a spherical aggregate embedded in a mortar matrix to form a specimen. In the past, Hansen has attempted to explain the complex behavior of the concrete made of lightweight-aggregates with the help of Goodier's formula. His work is notable, but it is a limited case of Goodier's general model which had been introduced, in his study on the concentration of stress around spherical and cylindrical inclusions and flaws. The Goodier's analysis may be applied to real materials as a rough estimate, when the mortar (paste, sand, and voids) is treated as a homogeneous elastic matrix surrounding elastic inclusions of coarse aggregates and no interaction among inclusions exists. This approach is somewhat unrealistic. It must be pointed out, however, that the stress-strain curves for lightweight concretes are rather straight compared with those for gravel concretes of the same strength. Under such conditions, failure takes place by splitting the mortar surrounding a weak piece of aggregate. For tractability, the problem has been solved for an elastic inclusion in an infinite space. Several models conformed to Goodier's conditions as much as possible were selected, and the experimental and analytical values were numerically compared in this paper. In the experiments several strain gauges were attached around the perimeter of an aggregate. The observed load-local strain behavior agreed reasonably well with that predicted by Goodier's analysis.
Amorphous polymers which have been deformed plastically at room temperature almost recover their original shapes at temperatures above their glass-transition temperature. The shape recovering behavior during raising temperature is significantly affected by the temperature distribution in the polymer specimens, which have essentially low thermal conductivity. In this paper, the influences of the lateral size of specimens and the surface temperature on the recovering behavior of poly (vinyl chloride) heated in an air oven were investigated experimentally and the results were compared with the numerical calculations obtained by using the equation of heat conduction. The results show that when the specimen is considered as a bundle of many fibers, the calculated shape recovery of tensile or torsional deformation agrees with the experimental results and the behavior of model described above also agrees with the experimental result of the specimen having localized neck.
A method to predict the time response of unidirectional glass fiber and plain woven glass cloth reinforced polyester laminates was described. The short term (20 minutes duration) creep test results of strip tension specimens with the load at various angles to the fiber direction were reported and compared to the analytical results. For the unidirectional laminates, it was shown that the materials were elastic at all stress levels when the fibers were in the load direction. On the other hand, when the load transverse to the fibers the viscoelastic response varying from a small amount at low stress level to a large amount at high stress level appeared even at room temperature. For off-axis specimens and plain woven laminates, the response was similar to the latter. Furthermore, the numerically predicted results were compared with the experimental results. The results showed that only two material informations were needed to predict the viscoelastic response of the composites: One is the viscoelastic response of the matrix resin and the other is the elastic constants of the glass fiber.
Creep fracture behaviour of 1.3Mn-0.5Mo-0.5Ni steel has been investigated metallographically using creep tested specimens with rupture times up to about 80000h in order to clarify creep fracture mechanisms and construct a creep fracture mechanism map. The results obtained are as follows: (1) The transition from transgranular to intergranular creep fracture was found to occur with increasing time to rupture. This transition in creep fracture modes leads to a decrease in rupture ductility and stress index of rupture life. (2) The intergranular creep fracture is caused by the formation and growth of grain boundary creep cavities, most of which are associated with grain boundary carbides. (3) The creep fracture mechanism map, which was constructed experimentally in stress-temperature space, indicates that the operating conditions of temperature and stress for the steel at steam power plants should be kept within the field of intergranular creep fracture due to cavitation. (4) The observed stress index and apparent activation energy of rupture life in the field of intergranular creep fracture are in reasonable agreement with the calculated values from the cavitation fracture model, which assumes that the number of cavities increases with creep strain and the growth of the cavities is controlled by grain boundary diffusion.
Recently, friction welded butt joint has come into wider use for many mechanical structural elements, e.g. small scale crank shaft, etc. However, there exists some uneasiness in the practical use of this type of joint because of lack of strength data under service load or fatigue load conditions. So, the authors planned to conduct a systematic study on fatigue behavior of this type of joint and have been carrying out a series of experiments by using some sorts of joint specimens composed of similar metallic material. As a part of this study, rotating bending fatigue tests were carried out to investigate the fatigue strength behavior of SUS 304/SUS 304 friction welded butt joint specimens. The results showed that the fatigue strength of the joint specimen was much lower than that of the base material specimen especially in the stress cycles range exceeding the critical number of stress cycles for the base material specimen. Furthermore, detailed observations on the fatigue fractured surface were done to give valid explanation to the characteristic strength behavior of the joint specimen revealed in this experiment. It is concluded that the lowering trend in fatigue strength of SUS 304/SUS 304 joint specimens depends on the metallurgical feature of the friction welded interface, in other words, that the boundary layer of fiber flow direction existing around the interface gives a detrimental effect on the fatigue strength of this type of joint.
For the purpose of studying how the torsional fatigue strength of steel shafts changes with the distance between a step and a key groove end, the completely reversed torsional fatigue tests were performed on the low carbon steel specimens having steps with a comparatively sharp fillet and a key groove, and the fatigue crack initiation and propagation were discussed macroscopically from the fatigue data obtained and the location of fracture. The conclusions obtained are as follows: (1) For the specimens with a key groove, the reversed torsional fatigue strength of the specimen with a groove end was about 10% lower than that of the specimen with a key groove extending over the reduced section of the specimen. (2) On the fatigue crack initiation in the specimen with a groove end, as long as the circular arc of the key end was located in the portion of fillet, there existed an interaction between two notches of a filleted step and a key groove (that is, the “double notch effect”). On the other hand, the distance between a step and a groove end did not directly influence the fatigue strength. (3) Fracture mostly occurred at a key end in the parallel portion (the reduced section) of the specimen. (4) The three-dimensional stress concentration appeared at the groove end not only from the shape change in the transverse cross-section but also from that along the longitudinal section of the specimen.
Fatigue crack growth tests of copper, very low-carbon steel, mild steel, stainless steel and aluminum alloys were conducted by using center-cracked specimens under elastic, elastic-plastic and gross yielding conditions. The growth rate of a fatigue crack was correlated to the ranges of J integral ΔJ and crack opening displacement Δφ250, where ΔJ was evaluated from the loading portion of hysteresis. loops of load against crack opening displacement at the crack center and Δφ250 was measured at the position 250μm behind the crack tip. The growth rate da/dN was expressed as a unique power function of ΔJ or Δφ250 for each material. The variance in the da/dN-ΔJ relation with materials was found to be minimum when da/dN was correlated to ΔJ/E(E=Young's modulus). The variance was even reduced if Δφ250 was taken as a parameter. The exponent in the da/dN-ΔJ relation tended to decrease from 2.3 to 1.4 as the yield strength of the material increased. In the region of rates between 3×10-7 and 5×10-5m/cycle, the fracture surfaces of copper, very low-carbon steel and stainless steel were covered almost entirely by ductile striations, whose spacing s coincided with the macroscopic growth rate da/dN. Since s was not proportional to ΔJ, the simple crack tip blunting model proposed previously was not enough to derive the fatigue crack growth law. Some discussion was made for a further refinement of the mechanics of crack growth by plastic blunting mechanism.
Fatigue crack growth behavior and its governing factors were investigated by analysing the test data obtained under K-increasing conditions on various structural materials. The fatigue crack growth rate curves exhibited a trilinear form in the so-called Region II. This trilinear form also appeared in the relationship of da/dn versus the effective stress intensity range ΔKeff and the transition points in the relationship corresponded to those in the plot of the crack opening ratio U against ΔKeff. Irrespective of materials, the effect of stress ratio on the crack growth rate can be well evaluated in terms of ΔKeff. The fracture ductility of material εf was found to exert a considerable effect on the fatigue crack growth rate and the following empirical equation was proposed to account for the effect of material properties on the crack growth rate; da/dn=c/√εf(ΔKeff/E)m
In order to investigate the statistical distribution and its characteristics (parameters of the distribution) of fatigue crack length at an arbitrary time during the process of fatigue crack propagation, pulsating-tension fatigue tests were carried out under the condition of the same constant stress amplitude on many specimens of a high-tension steel, and the results were discussed by means of the statistical analysis. In the first place, the constants in the Paris-Erdogan equation of fatigue crack propagation were randomized and the results obtained by computation were compared with the experimental results and discussed. Next, from these results a new parameter was considered, which is constant irrespective of crack length and represents the statistical variability of crack propagating-life. Finally, by using the method of Markov chain, it was revealed that this parameter really represented the variability of lives in the transition propability matrix of Markov chain, and thus the physical meaning was given for this parameter. It was also found that the above parameter was applicable for the crack propagating behaviour in both cases of constant and variable stress intensity factor ranges.
The temperature-impact value curves determined by the Charpy impact tests have been obtained for low carbon steel (SM41) subjected to prestrain tension of 0.15. The effects of prestrain on the ductile-brittle transition temperature, the maximum impact value and the slope in the transition region of the curve were studied. It was found that (1) the transition temperature rose in the range of 0 to 0.10 prestrain but fell in that of 0.12 to 0.15, and (2) the minimum value of the slope and the maximum impact value were both at approximately 0.10 prestrain. The dependence of the transition temperature upon prestrain was discussed by means of Stroh's theory, which is based on the probability of the dislocation source to break away from Cottrell's environment. The experimental results show that the dependence of the transition temperature upon prestrain can not be explained by the prestrain dependence of the activation energy for the dislocation source to break away from Cottrell's environment; rather the dependence can be qualitatively explained by the length of the dislocation source estimated from the dislocation distribution in the prestrained steel as observed by transmission electron microscopy. The dependence of the slope upon prestrain can be also qualitatively explained by the dislocation distribution.
Several experiments concerning the generation and propagation of a single stress pulse have been made for the purpose of investigating shock response of a multilayer strip plate. The generator of reproducible single shock pulse was developed using the electro-magnetic induction method. The stress amplitude and the pulse width were easily controlled. The stress pulse was observed by the dynamic photo-elasticity method. Measurements of reflection and transmission of stress pulse in a three-layer strip plate were made as a simple example to test shock response. Photo-elastic materials were used as an incident and a transmitting media and metals were used as an intermediate layer. Observations were made at intervals of 10μsec, and the reflection and transmission phenomena were found to depend on the relative characteristic impedance of the intermediate layer with respect to the incident medium as well as on the relative width of the intermediate layer with respect to the incident pulse. Moreover, a simple analysis was made based on the theory of reflection and transmission of plane waves at a boundary in infinite medium. For more detail discussion, it is necessary to analyze the data with consideration for frequency components of incident, reflected and transmitted pulses.
In order to analyze two- or three-dimensional stress, displacement or strain distribution from fringe patterns obtained by using photoelasticity, holographic interferometry or moire, an image processing system has been developed. This system employs an IC image memory, a personal computer and its peripheral devices, and so it is of low price. A program to analyze fringe patterns was written in consideration for interactive and wide use with reasonably high speed. As an example, a moire fringe pattern of powders during compaction in a T-shaped vessel was analyzed. Furthermore, a scanning moire technique was developed, in which the master grating lines are replaced by the scanning lines of a TV-camera. Use of the image processing and this scanning moire in conjunction with a mismatch technique allows measurement of both small and large strains from one image picture.