Journal of the Society of Materials Science, Japan
Online ISSN : 1880-7488
Print ISSN : 0514-5163
ISSN-L : 0514-5163
Volume 13 , Issue 135
Showing 1-18 articles out of 18 articles from the selected issue
  • 1964 Volume 13 Issue 135 Pages 906-914
    Published: December 15, 1964
    Released: June 03, 2009
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  • Kazuyoshi KAMACHI
    1964 Volume 13 Issue 135 Pages 915-917
    Published: December 15, 1964
    Released: June 03, 2009
    The method and technique of electroplating are so widely known that they are applied to industorial process without raising serious problems. But the plating of targets for demountable X-ray tubes requires methods other than plating for surface hardening and anti-corrosin process, and they must be used to convert electrons to X-rays. It requires compactness, high purity, and suitable thickness.
    Simple and economical methods of electroplating of Cr, Co, Mn and of measuring the thickness plated are discussed in this paper.
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  • Klaus KOLB, Eckard MACHERAUCH
    1964 Volume 13 Issue 135 Pages 918-919
    Published: December 15, 1964
    Released: June 03, 2009
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  • Klaus KOLB, Eckard MACHERAUCH
    1964 Volume 13 Issue 135 Pages 920-922
    Published: December 15, 1964
    Released: June 03, 2009
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  • Mitugi IWAMOTO, Hatutaro KIKUCHI
    1964 Volume 13 Issue 135 Pages 923-929
    Published: December 15, 1964
    Released: June 03, 2009
    To measure the lattice distortion from the diffraction pattern due to characteristic X-rays and there from to determine the residual stress is a very effective method of nondestructive inspection. In the industrial application of this method, it is necessary to preliminarily clarify the possible errors induced in the measurement.
    This method is supposed to cause various errors in measurements. Earlier1), geometrical errors in X-ray radiography and possible errors in distance measurements of diffraction ring were theoretically and experimentally discussed. A proposal was made, and it was reported that the experimental value of lattice distortion was far larger than its theoretical value. In the present paper, by way of solving these problems, it was experimented how the duration of exposure in radiography induces an error.
    As commonly practiced in the Glocker method and the sin2Ψ method and others, the lattice distortion in each orientation is found before determining the stress, this lattice distortion can be detected by radiographing the diffraction pattern with the specimen surface tilted at varied angles (Ψ) to the incident X-rays. Thereby, the distance measurement of diffraction ring has been made by means of a micro-photometer, and accordingly, the density of film back ground plays an important role. The films have no equal density of background, particularly in the films taken at heavily tilted angles there is a considerable difference in density between right and left even in the same piece of film.
    To find how in such conditions the measuring errors of diffraction rings occur from one another, vertical radiography with different film densities under different exposures was made and the results were analyzed. Through this analysis, it was revealed that the scattered ray had been mainly responsible for the errors. This scattered rays are divided into the primary one from the specimen surface and the secondary one reflected from the metal part like the film cassete. It is predictable that the latter has a larger bearing on the errors.
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  • Kazuo HONDA, Jyunichi ARIMA
    1964 Volume 13 Issue 135 Pages 930-937
    Published: December 15, 1964
    Released: June 03, 2009
    The stress measurement by X-rays is based on the variation of lattice spacings of metallic crystals due to stress. Therefore complicated problems concerning the theory and equipment are present in the practical application of this measurement. Recently, however, the experimental procedures of X-ray stress measurement are applied to many fields of engineering studies in consequence of the development of equipments as well as of the improvement in measuring method and theoretical background. We have investigated the X-ray stress measurement from the standpoint of engineering application.
    However, there are two sorts of problems regarding the X-ray stress measurement. One is that the X-ray stress measurement depends on the measurement of the local lattice strains due to heterogeneous deformation of the metallic crystals. Consequently it seems that the generation of these lattice strains is closely related to the deformation mechanism of the crystal grains. The other is that in the two phase alloys containing the α- and the β-phases, the plastic deformation is expected to appear preferentially in the α-phase due to the difference in yield stress or crystal lattice structure. Therefore, in regard to the X-ray stress measurement, it is necessary to discuss the problems of “Gefügespannungen”in relation to the mechanism of plastic deformation and the interrelation of elastic constants of the α- and the β-phases. In this connection, the authors carried out some experiments on Cu-Zn alloys containing the α- and the β-phases. One is the measurement of elastic constants of the α- and the β-grains, and the other is the measurement of residual stresses in these phases. In connection with the above experiments, the authors performed the observation of microstructure of the extended 6-4 brass plate specimen.
    Round bar specimens of 6-4 and 7-3 brasses were used in the experiments. After being finished, all the specimens were annealed at 400°C for 1hr in the air, and then the specimens were electopolished before being subjected to X-ray photography. The specimens were stressed stepwise by a tensile testing machine, and at several stages of applied stress, the CoKα1 beams were radiated to the center of the specimen surface in vertical and oblique incidences with several angles Ψ. Using the film technique, the changes in atomic distances of the α- and β-phases were measured by the conventional sin2Ψ method. The value of cosec θψ was calculated from the measurement of radius of diffraction ring, using a microphotometer of automatic recording type.
    At several stages of the applied stress, the relation between εψ and sin2ψ was obtained, and then the curve representing δε/δsin2ψ-σ (stress) relation was drawn by using the method of least square. Based on these diagrams, another curve of εψ=0 versus stress was drawn similarly. From the slopes of these lines, the elastic constants Were calculated for each phase. For the observation of microstructure of extended 6-4 brass, an optical microscope of 600 magnifications and an electron microscope of 10Å resolving power were used.
    The conclusions of the present study are as followes;
    (1) The elastic constants of the α-phase were measured by the X-ray technique using annealed 7-3 and 6-4 brasses. The values obtained were in fairly good agreement with those measured mechanically within the experimental errors. In the case of the specimens deformed plastically, the same results were obtained also.
    (2) On the contrary, for the β-phase of deformed 6-4 brass, the elastic constants obtained by X-rays showed a little divergence from those measured mechanically.
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    1964 Volume 13 Issue 135 Pages 938-943
    Published: December 15, 1964
    Released: June 03, 2009
    The X-ray stress measurement using a diffractometer specially designed for the purpose has recently been prevailing. Little or no experiment on X-ray stress measurement, however, has so far been made by means of an ordinary diffractometer.
    In this paper, the possibility of residual stress measurement by means of sin2ψ-method using a single pole counter diffractometer, Shimadzu GX-2, is discussed. In measuring the residual stress using this type of a diffractometer, the following two conditions must be fulfilled. One is that the specimen can be fixed at an arbitrary angle position, only the counter being made to scan. The other is that the counter can be shifted precisely in the radial direction of the goniometer with a change in ψ. The errors which may arise from this shift of the counter and from mis-setting of the specimen are estimated.
    Next, the results obtained from the experiments are reported, which were carried out on extended α- and (α+β)-brass specimens in order to confirm the so called surface effect, the reflecting plane dependence of residual stress values, and the“Gefügespannungen”which had been observed by many investigaters. The plate specimens were annealed at 550°C for 2hrs in an argon atmospher and were extended 3% statically. The thin layers were successively removed from both sides of the specimen. The residual stresses in α-brass and those in both α- and β-phases of (α+β)-brass on each layer near the specimen surface were determined by means of sin2ψ-method. The reflecting planes used were (420), (331), (400) and (311) planes of α-phase in α- and (α+β)-brasses, and (321) and (211) planes of β-phase in (α+β)-brass, respectively.
    The results are as follows
    (a) After the extension of 3%, the residual stress in α-brass specimen is compression on the surface, showing a tendency to change into tension in the interior of specimen. The reflecting plane dependence of residual stress values is found out on each layer. However, the stress distribution in the cross-section of specimen shows the similar aspect for each lattice plane used.
    (b) After the extension of (α+β)-brass specimen by 3%, α-phase remains in compression, while β-phase in tension. The reflecting plane dependence of residual stress values and the surface effect are observed as in α-brass specimen.
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  • Takeyoshi TAMARU, Kohei KOJIMA
    1964 Volume 13 Issue 135 Pages 944-948
    Published: December 15, 1964
    Released: June 03, 2009
    The data of stress determined by X-rays agree well with that obtained by the mechanical method in the macroelastic range. But the meaning of the residual lattice strain that is to be determined by X-rays as to the residual stress in metals subjected to plastic deformation is not yet sufficiently known. Especially in steel, the residual stress on the surface of the specimen after uniaxial plastic deformation shows higher compressive stress than in the interior by the so-called surface effect1) or the in homogeneity of strain hardening2), and the residual compressive stress is distributed uniformly over the cross section of the specimen. Moreover, there are some problems of“Gefügespannung”4), 5)due to the difference of the strength of ferrite phase and cementite phase3), the wave length of X-rays and the diffraction plane dependency etc. For the application of stress measurement by X-rays in the determination of the residual stress to the plastically deformed metal, it is important to elucidate these problems.
    After removal of load in each stage of uniaxial tensile deformation, in this paper, the residual stresses of the surface of several low carbon steel plates (contained 0.04%C, 0.06%C, 0.16%C, 0.21%C, 0.30%C) and the stress distribution over the cross section of specimens by electrolytic etching were determined by X-rays. The chemical composition and heat treatment of each specimen are shown in Table 1. The lattice strain was determined by sin2φ method from the photographic film of the diffraction line of (211) plane using CrKα1. Since the average ferrite grain size in the finished specimens was about 0.02-0.04mm, the diffraction line become spotty. To avoid this effect a specimen holder consisting of horizontal and vertical oscillation mechanism was prepared (Fig. 2).
    The residual stresses of the surface of the specimens above 0.06%C were all compressive and increased with increasing plastic deformation (Fig. 3). These compressive residual stresses were approximately proportional to the true stress obtained by mechanical test6). The proportional constant was nearly 0.2 (Fig. 6). From these results, on the contrary, it is shown that the residual stress of the surface can be estimated from the applied mechanical stress, but the surface stress of the steel up to 0.04%C is low and not proportional to the strain.
    The residual stress distribution over the cross section of each specimen was shown in Fig. 7. The residual stress of the specimens up to 0.16%C was higher on the surface or in the vicinity of the surface than in the interior. The residual stress distribution of specimens above 0.21%C was almost uniform. The difference of these distributions is considered not only to be affected by the carbon content but also by the plastic strain7).
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  • On the Residual Stresses due to Plastic Deformation under a Uniaxial and a Multiaxial Stress System
    Shuji TAIRA, Yasuo YOSHIOKA
    1964 Volume 13 Issue 135 Pages 949-956
    Published: December 15, 1964
    Released: June 03, 2009
    It is pointed out by the authors as the result of studies on the residual stresses of stretched and quenched carbon steel specimens by using X-ray method: 1) that thermal residual stress in the (211) crystal plane represents the macroscopic residual stress itself, 2) that it is considered that the compressive residual stress obtained by using the Cr-Kα beams in stretched carbon steel specimen includes the macroscopic residual stress due to the surface effect, and also the microscopic one due to the anisotropy of plastic deformation.
    It has been reported by many researchers that X-ray compressive residual stresses are observed on the plastically stretched carbon steel specimens. However, considering from the recently obtained experimental results, some contradictions to the discussions are often found since the past studies treated only the residual stress due to the uniaxial stretching, and scarcely dealt with the residual stresses caused by other processes. For this reason, the authors carried out experiments to examine the nature of X-ray residual stress in order to extend the method of X-ray stress measurement to practical use.
    The crystal plane dependence of residual stress in stretched or quenched specimen was investigated, and the biaxial residual stresses in the thin-walled tubular specimens caused by plastic deformation due to the internal pressure were measured.
    Iron and five sorts of carbon steels with carbon contents ranging between 0.06 and 1.10 percent were prepared as test materials. All the specimens were annealed after machining. Some of them were water-quenched from 600°C after being annealed, and these specimens include the residual stresses of purely thermal effect.
    The X-ray diffraction apparatus used was a parallel beam type X-ray stress analyser, and the diffraction lines of Co-Kα and Cr-Kα beams from (310) and (211) crystal planes, respectively, were automatically recorded.
    The results obtained in this study indicate interesting features as follows:
    1) The crystal plane dependence of residual stress is not seen in the quenched specimens, and the thermal residual stress can be accurately measured by means of X-rays.
    2) On the other hand, it is clearly observed in plastically deformed specimens. This result indicates that presence or absence of crystal plane dependence may be effected according to the difference of mechanism causing the residual stress.
    3) In addition, for plastically deformed specimens, compressive residual stress tends to approach a constant value at the center of the specimen. It is important to note that even in the iron specimen which consists of sole ferrite structure, residual compressive stress was observed in the core of the specimen.
    4) The plastic deformation under a uniaxial or multiaxial load stresses induces a uniaxial or a multiaxial residual stress system, respectively, of microscopic nature.
    Based on these results, the authors suppose at present that the cause of X-ray compressive residual stress of microscopic nature lies in the anisotropy of plastic deformation at room temperature, consequently, the diverse values of residual stress will be observed in different crystal planes.
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  • Kazuyoshi KAMACHI
    1964 Volume 13 Issue 135 Pages 957-959
    Published: December 15, 1964
    Released: June 03, 2009
    The residual stress and strain in deformed metals and alloys have remarkable effects upon the mechanical properties as well as physical and chemical properties, and many experiments have so far been made in the way of their measurement and studies.
    In terms of X-ray examination, the peak shift of X-ray diffraction rings are accounted for by the uniform change of lattice spacing, which is accepted as responsible for the residual stresses. The non-uniform distorsion of the lattice is also considered as responsible for the residual energy.
    To consider the relation between the residual strain, the stresses and the residual energy, stored energy of tension tested. specimens were measured. The material of the specimen is mild steel, having chemical compositions of 0.26 wt%C, 0.07% of Si, 0.49% of Mn, 0.042% of P and 0.02% of S.
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  • Hiromichi KAWAI
    1964 Volume 13 Issue 135 Pages 960-964
    Published: December 15, 1964
    Released: June 03, 2009
    The device of a dynamic X-ray diffractometer has been proposed here, principally based on the stroboscope-technique, to be used for observing the X-ray diffraction pattern at a particular phase of periodic deformation of crystalline specimens in a steady state.
    This technique is useful not only for determining the crystal lattice deformation and crystal orientation of the specimen under its highspeed periodic deformation, but also for determining the phase difference of the crystal deformation or orientation of the specimen from its bulk strain as a function of vibration frequency at a given temperature and as a function of temperature at a given frequency; i.e., the determination of the relaxation time of crystal deformation or orientation and its temperature dependency.
    The result of several experiments made on the crystal orientation of a medium density polyethylene has revealed the fact that the relaxation time of crystal orientation of the polyethylene is of an order of 0.1 sec. at 25°C., which is consistent with the frequency dispersion region of strain-optical coefficient of the polyethylene measured by Onogi et al. by means of the dynamic birefringence technique, and with the time dependent on the phenomena of low-angled light-scattering intensity measured by Erhardt et al. by means of the dynamic light-scattering technique.
    This technique may further serve for determining the rates of reversible strain-induced crystallization and reversible strain-induced crystal transitions and the rate of migration of crystal dislocations, twin-boundaries and stacking faults.
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  • Tomoharu YAMADA
    1964 Volume 13 Issue 135 Pages 965-969
    Published: December 15, 1964
    Released: June 03, 2009
    Twin-counter method different from the ordinary X-ray method of determination of residual stresses characterizes itself by the fact that the residual strains can be directly read out on the counting rate meter whose indication corresponds directly to a small shift in the position of an X-ray reflection line due to lattice strain.
    The Twin-counter consists of two semi-cylindrical G. M. counters which are symmetrically situated on both sides of a thin separator which serves as the common cathode. A beam of reflected X-ray from a specimen may be divided into two by this fine common cathode, and each counting rate due to the two inner counters may be adjusted by shifting the Twin-counter so that the out put of the differential rate meter connected to each counter becomes zero. Then, an out put of the counting rate meter corresponds to the position of an X-ray reflected line.
    Some experimental methods and examples for determinations of the residual principal stress and its distributions on the specimen surface are demonstrated by making practical application of such a character of the Twin-counter method.
    According to the basic principle of the X-ray method of stress measurement, the surface stress component σφ is given by the well known equation
    σφ=dp, ψ-d⊥/d⊥E/1+ν1/Sin2ψ.
    Now ψ is kept at constant different from the ordinary“Sin2ψ method”, while φ is changed as φ1, φ2, ……, φi, etc. by rotating the specimen around the axis normal to the specimen surface. Then, the following equation is obtained by subtracting σφj from σφi,
    σφiφj=dφi, ψ-dφj, ψ/d⊥E/1+ν1/Sin2ψ.
    If the value of (dφiψ-dφj, ψ) becomes maximum, the direction of principal stresses is the same as directions of φi and φj respectively. The angle in the direction of the principal stress, therefore, are found out from the experimental data with ease. If it can be estimated that one of the principal stresses σ1 is a tension or compression and the other σ2 is negligible small, σ1 is determined using the equation given above.
    Since the incident angle ψ is kept at constant during the experiment, the focusing circle in a back-reflection focusing technique does not change, and it does not change the irradiated area nor the depth of the penetration of X-rays in the specimen.
    For other applications of this Twin-counter method, the relative surface stress distribution may be continuously recorded by shifting the specimen.
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  • Hiroshi AIDA, Michio YAMAMOTO
    1964 Volume 13 Issue 135 Pages 970-977
    Published: December 15, 1964
    Released: June 03, 2009
    Generally, the results of X-ray stress measurement are influenced by surface conditions and material conditions. So two series of experiments have been carried out by the anothors using X-ray diffraction method with twin pole geiger-müller counter. First, the effects of surface conditions on the measured results have been studied to obtain the data on surface treating procedures. Then the reliability of measured values has been investigated for several heat treated materials to secure the possibility of industrial use of X-ray stress measurement. The results of above experiments are as follows.
    (1) It is important to flatten the specimen surface and to remove the plastically deformed layer that occurred due to the surface treatments, before the stress measurements was made by X-rays. It has been shown that the surface should not be more than JIS6S (as mild steel polished by emery paper #60∼100) in roughness, and that the plastically deformed layers due respectively to polishing by emery paper (#320∼#100), to grinding by portable grinder, and to machining by shaping machines, have depth of 30∼40μ, 140∼170μ and 60∼100μ accordingly.
    (2) Various heat treated materials including mild steel, 1Cr-1/2Mo steel and 21/4Cr-1Mo steel have been tested, and the effect of the profiles of X-ray diffraction pattern on the measured results has been investigated. It has been shown that the measured results become unreliable when the profiles of diffraction patterns become spotty, although the scatter of the measured results is small in the case of good profiles of diffraction patterns. And it has been found that the measured values of stresses become considerably reliable, even if the case of Kα doublets are in distinguishable, when the wider receiving slits are used.
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  • Fumiaki KANZAKI, Noboru NAWATA, Hajime KITAGAWA
    1964 Volume 13 Issue 135 Pages 978-983
    Published: December 15, 1964
    Released: June 03, 2009
    In this paper is described whether the X-ray stress measurement method can be employed for the skin-pass process control of cold-rolled steel strip by examining the relation between the reduction rate of the skin-passed steel strip and its surface residual stress measured by X-ray diffraction. We also examined the internal stress distribution of some kinds of skin-passed steel strip.
    Measurement were carried out using parallel beam X-ray with sollar slits, and a scintillation counter was employed as a detector. JIS, SPC-1, and SPC-3 grades of cold-rolled steel strip were used in order to measure the relation between reduction rate and surface residual stress, and the reduction rate were varied from 0.3% to 2.5%.
    For the materials undergoing the heaviest reduction, the diffraction angle differences from 2θ0 (2θ0: diffraction angle on φ=0) were measured and these values were plotted in the axis of the ordinate and the values of sin2φ in the axis of the abscissa. As the angle differences and the values of sin2φ showed a linear relation, we applied the two point method, usually called“Perpendicular-45°+η”method.
    For the skin-pass reduction, each residual stress showed a similar inclination on the surface of the steel strip. In the case of light reduction, residual stress becomes compression and, in the case of heavy reduction, it becomes tension. (cf. Figs. 3, 4 and 5).
    From the results of our experiments, we conclude as follows.
    The surface residual stress of skin-passed materials depends upon their“stress-strain curves” before rolling, especially upon the behavior of the neighboring part of yield-point. Therefore, if the X-ray stress measurement method is to be employed for skin-pass process control, it is considered necessary to grasp a full picture of the form of the stress-strain curve and check deviations from the typical curve. And it is also essential to keep the deviations as small as possible and to establish the relation between the skin-pass reduction and the residual stress on the materials having the typical curve.
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  • Yasunori MURAKAMI, Toshio KAWABE, Isao IWASAKI
    1964 Volume 13 Issue 135 Pages 984-991
    Published: December 15, 1964
    Released: June 03, 2009
    The accuracy of stress measurement by X-rays has been improved remarkably through recent years. Active researches have been conducted in many laboratories, and as a result the measured stress values have come to the stage of giving a sufficient reliability. However, there still remain some problems which must be further investigated.
    In this study, as one of the application problems, the authors took up the problem of welding residual stresses. In connection with this subject, a number of studies have hitherto been made. But there have been few works so far that dealt with the residual stress distributions measured by the X-ray method.
    The test piece used was a mild steel plate (SS41) with the dimension of 140×70×4.5mm, and two pieces were butt welded together under the groove angle of 75°by an ordinary A C arc welder, forming a specimen of square type. The welding consisted of two passes on the surface and one pass of reinforcing bead on the back.
    The X-ray stress measurement was carried out by the film method using the Glocker, s technique of vertical and 45°oblique incidences. At first, CoKα beams were used, but the diffraction lines showed a considerable broadening. Therefore, CrKα radiation was utilized, and in this case fairly sharp diffraction lines were obtained. The distribution curves of diffraction intensity were drawn by an automatic recording microphotometer. The peaks of these curves were determined, for convenience' sake, by the method of half breadth at the half height. The residual stresses were calculated by the following formula,
    The residual stresses were measured in two directions, parallel and perpendicular to the bead, at many points both on the surface and back, and the distribution curves of them were drawn. The results on the surface showed, in contrast to the ordinary results for the plate without a reinforcing bead, compressive residual stresses in the vicinity of the bead and tensile stresses near the edge in both cases of the measurements in the two directions. On the other hand, the results on the back were reverse to the above case. This effect of the reinforcing bead is worthy of note.
    For the measurement of welding residual stresses, the Gunnert method or the Mathar method has been widely utilized so far. Consequently, for the purpose of comparing the measured stress values, the Mathar method was also applied to the present specimens. The Mathar method consists of drilling a small hole in the sample and measuring the deformation around the hole. The drill used was of 6mm diameter, and for the measurement of strain four electric resistance wire gages with the gage length of 6mm were pasted on the specimen, each two being attached in the direction parallel and normal to the bead respectively. The calibration test was conducted a priori, and based on this result the residual stresses were calculated according to the formula given by Riparbelli. The Mathar method was applied, as before, to several points on the surface and back, and the results were compared with those of the X-ray method. The stress values obtained by the Mathar method showed a little scattering. On the whole, however, these values were a little smaller than those measured by the X-ray method. This result seems to be natural, since the stress value obtained by the Mathar method gives the average over the distance of the gage length in contrast to the local stress value measured by the X-ray method.
    Next, on the supposition of the stress repetition of an extremely low cycle as in the case of a boiler drum, the change in residual stresses due to the repeated stressing of a very low cycle was investigated. Another specimen with the dimension of 140×40×4.5mm, butt welded along the center line parallel to the short side of 40mm was prepared for this experiment.
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  • On an Explanation of the Diffraction Plane Dependence of the Change in Half-Value Breadth
    Shuji TAIRA, Kazuo HONDA, Takeji ABE
    1964 Volume 13 Issue 135 Pages 992-998
    Published: December 15, 1964
    Released: June 03, 2009
    In the previous papers, the authors have reported on the change in half-value breadth of diffraction line of (200), (310), (211) and (110) atomic planes in fatigue process by using CoKα radiation. It was found that the change in half-value breadth of diffraction line of (200) atomic plane was the largest, while that of (110) plane was the smallest, although general mode of the change in half-value breadth was quite similar. At the same time we studied the changes in residual stress and microstructure during fatigue process, and we considered qualitatively, on the basis of the experiments, that the change in half-value breadth was correlated to the slip mechanism of crystal in fatigue phenomena.
    In this paper, an interpretation is presented on the diffraction plane dependence of the change in half-value breadth, which is based on the idea that each crystal in the polycrystalline aggregates is particularly fitted for slip according to its orientation. In the discussion, it is assumed that the diffraction planes lie in parallel with the specimen surface according to the experimental condition of goniometer and that the X-rays diffracted by severely slipped crystals have large line broadening, while those by unslipped crystals remain as sharp.
    The orientation factor μ is given by
    where, φ: the angle between slip plane normal and stress axis
    α: the angle between slip direction and stress axis
    In order to get the mean value of μ of an atomic plane with respect to a slip system, μ is intergrated with respect to λ, where λ is the angle of the direction of the stress axis to the orientation of each crystal, that is,
    where, λ0=0, λn=2π
    Calculating μ of the atomic planes (200), (310), (211) and (110) with respect to each of the three slip systems {110}, {211} and {321}, and taking the maximum values of μ for each atomic plane, we have 0.482, 0.469, 0.460 and 0.435 for (200), (310), (211) and (110), respectively.
    On the other hand, the values of μ have been obtained by the graphical method. The distribution of the orientation factor μ has been determined on stereographic projection by the other author. The geometrical orientation of probable diffraction plane can be determined on the same figure as a trace of orientation. Using this figure, we can determine the distribution of μ along the trace of orientation. From this, we decided the mean value of μ for the aforesaid atomic planes at 0.485, 0.486, 0.484 and 0.436 corresponding to (200), (310), (211) and (110) diffraction planes, respectively. μ values determined by both the methods of calculation and graphical procedure are tabulated, and it is found that μ values are very close between both the methods. After all, we see that μ of (200) plane is the largest and that of (110) plane is the smallest. It is expected, therefore, that μ is one of the important factors which affect the diffraction plane dependence of the change in half-value breadth during the fatigue process.
    The above discussion is based on the observation of half-value breadth of diffraction lines from atomic planes parallel to the surface. It is probable that, if the above interpretation is right, the diffraction plane dependence for atomic planes not parallel to the surface would be different from the above observation. This has been proved by the experiment.
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  • Shigetsune AOYAMA, Hirohiko NAMIKAWA
    1964 Volume 13 Issue 135 Pages 999-1005
    Published: December 15, 1964
    Released: June 03, 2009
    In the first place, several statical tension and bending tests were carried out ranging from the elastic to the plastic with annealed specimens, and the surface stress and the half-value breadth were measured by X-rays at several steps of strain during and after the loading.
    Then, completely reversed bending fatigue tests ranging from high to low load were performed with annealed, pre-pulled and shot peened specimens. The residual stress and the half-value breadth were measured by X-rays at intervals during the fatigue process together with hardness measurement.
    The results obtained are as follows.
    1. In the statical tension tests, the residual stress was observed immediately after the nominal stress exceeded the tensile yield point, and the increase of half-value breadth or hardness started at the same time. In the case of bending tests, although the residual stress began to increase at the stress level near the tensile yield point, the increase of half-value breadth or hardness was not observed till the yield in bending took place.
    2. During the reversed bending tests under high loads, the initial residual stresses varied intensely in the first few cycles, and faded away prior to fracture in the case of pre-pulled as well as shot peened specimens.
    3. By the action of reversed bending under low loads, the initial residual stresses of pre-pulled specimens diminished with ease and faded away, but those of shot peened specimens decreased gradually according to the stress levels, and remained almost constant under the stress level of the endurance limit.
    4. The half-value breadth and hardness measured at intervals during fatigue process were found to keep a fairly good linear relation.
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  • On the Changes in Half-Value Breadth and Residual Stress of 6-4 Brass to Stress Cycles
    Kazuo HONDA, Junichi ARIMA, Tetsuro KONAGA
    1964 Volume 13 Issue 135 Pages 1006-1012
    Published: December 15, 1964
    Released: June 03, 2009
    In the field of mechanical engineering, the need for a simple but effective way of evaluating the fatigue strength and life of structural materials is an important problem with which the design engineers have faced. Accordingly, a considerable amount of investigations have been made in this field. However, the basic nature of fatigue damage and the conditions which lead to the initiation and propagation of fatigue cracks are not sufficiently understood. Nor any satisfactory method of assessing the exact state of fatigue damage has yet been found.
    In order to approach the problem of understanding the response of materials to various external forces, in this connection, the authors, considering it to be important to combine many fields of information, have investigated the fatigue damage of metals under various conditions of stress by employing the X-ray technique. Namely, the authors have studied the mechanism of fatigue of metals by observing the changes in half-value breadth, residual stress and micro-structure under constant and varying stress amplitudes with or without mean stresses. Some investigations1)∼3) have been performed to study the relation between the changes in half-value breadth and the number of stress cycles. They offered a certain interesting knowledge on the behaviour of materials under cyclic stresses and a reliable means for predicting the fatigue life in principle. In the other series of experiments, 4)∼6) the authors have made discussions on the changes in half-value breadth in relation to the basic mechanism of fatigue, and also suggested a noticeable information to attack the fatigue problem in the future.
    It is clear at present, however, that the values of half-value breadth and residual stress are affected by the type of internal stress state seriously.7)∼9) For example, in steel, the iron carbide (Fe3C) lamella in ferrite may be in equilibrium with the matrix under a certain condition, that is, when it is formed or annealed, but upon cooling to room temperature or by plastic deformation, extremely high-locked stresses develop in the surrounding matrix because of the difference in some elastic and plastic properties or in thermal expansion coefficient. Really, the presence of the so-called “Gefügespannungen”has been pointed out, and it is considered to be due to the difference in the yield stresses of the various phases coexisting in an alloy.10)∼12) Therefore, if we consider that the “Gefügespannungen”are caused by the progress of fatigue slips and the growth of micro-cracks in certain grains of the phase, they may contribute to the behaviour of line broadening and the state of residual stress in the fatigue process.
    For these reasons, in the present paper, the authors attemped to investigate the fatigue mechanism of metals containing the α- and the β-phases (6-4 brass) in relation to the“Gefügespannungen”, and carried out some experiments on the changes in the half-value breadth and residual stress due to stress repetitions using the (α+β) brass. The conclusions obtained are as follows:
    (1) The general feature of the changes in the half-value breadth of the α- and the β-phases during the stress repetitions is quite similar to that of the (310) diffraction lines, which was pointed out previously on annealed carbon steel.13) However, the (310) and (321) diffraction line widths of the β-phase show changes greater than any others, while those of (400), (420) and (331) diffraction lines of the α-phase are very small in the fatigue process.
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