In this paper, the new type X-ray apparatus for stress measurement is described, specially designed to measure the stress of the large unmovable samples.
After the light-weight measuring stand is set to the point to be measured, the X-ray tube head, which is completely balanced in weight for free setting, is fixed to the stand magnetically, so the setting action is very easy compared with a conventional apparatus.
This apparatus can be used as both the photographic method and the G.M. counter method, and the useful scanning diffraction angle 2θ is from 142° to 170° instead of 165° in a conventional one.
Designed to make it fit for use in the field service, the whole unit is mounted on one cart containing the cooling tank for the X-ray tube.

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For the X-ray measurement of the residual stress of hardened steel, as a consequence of line broadening, Koistinen proposed the necessity of using the correction factors such as the Lorentzpolarization factor and the absorption factor.
Examination of these correction factors was made, using the specimens freed from residual stress.
Comparison between strain gage measurement and X-ray measurement of applied stresses was also made. Methods of making the stress free specimens were:
(1) Hot bath quenching (to minimize transformation stress)
(2) Thinning of a massive plate by chemical polishing (to relieve residual stress)
(3) Magnetic separation of grinding chips of hardened steel.
As a result of experiments for stress free state, raw data showed compressive strain, while the data corrected for background and LPA showed zero and somewhat tensile strain respectively.
Under loading conditions, the strain measured by X-ray, regardless of correction factors, corresponded to the applied stress within the error of 10kg/mm². As a consequence, for measuring residual stress of hardened steel, it is enough to make merely the background correction, using (1+ν)/E=5.47×10^-5mm²/kg

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A stress-strain analysis of single cubic crystal is developed which utilizes the strain data supplied by the X-ray back reflection divergent beam method. The principal strains and their direction are determined, and the three dimentional stress-strain configuration is obtained from these data. The stored energy of the crystal is also deduced from a knowledge of the stress-strain configuration.
This analysis is applied to the study of the characteristics of various Cu-alloy crystals after various deformation and annealing process.

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There are many kinds of techniques in X-ray stress measurement, each of which has its own advantage for practical purposes.
But there has been no investigation made so far evaluating the accuracy of various techniques of X-ray stress measurement.
In the present report, the measurements about an identically pulled specimen on the diffractometer by different kinds of the counter methods were performed and their resolving powers evaluated, the maximum intensity to back ground ratios, d values and stresses were obtained.
The results are as follows:
(1) The parafocusing method has higher resolving power and more than twice the diffraction intensity by the parallel beam method.
(2) By the parafocusing method with a specimen fixed, good results are not obtained.
(3) In practice, the parallel beam method and the θ-2θ method of parafocusing have good agreements with the applied stresses.
(4) By the θ-2θ methods by means of the parallel beam and by parafocusing method more exact stress values are obtained, and especially in the case of the parafocusing method the automatic focus tracing apparatus is needed.

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The authors have carried out fundamental studies on the stress measurement by means of X-rays for the purpose of extending their application to practical engineering problems. One of them is for the improvement of the accuracy of stress measurement. In place of taking the shift of the peak position of diffraction profile for measuring lattice strain, the authors had previously proposed a new method of separation of Kα₁ component from Kα doublet using Fourier analysis for the improvement of accuracy of X-ray stress measurement for a sample with a broad diffraction profile. This method is characterized as being applicable to the measurement of peak position of diffraction profiles with various shapes including broad ones.
However, the numerical calculation of this method is exceedingly complicated because the Fourier analysis is introduced in the measuring process. For this reason, a convenient method has been devised for the measurement of stress, which is by measuring the center of gravity of Kα doublet without use of Fourier series, keeping on the advantages of above mentioned method, was proposed. The calculation of the center of gravity can be easily and quickly performed as compared with the previous case.
Moreover the effect of Lorentz polarization and the absorption factors on the measured stress should be also discussed in the case of the measuring sample which has a large amount of residual stress and shows a broad diffraction profile. From this point of view, the authors previously discussed the effect of both factors (LPA factor) and reported that these effects on the measured stress are remarkable when the specimen has a broad diffraction profile and a large amount of residual stress. However, the quantitative effect of LPA factor on the stress value should be known because the calculation at each measurement are very complicated.
In the present study, the authors discussed on the quantitative effect of LPA factor on the stress value by using the half-value breadth of Kα doublet as a parameter.
The following assumptions were used; (1) The intensity distribution curves φ₁(x)_LPA and φ₂(x)_LPA, which are corrected by LPA factor, obtained from Kα₁ and Kα₂ radiations, respectively, are represented by Gaussian distribution curves. (2) The following relation holds between φ₁(x)_LPA and φ₂(x)_LPA.
Φ(x)_LPA=φ₁(x)_LPA+φ₂(x)_LPA, φ₂(x)_LPA=kφ₁(x/Δx)_LPA,
where k is a constant, Δx is the distance between the peak position of the intensity curves diffracted from Kα₁ and Kα₂ radiations, and Φ(x)_LPA is the intensity curve which is corrected Φ(x) diffraction curve by using LPA factor.
If the intensity distribution curve φ₁(x)_LPA, the value of peak position and the half-value breadth are given, Φ(x) curve can be composed. The relation between the gravitation center of Φ(x) and the peak position of φ₁(x)_LPA, and between the half-value breadths of Φ(x) and φ₁(x)_LPA are obtained. Furthermore, when the stress value σ_1.LPA measured from φ₁(x)_LPA is given, Bragg's angle (peak position of φ₁(x)_LPA) can be calculated from the fundamental equation of stress measurement by means of X-rays and Bragg's equation. Therefore, the gravitation center of Φ(x) is calculated and then stress σ determined from Φ(x) is obtained.

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Beiträge des Instituts für Werkstoffkunde der Technischen Hochschule Aachen zur röntgenographischen Spannungsmessung aus den letzten Jahren wurden zu folgenden Problemen gegeben: Zur Kopplung der Einzelkristallite in einem vielkristallinen Haufwerk, zur Berechnung der orientierungsabhängigen vielkristallinen Elastizitätskonstanten von homogenen und heterogenen Werkstoffen, zur Entstehung und zur Ausbildung der sogenannten Gefügeoder Verformungseigenspannungen nach plastischer Verformung homogener und heterogener Werkstoffe.

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The X-ray diffraction techniques have remarkably been developed and have been recognized as a valid experimental means in the fields of both fundamental and applicational researches concerning the strength of engineering metallic materials. The techniques, however, have been mainly applied to the studies on the strength of steels and light metals, and hardly been applied to the studies on inhomogeneous metallic materials in spite of so much expectation being made in this line, for example to establish the method of X-ray stress measurement.
Cast iron, an example of inhomogeneous metallic materials, has graphite as a part of its structure, so that the deformation behavior is complicated and its mechanical properties are difficult to be defined, as compared with ordinary carbon steel. Many investigations have been made on the effect of graphite on the strength of cast iron. It has been considered that the strength of cast iron is mainly subjected to stress concentration effect around graphite and to decrease in effective cross sectional area due to graphite. However, the above idea has not yet been verified experimentally.
Cast iron is composed of three phases in the structure in general, which are ferrite, cementite and graphite. Therefore, it is advantageous to know the deformation behavior of each phase. The X-ray diffraction technique may be available for this purpose, since the diffraction line can be obtained from only ferritic phase.
As a series of the studies on the deformation mechanism of inhomogeneous metallic materials by the X-ray diffraction techniques, the authors propose to present in this paper a report of the investigations conducted on spheroidal graphite cast iron with pearlitic matrix. The changes in lattice strain during and after stress cycles on the tensile or on the compressive surface of the plate bending specimens were mainly measured.
Many interesting features were obtained from the experimental results, and the conclusions are as follows:
(1) The deformation behavior of test material is very complicated, and local plastic deformation appears in the matrix due to stress concentration effect and decrease in effective cross sectional area caused by graphite under even low tensile stress of about 10kg/mm². This plastically deformed area spreads with stress cycles until it reaches the limit.
(2) On the other hand, the deformation of graphite itself, the formation of voids around graphite, and the formation and opening of cracks during loading are also considered to make up the tensile deformation of cast iron in addition to the elastic and the plastic deformation of the matrix.
(3) In the case of compression, such characteristic features as in the case of tension do not occur.
(4) The X-ray elastic modulus of cast iron can be measured after 3 to 10 times of stress cycles with the same stress amplitude for an annealed specimen. However, it is necessary to investigate further on the possibility of using this modulus for different stress levels, especially for practical X-ray stress measurement on cast iron.

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It is well known that the mechanical properties of the iron castings are much affected by graphite in the ferrous matrix. Particularly, the apparent modulus of elasticity of the iron casting varies widely with the quantity, distribution, size and shape of graphite. By the X-ray diffraction method, the elastic strain near the surface of specimen can be measured non-destructively. The X-ray stress measurement, therefore, seems to be applicable to the study of the mechanical properties of iron castings. It is not clear, however, in case of X-ray measurement of iron castings whether the sharp diffraction pattern can be obtained or how the measured stress can be related to the applied stress.
The surface stresses of the plate specimens of gray iron castings with fine and coarse flake graphite and malleable iron casting were measured by X-rays, in tension and compression side respectively, at several loaded and unloaded steps in uniform bending. The relations between the nominal stress and the measured stress by X-rays were investigated with reference to the mechanical properties of iron castings.
Nominal bending stress and measured stress by X-rays showed linear relations, both in tension and compression side, till the nominal stress reached near the yield point or 0.2% offset point of statical tension or compression tests. In the case of gray iron casting with fine flake graphite or malleable iron casting, the measured stress by Co-Kα radiation well agreed with the nominal stress, where E=21000kg/mm² and ν=0.28. In gray iron casting with coarse flake graphite, the total surface strain of tension side extremely differed from that of the compression side, and the stress measured by X-rays was observed lower on the tension side and higher on the compression side than the nominal stress. The measured stress by Cr-Kα radiation always appeared to be a little lower than the stress by Co-Kα.

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The subject of inelastic buckling of columns and flat plates has been studied by several investigators.¹⁾ Residual stresses have considerable effects on the inelastic buckling strength of columns, and several researches have hitherto been reported on this problem.³⁾⁴⁾ Especially, Osgood made a clear analysis on the column with a simple rectangular cross section, assuming an ideally plastic material and an unfavorable distribution of residual stress, which showed a remarkable reduction of column strength.²⁾
The authors extended the analysis to the case of favorable distribution of residual stress, and also to the case of material with a linear strain-hardening characteristic. Although the analysis failed to give an explicit expression of the column strength, the column curves could be drawn by taking successively arbitrary values for the amount of spread of the plastic region. The theoretical column curves showed a noteworthy difference between the two cases of favorable and unfavorable distributions of residual stress.
Experiments were carried out to verify the analysis. Two sorts of materials, low and medium carbon steels, were used as specimens. The dimension of the cross section was 6×9mm, the length being variously changed to give the slenderness ratios from about 40 to 100. The specimens were tested in a special device prepared for this purpose. The transverse deflection as well as the axial diaplacement were measured by two dial gages, respectively. As the treatment introducing residual stresses, low temperature quenching (quenched from 700°C into ice-water) and machining by a shaper (depth of cut was 1mm) were adopted, of course, the former giving unfavorable and the latter favorable distributions of residual stress. The residual stress distribution was measured by the X-ray film method, using CrKα beams. Thin layers were etched off successively from both sides of the specimen, and the surface residual stress was measured each time by the sin²ψ method. The original distribution of residual stress was obtained by using the correction formula.⁵⁾ The experimental results showed considerably lower values as compared with the theoretical ones, due probably to the eccentricity of axial loading and the initial curvature of the column etc., however, a marked effect of residual stress distribution on the column strength was verified.

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The pulsating tension test by means of a Losenhausen type fatigue machine, (where maximum tensile stress is 35kg/mm², and minimum tensile stress is 4kg/mm²) was performed of the 50kg/mm² high tensile strength steel. And we measured surface residual stress at N=10⁵, 2×10⁵, 3×10⁵, 4×10⁵, 5×10⁵, 7.5×10⁵, 10⁶, 2×10⁶, 3×10⁶, breakdown, (where N means the cycles to fracture)
To determine the surface residual stresses, we used parallel beam X-ray diffraction method.
As our result, at the center of the specimen, the behavior of the surface residual stress relating to stress repetitions showed the resembled inclination as reported before by other authors using other fatigue machines.
The relations between the surface residual stresses and the stress repetitions of other grade of high tensile strength steels (especially, the tempered high tensile strength steels) remain to be confirmed hereafter.

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As part of the program of the cooperative researches sponsored by the Society of Materials Science, Japan, we have carried out the test in our laboratories in which the different heat treatments were performed for carbon steel and chrome-molybdenum steel, and the variation of residual stress and half-value breadth in the fatigue process was estimated. Among them, the test results on induction quenched materials are mentioned in this report. As for the variation of residual stress and half-value breadth, various test results had hitherto been reported from several laboratories. The final object of those researches as production makers is to grasp the fatigue process of real production parts, that is to say, to predict the break-down. Therefore we have continued for several years the basic tests for putting the X-ray residual stress measurement to practical use. As a result, it was found that it was difficult to predict the break-down of real production parts. Accordingly the other test method (Sonic test) was utilized jointly with the above mentioned method. Consequently we have attained to the following conclusions.
(1) Residual stress, when repeated stress is over the fatigue limit, varies rapidly at an early stage of fatigue, and, after that, does not vary remarkably until break-down. When the repeated stress is under the fatigue limit, nothing but variation of tolerance is observed.
(2) In the diffraction pattern photographed at the measurement of residual stress, obvious change of repeated stress, when it is over the fatigue limit, is observed before and after the fatigue test.
(3) The result of sonic test does not vary so remarkably at the early stage of fatigue, when the repeated stress is over the fatigue limit, that is different from the above mentioned residual stress. But when it approaches the fracture point, it varies suddenly. Also, when the repeated stress is under the fatigue limit, little variation is observed.
(4) The expected object of the present tests was achieved by the above mentioned results; As for the early stage of fatigue, the variation of residual stress and half-value breadth are measured by X-ray method. As for the final stage of fatigue, it will be concluded that it is possible to grasp the fatigue process and predict the fracture.
(5) Although the real production parts were not utilized for the basic test this time, it is expected that X-ray method and sonic test will be jointly used to observe the fatigue process of real production parts for the future plan.

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The mechanism of fatigue fracture in metallic material is thought to be independent of its initial condition in itself. In other words, a monotonously varing parameter, which represents the fatigue progress of material with any initial treatment, should be considered. Considering this, the authors intended to study on crystal deformation during the fatigue process of low-carbon steel specimens, which were treated in a different manner before the fatigue test, by means of the back-reflection X-ray microbeam diffraction technique because this technique made it possible to perform an quantative investigation on deformation of grain and subgrain distinctively.
In this publication, they dealt with the results of investigation on the fatigue process preceding the macro crack initiation of cold-rolled low-carbon steel specimens with different reduction percent. They were itemized as follow.
(1) The number of sharp spots in an arc diffracted from a grain increased and the intensity of its back ground darkness decreased relatively, as the fatigue process progressed. On the other hand, an arc diffracted from a specimen subjected to cyclic stress under the fatigue limit made no considerable change.
This was observed to de regardless to the reduction percent of cold-rolling.
(2) Simultaneously with the appearance of sharp spots in a diffracted arc, persistent slip bands came within the scope of an optical microscopic examination during the fatigue process.
(3) During the fatigue process the micro lattice strain range within one grain of a heavily cold-rolled specimen changed differently from that of a lightly cold-rolled one. In the former case it showed a rapid decrease in the early stage and then its diminution became gradual. On the contrary, in the latter case it increased abruptly first and it was followed by gradual increase.
The micro lattice strain range within one subgrain of lightly cold-rolled specimens tended to decrease with some fluctuation of first stage. While that of heavily cold-rolled ones showed an abrupt decrease in the early stage and then it made no considerable change.
(4) The subgrain size tended to be smaller and the total misorientation within one grain increased during the fatigue process, although those changes were not outstanding.
(5) Crystal deformation differed from grain to grain in the degree of its progress during the fatigue process.
In the next publication, models of crystal deformation during the fatigue process are to be proposed and the mechanism of fatigue fracture of cold-rolled low-carbon steel specimens is to be discussed in relation to the case of annealed ones, being based on the above-mentioned results.

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By the use of Soller slit in the primary beam and a line source of characteristic X-rays, the X-ray diffraction microscopy is extended to allow the detection of imperfection in a crystal lattice. A Soller slit creates a set of virtual X-ray sources. A large number of rays cross at the center of each cell, so that the vertically divergent beam emerging from each cell may be said to issue from the virtual source located at the center of each cell. At the same time the rays are diverging horizontally from the actual source, so that the virtual source is actually a short horizontal line through the center of each cell, there being one virtual source for each cell of the Soller slit.
This technique has the advantage of allowing the diffraction patterns from distorted and undistorted region in a crystal lattice to be recorded on the large surface by taking a single photograph.
This new technique is applied in the present investigation to a study of the deformation of aluminium single crystal, and it is revealed that the clustered slip regions are rotated relative to matrices after tensile deformation.

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Cheap, mass-produced rigid PVC can serve as substitute for metals and its applications as pipes are steadily increasing.
The fatigue strength of rigid PVC pipe under simulated service conditions has been investigated, and the characteristic of its deformation studied by X-ray diffraction. The following results have been found;
(1) Like that of other high polymers, the fatigue strength of rigid PVC depends on the temperature. Its notch-sensitivity under fatigue is affected by its shape and loading stress.
(2) The characteristic of its deformation can be quantitatively evaluated by annealing the material at various temperatures before and after the working, taking note of its diffraction halo every time by exposing the material to the characteristic X-rays, and thereby comparing the changes in diffraction halo corresponding to the changes in the annealing temperature.
Through microstructure investigation of tensile deformation and fatigue deformation by this method, it has been confirmed that these deformations, just like those in metals, have different characteristics.

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The shadow image technique was applied to the measurement of the current density distribution, and the power density and the minimum spot diameter in the focal point of the electron beam was calculated. The actual microfocus X-ray unit was established on the basis of the theory of the telefocus electron beam one-step reducing technique. The electron beam traces emitted from the telefocus four-pole electron gun of the unit were obtained by means of a copper plate contamination technique. The power density and the minimum spot diameter on the target were measured, which met the requirement of the microfocus unit, which features large current capacity and sharp-current density distribution.
In the case of in-focus, current density distribution increased in inverse proportion to r^4/3 and spherical aberration of the reducing lens relates to a form of distribution. Power density around the least confusion circle approximates 10⁵W/mm².
The minimum diameter of the X-ray source was estimated at 10μφ, and the spot size of an electron beam was considered smaller because there was back-scattering.
Because the outside diameter of the unit around the focus point was lessened and the X-ray outlet could be located near the X-ray source by employing the long-focus magnetic lens (f: 13cm) in the tele-focus electron gun of the actual unit, efficiency as an X-ray source was improved far better than those of other X-ray units.
The application for the crystal structural analysis of single crystal plates through the divergent X-ray beam radiated from the X-ray source of 10 microns in diameter were indicated with some examples.

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