Previously we had introduced an X-ray stress measuring apparatus to be used in field service, specially designed to measure the stress of large unmovable samples or abnormally shaped samples. To follow this up we have completed its development in designing a goniometer to make it possible to test or examine its stress measurement.
The goniometer is designed to make precise measurement taking the following errors into account.
(1) The error of the sample positioning.
(2) The mechanical errors of the goniometer itself.
(3) The fluctuation of the X-ray output.
(4) The statistical fluctuation of the GM counter and the data of the measurement by this apparatus have in proved its precision percentage.
In this paper particular accounts are given of the X-ray goniometer for measurement of stress.
The distinctive features of this apparatus are mentioned below:
(1) The positioning of the sample is easy.
(2) It has precise mechanism.
(3) The parallel beam method is adopted.
(4) It is applicable to simultaneous measurement both by the film method and by the GM counting method.
(5) A slender X-ray tube extends the range of making effective scanning of angles.
(6) This apparatus can be connected to the X-ray diffractometer.
Some errors are estimated in the measurement of assumed conditions in this paper.

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In this paper, report is made it the pulsating tension tests which were performed by means of a Losenhausen type fatigue machine of the 80kg/mm² tempered high tensile strength steel.
On each of them, two sorts of specimens were tested; the specimens whose surface was smooth, and the specimens with 3mmφ hole (α=2.8).
We measured the surface residual stress at N₅=10⁵, 2×10⁵, 3×10⁵, 4×10⁵, 5×10⁵, 7.5×10⁵, 10⁶, 2×10⁶, ……, break-down, or 2×10⁵, 4×10⁵, 6×10⁵, 8×10⁵, 10⁶, 2×10⁶, ……, break-down, (where N means the repetition number).
To determine the surface residual stress, we used the paralell beam X-ray diffraction method.
As the result, on 80kg/mm² tempered high tensile strength steel, the surface residual stress of the specimen little varied, whether break-down or not.
In the case of break-down, the reason why the surface residual stress scarcely varied, is considered as follows; (1) the work hardening coefficient is smaller, (2) carbides' configuration and their distribution in steel are different from others, (3) phase difference from other steels (that is, tempered martensites is much more than ferrite.).
The half value breadth of the profile became larger in the neighbourhood of the break-down repetition numbers.

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The X-ray radiation area is required to be small so as to measure the X-ray residual stresses of rolling surface of ball bearing, balls and rollers. In this case, photo method is more effective than the counter method.
Quenched bearing steel presents greatly diffused diffraction pattern, however, so that it is difficult to measure the X-ray residual stresses with high reliability. In order to improve the reliability of X-ray stress measurement for accuracy in the photo method, we have investigated on factors of the error in the photo method. In the photo method, remarkable factors which reduce reliability for accuracy exist in the X-ray photographic technique.
One of them is an error induced during the determination of the center of diffraction ring. Another problem is difficulties of determining representative position from intensity curve for its broadening.
On the correlation of the X-ray and the mechanical stress and reproducibility of the X-ray stress, we investigated the effects of three methods in which the center of diffraction ring is to be determined. They are as follows:
(1) a method in which the center of punch hall is assumed to be the center of diffraction ring.
(2) a method in which tin powder is used as standard specimen.
(3) a new method invented by the authors.
A new method that the same half-round of diffraction ring is twice exposed on a film rotated at the angle of 180 degrees between the first exposure and the second, named "Twice Exposure Photographic Method", has great effect on improving the reliability of X-ray stress measurement.
It shows only ±3kg/mm² scattering in reproducibility and correspondence to the mechanical stress, although other two methods shows ±8-15kg/mm² in measuring quenched bearing steel.
Considering these results, two factors previously mentioned are really important and are eliminated by our new "Twice Exposure Method".

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The residual stresses of the hardened high carbon steels are very sensitive to grinding processes, and the stress gradients near the ground surface are found to be very steep. In the suitably ground surfaces of middle carbon steels which are case-hardened by the high-frequency induction heat treatment, there is no appearance of the tensile residual stress, but under the unsuitable grinding conditions, tensile stresses are discovered at about 10 to 30μ depth under the ground surfaces. These residual stresses can be satisfactorily measured by the X-ray diffraction technique, on successively electropolished surfaces.
However, the penetration depth of X-rays must be taken into consideration because the stress varies in the distance of X-ray penetration. With Cr-Kα-rays the very thin surface stress could be determined, because they are heavily attenuated in steel. With more penetrable X-rays, Co-Kα, Fe-Kα and Mo-Kα, the measured stresses are influenced by the steep gradient of stresses. These relations are discussed theoretically and experimental results using Fe-Kα and Cr-Kα are compared, and it is shown that the 2θ-sin²ψ plot for Fe-Kα is not in a straight line because of the stress gradient.
It is discovered that these facts can be utilized for the non-destructive measurement of tensile stresses whick may be existent just under the unsuitably ground surfaces. In the usual method the stress is measured on the electro-polished surface and it gives some failures to the precisely ground surfaces, but using the more penetrable X-ray, Fe-Kα, the stress under the surface is estimated from the non treated surface.

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It has been generally accepted that X-ray stress measurement of very coarse polycrystalline materials is difficult because of their spotty X-ray diffraction patterns.
In this paper, we propose to discuss the θ-2θ and the fixed specimen method, and verify experimentally which method is more profitable for measuring stress of the specimen with very coarse grain.
The results obtained are as follows:
(1) The fixed specimen method is inadequate for coarse polycrystalline materials.
(2) By the θ-2θ method it is ultimately possible to measure accurately the stresses on materials having such a large average grain size as 200μ.
(3) The experimentally obtained X-ray elastic constants E/(I+ν) are almost invariable for materials having average grain size from 5μ to 120μ.

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It is well known that the internal stress in electrodeposited metals is varied by the electrolytic conditions and the internal stress effects on some properties of the electrodeposited metals.
Therefore, it is important to measure the internal stress in electrodeposited metals. Hitherto, many workers have developed the methods to measure the internal stress in electrodeposited metals. The principles of those methods are based on the measurement of deflection of a thin strip or a spiral helix which is electrodeposited on the one side. These methods do not give a direct information on the lattice deformation in electrodeposited metals.
The X-ray diffraction methods are expected to give more exact information on the lattice distortion in electrodeposited metals. Recently, a number of X-ray diffraction methods for stress measurements have been developed in the field of the testings for metallic materials. The authors applied these X-ray diffraction methods to measure the internal stresses in electrodeposited chromium. In order to measure the internal stress of the first type (macro stress) in electrodeposited chromium by Sin²ψ method, the authors modified an ordinary diffractometer to be fulfilled the following conditions: (1) the specimen axis can be fixed at an arbitrary angle, the receiving slit and the GM tube being made to scan. (2) the receiving slit and the GM tube can be slided precisely to the focusing point in the radial direction of the goniometer which corresponds to the value of ψ₀. The errors in this stress measurement which is apt to be caused by the sliding of the receiving slit and the GM tube were determined at 2θ=0°, and the influence of deviation in the position of the receiving slit from the focusing point on the measured value of stress was discussed by measuring the stress free iron powder. In measuring the internal stress of the second and third type (micro strains) in the electrodeposited chromium, the half-value breadth of several diffraction lines were measured by using Cu-Kα radiation and Hall's equation was applied to determine the micro strains.
The chromium was plated on annealed copper plate from a bath containing CrO₃:250g/l, H₂SO₄:2.5g/l and current density was 60A/dm². The range of thickness of the deposits was from 10 to 30μ.
From the experimental results, the following conclusions were derived.
(1) It was confirmed to be possible to measure accurately the internal stress of the first type by using the modified diffractometer.
(2) It was found that the internal stress of the first type in electrodeposited chromium measured by Sin²ψ methed on (211) diffraction line with Cr-Kα radiation was tensile stress at bath temperature range of 40-65°C, and the stress decreased with increasing bath temperature, and above 70°C the stress was compressive stress.
(3) The half-value breadth of (211) diffraction line with Cr-Kα1 radiation decreased with increasing bath temperature from 40°C to 75°C.
(4) It was found that the internal stress of the second and third type was a maximum at bath temperatures of 40-50°C. This tendency corresponded to the results of deflection obtained by a thin strip contractometer which showed a maximum value at bath temperatures of 40-50°C.

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The heat-treated materials have residual strains both "micro" and "macro" coexisting in them. The residual stress must generally be measured either by the X-ray method or by the cutting method with the use of a wire strain gage. It is necessary that the mutual relation of the residual stresses respectively obtained by these two methods will be made clear. There are but few data, however, as have so far been hitherto collected with this requirement in view, about the property of residual stress of heat-treated materials. A report is presented in this paper of the measurement of the residual stress variation on the surface of the induction hardened steel, both by the X-ray method and also by the cutting method with the use of the strain gage.
It has consequently been made evident that there is complicated mutual relation between the "macro" residual stress and the "micro" residual strain, and that the difference in the residual stress value when the stress is measured by the X-ray method from what it is when the stress is measured by the cutting method with the use of the strain gage comes from the "micro" residual strain. The effect of the difference is remarkable when there is larger "macro" residual stress. When the residual stress value of the induction hardened materials is measured by the X-ray method, it is important that the effect of the "micro" strain variation on the "macro" residual stress will be taken into consideration.

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Residual stresses of considerable magnitude are generally introduced near the surface layers of machine components by the machining operation. These residual stresses are deleterious from the standpoint of precise finishing, and also have some effects on the fatigue strength. Therefore, the measurement of these stresses is an important subject for machine manufacturers. Several studies have been reported concerning the residual stresses produced by the machining operation, such as turning, shapering, milling and grinding etc^1)-3).
In this study, the surface residual stresses due to the milling operation were measured with X-rays under several conditions such as the cutting speed, the feeding and the depth of cut. Flat plate specimens of a low carbon steel and a high tensile strength steel were used, and one surface of the specimen was cut with a plain milling cutter of 25° spiral angle under the cooling action of oil lubricant. The X-ray apparatus used was of parallel beam type with GM counter, and CoKα beams were used throughout this experiment. The residual stresses were measured by the sinsin2ψmethod in the cutting direction as well as in the transverse direction. The distribution of residual stress near the surface was examined by etching off a thin layer successively from the machined surface and by utilizing the correction formula⁴⁾. The changes in the half-value breadth due to successive removal of surface layers and in hardness were also investigated.
The conclusions obtained in this study may be summarized as follows. The increase in the cutting speed has the effect of decreasing the tensile residual stress, on the contrary, the increase in the feeding exerts such influence as to raise the residual stress toward the tension side. On the other hand, the residual stress tends to maintain nearly a constant value despite of the increase in the depth of cut. The region of monotonous decrease in the half-value breadth and hardness which may be considered to represent the domain of deteriorated surface layers⁶⁾, was in approximate coincidence with the range in which the residual stress distribution showed a remarkable change.

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The residual lattice strains in plastically extended polycrystalline iron and steels have been measured using X-ray diffraction methods, and their 'surface effect'⁵), 'plane dependency, ' that is, the difference of the stresses measured from the peak shift of diffraction lines for various planes using different X-ray wave lengths, and 'Gefugespannungen'⁶) have been quantitatively discussed.
The chemical composition of materials and the shape of specimens are shown in Table I and Fig. 1. The grain size of pure iron is about 150-200μ. Steel 1 is a tool steel which has the lamellar pearlitic structure. Steel 2 is the high carbon chrome steel (SUJ 2) which has the spheroidized pearlite. The results reported here are summarized as follows:
(1) In every case, the changes in lattice constants are found to be approximately linear with sin²ψ, and the scatter about the straight lines is small. There is no evidence within the range of the experimental error to confirm that this is the effect of the second kind of lattice strains¹⁰⁾ or others¹¹⁾¹²⁾.
(2) The 'plane dependency' is not sufficiently explained by the correction of the elastic constants attributing it to the elastic anisotropy.
(3) In the case of the pure iron, the 'surface effect' is clearly seen. It disappears as the specimen is thinned by electropolishing till it is about 0.2mm (Fig. 11).
(4) The 'plane dependency' of the residual stresses has been recognized in the case of pure iron (Fig. 4-11). Especially, it is recognized that the stresses for the (220) planes are tension, but the stresses for the (310) planes are compression in the range of initial deformation or in the interior of the specimen prestrained. The effect of 'plane dependency' for the (211) planes is small.It is conceivable that the stresses obtained for the (211) planes are nearly comparable to the mechanical stresses when 'Gefügespannungen' are neglected.
(5) It is considered that the residual stresses produced by the plastic deformation may be explaned by three processes, that is, the 'surface effect', the 'plane dependency' and Gefügespannungen'.

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In the field of mechanical engineering, the materials which commonly have been used are alloys that consist of many phases. It may be easily imagined that each phase of them shows the extremly complicated deformation under applicated stress. Thus, the external strain of the specimen is the mean value of the strain in each phase. In order understand the responses in each phase of the material to externally applied stress, the authors have adopted two phase alloys, (α+β) brass which is the simplest of them. Noticing the α-and β-phases, they have made study of (α+β) brass, and put particular emphasis on the change in the half-value of X-ray diffraction line during the fatigue process. To make clear the character of mechanism of crystal deformation in fatigue, the change in the diffraction line widths on a few lattice planes has been examined. Such examination has also been attempted during the plastic deformation process.
From those experiments results the following have been obtained.
(1) (310) and (321) diffraction line widths in the β-phase are greater than those of (400), (420) and (331) of the diffraction lines in the α-phase under the fatigue and stretching processes.
(2) In order to account for the crystal lattice plane dependency of the diffraction line widths in the α-phase, the authors have adopted an idea of the orientation factor which is calculated for each lattice plane. It is found in consequence that during the tensile deformation the crystal plane dependency of the changes is sufficiently accounted for by the values of the orientation factor, while during fatigue process it is accounted for by them and the effects of the crack initiation.
(3) The change in the residual stress of the α-phase due to stress repetitions show the same behaviour as those of plain carbon steel; the compressive residual stress appear in the first stage of fatigue and then decrease abruptly. On the othor hand, in the β-phase of the same material the tensile residual stress is generated in the first stage of fatigue, and in the second stage it decreases steeply. Thereafter no change occurs.
(4) In the observation of slip markings in the α-phase by means of optical microscope, it has been found that they are intensified gradually with increase in the number of stress repetition, while in the β-phase, no obvious slip phenomena has been observed.
Further, in pursuing those investigations, the authors have adopted back-reflection X-ray micro beam and electron microscopy techniques.
The information on fatigue mechanism supplied by the study of change in the half-value width as mentioned above gives us many suggestions on the change in micro-structure of materials under fatigue process. It is necessary to direct the light on the micromechanism because of such local nature of fatigue mechanism. The half-value breadth read from the diffraction lines taken by the ordinary beam is inevitably the mean value of radial breadth from many crystal grains and its variation includes various physical factors, although it has many advantages for detecting fatigue damages that have been observed in cyclically stressed materials.
In the present study, it is intended to apply the back-reflection X-ray micro beam technique to the observation of each crystal grain of material during fatigue process, in order to interpret the change in the half-value breadth under fatigue process of (α+β) brass.

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It is considered that the process of fatigue fracture could be arranged the three classes, i.e., crack initiation, crack propagation and fracture. Of these the second process is important from the following point of view.
(1) As has so far been reported in many publications, the importance of crack propagation process in total fatigue life increases in proportion to the increase in the stress concentration factors.
(2) The non-propagating crack is out of all consideration so far as is concerned.
Summarizing the studies that have so far been made relevant to the propagation process under cycling stress, it may be divided into two classes. (1) The macroscopic approach concerning the relationship of the velocity of crack propagation and the applied stress. (2) The theoretical approach which deals with the analysis of the modelled mechanism of crack propagation.
Neither the macroscopic nor the theoretical approach is adequate, however, to give full accounts of such phenomena as crack initiation and crack propagation.
For this reason studies on the crack propagation in the course of fatigue process have been made from the microscopic point of view by Holden, Grosskreutz, McEvily, Wood, Taira, at al., using the electron microscopy or the back-reflection X-ray micro beam techniques.
Holden reported the relation of the crack length and the extension of plastic region at the tip of the crack. Grosskreutz, Wood and Taira revealed the relation of the mechanism of the crack propagation or the fatigue fracture and the substructure surrounding the tip of the crack.
But as the direct observation of the crack tip is very hard even by means of electron microscopy technically, there have been but few observations so far published on it.
Considering it, the authors have intended to study on the crystal deformation at the tip of the propagating and non-propagating cracks during fatigue process of pure copper and low carbon steel specimens with notches by means of electron microscopy and the back-reflection X-ray micro beam diffraction technique. The electron microscopy technique has been used to obtain the qualitative information on the subject, and the back-reflection X-ray micro beam diffraction technique has been used to perform quantitative investigation on it.
The synopsis of this paper is as follows;
(1) Cracks started in the trace of the slip stratum, and eventually spread along the persistent slip band. Non-propagating cracks stopped at the first grain or its boundary.
(2) The extension of the plastic region ahead of the propagating crack tip observed by the electron microscopy is larger than that of non-propagating crack.
(3) The quantitative investigation by means of the back-reflection X-ray micro beam diffraction technique points out that the value of the micro lattice strain and of the misorientation ahead of the propagating crack tip decreases steeply at the place about 0.2mm of distance from the crack tip. This value is equal to that ahead of the non-propagating crack tip.
(4) The plastic region at 0.2mm of distance from the tip of the propagating crack correlates well with the place at the tip of the propagating crack observed by means of replication electron microscopy.

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Recently, tufftrided steel is widely used as the structural material of machine parts since it has many advantageous properties such as high fatigue-resistance and wearing-resistance and, further, shortening the treatment time as compared with that of the conventional nitriding. It is generally known that the improvement of fatigue property depends on the cause of the residual compressive stresses the intermetallic compound and the diffusion layers near the surface and the increase of hardness. However, the degree of contribution of these factors to fatigue property is not clear.
From this point of view, as a part of studies in series on the fatigue fracture of the tufftrided steel, the authors have carried out in this present study several investigations on the residual stresses in the tufftrided steel using the improved X-ray diffraction technique.
The specimen used in this investigation was a S15C low carbon steel, and as was the case with all specimens, was annealed after forming and then tufftrided. The composition of salt bath far tufftriding was composed of 46.8%-KCN, 45.5%-KCNO and 0.05%-Na4Fe(CN)6. The temperature of this salt bath was kept at 570°C and the specimen was water-quenched after soaking in this salt bath for 90 minutes. By this treatment, the intermetallic compound layer composed of ε-Fe3N with thickness of about 7μ and the diffusion layer of 0.8mm thickness was formed on the surface layer and its neighbouring layer of the specimen.
As the examination process, the residual stress distribution was first measured by means of X-rays as well as mechanically for the purpose of observing the nature of the residual stress in the tufftrided steel. Then the change in residual stresses due to alternating stressing was observed and the contribution of residual stresses to the improvement of fatigue limit was discussed.
The results obtained in this study indicate interesting features as follows:
(1) The strength of steel, especially in fatigue property, has been remarkably improved by trufftriding and quenching. However, it decreases if nitrided materials have been precipitated in the diffusion layers by tempering. For this reason, the water-quenching should be performed as quickly as possible after tufftriding in order to prevent their precipitation.
(2) During the measurement of residual stresses in tufftrided steel by means of X-rays, the macroscopic residual stress itself has been observed. Almost all residual stress in tufftrided steel is influenced by the thermal stress by water-quenching and the residual stress induced by nitriding is small.
(3) No change in residual stress of surface layer has been observed during the fatigue process. It is considered that this non-fading property is a character of tufftrided steel.
(4) The degree of contribution of residual stresses due to cyclic stressing is about 30%. It is considered that the factors such as diffusion layers and the increase in hardness give more effective contributions.

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Fatigue fracture occurs in any kinds of engineering materials, cold-rolled ones, heat-treated ones, etc. It is considered to be very significant to find out a monotonously varing parameter which represents fatigue progress of these materials, in understanding the mechanism of fatigue fracture as well as in the prediction of fracture by fatigue. For this purpose, the authors have set about a series of studies on microstructural change during the fatigue process of low-carbon steel specimens, which are treated in different manners before fatigue test, by means of back-reflection X-ray microbeam diffraction technique. In the previous papers, the fatigue process preceding macro crack initiation of annealed or cold-rolled specimens was investigated.
In this paper, the specimens were initially quench-aged and fatigue process preceding macro crack initiation of these specimens was studied. It was intended to find out the feature characterizing the fatigue process in three kinds of materials, the annealed, the cold-rolled and the quenchaged steels and their features are briefly described in articles (1)-(4). The causes for the increasement in fatigue strength of quench-aged steel was discussed and the results are summarized in article (5).
(1) In the early stage of fatigue process, the micro lattice strain range within a grain changes notably. The total misorientation β increases while the subgrain size t decreases rather slowly. As fatigue proceeds, the micro lattice strain range within a subgrain decreases and t continuous to decrease more slowly, although β takes nearly constant value. The width of subboundaries are narrowed. As macro crack initiation is coming near, the changes of these quantities begin to diminish. Therefore, the rearrangement of dislocations to develop substructure is a chracterizing feature of the later stage of fatigue process.
The degree of the development of substructure can be used as one of the crystallographic parameters which express the degree of progress in "fatigue damage" of cyclically stressed specimens with any initial state.
(2) Excess dislocation density in a subgrain at the number of stress cycles of macro crack initiation takes the small value of 2-5×108 lines/cmcm2. The amount of increase in excess dislocation density at subboundaries during the fatigue process till crack initiation is of the same order notwithstanding the variety of initial state.
(3) During the fatigue process of specimens cyclically stressed above fatigue limit, well-developed substructure is observed in severely deformed grains at the same stage as the appearance of persistent slip bands. A crack takes place, at last, at the place of some persistent slip bands. On the other hand, the diffraction patterns reflected from grains without persistent slip bands do not show a notable difference from the initial patterns. From these points of view, it can be said that well-developed substructure plays an important role in crack initiation.
(4) The degree of fatigue progress in cyclically stressed specimens is observed to differ from grain to grain, even if these grains are located in the same irradiated area of X-ray microbeam. This implies that there is no remarkable interaction between the adjacent grains, at least until the macro crack initiation of high cycle fatigue.
(5) The structural causes for the improvement in fatigue strength are listed as follows; the initial locking of dislocations, the highness of frictional stress and the rapidness of work-hardening rate. These facts reveal the difficulty of dislocation movement mainly in the early stage of fatigue process.

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It is well known that X-ray diffraction breadth varies with stress cycles. Let the variation of breadth be designated by y=b/B-1, where b is breadth after any number of stress cycles, and B is its initial value. In order to analyze the fatigue process, the equation for the breadth variation was introduced by the authors. The equation is constructed with two parts. One expresses a quickly increasing part of breadth in early fatigue cycles, and corresponds with workhardening process. If the variation is denoted y1, the equation is as follows where k1 and m1 are constants, n is the number of stress cycles, σ1 is designated as σ1=σ-0.7σw, σis the stress amplitude and σw is the endurance limit. The other one expresses the slowly increasing part of that over the whole fatigue life, and it corresponds with fatigue damage process. If the value is denoted y2, the equation is as follows where k, A, D and m are constants. S-N curve can be represented with the following equation under constant amplitude loadings.
The constants A, D and m are the same as those mentioned above, and can be determined from the fatiguc tests. The variation of breadth y is represented with sum of y1 and y2.
The tested material was 0.10%C steel which was annealed at 700°C for 2hr. For the X-ray apparatus CoKα line was used. The distance between the specimen and the film was 70mm.
In the present experiment, when the variation of breadth increased until y=0.19, the material fractured in the case not only of constant amplitude test but also of sinusoidally varying amplitude test. The measurement values and calculated curves agreed well with each other.

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The diffraction patterns obtained by the back reflection divergent X-ray method are analogous to the well known Kossel patterns, in which each ellipse consisting of Kα₁ and Kα₂ lines corresponds to the definite set of (hkl) planes. Crystallographic orientation may be determined rapidly and exactly with these pseudo Kossel patterns compared with the ordinary X-ray technique.
The diffraction line is indexed by measuring the following Parameters; (1) the distance between the doublet on the film and the two consecutive film positions in the multiple exposure technique; (2) the length of the major or the minor axis in an ellipse and the specimen-to-target and the targetto-film distances.
The crystallographic orientation of a specimen can be determined to an accuracy of the order of 0.01° by measuring the parameters of more than two sets of (hkl) planes.

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The behaviour of the individual grain and that of the inside grain of the specimen deformed by tension were investigated by the back reflection divergent X-ray beam method, to confirm their correlation with the behaviour of the specimen as a whole.
Coarse-grained polycrystalline plate specimens of low carbon steel were prepared by the strainannealing method. The grain sizes of the specimens were about 1.7, 7 and 5mm for sample A, B and C respectively.
The horizontal type capillary X-ray tube apparatus (Rigaku Denki make) was used to obtain Fe-Kα radiation.
First, to examine the structural change of crystals, pseudo-Kossel patterns were taken with the samples A and B at several stages of strain after the load were removed. Stresses and strains of specimens were also measured simultaneously to provide the nominal stress-strain diagram.
Then, the relative lattice rotation was examined in an unstrained and strained state at two different positions in a grain with sample C.
It was observed that the pseudo-Kossel patterns became irregular with deformation, showing local line broadening, kinking and shifting, when the specimens were stretched over the proportional limit, and that the diffraction lines broadened as a whole in the state of greater deformation.
In the range between the proportional limit and the stress level at which linear hardening in the load-elongation diagram started, the kinking, shifting and broadening of the diffraction lines increased.
When the specimen was deformed by tension, the relative lattice rotation was observed at two different positions in a grain, in the early stage of plastic deformation.
In the stress range corresponding to the linear hardening, most diffraction lines of the obtained pseudo-Kossel patterns showed kinking, shifting and broadening, irrespective of the kinds of latticeplane.
It was seen from these results that in the load-elongation diagram, the curved range between the proportional limit and the stress level at which linear hardening started was caused by the fact that the load elastically supported by individual grain or different part of a grain was different from each other.

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Cast iron is taken as a typical example of inhomogeneous metallic materials. It has graphite in its structure and its complex structure causes complicated deformation mechanism in microscopic scope during loading. However, the mechanical behavior of cast iron has not been sufficiently interpreted in terms of microscopic mechanism of deformation. Because of lack of usable information, the designing of machine parts made of cast iron is obliged to follow so-called experience, although various sorts of cast iron are widely used in engineering equipments and machines.
In the present paper, it is intended to elucidate the microscopic deformation mechanism of cast iron by observing the relation of macroscopic deformation behavior, which is determined by tension and compression test, to the deformation characteristics of atomic planes of ferritic matrix observed by X-ray diffraction technique.
The deformation behavior of spheroidal graphite cast iron with pearlitic matrix was discussed in the previous paper on the basis of lattice strain measured by Co-Kα radiation and the change in half-value breadth. In the previous investigation, the local plastic deformation in the matrix around graphite and the reduction of the effective cross sectional area caused by graphite were observed even under low tensile stress. It was reported, moreover, that the X-ray elastic modulus of cast iron was measured with confidence after 3 to 10 stress cycles for annealed specimens.
This paper is to present the results of the further experiments, and it is a supplement to the previous investigations. The crystal plane dependence of lattice strain or elastic constants of spheroidal graphite cast iron with pearlitic matrix is observed by using Co-Kα and Cr-Kα radiations.The difference of deformation behaviors between the spheroidal and the flake graphite cast iron has been studied by employing the X-ray method as well as the optical microscope. The X-ray elastic constants for stress measurement on cast iron are also calculated from the obtained results.
The following conclusions have been obtained:
(1) The characteristic deformation behavior of spheroidal graphite cast iron reported in the previous paper is confirmed again by Cr-Kα measurements and by the observation with optical microscope.
(2) The crystal plane dependence of lattice strain occurs under stress more than about 15kg/mm² for spheroidal graphite cast iron with larger values of lattice strain on (310) planes than those on (211) planes.
(3) Spheroidal graphite cast iron have almost the same deformation mechanisms as flake graphite cast iron in substance. That is, the formation of cracks is made in the matrix by means of high stress concentration effect.
(4) For the X-ray elastic constants of cast iron, the values should be used as they are obtained by submitting an annealed specimen to 3 to 10 stress cycles.
The elastic constants obtained by the X-ray method is different from those obtained by the mechanical method. And there is great difference in value between cast iron and iron or steel. Therefore, much caution should be taken in estimating the elastic constants in the X-ray stress measurement on cast iron.

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Hardness value is taken as one of the most important fundamental characteristics of materials. It has been reported, however, that the hardness of metals is influenced by the existing applied or residual stress in materials and so the hardness value measured under stressed state is vague in meaning. In this paper the effect of macroscopic stress on hardness was studied in several annealed carbon steels which had different carbon contents. Stresses on the surface of specimens which were uniaxially or biaxially stressed by bending, were measured by the X-ray technique, and Vickers hardnesses were measured near the points where stresses were measured. We employed the X-ray technique because it was necessary to measure nondestructively the stresses including residual stresses, and this object was attained only by the X-ray technique.
As the result, it was found that the dependence of hardness on the existing macroscopic stress differed according to the sort of materials; and that hard steels were affected by stress more than soft steels in hardness. And the effect of biaxial stress on hardness is greater than that of uniaxial stress. The diagonal length ratio of Vickers indentation along, and perpendicular to, the direction of uniaxial stress depends on the magnitude of stress, and also on the sort of materials.

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The relation between the residual stress and the injury on the ground surface of hardened ball bearing steel was investigated. Ring specimens were hardened and tempered to Rockwell C62. The grinding of the internal surface was worked on a Heald constant force internal grinding machine under a series of severe operating conditions. The residual stresses were measured by the X-ray method, using a Geiger counter diffractometer with CrKα radiation.
According as the normal force of grinding varied from 0.5 to 3.5kg/mm, the surface residual stress changed almost linearly from a compressive value of about 10kg/mm² to a tensile value of 90kg/mm². A marked decrease of the half-height breadth was also observed with increasing tensile stress. By macroetching with hot hydrochloric acid, etch cracks were developed on the surface where the tensile residual stress exceeded the value of 50kg/mm².
To ascertain whether the surface residual stress depends upon the cutting action or on the frictional heat, the rubbing experiment of steel was made with alumina ceramics and superfinishing stone. After rubbing 10sec. with alumina ceramics, the residual stress varied with increasing load from a compressive value of about 50kg/mm² to a tensile value of 50kg/mm², as in the case of constant force grinding. Decrease of the half-height breadth was also observed when the residual stress became tensile. On the other-hand, in the case of superfinishing stone, the compressive stresses of the order of 50kg/mm² were always obtained. No decrease of the half-height breadth was observed in the range of the experiment.
Since the cutting action is very poor in both cases, it is considered that the tensile residual stress is mainly due to the frictional heat. In case the frictional heat should be neglected, the compressive residual stress would be generated by the plastic deformation in very thin surface layers. In the case of superfinishing stone, as the abrasive grains are easily detached by a small frictional force, evolution of the frictional heat will not be enough to introduce the tensile residual stress.
Tempering above 150°C decreases the tensile residual stresses and raises somewhat the critical stress of etch cracks.

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The sintered materials have recently come to be extensively applied in various fields by the continued improvement of their properties. It must be emphasized, however, that some mechanical properties of sintered materials are inferior to those of materials produced by machining bar stock. To improve those properties, the evaluating method for the properties must be established. For example, the inferiority in toughness of the sintered materials has been a deterrent in some applications, and there has been no correct evaluating method for the toughness of sintered materials. The X-ray diffraction techniques may be available for these purposes. However, little has been done in the application of the X-ray techniques as evaluating method for the properties of sintered materials.
In this investigation, the diffraction patterns of iron powder, ferrous compacts, and ferrous sintered specimens were taken, and their half-value breadth was measured. Besides, a similar X-ray examination of the specimens was carried out after their bending test. The results obtained are as follows:
(1) The lattice strain of iron compact induced by the compaction disappears easily by the sintering. In the case of mixed powder compact, the diffraction pattern gives a broad line after the sintering corresponding to the insufficient inter-diffusion during sintering, and the changes in the half-value breadth may be good indication of the degree of inter-diffusion.
(2) The diffraction patterns taken at the portion near the fractured surface give good information on the toughness of sintered materials. By this method, the correct value is obtained of the increase of toughness by high temperature sintering, and of the effect of copper and nickel on the toughness of sintered ferrous materials.

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