In this paper is described the X-ray stress camera specially designed for stress measurement by a photographic method. This apparatus may be used by either grocker's method, Schaals Method or sin2φ method. We tried to record a diffraction pattern in a short time's exposure, using a specially designed short anode X-ray tube, with reduced distance between the object and the focus. The microphotometer, the film puncher and the electro polisher are also developed in consequence.
It is a matter of common knowledge that there are two ways, namely counter method and photo method, to measure X-ray residual stresses. it is a recent tendency that reinforcement of the counter method by a photographical method has been gradually prevailing at laboratories. At the same time, the manufactures of X-ray stress measuring apparatuses are trying to adapt the photo method every way. To cope with the above-mentioned situation, “Konishiroku”and“Fuji”, both Japanese typical makers of X-ray films that form the basis of the photo method, have made efforts to review X-ray films, and carried out sufficient testings on X-ray films for both industrial and medical uses. However, there are few data for X-ray area concerning the measurement of X-ray residual stresses. Therefore, our laboratory investigated in photo sensitivity, grain size, fixing time and the like, for five varieties of Types N, S, Y, RR, and R films, which are altogether the products of the“Konishiroku”, and carried out testings to determine the X-ray film best suited for the measurement of X-ray residual stresses. Putting their results together, Type N is superior to any other types in sensitivity and contrast, while it is very much inferior to any other types in grain size and fixing time. Type-S is inferior to Type N in sensitivity, and about equal in contrast, while the former is very much superior to the latter in grain size and fixing time. Type Y is shorter than any other types in fixing time, while it is equal to Type S and very much superior to Type N in grain size. Although Types RR and R are characterized as excellent in contrast in their maker's catalog, it has been proved that even when 30 minutes' exposure has been processed in such a condition as when it is used by us, they did not turn in the straight line area, so such films are not of any practical use. Therefore, it has been concluded that Type S is the best one for use in the measurement of X-ray residual stresses, because it is superior in contrast, grain size and fixing time, though it is a little inferior to the best Type N in sensitivity. Furthermore, in the process of these tests, has been ascertained again the efficiency of X-ray filter, that was reported in the special issue of the Society Journal last year, concerning X-ray stress measurement as mentioned below. According the to the characteristic density curve of X-ray film shown when the X-ray filter is not used, the density of diffraction line becomes high in a short time, while the density of the background becomes high. Therefore, the value of the density of diffraction line minus the background density namely the effective density decreases. However, in the case of the characteristic curve of X-ray film with the use of the X-ray filter, the density of diffraction line does not become so high in a short time. But as the density of background does not become high, even if the exposure time becomes longer, the latter is superior to the former in the effective density and contrast. As a result, it has been made clear that the efficiency of such an X-ray filter is to be greatly enhanced by setting it before the X-ray film, so as to absorb the diffused reflection of X-ray besides making the characteristic X-ray, unicolorous which is the main purpose of this filter.
It is well known that various kinds of residual stress are found to exist in extended metal and alloy specimens by means of X-ray technique. One of them has been ascribed to the difference in the yield stress of crystals between the specimen surface and its interior (surface effect). The residual stress due to the difference in the yield stress among the crystals constituting a polycrystalline agregate has also been reported. Another one called “Gefügespannungen”has been considered to be due to the difference in the yield stress of the various phases coexisting in an alloy. As regards the“Gefügespannungen”, however, only the qualitative result on steel consisting of ferrite- and cementite-phases has so far been published. The present study is designed to obtain the direct X-ray evidence for the presence of the “Gefügespannungen”. As an example of the two phase alloys, (α+β)-brass rod specimens were used. They were annealed at 550°C for 2hr in an argon atmosphere. Having been confirmed that there exists no residual stress in an annealed state, the specimens were extended statically. The residual stress in α- and β- phases on each layer near the specimen surface was determined nsing sin2ψ-method. Throughout the experiments the X-ray film technique using Co-Kα characteristic radiation was adopted. The results obtatined are as follows: (a) After the extension of 3% α-phase remains in compression, while, β-phase in tension. The result seems to give a direct evidence for the“Gefügespannungen”. (b) In spite of the presence of the“Gefügespannungen”, there exists macroscopic compressional stress on each layer near the specimen surface. This may be due to the surface effect. (c) Residual stress after 10% elongation could not be determined because of the extraordinary broadening of diffraction lines, especially of those from β-phase. The results reported here are also certified by the experiments in progress using an X-ray diffractometer, the results of which will be described elsewhere in future, together with the results concerning the dependence of residual stress values on reflecting planes.
The X-ray method of stress measurement is taken as a unique method of non-destructive measurement of local stress. Recently the experimental technique and the theory of stress measurement by X-rays have been greatly improved. From the results of recent study, it is understood that the mechanically applied stress with in the elastic limit can be measured by X-rays with sufficient accuracy. In the case of measurement of residual stress by means of X-rays, however, there remains a question whether the stress measured by X-rays represents the macroscopic residual stress itself. Since the lattice spacing is taken as the gauge length for measurement of strain, it is plausible that the microscopic nature as well as the macroscopic nature are included in the value of the stress obtained. In the present study, experiments were carried out to find the influence of microscopic nature on the valuation of residual stress by X-rays using stretched plate specimens of carbon steels. Eight sorts of carbon steels with carbon content ranging between 0.14 and 1.00 percent were used as the material of the specimens. All the specimens were annealed after the forming. The plastic tensile strain of a quarter and a half of the strain at the maximum load in tensile test was given for every material, and residual stress measurement was made by X-rays and mechanical methods for the stretched specimens. It was intended to compare the distributions of residual stress determined by both these methods. As the X-ray diffraction apparatus, an automitic X-ray stress analyzer of the parallel beam type with the Geiger-Müller counter tube was used. The Cr-Kα radiation was employed, which gave diffraction from the (211) crystal planes of carbon steel. For the purpose of determining the distribution of residual stress by X-rays, a thin layer was successively removed on both the surfaces of the plate specimen, and the stress on the revealed surface was measured. On the other hand, the macroscopic residual stress was measured by the conventional mechanical method of successively removing of thin layers only on one side of the specimen. The obtained results are summarized as follows: - 1) Compressive residual stress is observed in the surface layers of the stretched specimens, and its value seems to be independent of the stretched strains. 2) The accuracy of the stress value by X-rays measured by the sin2ψ method is sufficiently reliable. 3) The residual stress on the surface of the stretched specimens by X-rays shows non-uniformity from place to place of the surface. It is considered that the non-uniformity of stress value by X-rays must be taken into consideration in the comparison of the stress measured by X-rays with that measured by mechanical means. 4) The compressive residual stress measured by the X-ray method increases with the increase of carbon contents both on the surface layers and at the core of the specimen. If the stress value by X-rays represents only the macroscopic residual stress, it must converge to zero at an infinitely small thickness after the successive removal of layers from both the surfaces. However, the experimental result shows the existence of compressive residual stress in such a case. Therefore, it is considered that the residual stress measured by X-rays in the stretched carbon steel includes the macroscopic residual stress caused by the surface effect and also the microscopic nature due to the plastic deformation, and the cause of the discrepancy between the X-rays and the macroscopic residual stress in the stretched carbon streel cannot be explained by the criterion of the phase stress (Gefügespannung) alone.
During the recent years, much progress has been made in the metallurgical field, more particularly in investigation to detemine with X-rays the internal stress of metals and in the accuracy of its detection with the improved experimental procedure and the equipment for measusement of stress with X-rays. But, there are some problems relative to the microstress obtained by X-rays and the macrostress by mechanical methods. Considerable agreement of both the stresses in the macro-elastic range is recognized. In the measurement of residual stress in the material subject to plastic deformation the diffraction plane dependency, the broadening of the diffraction pattern, “Gefügespannungen” etc. are important factors in the measurement of stress with X-rays to determine the residual lattice strains of certain grains in the specimen selectively. Many investigators pointed out that, after uniaxial plastic deformation, the surface of metals shows residual compressive stress, the so-called surface effect. These factors must be considered even in determining the surface stress by X-rays in the low carbon steel after various plastic detormation. At each stage after the uniaxial plastic deformation, the residual stress obtained by the lattice strains determined by the diffraction lines of the(310), (211) and (220) planes using Cokα1, CrKα1 and FeKα1, respectively on the surface of the low carbon steel plates is compressive, and increases rapidly up to plastic strain ε≅6%, and thereafter increases slowly. The breadth of the diffraction line increases correspondently to the residual stress. The residual axial stress distributed over the cross section of the plate was determined by means of etching, and measured by X-rays or by strain gauge. The results showed that the compressive residual stress on the surface layers balanced to the tensile stress in the interior of the specimen when we used strain gauge, but lost balance when we used X-rays. When the thickness of the specimen approached zero after successive etchings, the residual compressive stress obtained by X-rays diminished, but some compressive stress remained still on their layers. The maximum compressive stress was not observed on the surface, but was latent in the interior near the surface. It is considered from these results that “Gefügespannungen” due to the existence of the cementite and ferrite phase seems to play an important role. In determining the breadth of the diffraction line, measurement was made from the differential curve of the diffraction contour by the twin pole Geiger-Müller counter as mentioned in The Third International Conference on Non-destructive Testing 1960. A new method is mentioned. The differential curve obtained by the twin pole Geiger-Muller counter method shows zero on the peak position of the intensity curve of the X-ray diffraction and a peak on the position of the maximum slope of the intensity curve. The angle between these two positions corresponds to half the width of the intensity curve. Thus the influence of the variation of the intensity of the X-ray source which is one of the most serious problems in usual counter method became small, and we could measure the width easily even though the diffraction line was broad in the plastic deformation.
It has been reported in the previous paper of the authors that owing to the recent trend in the remarkable development of the X-ray apparatus and improved method of measurement, the stress in metallic materials can be measured with sufficient accuracy. A good correlation is found between the mechanically induced stress and that measured by X-rays where the conventional elastic constant is used in the calculation. There are some problems left, however, that need further investigation, for example, the problem of elastic anisotropy. This problem was discussed by some investigators, for instance, Möller, Greenough and Macherauch, and it was shown that the lattice strains are dependent on the diffracting planes of metallic crystals even in the elastic state, that is, there exists elastic anisotropy. For this reason, it is proposed that the elastic constant measured by the X-ray method should be used instead of that obtained mechanically for the stress measurement by X-rays. The metallic materials in practical use are polycrystalline, and the average strain of a number of crystals favorably oriented with respect to the characteristic X-rays is measured in the X-ray procedure. The lattice strain is likely to differ according to the lattice plane in each crystal. In order to clarify this problem, the authors measured the elastic constant by the X-ray method and compared it with that obtained by the mechanical means using carbon steels with various carbon contents. In this paper, the accuracy of the measurement of the elastic constant by X-rays is reported, and the stress calculated by using the elastic constant of X-rays is compard with that applied mechanically. Round bar specimens 6mm in dia. and 110mm in length were used in this experiment. All the specimens were annealed before being subjected to X-ray photography. The specimens were stressed stepwise by the tensile testing machine, and at several stages of applied stress, CoKα1 beams were radiated to the center of the specimen surface in vertical and oblique incidence with several angles ψ. The Stress was measured by the conventional Sin2ψ method using the film technique. The value of cosecθψ was calculated from the measurement of the radius of the diffraction ring using an automatic recording type microphotometer. In this experiment, it was required that because of the round bar type of the specimen, the effect of curvature of the radiated surface on the measured stress was taken into account. Accordingly, as a preliminary experiment, this effect was examined on the annealed specimen of 0.1% carbon steel. From the slope of the lattic strain (εψ)-sin2ψdiagram for several applied stress, ∂ε/∂ sin2ψ-stress curve was drawn by using the method of least square. Based on this diagram, another curve of εψ=0 versus stress was drawn as above. From these slopes the elastic constant was calculated for each material. The conclusions of the present study are as follows. The result shows that the error is within the range of ±600kg/mm2 as compared with the value measured mechanically for all the specimens of different carbon steels. Therefore, it may be said that for CoKα1 radiation the error of the calculated stress between the case where the elastic constant obtained by the X-rays is employed and the case where the mechanical method is used is within the range of ±3%, in other words, within the range of experimental errors. The present results are in accordance with those of the previous studies. However, in general, it may be considered that elastic anisotropy is present in the industrial metallic materials. Consequently, the effect of elastic anisotropy on the stress measurement needs further investigation by examining the cases of different characteristic X-rays
A new method of stress measurement by X-ray is proposed. The apparatus of the method consists of two parts; a camera and the supporter of the X-ray tube, combined with the camera. The camera is cylindrical and has cylindrical film around the axis which is strictly coincident with the incidental X-ray beam. The back reflected the X-ray patterns generally form corns around the axis of the incidental X-ray beam, and the intersections of these cones with the plat film make rings which are known as Debye Scherrer rings rings. When the materials are void of stress these rings become perfect circles on the film and appear as straight lines on the developed film, in the case of the cylindrical film. But if there is stress operating or some residual stress locked in the material, these cones are not perfect, but are deformed and the center is shifted. Then the diffracted and recorded patterns on the cylindrical film would appear as complicated biquadratic curves as the result of the intersection of the two quadratic curved surfaces. Then the existence of stress can be judged from a glance at the developed film. This is the most convenient point. Another point is that there is no need to measure the exact distance between the film and the specimen surface, as is seen in the following equation. σx=1/2RE/(1+ν)·1/tanθ·sin2θ·ΔDD ΔDD=ΔD+-ΔD-=(D+-Ds)-(D--Ds) (From figure) E: elastic modulus ν: poissons' ratio R: camera constant This equation does not include the term of the distance between the film and the specimen-surface. These two characteristics resemble the Schoal method (flat plate method), but in the present method the required exposure time is only one half of the Schaals' method. The latter must have two times, exposures that on the first half of film and next on the covered half of it.
Sachs' method is generally used as a means to explore the residual stress distribution of various cylindrical steel, but this method is practically inapplicable to the steel products, as it is a destructive method. This is a serious drawback from a practical viewpoint. It is generally said that some kind of residual stress affects the fatigue strength of machine parts. Therefore, it is particularly desirable to resort to a non-destructive method in order to explore the residual stress distribution inside the steel that forms machine parts. As one of the non-destructive methods, there is stress measurement by X-rays, and the surface stress of any product can be measured directly by this means. But the stress measurement by X-rays alone is not adequate yet to know the value of residual stress inside of the steel that forms machine parts. The authers have reported previously the method of calculating residual stress which is incidental to the heat treatment inside cylindrical steel with the phase transformations in consideration. If the value of the surface residual stress is obtained by the X-ray method and is used as a measure of quantitative check of such calculation results, such a calculation method will have practical utility. But it is sometimes necessary to use Sachs' method to ascertain experimentally the truth of the result reached by the X-ray method. What is the relation then between the surface stress value obtained by the X-ray method and the stress distribution obtained by Sachs' method? Is there good agreement between both the results obtained by X-rays and Sachs' method? In this report are mentioned some experiments which have been made on this problem and the results there of. Conclusively, it may be stated as follows; (1) Test was made of reproducibility of the average value obtained from the four values measured by the X-ray method. Although the two average values of the two independent measurements show good agreement, there is considerable scattering among the values individually measured which is considered not to be attributed only to technical error but also to crystalline inhomogenity. (2) There is some disagreement between the the surface stress value obtained by X-ray method (at 0.25mm depth from outer surface) and the surface stress value obtained by Sachs' method (at 2.5mm depth from outer surface). It is shown in this test that |σS|>|σX| This discrepancy is not to be approved in the procedure of testing materials. (3) The above mentioned disagreement can only be accounted for by the hypothesis either that some specially steep stress gradient occurs due to heat treatment of the material or that there is some essential difference which inhibits treating σS and σX as the quantity of the same class. This problem requires further experiments to be made with high precision and more data to be collected therefore.
It is a recent remarkable tendency that the method of X-ray stress measurement by means of X-rays has come to be widely utilized in many laboratories. It is also a fact, however, that some experimenters concerned with this measurement have still some doubts about its accuracy. The results of the experiments carried out in our laboratory, as was reported last year in the special issue of this society pertaining to the measurement of stress by X-rays, showed a high accuracy in the measurement. This high accuracy is considered to have been established as a result of the confirmation that the condition of the specimen surface has an important effect on the accuracy in the measurement of stress by X-rays, which was obtained through a number of investigations in our laboratory. Some literature concerning the measurement of stress by X-rays, however, treat the influence of the surface condition lightly. Accordingly, in order to make this point clear, experiments were carried out using the specimens with various surface conditions. As a result, it was found that the stress measured in the specimens with fine surfaces is in good agreement with the load stress, while that of the specimens with rough surfaces show discrepancies. Besides, as regards the residual stress, the measured values of the specimens with fine surfaces were found to be larger than those of the specimens with rough surfaces. The difference between both the measured values became larger as residual stress increased. The reason why the measured values show differences according to the conditions of the specimen surface might be ascribed to the circumstance that they may have some connection with the depth of penetration of X-rays. In case the specimen surface is rough, the real stress value may not be obtained for the shallow penetration of X-rays, because the stress in the projected area is relieved. Therefore, the specimen surface must always be flat and smooth However most specimens in our use are far from satisfying this condition. Consequently, polishing method is used to obtain a smooth surface, but in the course of polishing stress is introduced, resulting in the shift of the true stress value. In order to eliminate this stress in processing, etching methods by means of chemicals such as hydrochloric or nitric acid have been employed so far. Experiments, however, have shown no good results on the chemically etched surfaces. In our laboratory, therefore, taking the flatness of the specimen surface after the removal of stress in processing into consideration, electrolytic polishing method has been adopted, as was reported in the special issue of this society concerning the measurement of stress by X-rays. Besides, an electrolytic polishing apparatus was manufactured which is capable of eliminating the stress in processing in any specimen in a short time and which is used in our laboratory. This report contains the results obtained for the case in which Cr-Kα rays were employed as characteristic X-rays. If Co-Kα rays with a different penetration depth from that of Cr-Kα rays were used, the results might be somewhat different from this report. But it remains a common requirement that the specimen surface should be flat and smooth. As regards the relation between the roughness of the specimen surface Co-Kα rays, the authors will further their researches and await another opportuuity to report the result.
The measurement of residual stress by X-rays is utilized nowadays in many laboratories in consequence of the considerable improvement made in the accuracy of measurement brought about recently by the remarkable development of the X-ray diffraction apparatus and the accessory measuring devices. It is becoming one of the powerful methods of residual stress measurement. One of the authors has investigated the change in residual stress due to fatigue stressing, and found that a linear law of fading of residual stress holds in the range except in the early stage of repeated stressing. In this paper, the change in residual stress due to repeated impact is reported, and the application of the linear law of residual stress fading to the present case is examined. Two sorts of plate specimens were used, the one was of notched type using a low carbon steel (0.08% C), and the other was of unnotched type employing a high carbon steel(0.55% C). With the former, residual stress was introduced by plastic stretching, and with the latter by low temperature quenching. The specimens were put into a groove cut on the surface of a hard wood so as to be supported at both ends. Impact loading was given to the central parts of the specimens by a simple device of dropping a weight. The speed of cyclic impact was made to be 22 blows per minute by using a disc attached with a claw, which was rotated at 22rpm by the motor through reduction gears. Stress measurement by X-rays was carried out by the film method using the Glocker's technique of vertical and 45° oblique incidences. CoKα beams were used and the distribution curves of diffraction intensity were drawn by an automatic recording microphotometer. The residual stresses were calculated by the following formula: σ=K(cosecθψ-cosecθ⊥) where K=sinθ0E/1+ν·1/sin2ψ The residual stresses were measured at three stages of blow numbers of 500, 1000 and 2000 as well as at the initial state. As was expected, residual stresses decreased gradually with the increase of blow numbers for both the notched and unnotched specimens. It may supposed that the specimens were subjected to a fatigue stressing of pulsating bending of a low cyclic speed. The fading of residual stresses in the present experiment might be explained by the above fatigue phenomenon. Besides, another fatigue phenomenon due to the propagation of stress waves of tension and compression through the thickness of the specimen might be taken into consideration. The duration of impact in the present experiment, however, is infinitesimally small, therefore, the fatigue phenomenon of this sort is considered to play little role in diminishing the residual stress. Taking the ratio of residual stress σ/σ0 (σ0 and σ are the initial and the current value, respectively) as ordinate and the ratio of blow numbers n/N (n is the current number and N is taken as the final number of 2000) as abscissa, a linear relationship was obtained for both specimens, as in the previous case of fatigue stressing. It is a noticeable fact, however, that the linear law held in the earlier period of impact stress repetitions. Be the matter as it may, it may be said that the linear law of residual stress fading holds also for the case of impact repetitions. Experiments were made under another impact load using a larger weight, and as was naturally expected, the fading of residual stress was greater. This tendency was especially remarkable in the earlier stage of blow repetitions. In this case also, the linear law of residual stress fading was seen to hold.
In the previous papers the authers pointed out, using annealed low carbon steel plates, that slip lines appear in a quite localized region close to the notch root at a very early stage of fatigue process. In the next stage the slip lines develop wider and longer progressively until a macroscopic crack is initiated. On the other hand, the half-value breadth of X-ray diffraction line at the notch root increases rapidly at an early stage of fatigue, then gradually in the next stage and near the crack initiation it increases rapidly again. After the crack initiation the half-value breadth increases considerably. The correlation of the changes in micro-structure and the half-value breadth for the notched specimen are similar to the case of fatigue in the unnotched specimen. Considering these experimental results, it is suggested that the fundamental difference of the mechanism of fatigue fracture is not found between the notched and unnotched specimens. However, it is reported by many investigators that the fatigue strength of the notched specimen which is charactarized by the initiation of the crack is larger as compared with the predicted value of strength of the unnotched specimen divided by stress concentration factor. In order to interpret the discrepancy of fatigue strength between the notched and unnotched specimens, it is intended to take the discrepancy to be attributed to the behaviour of residual stress in fatigue process. Hence, one of the authers pointed out from the X-ray study on fatigue of the unnotched specimen of annealed low carbon steel plate that the compressive residual stress that appears on the surface increases rapidly at an early period of cyclic stressing, but in the next stage of fatigue it decreases suddenly, thereafter its diminuation proceeds gradually until fracture occurs. It is considered that such a change in residual stress may occur in the case of fatigue in the notched specimens, and stress gradient at the notch root should give an influence on the change in residual stress. In the present paper, the results of measurement of residual stress and applied stress at the notch root at several stages of fatigue process are presented, andthe in fluence of residual stress on fatigue endurance of the notched and unnotched specimens are discussed. The specimens used were 0.16% C carbon steel plates having 90-deg. V notches, and were annealed and electropolished after machining. The condition of applied stress was a fully reversed bending stress. For determining the stress value by X-ray the so-called sin2ψ method was adopted. Since the fatigue fracture occurs at a very localized region in the vicinity of the notch root, an application of X-ray method of stress measurement to such a notched specimen is very effective, because the X-ray method of stress measurement is eligible to measure such a localized stress. The obtained results are summerized as follows: (1) The value of the compressive residual stress that is generated during fatigue process increases as stress concentration factor of the specinen increases. And the residual stress acts on the actual stress condition as the mean stress. (2) These results suggest that the residual stress makes an important contribution to the increase of fatigue endurance with the increase of stress concentration factor. (3) The fatigue crack can support the compressive load, while it can not support the tensile load. Consequently, it is considered that the stress condition at the tip of crack is a repeated stress with the mean tensile stress.
The macroscopic theory of fracture as developed by Ludwick, Druidenkov and Orowan making distinction between ductile fracture and brittle fracture point out that brittle fracture results when flow curves cross the supposed brittle fracture curve, and ductile fracture results, when flow curves cross the ductile fracture curve. On this theory the initiation mechamism of brittle fracture isconsidered according to the Griffith's theory and no consideration is made on ductile deformation to fracture. On the other hand in the microscopical study of fracture, much effort has been made to make clear the formation of crack nuclens. From many observations, several models of pile up dislocations to develop the cracks have been reported by Zener, Orowan, Stroh, Cottrell, Mott and by some other reseachers. But these theories of two groups have been developed independently, and few attempts have been made to establish a consistent theory to combine these two thoroughly. This paper is an experimental report of the study to make clear the relation between brittle fracture and ductile deformation to fracture, using the X-ray diffraction methods. In the study the X-ray apparatus with back refrection devise was used, and X-ray micro beam technique was employed and improved mecro beam cameras were designed and constructed by the author. In this way information was obtained about the heavily deformed state of the material and about the transitions of fracture mode from ductils to brittle. As the results of the X-ray experiments thus made with the use of these comeras, measurements were made of the size of fragmentatedcrystalline particles, the misorientation between them and the dislocation density of the fractured parts and considerations were made also of fracture and ductile deformation.