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Residual stress on the weld metal of nickel based alloy was evaluated through x-ray diffraction and metallurgical study of the microstructure. Weld metal specimens were prepared from Alloy182 (JIS DNiCrFe-3) and Alloy132 (JIS DNiCrFe-1J) deposited on a steel plate. X-ray diffraction results show a strong [100] preferred orientation nearly normal to the surface of the weld metal. Crystallographic consideration predicts that dominant 311 diffractions appear around 25.2 and 72.5 degrees of ψ angle. For each diffraction, the peak shift was measured at the ψ angle showing the maximum diffraction intensity, using the side-inclination method (ψ-goniometer method) with a Mn x-ray tube and a PSPC (position sensitive proportional counter). The residual stress was determined by the peak shifts according to the two tilt method. The x-ray stress constant, K, on Alloy 182 was determined experimentally. The depth profile of the residual stress was measured on the ground specimens with and without laser peening. Tensile residual stress due to the grinding work is observed in the surface layer of the unpeened specimen; however it changes to compressive after laser peening. The overall behavior of the depth profile of laser peened material agrees well with that of Alloy600 base metal measured in the previous studies, where the compressive residual stress with several hundred MPa at the surface gradually decreases and reaches to around 0MPa at the depth of about 1 mm.

X-ray stress measurements in a local area of a single crystal silicon were carried out using synchrotron radiation. In the experiment, the beam line 3A (BL3A) in the Photon Factory of the High Energy Accelerator Research Organization, Tsukuba, Japan, was utilized. The χψ-oscillation method was used as the oscillation method of a specimen for detecting a perfect diffraction profile. In the case of using synchrotron radiation, a wavelength can be selected using a monochromater so that the diffraction angle may become high angle where the highly-accurate strain measurement is possible. Therefore, accuracy of the stress measurement is improved more than using characteristic X-rays. The stresses in three steps were applied on a specimen using a four-point bending device. The diffraction angles of three different diffraction planes were measured in each step using the φ50μm collimator, and the stresses were calculated from the peak shift. The measured stresses agreed well with the applied stresses evaluated using a strain gage. Also, the stress distribution near the edge of the circular hole of the diameter of 400μm which was made on a single crystal silicon was measured using the φ30μm collimator. The stress was applied using a four-point bending device, and the stresses were measured at five points from the edge of the circular hole to 240μm. The measured stress distributions agreed with the FEM result. However it is necessary that the beam size is more decreased in order to obtain the stress distributions more accurately.

We used X-ray diffraction method using Synchrotron radiation (SR) for solving residual stress in composite material. Diffraction planes with arbitrary diffraction angle were measured. Moreover, there is a characteristic that the different diffraction planes at same 2θ angle were obtained using SR with different wave length. In this study, effects of penetration depth on an X-ray parameter of the composite material were examined. First of all, the X-ray elastic constant of the single-phase body (PXEC) was measured for the evaluation of the phase stress. Next, the elastic deformation behavior of phase stress in the matrix phase was evaluated, and the influence of the second phase particle was investigated. Residual phase stress of each phase in the fracture surface is measured as an application example for the X-ray Fractography. The relation between the stress intensity factor and TiN volume fraction was examined.Trying to fracture toughness test in composite material, we discussed influence of fracture toughness value on residual stress. Deformation behavior of softer matrix phase was controlled by hard second phase particle under macroscopic tensile stress. It was found that residual stresses in the fracture surface were relaxed on the surface.Furthermore, there is the correlation between the stress intensity factor at the fracture and the phase stress in the matrix phase.

The residual stress distributions just beneath the fatigue fracture surface were measured using synchrotron radiation with three different wavelengths, i.e., three different penetration depths. The residual stress distributions were estimated from three kinds of diffraction data by the following process. First, a temporary residualstress distribution in the depth direction is assumed. Theoretical 2θ-sin2Ψ diagrams for each wavelength, where each has a different penetration depth, are calculated by the cosΨ method developed by one of the authors. The sum total of the differences between the theoretical and experimental values of the diffraction angle in 2θ-sin2Ψ diagrams is calculated. This total value is minimized by changing the assumed stress distribution by the quasi-Newton optimization method. Finally, optimized 2θ-sin2Ψ diagrams for each penetration depth and detailed stress distribution are determined. The true surface residual stress is obtained from this stress distribution.No effect of load ratio R(=Pmin/Pmax) on the residual stresses of the fatigue fracture surfaces in low-carbon steels was observed when the sin2Ψ method was used for stress measurement. However, the residual stresses became higher with increasing R when these were measured by the proposed method. On the basis of this, the stress intensity factor range, ΔK, can be estimated from the residual stress on the fatigue fracture surface.

The residual stress distributions just beneath the fatigue fracture surface were measured using synchrotron radiation of three different wavelengths having three different penetration depths. The residual stress distributions were estimated from these three diffraction data by the following process. First, a temporary residual stress distribution in the depth direction is assumed. Theoretical 2θ-sin2ψ diagrams for each wavelength are calculated by the cosψ method developed by one of the authors. The total of the differences between the theoretical and experimental values of the diffraction angle in 2θ-sin2ψ diagrams is calculated. This total value is minimized by changing the assumed stress distribution using the quasi-Newton optimization method. Finally, the optimized 2θ-sin2ψ diagrams for each diffraction and the detailed stress distribution are determined. The true surface residual stress is obtained from this stress distribution. No effect of the load ratio R (=Pmin/Pmax) on the residual stress of the fatigue fracture surface in low-carbon steels was observed when the sin2ψ method was used for stress measurement. However, it was found in this synchrotron study that the residual stress became higher with increasing R. On the basis of this, the stress intensity factor range, ΔK, can be estimated from the residual stress on the fatigue fracture surface.

Stresses in a single crystal specimen or any individual grain of polycrystal specimen were measuerd by the use of one dimensional position sensitive proportional counter (PSPC). A problem on such project is how to measure stresses experimentally because continuous Debye-Scherrer (DS) diffraction ring is only just a spot from a grain and appeared on an imaginary DS circle from polycrystal specimen. Therefore, it is important to convert from such a spot to measurable diffraction curve. We adopted a PSPC and a specimen oscillating mechanism in the present study.Large grained 3% silicone iron specimens were prepared and 211 diffractions on each grain under elastic loading were measured by Cr-Kα x-rays radiation after determination of orientation (n1n2n3) [w1w2w3] on each grain by Laue method. A specimen stage with the ψ and φ rotating attachment was oscillated upon the x-ray irradiated point on the specimen surface in ψ and ψ+90°directions by the use of two stepping motors. The oscillating areas were ±3°in the ψ direction and ±0.5°in the ψ+90°direction, respectively and a measurable diffraction intensity, curve from a DS spot was converted by this operation.Stresses under uniaxial loading were measured by this technique and we concluded that stresses in a grain can be measured without the use of lattice parameters on the non-stresses condition.

There are several investigations on the behavior of residual stress during fatigue process. It is, however, difficult to detect the crack initiation from the change in residual stress because of no significant change in residual stress through the fatigue process. The purpose of this investigation is to detect the fatigue damage from the change in actual stress measured by X-ray diffraction technique during fatigue test. In this paper, a cantilever type rotary bending test machine was developed for an X-ray stress analysis based on Single Exposure Technique. The actual stress at the maximum tensile applied stress was measured to failure during cyclic loading.The actual stress was keeping stable with increasing number of cycles until crack initiation, and this behaivior was independent of stress amplitude. After the crack initiation, it decreased suddenly with crack propagation because of stress relaxation at the crack. These results show that the change in actual stress at the maximum tensile applied stress has much higher sensitivity to detect crack initiation than one in residual stress. In-situ X-ray observation of actual stress during fatigue test is useful to detect fatigue damage.

X-ray stress measurements for isotropic polycrystalline are materials are usually carried out by the sin2ψ method under the assumption of no stress gradient in X-ray penetration depth. When a steep stress gradient exists in the vicinity of surface layer, however, non-linear sin2ψ relation is observed and the sin2ψ method cannot be applied on such cases. Although several X-ray stress analyzers have been developed for materials with steep stress gradient in the surface layer, it is desirable to use diffraction data at higher incident angles of ψ0 as possible as close on 90 degrees in order to determine the both values of surface stress and stress gradient with high accuracy.In the present study, an X-ray stress analyzer based on Ω geometry was fabricated to enable X-ray incidence at higher angle of ψ0. The X-ray detector was positioned on -η side against X-ray incident beam. Both of the residual surface stress and stress gradient were determined by use of the cosψ method on shot-peened steel and silicon nitride specimens. This prototype stress analyzer was found effective to perform a biaxial or triaxial stress analysis.

This investigation was made in order to find out a distribution of residual stress on the surfaces ground under various grinding conditions obtained by changing an actual depth of cut, number of grinding and a grinding process under a constant state of a chip cross sectional area. The surfaces of the specimens were ground by only up cut, only down cut and both up and down cut, respectively. The experimental data were analyzed by using both the Dolle-Hauk method and the integral method which takes into account of the stress gradient.As a result, the residual stress on the surface of one pass grinding showed higher tensile stress when a larger actual depth of cut took place. And the residual stress of down cut grinding was higher than that of up cut. By repeating another re-grinding on the same surface, the residual stress translated into a compressive stress and then converged into a certain level. On the contrary, the stress gradient changed to positive side in such case.

When the X-ray stress analysis is performed by using a position sensitive proportional counter (PSPC), a parabolic (curved) background line is obtained on the X-ray diffraction profile because of geometrical problem of PSPC and absorption of X-rays. Since such phenomenon is especially remarkable in the broadened profile, it is necessary to correct it to a straight background for measuring a diffraction angle or a half-value breadth with high accuracy.This paper analyzes such curvature of background line of the profile and suggests a correction method to linearize the background line.The results obtained are summarized as follows:1) The intensities at the both ends of effective length of the PSPC decreased because of the tilt incidence of X-ray beam.2) The correcting factor for the linearization of the background line was essentially the inverse of background intensity. However, because the background is apt to scatter due to the statistical property of X-rays, such factor was determined by smoothing the inverse of the scattering X-ray intensity obtained from a glass plate.3) By correcting the background line, the half-value breadth was able to be measured as a constant value wherever the starting points for determining the background line by digital calculation were positioned.4) On the other hand, the correction was not necessary on the stress measurement.

A new principle of X-ray stress evaluation for a sample with steep stress gradient has been prosed. The feature of this method is that the stress is determined by using so-called φ-method based on the change of φ-angle and thus has no effect on the penetration depth of X-rays. The procedure is as follows; firstly, an average stress within the penetration depth of X-rays is determined by changing only φ angle under a fixed ψ angle, and then a distribution of the average stress vs. the penetration depth of X-rays is detected by repeating the similar procedure at different ψ angles.The following conclusions were found out as the result of residual stress measurements on a carbon steel of type S55C polished by emery paper. This method is practical enough to use for a plane stress problem. And the assumption of a linear stress gradient adopted in the authors' previous investgations is valid. In case of a triaxial stress analysis, this method is effective for the solution of three shearing stresses. However, three normal stresses can not be solved perfectly except particular ψ angles.

A position-sensitive proportional counter suitable for the X-ray stress analysis has been developed and residual stress in austenite steel was measured with an apparatus which uses this PSPC system.The detector was designed to have a good angular resolution overall the counter length for diffracted X-ray beams and a high counting rate. The mean angular resolution measured was about 0.2° in 2θ (FWHM), and the maximum allowable counting rate reached about 40000cps. The time required for the data accumulation was shortened to about one-tenth of that of the conventional counter method.It is generally said that the X-ray stress measurement of austenite steel should be performed on its γFe(311) diffraction plane by using Cr-Kβ radiation and the measurement on γFe(220) should be avoided because the strain sensitivity on γFe(220) diffraction plane is less than that on γFe(311) one. However, the precision of stress determined on γFe(220) was better than that on γFe(311), if Bragg's angles were measured at many ψ angles.

In the field of X-ray stress measurement of polycrystalline materials, a diffraction plane at higher Bragg angle has to be selected in order to obtain the precise value of stress. However, the stress measurement on an optional (hkl) plane desired is not always possible because the X-ray beam exited from a metal target has a dispersive wave length.Recently, we have been able to use the synchrotron radiation source (SR) as an excellent X-ray source. In Japan, the facility of synchrotron radiation (Photon Factory, PF) was constructed in the National Laboratory for High Energy Physics (KEK) at Tsukuba academic city. The use of this SR enables the stress measurements on many (hkl) planes with high accuracy in the higher Bragg angle region by providing an X-ray beam having an optional wave length.We have started the X-ray stress analysis by use of the synchrotron radiation source. This paper reports the system of measurement and some results of preliminaly experiments.Since a monochromatic X-ray beam is required for the stress measurement, we used a beam line which consists of a double crystal monochrometer and a focusing mirror. X-rays between 4KeV (λ=0.31nm) and 10KeV (λ=0.12nm) are available with this optical system. We adopted a constant Bragg angle of 2θ=154° for all the diffraction planes. A PSPC having a carbon fiber anode is made and used as a detector with the use of a fast digital signal processor.We could observe the diffraction profiles from (200), (211), (220), (310) and (321) crystal plane of alpha iron, respectively, and the residual stresses in these planes except the (200) plane were measured with high accuracy in a short time.Such feature especially suits the stress analysis of the material which has preferred orientation or stress gradient.

The X-ray microbeam diffraction technique is a powerful method for observation of substructures in metallic materials, because of its ability to measure the microstructural changes in a localized region quantitatively and non-destructively. In recent years, the microstructure in the vicinity of fatigue crack tip has been investigated by using this technique and the mechanism of crack propagation has been discussed based on the results obtained. However, the correlation of the X-ray microbeam diffraction patterns and the microstructures observed by the other methods has not been made sufficiently clear.In the present study, the X-ray microbeam diffraction patterns from deformed specimens were compared with the substructures photographed by means of transmission electron microscopy.The material used was 0.12% carbon steel, and the low cycle fatigue test, the high cycle fatigue test and the impact test were performed to form substructures in the specimens.A good correlation was obtained qualitatively between the X-ray microbeam patterns and substructures in both the low cycle fatigued and impacted specimens. It was possible to distinguish the mode of substructure through X-ray microbeam diffraction patterns.A disagreement existed, however, between the values of subgrain size obtained by different analytical methods. It is considered that getting agreement between these values is difficult in the present stage, because of the assumptions on analyses. But the subgrain size should be a good parameter representing the plastic deformation, if an analytical method suitable for the mode of diffraction pattern is adopted.

Recently, a synchrotron radiation source (SR) has become available as an excellent X-ray source. X-rays from SR (XSR) have following features: (1) high intensity, (2) optional wavelength with narrow width is obtained when monochromater is used, and (3) small divergency. These provide the accurate stress measurements on many (hkl) planes in the higher Bragg angle region since the X-rays with optional wavelength can be selected. Such features of SR are most suitable for the stress analysis for materials having preferred orientations.In this study, the stress in cold rolled steel specimens having the preferred orientation was measured by X-rays from the synchrotron radiation source. The results obtained are summarized as follows:(1) The diffractions from (211), (220) and (321) planes were obtained separately with high accuracy in a short time.(2) The stress in the textured steels was evaluated by an analytical method utilizing more than one diffraction plane belonging to one zone axis. This was found to be a suitable method for the stress analysis by use of XSR because the stresses in various lattice planes can be obtained with the same accuracy.(3) The X-ray elastic constant measured experimentally agreed well with the analytical value calculated from single crystal compliances.

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-Muller 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 (Gefugespannung) alone.

The authors have pointed out in their previous papers that both the accuracy and reliability of X-ray residual stress value on the samples with narrow breadth of X-ray diffraction profile were sufficiently good. However, no results on the sample whose X-ray diffraction profile is very broad have yet been obtained. As the measurement of peak position of X-ray diffraction profile, although the half-value breadth method can be employed and good results were obtained in the case of sharp diffraction profile, this method cannot be applied to the case of broad diffraction profiles, because the back ground line of the profile cannot be clearly determined. Consequently, it is considered that the accuracy of the stress value obtained is not sufficiently good. Therefore, it is necessary to develop a new method for the measurement of the peak position of diffraction profiles.In addition to this problem, the effect of Kα2 component on the measuring stress ought to be considered. Furthermore, the effect of the Lorentz polarization factor and the absorption factor should be taken into account when the measuring sample has a large amount of residual stress with a broad diffraction profile.In the present study, the authors attempted to separate the Kα1 component from Kα doublet by using Fourier analysis so that this procedure may be applied to any shape of profile, and so they discussed the effects of the Lorentz polarization factor on the stress value.For the determination of the peak position, first, two assumptions were made as follows:-1) The intensity distribution curve actually observed Φ(x) is given by the sum of the intensity distribution curves φ1(x)and φ2(x) diffracted from Kα1 and Kα2 radiations, respectively. 2) The following relation holds between φ1(x) and φ2(x), φ2(x)=kφ1(x-Δx)where k is a constant and Δx is the distance between the peak positions of the intensity curves diffracted from Kα1 and Kα2 radiations. Next, the intensity distribution curves Φ(x) and φ1(x) were represented by the Fourier series respectively, and φ1(x) was separated from Φ(x), and the Lorentz polarization factor was inducted into φ1(x). Lastly, the peak position of intensity distribution curve obtained by the above manner was determined by the parabola fitting method. These calculations were carried out by the digital computer.By using this method, the residual stresses on the some samples were measured, and on the basis of the experimental results, the following conclusions were derived.(1) It is considered that the effect of Kα doublet can be ignored from the view point of the accuracy of stress value even if the value of residual stress is large.(2) It is supposed on the other hand that the effect of the Lorentz polarization factor on the measured stress is remarkable especially for the specimen which has a broad profile. However, when the half-value breadth of the profile given by Kα doublet is less than 3°, it may be considered that this effect can be neglected.(3) By separating the Kα doublet and then correcting the Lorentz polarization factor, the X-ray residual stress on the shot peened carbon steel specimen agrees fairly well with the mechanical one, compared with the X-ray residual stress obtained by the raw data.(4) Although the effect of Kα doublet can be neglected, it is considered that this method has the characteristic of being suitable to the measurement of the peak position of diffraction profiles with whatever shapes including broad ones.

The authors previously reported on the behaviour of residual stress and change in microstructure due to cyclic stressing by rotary bending of tufftrided carbon steel specimens. They also pointed out that no change was observed in residual stress and microstructure on the surface layer of the specimen during the fatigue process. The strength of tufftrided steel was influenced by the amount of precipitation of nitriding materials in the matrix.In order to clarify the improved mechanism of fatigue-resistance of tufftrided steel, however, it is required that more detailed investigation will be made. It is especially important to make inquiry of the effects of mean stress superposed to the cyclic stresses and the contribution of residual stress. Investigation was therefore made of the fatigue limit and the fatigue life on the alternate bending with mean stress, and of the change in residual stress during the fatigue process.Plate type 0.07% carbon steel specimens were used as the experimental material, and these specimens, after being machined and annealed, were tufftrided at 570°C for 90min. The alternate stress and mean stress were applied to the specimen by Schenck type reversed bending fatigue testing machine. The residual stress in the specimen surface on the way of fatigue process were measured by X-rays. By taking the residual stress as a mean stress and by calculating the equivalent stress amplitude in reversed bending, the contributions of residual stress to the fatigue limit and the fatigue life were studied. An ideal S-N curve, which did not include the influence of residual stress, was introduced.The results of the experiment and discussions thereanent are summarized as follows:(1) Both the fatigue limit and the fatigue life decrease as the mean stress increases. The fatigue limit in the case of supeprosed mean stress coincides with the initiation of plastic deformation.(2) The compressive residual stress in the specimen surface, where the tensile mean stress is loaded with cyclic stress, almost disappears in the initial stage of fatigue life. On the other hand, the residual stress on the compression side slightly decreases at about-20kg/mm2 in the initial stage, but this value remains to the fracture. It is considered that there is no contribution of compressive residual stress of the fatigue strength.(3) Based on the ideal S-N curve, the contribution of residual stress to fatigue limit which is improved by tufftriding is about 14∼30% in case the fatigue is caused by reverse bending.On the other hand, it is evident that 50∼90% of the whole fatigue life is influenced by the compressive residual stress.

The requirement for the standard block for hardness is that it has a designated hardness over the whole surface and must reproduce the same value at each test.In the indentation hardness test, however, plastic deformation is also produced inevitably by repeating tests on the same block, and it affects the standard value of hardness. It is important to know how long the initial designated hardness may be retained.The author measured, on the Rockwell hardness test block, 1) the change of hardness, 2) the residual strain and 3) the change of residual stress on the surface due to repetition of test, using electric wire strain meter, optical flat and X-ray method, and obtained the followings as the test results:(1) In the process of successive indentation, three stages of hardness change were observed; until fifty times of indentation, two groups were observed for hardness, one which increases slightly, and the other, which shows no changes, and thereafter there appears no change in hardness till one hundred and fifty times of indentation. Over that number of indentation, it is likely that the hardness will increase.(2) Over the back side of the block, residual compressive strain was observed It was greater for softer materials, and greater as well when the standard block was of smaller thickness.(3) On the testing surface, residual compressive stress was observed. The stress increased as the number of indentation increases.(4) The reliable value of standard hardness is obtained after indentations of fifty times. The block, subjected to indentation of more than one hundred and fifty times, gives an incorrect value of hardness.

Stress measurement by X-ray diffraction has certainly definite advantages. It is the only nondestructive method of determining the residual stress in metallic materials. Another feature is the fact that the localized stress can be measured by this method.In the field of mechanical and structure engineerings, it is said that residual stress in products is the problem of importance in the process of production and also in performance. The distribution of residual stress in these materials is in many cases determined by employing the destructive method, although this method has a little reliability in view of experimental procedure and has adaptability to very limited sort of materials.Recently the experimental technique of X-ray stress measurement has been surprisingly improved in our country and the field of its application is very much enlarged.In this connection, in the present paper, some methods of determination of residual stress by means of X-ray diffraction are demonstrated, by taking examples of specimen in the shape of plate and cylindrical bar. The equations for the calculation of residual stress are as follows:(1) plate (the case of symmetrical residual stress distribution)where σ: residual stress at a distance a from surface. σX: measured residual stress by X-ray at the layer a. h: thickness of plate.(2) plate (the case of unsymmetrical residual stress distribution)where σ: residual stress at a distance a from the top surface.σX: measured residual stress by X-ray method at the layer a.σbs: initial residual stress at the bottom surface.σba: residual stress at the bottom surface after removing the depth a.(3) cylindrical barwhere σz, σt, σr: axial, tangential and radial direction residual stress at the radius r.σzX, σtX: axial and tangential direction residual stress by X-ray method at the radius r after removing from surface a to r.It has been found from the result of present study that among the past investigations on the measurement of residual stress by means of X-ray are many problems open to questions about interpretation of the obtained results.

It has been pointed out by many researchers that substructure affects crack propagation in case of fatigue of metallic materials. However, the materials used in the past investigations were mostly homogeneous, and the microscopic behaviour of surface hardened materials such as tufftrided steel is only little known.In the present study, some investigations were made to obtain the relation between the crack propagation and substructure of tufftrided steel specimens with notch root through the observations of the crack propagation and the change in substructure in the vicinity of notch root and crack during the fatigue process by using the back reflection X-ray microbeam diffraction technique.The results obtained are summarized as follows;(1) The life to fracture or the period preceeding crack initiation of a tufftrided steel specimen increases remarkably as compared with that of a non-tufftrided steel specimen under the same stress amplitude.(2) The crack initiates at a comparatively early stage in the life to fracture and grows rapidly. However, when the crack tip passes through the position 1∼2mm away from the notch root, the crack propagation rate gradually decreases.(3) The substructure had already formed at the places with high content of soluted nitrogen after tufftriding, and the same substructure can be observed in the vicinity of crack tips irrespective of crack length.(4) It is evident from the observations by microbeam X-rays and by a scanning electron microscope that the plastically deformed area in the vicinity of crack in the tufftrided steel is very small and the magnitude of deformation of each crystal is also small as compared with that in the non-tufftrided steel.