Development of Residual Stress Measurement Apparatus by Neutron Diffraction and Its Application to Bent Carbon Steel

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(1)｢材料｣ (Journal of the Society of Materials Science, Japan), Vol. 70, No. 5, pp. 353-360, May 2021. Technical Review. Development of Residual Stress Measurement Apparatus by Neutron Diffraction and Its Application to Bent Carbon Steel Makoto HAYASHI*, Shinobu OKIDO**, Nobuaki MINAKAWA*** and Yukio MORII****. To establish the measuring technique of neutron diffraction for the internal residual stress distribution in a structural component, a neutron diffraction apparatus was designed and manufactured in Japan Research Reactor No.3 (JRR-3). At the first step of measurement, basic characteristics of the diffractometer was evaluated. The incident neutron beam flux was 104 n/cm2/s and the Full Width at Half Maximum (FWHM) of diffracted neutron profile was about 0.3 degree. This indicates that the manufactured neutron diffractometer is capable for the residual stress measurement. As the first application of the neutron diffraction measurement, the residual stress distribution in plastically bent carbon steel plate was measured. A typical compressive-tensile-compressive-tensile residual stress pattern in the tangential direction in the bent plate was confirmed. The maximum stress near the surface was about 180 MPa. This means that the technique for residual stress measurement by neutron diffraction method can be established in Japan. Key words: Neutron diffraction, Diffractometer, Residual stress, Carbon steel, Plastic deformation. 1 Introduction Stress corrosion cracking or fatigue crack initiates and propagates near a welded junction in pipes and structural components of nuclear power plant due to high residual stress caused by welding. When the crack propagates inside, the residual stress re-distributes in the crack ligament. This changes the crack growth behavior. In order to estimate the remained crack growth life, the re-distributed residual stress distribution has to be evaluated. Although the X-ray diffraction method is widely used to accurately measure the residual stress in various kinds of materials, the penetration depth of X-ray is only about 20 m from the surface for the carbon steel using Cr-K X-ray, so that the residual stress inside the structure cannot be measured. On the other hand, penetration depth of the neutron exceeds several tens of mm. Thus the neutron diffraction is the only method available to non-destructively determine the residual stresses inside weldments 1),2). The residual stress measurements of structural components by the neutron diffraction method have been made last several decades in Europe and North-America 3)-5). Since the residual stress measurement by the neutron diffraction needs a powerful neutron source, however, the measuring technique for the residual stress by neutron diffraction has not been established in Japan. Accordingly a residual stress analyzer was designed and manufactured in Japan Research Reactor No.3 (JRR-3) of Tokai Establishment, Japan Atomic Energy Research Institute (now Nuclear Science Research Institute, Japan Atomic Energy Agency),. and it was named as RESA (Residual Stress Analyzer). At first a basic measurement was conducted as mentioned in this review. Based on several residual stress measurements 6),7), new residual stress measurement apparatus named as “TAKUMI” has been established in J-PARC MLF. It has been widely used for evaluation of phase stresses and residual stresses in the structural components 8),9). So far, residual strains were measured in almost all of the previous studies on the neutron diffraction, or obtained residual strains were converted to residual stresses using macroscopic elastic constants 2). Since the elastic constants depend on the diffraction planes 10),11), however, the authors have studied this dependency for ferritic steel 12). The results showed that Young’s modulus of hhl (211, 220, 110) diffraction was 243GPa, that of 200 diffraction was 188 GPa and that of 222 diffraction was 268 GPa. These values coincide with the calculated values using Kröner elastic model for single crystal 13)-16), if modified using the Young’s modulus ratio between the objective material and the single crystal. The authors also examined the spatial distribution of residual stresses in a socket welded joint and 4 inch butt welded pipe joint and found a good agreement between the neutron diffraction method and the X-ray diffraction method or the strain gauge method 17),18). The above mentioned results were obtained using the neutron diffraction apparatus of L3 diffractometer in NRU reactor in Chalk River Laboratories of AECL (Atomic Energy of Canada Limited.). In order to establish the residual stress measuring technique by neutron diffraction, a diffraction. + *. Received Apr. 14, 2020 2021 The Society of Materials Science, Japan Member: Mechanical Engineering Research Laboratory, Hitachi, Ltd. (now R&D Division, AIDA ENGINEERING LTD. Sagamihara, Kanagawa, 252-0134, Japan) ** Member: Mechanical Engineering Research Laboratory, Hitachi, Ltd. (now Hitachi-GE Nuclear Energy, Ltd. Hitachi, Ibaraki, 317-0073, Japan) *** Member: Nuclear Science Research Institute, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan (died in 2016) **** Member: Nuclear Science Research Institute, Japan Atomic Energy Agency (now Radiation Application Development Association, Tokai, Ibaraki, 319-1106, Japan). 01-13012-(p.353-360).indd. 353. 2021/03/11. 15:01:03.

(2) 354. M. Hayashi, S. Okido, N. Minakawa, Y. Morii. apparatus was designed and manufactured in JRR-3, and a basic measurement was conducted. In this review the outline of neutron diffraction apparatus, basic characteristics of the diffractometer and the measurement of the residual stress distributions in plastically bent carbon steel plate were described 19). 2 Neutron Diffraction Measurement. Neutron diffraction is a method for measuring the spacing d between the atomic planes of a crystal lattice. A neutron beam of a known wavelength λ is diffracted from its incident direction by a scattering angle 2θ according to Bragg’s law,  = 2d sinθ. (1) By scanning a detector through a range of scattering angles, a profile of neutron counts versus 2θ is obtained. Here, λ is wavelength of neutron beam, d is lattice spacing and θ is diffraction angle. When the lattice spacing changes due to the residual stress or the applied stress, the diffraction angle changes. Through the differentiation of eq.(1), lattice strain  can be calculated by the following equation,  = Δd/d = (do - d)/do = -cot・Δθ (2) Here d0 means stress free lattice spacing. Actually d0 is measured in small samples cut from the objective measurement positions in the structure and annealed for the stress relief. Usually carbon steel is annealed at 625℃ for two hours and furnace-cooled down to 200℃, and then cooled in air. In X-ray diffraction, sin2 method is usually employed and stress free lattice spacing d0 is not necessary 12). While the peak position of diffracted profile is determined by half-value center point method in X-ray diffraction method, the peak position is determined by the center of Gaussian approximated diffraction profile in this experiment. Strain components are measured in a direction that bisects the incident and diffracted neutron beams. To obtain values of strain in the axial (A), radial (R) and hoop (H) directions of a tubular material, the tube must be reoriented to place this bisector in the required direction. With the three directional strain A, R and  measured at each location, three directional residual stresses, , R and H, can be calculated through a generalized Hook’s law,. 3 Neutron Diffraction Apparatus An outline of JRR-3 in Tokai Establishment of Japan Atomic Energy Research Institute is shown in Fig.1. The swimming pool type 20 MW reactor main body is established in the reactor hall in the left side in the figure. In the surroundings of the reactor various kinds of diffraction apparatus G1-G6 and 7R are set. They are used for the studies to clarify the function mechanisms of high temperature superconducting and spintronic materials. Three cold neutron beam lines C1-C3 and two thermal neutron beam lines T1 and T2 are set up in the right side guide hall. Many diffraction apparatus and small angle scattering apparatus are located along the beam lines. In this study the diffraction apparatus named DIVE set at T2-1 was reconstructed and changed to the residual stress measuring apparatus named as RESA (REsidual Stress Analyzer).. Fig.1 Outline of Japan Research Reactor No.3 (JRR-3). For the reference, the neutron spectrum of the thermal neutron beam line T1 is shown in Fig.2. The ordinate is neutron intensity in arbitrary scale and the abscissa is neutron wavelength  in nm. As can be seen in the figure, neutron intensity is strong for  from 0.1 nm to 0.35 nm and takes the maximum value around 0.19 nm. Since the appropriate neutron wavelength for the crystal structure analysis ranges from 0.15 nm to 0.2 nm, the neutron spectrum shown in Fig.2 is suitable for the residual stress measurements of carbon steel, stainless steel, aluminum and copper alloys.. . E 1+. 1-2. E 1+. 1-2.  = ───[ + ─── (A+R+)]. . R = ───[R + ─── (A +R+H)]. . E H + ─── (A +R+H)] H= ───[ 1+. 1-2. (3). where E is Young’s modulus,  is Poisson’s ratio, and the subscripts indicate components of strain and stress. These elastic constants depend on the diffraction plane. The authors revealed that the proper elastic constants were E=243GPa and =0.28 for strain determined from shifts in the 112 diffraction peak for ferritic steel.. 01-13012-(p.353-360).indd. 354. Fig.2 Neutron spectrum of thermal neutron beam at T1 line. The outline of neutron diffraction apparatus is shown in Fig.3. The neutron flux in the thermal neutron guide is 108 n/cm2/sec. The neutron beam is monochromized by. 2021/03/11. 15:01:04.

(3) Development of Residual Stress Measurement Apparatus by Neutron Diffraction and Its Application to Bent Carbon Steel. 355. monochromator made of piled carbon. The obtained wavelength ranges from 0.1 nm to 0.2 nm and the neutron flux is about 106 n/cm2/sec. After the monochromation the neutron beam passes through the 3 m long guide tube made of aluminum. The incident neutron beam size is determined by B4C rubber slit, the size of which is 30 mm square, located inside of the aluminum beam guide and Cd plate slit set at the end of the aluminum beam guide. The tip of aluminum beam guide can expand and contract. The neutron flux at the Cd slit is about 104 n/c2/sec. This flux is sufficient for the residual stress measurement. Fig.5 Photograph of goniometer mounted on diffractometer.. Fig.3 Outline of neutron diffraction apparatus established at JRR-3. The measured sample is mounted on a computercontrolled XYZ-translator fixed on the diffractometer and can be placed at a selected locations within the sample. Thus a spatial map of strain is constructed. The diffracted neutron beam pass through the receiving Cd slit and detected with the one dimensional position sensitive detector. Its aparture width is 5 mm and 100 mm long. The overview of neutron diffraction apparatus and XYZ-translator are shown in Figs.4 and 5 respectively. In Fig.4 the monochromator is set at upper side, and an incident beam guide comes from the upper side and a diffraction beam guide is at left side. The sizes and configurations of slit made of Cd set both at the neutron beam guide are arbitrarily changeable.. Incident Beam Slit Neutron Sample Diffraction Beam Slit. 3-Axis Goniometer Fig.4 Overview of neutron diffraction apparatus at T2-1.. 01-13012-(p.353-360).indd. 355. A measurement and control system for the neutron diffraction is shown in Fig.6. A main controller is connected with a motor driving controller and a multi-channel analyzer through GP-IB. The diffractometer and the translater, in other words, goniometer are driven through motor driving controller. The diffractometer is scanned in 2θ direction and goniometer can be driven in X, Y and Z direction independently. Accordingly, once the original position of measuring sample is set, the sample is automatically moved and the diffraction profile at the desired position can be measured. The diffracted neutron detected with the mono-dimensional position sensitive detector is analyzed by the multi-channel analyzer. The analyzed data is transmitted to the main controller and it converted to the relationship between the diffraction intensity and the diffraction angle. Equipment of RESA Goniometer : X,Y,Z Diffractometer:2θ. Motor driver. 1-Dimensional counter. Motor driver controller. Multi-channel analyzer. Main controller GP-IB unit Ethernet Line. Fig.6 Measurement and control system for neutron diffraction apparatus. Specifications of mono-dimensional position sensitive neutron detector is shown in Table 1. In order to improve the detectability and spatial resolution and reduce the γ-ray cross-section, 3He-CF4 gas is full-filled at 800 kPa in the detector. Aparture window is made of 2.5 mm thick aluminum. Furthermore, multi-electrodes wire made of metal are employed for the high detectability and the long life. Active length of the detector is 100 mm. Since the active length is 100 mm and the spatial resolution is 100 pixels, pixel size is 1 mm. The detection efficiency is 52% for =0.1. 2021/03/11. 15:01:04.

(4) 356. M. Hayashi, S. Okido, N. Minakawa, Y. Morii. nm neutron and 78% for =0.2 nm neutron respectively. The usage of wavelength of 0.1 to 0.2 nm neutron in this experiment means relatively high detectability. The function of mono-dimensional position sensitive detector was confirmed. The relationship between channel number of multi-channel analyzer and diffraction angle obtained by using a standard powder sample is shown in Fig.7. The figure reveals that the channel number is in proportion to the diffraction angle for the diffraction angle of 2=±1.7 degree. Table 1. Specification of mono-dimensional position sensitive detector.. angle of incident neutron beam should be small for decreasing the FWHM. At that time, the diffraction beam intensity decreases and the measurement time increases. This leads to decrease of accuracy from the view point of statics. Thus the appropriate FWHM should be controlled. In Fig.9, A1 is divergent angle between guide tube T2 and monochromator, A2 is divergent angle between monochromator and sample, A3 is divergent angle between sample and detector, B is curveture angle of monochromator crystals, and m is diffraction angle at monochromator. Figure 9 is obtained for m of 73.12 degree. FWHM takes the minimum value of 0.33 degree at the diffraction angle of 2=43 degrees.. Neutron counts (X103 counts). 12. 11. 10. 9. 8 -2.0 500. 1.0. 300 200. 0.8. 100 0 -2.0. -1.5. -1.0. -0.5. 0 0.5 2 (deg). 1.0. 1.5. 2.0. Fig.7 Relationship between channel number of multi-channel analyzer and diffraction angle. The result of detection efficiency of detector is shown in Fig.8. The ordinate is neutron counts for several seconds and the abscissa is diffraction angle 2θ. Although the neutron counts are a little bit scattered, almost equal detection efficiency can be obtained for the diffraction angle of 2=±1.5 degree. Dependency of full width at half maximum (FWHM) of diffracted neutron profile obtained by the neutron diffraction apparatus shown in Fig.3 is shown in Fig.9. Here FWHM was calculated using Cagliotti’s equation 20). In the residual stress measurement by the neutron diffraction, the peak shift gives the residual strain as shown in eq.(2) and it is converted to the residual stress through eq.(3). This indicates that the narrower FWHM, the more accurate residual stress. The divergent. 356. FWHM (deg). Channel (ch). -1.0. -0.5. 0 0.5 2 (deg). 1.0. 1.5. 2.0. Fig.8 Detection efficiency of mono-dimensional position sensitive detector.. 400. 01-13012-(p.353-360).indd. -1.5. A1=0.25deg A2=0.3deg A3=0.3deg B=0.5deg m=73.12deg. 0.6. 0.4. 0.2 20. 40. 60 80 2 (deg). 100. 120. Fig.9 Dependency of FWHM on diffraction angle. 110 diffraction profile obtained from the annealed carbon steel is shown in Fig.10. The diffraction profile is approximated by the Gaussian distribution (solid curve) and the peak position is determined. The calculated peak position is 58.889 degree in 2θ. This means the lattice constant is 0.286105 nm, and it is a little bit smaller than that of pure iron of 0.28644 nm. FWHM in Fig.10 is 0.293 degree and it nearly coincides with the calculated value shown in Fig.9.. 2021/03/11. 15:01:05.

(5) 357. Development of Residual Stress Measurement Apparatus by Neutron Diffraction and Its Application to Bent Carbon Steel. 500 Annealed material Peak position=58.889deg FWHM=0.293deg. Intensity (counts). 400 300 200. 100 0 58.0. 58.5. 59.0 2 (deg). 59.5. 60.0. Fig.10 110 diffraction profile obtained in annealed carbon steel plate. 4 Residual Stress in Plastically Bent Carbon Steel Plate. steel plate is shown in Fig.11 and the residual stress measured region was shown in Fig.12. Because the residual strain in the three directions has to be measured in the neutron diffraction stress measurement, as shown in eq.(3), the residual strains in X direction (tangential direction), Y direction (thickness direction) and Z direction (width direction) were measured. The appearance of residual stress measurement of bent carbon steel plate is shown in Fig.13. The incident beam slit and the diffraction beam slit are seen at right and left side respectively in the figure. The slit sizes are 4 mm in diameter. The bent carbon steel is mounted on the three axis goniometer. In Fig.13, the residual strain is measured in X (tangential) direction. The measured pitches are 2 mm in the thickness direction and 5 mm in the width direction. Then the total number of measured position is 66.. Detector Neutron. The basic characteristics of the neutron diffraction apparatus were verified. In order to confirm the measuring function the residual stress distribution. Incident beam slit. Diffraction beam slit. Sample 3-axis Goniometer Fig.13 Appearance of residual stress measurement in bent carbon steel.. 500. Measured section. 200 Annealed material Bent material. Fig.12 Residual stress measured region in bent carbon steel plate.. inside a plastically bent carbon steel plate (JIS SM400) was measured. Thickness of the plate was 10 mm and width was 50 mm. The plate was forcefully bent with the radius of 40 mm at the internal side using a jig of which radius was 40 mm. The appearance of the bent. 01-13012-(p.353-360).indd. 357. Intensity (counts). 400.  =0.034deg =5.4x10-4. 150. 300 100 200. 0 58.0. 50. . 100. 58.5. 59.0 2 (deg). 59.5. Intensity (counts). Fig.11 Appearance of bent carbon steel plate.. For the measurement of thickness directional strain, the 3-axis goniometer was rotated 90 degrees from the condition shown in Fig.13. For the measurement of width directional strain another shaped supporting jig was used. Measurement time is about 1 hour for each strain measurement. 110 diffraction profiles obtained in the annealed and plastically bent carbon steel are shown in Fig.14. In the figure, open circles show the profile measured in annealed steel and solid circles show the profile measured in the bent steel. The peak position of the bent steel shifts 0.034 degree to higher angle side compared with the annealed steel. This peak shift. 0 60.0. Fig.14 110 diffraction profiles obtained in annealed and plastically bent carbon steel.. 2021/03/11. 15:01:06.

(6) 358. M. Hayashi, S. Okido, N. Minakawa, Y. Morii. corresponds to the tensile strain of 5.4 x10-4 strain. The three dimensional expression of the residual strain in the tangential direction is shown in Fig.15. The origin of the thickness direction is inner side of plastic bending deformation. Since the inner side is deformed to compressive side and spring backed to tensile, about 0.1% tensile residual strain remains. The tensile strain changes to the compressive side at about 3 mm from the surface, and it changes to the tensile side again from the plate thickness center. About 0.06% compressive residual strain remains outside surface. Similarly the residual strain distributions in the width and thickness directions, and the residual stresses are calculated using eq.(3). The tangential residual stress distribution is shown in Fig.16. In the figure the residual stress distribution in the whole cross section is illustrated. As a whole, the tangential residual stress distribution becomes tensile-compressive-tensile-compressive from the inside to outside of bending deformation. However, the extraordinary residual stresses are obtained at the four corners of the measured section, depending on the constraint of bending deformation. This kind of extraordinary distribution could be understood from the deformation condition as can be seen in Fig.11, and it seems due to saddle shaped deformation with the low constrains at the free surface of both end side of width direction. Since the extraordinary stress distribution is obtained about 10 to 15 mm from the end surface, accordingly the residual stress distribution except that kind area is shown in Fig.17. The residual stress in the tangential direction in the bent steel takes typical compressive-tensile-compressive-tensile pattern from inside to outside of the bent plate. The absolute. Fig.15 Residual strain distribution in tangential direction.. Fig.16 Residual stress distribution in tangential direction at the central whole cross section.. 01-13012-(p.353-360).indd. 358. values both at the inside and outside surfaces ranges from 120 to 180 MPa. These values are relatively lower than those expected from the degree of plastic deformation. One of the reasons is that relatively large 4 mm neutron beam slit size gives an averaged value in the measured volume of 2 times 4 mm block at the surface area.. Fig.17 Residual stress distribution in tangential at the center region of cross section. As described before, two dimensional distribution of the residual stresses in the three directions in the plastically bent carbon steel can be evaluated with relatively good accuracy. Especially, the typical compressive-tensile-compressive-tensile residual stress pattern can be obtained from the inside to the outside of the bent steel plate. This means the technique for the residual stress measurement technology by the neutron diffraction is considered to be established in Japan. 5 Conclusions To establish the measuring technique of neutron diffraction method for the internal residual stress distribution in a structural component, a diffraction apparatus was designed and manufactured in JRR-3 (Japan Research Reactor No.3) and applied to the residual stress measurement in the bent carbon steel. The results are summarized as follows. (1) The neutron diffraction apparatus was designed and manufactured at the thermal neutron beam line in JRR-3. (2) At the first step of measurement, basic characteristics of the diffractometer was evaluated. The incident neutron beam flux was about 104 n/cm2/sec and FWHM was about 0.3 degree. This indicates that the manufactured diffractometer is capable for the residual stress measurement. (3) As the first application of the neutron diffraction measurement, the residual stress distributions in plastically bent carbon steel plate were measured. Typical compressive-tensile-compressive-tensile residual stress in tangential direction in the bent plane was measured. (4) The above results means the technique for the residual stress measurement by neutron diffraction method can be established in Japan.. 2021/03/11. 15:01:07.

(7) Development of Residual Stress Measurement Apparatus by Neutron Diffraction and Its Application to Bent Carbon Steel. References 1). J. Faber (Private Letter). L. Pintschovious, V. Jung, E. Macjeraich and O. Vohringer,. 12) “Standards for X-ray stress measurement”, The Society of. “Residual stress measurements by means of neutron diffraction”, Mat. Sci, & Eng., 61, pp.43-50 (1983) 2). 3). Materials Science, Japan (1987) 13) M. Hayashi, M. Ishiwata, N. Minakawa, S. Funahashi and J. H.. A. J. Allen, M. T. Hutchings, C. G.Windsor and C. Andreani,. Root, “Diffraction plane dependence of elastic constants in. “Neutron diffraction methods for the study of residual stress. ferritic steel in neutron diffraction stress measurement”, Journal. fields”, Advances in Physics, 34, pp.445-473 (1985). of the Society of Materials Science, Japan, 44, pp.1115-1120. A. Stacey, H. J. MacGillivary, G. A. Webster, P.J. Webster and K. R. A. Ziebeck, “Measurement of residual stresses by neutron. 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Appendix Before and after the development of RESA, the authors have applied the neutron diffraction method to many structural component and materials. The followings are list of published papers concerning to the measurements of residual stress and textures. a) T. M. Holden, J. H. Root, R. A. Holt and M. Hayashi, “Neutron diffraction measurements of stress”, Physica B, 213&214, pp.793-796 (1995) b) J. H. Root, C. E. Coleman, J. W. Bowden and M. Hayashi, “Residual stresses in steel and zirconium weldments”, J. Pressure Vessel Technology, 119, pp.137-141 (1997) c) M. Hayashi, H. Kimoto, H. Michishita, and J. H. Root, “Measurement of texture and elastic constants of Zr-2.5%Nb alloy by neutron diffraction”, Journal of the Society of Materials Science, Japan, 46, pp.743–749 (1997) d) Y. Akiniwa, K. Tanaka, T. Takezono, M. Hayashi, N. Minakawa and Y. Morii, “Neutron and X-ray diffraction measurements of phase stresses in SiC particulate reinforced aluminum. 01-13012-(p.353-360).indd. 359. e). f). g). h). composite”, Journal of the Society of Materials Science, Japan, 47, pp.755-761 (1998) M. Hayashi, M. Ishiwata, Y. Morii N. Minakawa and J. H. Root, “Residual stress distribution in carbon steel pipe welded joints measured by neutron diffraction” Materials Science Research International, 6, pp.287-294 (2000) M. Hayashi, S. Okido, Y. Morii and N. MInakawa, “Measurement of residual stress in structural components by neutron diffraction”, Materials Science Research International, Special Technical Publication-1, pp.418-423 (2001) M. Hayashi, S. Okido, Y. Morii, N. Minakawa and J. H. Root, “Residual Stress Measurements of Structural Components by Neutron Diffraction and Proposal of Measurement Standard”, Materials Science Forum, 426-432, pp.3969-3974 (2003) S. Ohkido, M. Hayashi, Y. Akiniwa, K. Tanaka, N. Minakawa and Y. Morii, “Residual stress measurement in shrink fitted component in textured Al alloy by neutron diffraction method”, Journal of the Society of Materials Science, Japan, 54, pp.333-338 (2005). 2021/03/11. 15:01:07.

(8) 360. M. Hayashi, S. Okido, N. Minakawa, Y. Morii. i) S. Okido, M. Hayashi, N. Minakawa, Y. Morri and K. Ando, “Evaluation of residual stress distribution of butt-welded pipe and redistribution behavior with crack extension using neutron diffraction method”, Journal of Pressure Technology, 43, pp.208-215 (2005) j) M. Hayashi, Y. Morii, T. Saito, H. Suzuki and A. Moriai, “Residual stress measurement in aluminum engine block”, Journal of the Society of Materials Science, Japan, 60, pp.624–629 (2011) k) M. Hayashi and J.H. Root,”Effect of Miss-alignment on Residual Stress in Carbon Steel Socket Welded Joint. Journal of the Society of Materials Science, Japan, 63, pp.602–607 (2014) l) Y. Onuki, A. Hoshikawa, s. Sato, P. Xu, T. Ishigaki, Y. Saito, H. Todoroki and M. Hayashi, “Rapid measurement scheme for texture in cubic metallic materials using time-of-flight neutron diffraction at iMATERIA”, J. Applied Crystallography, 49, pp.1579-1584 (2016) m) M. Hayashi, J. H. Root, R. B. Rogge and P. Xu, “Evaluation of Residual Stress Relaxation in a Rolled Joint by Neutron Diffraction”, Quantum Beam Science, 2 (2018) 21 n) M. Hayashi, S. Okido and H. Suzuki, “Residual stress distributions in water jet peened type 304 stainless steel”, Quantum Beam Science, 4, (2020) 18 The representative results are described in the following. There exists diffraction plane dependency of elastic constants. So the diffraction plane dependency of measuring material has to be examined using the tensile specimen the chemical compositions of which are the same with the measuring material. However, it takes several days. The authors calculated Young’s moduli in single crystal using Kroner model, modified them based on the ratio of bulk Young’s modulus and the Young’s modulus of single crystal and compared them with the measured values. The relationship between estimated and measured Young’s moduli in carbon steel, austenitic stainless steel, aluminum alloy and Zr-2.5%Nb alloy is shown in Fig.A. The estimated values well agree with the measured values.. measured by the X-ray. So the surface layer stress distribution with steep stress gradient can be evaluated even by the neutron diffraction method.. Fig.A Relationship between estimated and measured Young’s moduli in several materials.. Fig.B Pseudo peak shifts due to gauge volume deviating from measurement sample.. Thus the diffraction plane dependency can be easily determined by the Kröner model calculation and the tensile testing. This is very much cost and time saving method. When the gauge volume deviates from the sample in the residual stress measurement for the surface layer using neutron diffraction, a pseudo peak. shift occurs and accurate stress distribution cannot be evaluated. Therefore, the pseudo peak shift has to be measured under the same conditions as in the case of actual residual stress measurement using a sample in an unstressed state. The pseud peak shifts obtained are shown in Fig. B. The pseud peak shifts depend on the diffraction conditions. In the figure the peak shifts for the reflection in z direction and the transmission in x and y directions are shown. The residual stress distributions in near-surface of water jet peened type 304 stainless steel plate considering the pseud peak shift are shown in Figure C. The residual stress distribution in x direction measured by the sequential polishing X-ray diffraction method is also shown in Fig. C. The residual stress distribution in x direction measured by the neutron diffraction well agrees with that. 01-13012-(p.353-360).indd. 360. Fig.C Residual stress distributions in near-surface of water jet peened type 304 stainless steel plate considering the pseud peak shift. 2021/03/11. 15:01:07.

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