X-ray stress measurements are widely used as one of the most powerful nondestructive tools to measure residual stress in polycrystalline solids. In most cases, the sin2ψ method has been adapted to determine the stress. In recent years, the cos α method attracts engineers as a new method to measure the stress using two-dimensional detectors, such as imaging plates (IP). The present article is the part one of the review of state of the art of the cos α method. The principle of the method was originally proposed in Japan and has been developed in cooperative works in the Society of Materials Science, Japan. The strain is determined from the whole Debye-Scherrer ring recorded on IP by single exposure of X-rays as a function of the orientation angle α. In one measurement, the normal stress is determined by cos α diagrams and the shear stress by sin α diagrams, without knowing the exact value of stress-free diffraction angle. A commercial portable stress analyzer adapting the cos α method shortens the measurement time to about 1min. In the present article, the history of the development of the cos α method is covered and fundamentals of the method are presented. The advantages of the cos α method are highlighted in comparison with the other methods of X-ray stress determination.
The cos α method utilizes the whole Debye-Scherrer ring recorded on a two-dimensional detector taken by single exposure of X-rays to determine the normal and shear stresses. The simple optical system of the cos α method makes stress analyzers smaller, lighter, and handier to use for on-site measurements. Part 2 of this review describes several precautions of the measurement procedure to acquire accurate stress values in short time. The accuracy of the stress measurement of the cos α method has been confirmed to be equivalent to that of the sin2ψ method for various metals. The shear stress as well as normal stress is determined by single exposure. Various advantages of the cos α method are clarified in the experimental procedure of stress determination. Spotty Debye-Scherrer rings obtained from coarse-grained metals sometimes hamper accurate stress determination. To overcome such difficulty, several possible techniques including the oscillations of beam and specimen are proposed, together with new analysis method for stress determination specific to coarse-grained materials. Applications of the cos α method to welded members are presented, together with the future perspective of the method.
The investigation was made on the phenomena observed in the X-ray stress measurement on a curved surface by the cos α method. Numerical analysis was performed simulating the cos α method for the circumferential stress and the axial stress on a cylindrical surface. The X-ray residual stress measurements by the cos α method and the sin2ψ method were carried out respectively for the blasted surface of round steel bars with various diameters. It was found that the debye ring turned oval and the slope of cos α diagram decreased as the ratio of the X-ray beam size to the bar diameter increased, i.e. the magnitude of the measured stress was smaller than that of actual one. These tendencies were remarkable in the circumferential stress measurement. With respect to the relation between the X-ray beam size and the measured value of stress, the difference between the cos α method and the sin2ψ method was found to be small. The measurement error due to a cylindrical surface was negligible when the X-ray beam size was less than 1/3 of the diameter.
The core steel part “NAKAGO” in the hilt of the Japanese short sword “TANTO” was used. This sword was made by one sword craftsman. The surface of the core steel part was machined manually by him using some hardened files. After hand-filing, the filed mark lines were remained on the finished surface. In this study, the 2θ-sin2ψ diagrams as a function of φ-angle from Fe-211 plane using Cr-Kα radiation were measured near the filed surface. The residual stress field near the filed surface of “NAKAGO” was determined. As a result, the typical 2θ-sin2ψ diagrams from the filed and electrolytic polished surfaces show the ψ-splitting phenomena. The compressive residual stresses, σ11, σ22 and σ12, of about -208, -235 and -8.11 MPa were found to be generated on the in-plane polished surface parallel and perpendicular to the average filed line. And the microscopic shear residual stresses having stress gradients, σ13 and σ23, of about 28.7 and 2.88 MPa were also generated on the out-plane. It was concluded that the surface layer of the core steel part "NAKAGO" could be strengthened by this biaxial compressive residual stress field induced by hand-filing.
The excessive tensile residual stress generated by welding after surface machining may be an important factor to cause stress corrosion cracking (SCC) in nuclear power plants. Therefore we need to understand and control the residual stress distribution appropriately. In this study, residual stress distributions within surface machined layer generated by surface machining and sequential welding were evaluated by X-ray diffraction method. Depth directional distributions were also investigated by electrolytic polishing. In addition, to consider the effect of work hardened layer on the residual stress distributions, we also measured full width at half maximum (FWHM) obtained from X-ray diffraction. Testing material was a low-carbon austenitic stainless steel type SUS316L. Test specimens were prepared by surface machining with different cutting conditions. Then, bead-on-plate welding under the same welding condition was carried out on the test specimens with different surface machined layer. As a result, the tensile residual stress generated by surface machining increased with increasing cutting speed and showed nearly uniform distributions on the surface. Furthermore, the tensile residual stress drastically decreased with increasing measurement depth within surface machined layer. Then, the residual stress approached 0MPa after the compressive value showed. FWHM also decreased drastically with increasing measurement depth and almost constant value from a certain depth, which was almost equal regardless of the machining condition, within surface machined layer in all specimens. After welding, the transverse distribution of the longitudinal residual stress varied in the area apart from the weld center according to machining conditions and had a maximum value in heat affected zone. The magnitude of the maximum residual stress was almost equal regardless of the machining condition and decreased with increasing measurement depth within surface machined layer. Finally, the residual stress distributions were almost same in deeper depth than that showing a constant value of FWHM.
In the shot peening process, the residual stress on the shot-peened surface and its distribution under the surface are important evaluation items for the high value-added surface creation. In this paper, it was proposed that the residual stress distribution under the shot-peened surface for a thin plate was non-destructively estimated from the measured value of residual stress on the surface and that of the arc height, by applying the theory of linear thermal stress analysis for a thin plate. The analyzed residual stress profile showed good agreement with that of the experimental results obtained from the surface removal by electro-polishing. From the results of analysis, it was found that the depth of compressive residual stress (the depth which changes from the compressive stress to the tensile stress), the residual stress at the depth of the inherent strain and the residual stress on the opposite surface to the shot-peened surface characterizing the profile of residual stress distribution had a relationship with the ratio of a thickness of plate to an inherent strain depth.
The X-ray diffraction technique is widely used for measuring the residual stress on metal surfaces. Since the penetration depth of X-rays is shallow, the surface removal method has been adapted to measure the in-depth distribution of the residual stress. The measured stress distribution needs to be corrected to take into account of the redistribution due to surface removal. In this study, the correction of measured stress was performed using finite element analysis (FEA). For FEA, we prepared multi-layer solids with differential thermal coefficients of expansion. Uniform temperature change caused continuous residual stress distribution in the solids. Step-by-step surface layer removal of a flat plate and a cylinder was carried out in simulation, and then the matrices for stress correction were obtained. FEA correction for entire surface layer removal was confirmed to be identical to the theoretical solution. In the case of local surface removal, it was clarified that the correction matrix obtained for a particular residual stress distribution is applicable to arbitrary stress distribution. Using this method, the difference in the stress correction for entire surface layer removal and local surface removal was determined and it was applied to residual stress distribution correction for a carburized steel bar. Moreover, we have discussed in depth how the stress correction for the entire surface layer removal can be applied for the local surface removal.
The yield stress of metals increases in proportion to the square root of dislocation density; this relationship is known as the Bailey-Hirsch relation. The increase in yield stress Δσ is expressed as a function of the shear modulus G, the Burgers vector of dislocation b, and dislocation density ρ using the equation: Δσ=αGb√ρ. Here, α denotes the dislocation strengthening coefficient. Research using transmission electron micrographs has revealed a linear relationship between √ρ and Δσ. Various values from 0.77 to 1.4 were reported for α in cold-worked iron, but the equation Δσ≒1.8×10-8 √ρ (α=0.9) has been established as applying to a variety of situations. On the other hand, the micro-strain ε has been measured via the Williamson-Hall method for two kinds of cold-worked iron: 0.001%C steel and 0.0056%C steel, with grain sizes of 120 μm and 50 μm, respectively. Plastic strain was induced by cold rolling up to a thickness reduction of 90%. The work hardening behavior is significantly different between these two steels but it was found that Δσ can be calculated for both using the equation Δσ[GPa] = 220×ε. From these results, the conversion equation; ρ[m-2] ≒ 1.5×1020 ε2 was introduced to relate ε and ρ. As a result, it was confirmed that the Bailey-Hirsch relation can be treated as a common standard for understanding of dislocation density, regardless of the measurement methods employed.
Composite materials made from two or more different components are widely used in fields ranging from semiconductor devices to mechanical structural materials. Depending on the environment, this construction material may be subjected to mechanical loads and thermal stress, and this may lead to problems such as delamination. The occurrence of such delamination is expected to be strongly dependent on the residual stress subjected to loading processes. In the present study, the influence of a repeated tensile bending load on the residual stress in the Cu film and the carbon steel in Cu-coated steel was investigated. In the absence of a Cu coating, it was shown that the residual stress in the steel changed to the compression side due to the application of a repeated tensile bending load. Furthermore, the magnitude of the compressive stress increased as the surface roughness of the substrate decreased. In the case of the Cu-coated steel under the same load, the residual stress was slightly tensile stress decreased, but its magnitude did not depend on the surface roughness. In the Cu coating itself, the residual stress was originally tensile, but its magnitude decreased under repeated loading. This decrease was much more significant when the surface roughness of the substrate was low.