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Technical Note
X-Ray Residual Stress Measurement of Austenitic Stainless Steel Based on Fourier Analysis Toshiyuki Miyazaki* and Toshihiko Sasaki Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan Received February 24, 2015 Accepted for Publication August 20, 2015 http://dx.doi.org/10.13182/NT15-25
Abstract — In a previous study, the authors introduced a new nondestructive method to measure stress with a two-dimensional X-ray diffraction image. This method was tested on a carbon steel specimen. To apply this method to the structures of nuclear power plants, it is essential to show that the residual stress of austenitic stainless steel can be measured. We report on an experiment in which the method was used to measure the stress in austenitic stainless steel standards. The results were consistent with the specification of the stress standard and the conventional sin2 method. We conclude that the proposed method is promising for residual stress measurement of austenitic stainless steels. Keywords — X-ray, residual stress measurement, stainless steel. Note — Some figures may be in color only in the electronic version.
I. INTRODUCTION X-ray diffraction is a nondestructive tool for investigating residual stress in materials. Among the various X-ray stress measurement methods, the cos ␣ method1 can determine the stress with a single X-ray irradiation. This enables a shorter measurement time and simpler measurement system compared with the conventional sin2 method (for example, see Ref. 2). The introduction of an image plate (IP) as an imaging detector3 and improvement of the method4 have meant that the method can achieve the same accuracy as the sin2 method. The authors have reported5 on a new method based on Fourier analysis of the Debye-Scherrer rings (D-S rings) and demonstrated that it is a generalization of the cos ␣ method. This method was applied to a carbon steel specimen, and its capability to determine the stress was demonstrated. The purpose of the present study is to demonstrate that this new method is also applicable to austenitic stainless steels that are widely used in nuclear power plants. To apply the method, we used two characteristic X-rays. One is the Cr-K characteristic X-ray commonly used to examine ferritic *E-mail:
[email protected]
steel, and the other is Mn-K␣. Oguiso6 showed that Mn-K␣ with the sin2 method improves the accuracy of stress measurements conducted on austenitic stainless steel. More recently, Wang et al.7 demonstrated that the cos ␣ method can be used on nickel-based weld metal and Type 304 stainless steel (Type 304). We applied the new method using Cr-K and Mn-K␣ characteristic X-rays to stress standards made of Type 304 and Type 316L stainless steel (Type 316L).
II. THEORY Figure 1 shows the arrangement of the stress measurement. The term is the complement of the diffraction angle ( ⬅ /2 ⫺ ). The term 0 is the angle between the specimen surface normal and the X-ray incident angle (note that this 0 differs from the of the sin2 method). When the specimen is in the plane stress condition, the normal strain along the direction of the circumference angle ␣ of the D-S ring can be described as (␣) ⫽ a0 ⫹ a1 cos ␣ ⫹ b1 sin ␣ ⫹ a2 cos 2␣ ⫹ b2 sin 2␣ .
(1)
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2E 1 ·a . 1 ⫹ sin 2 sin 20 1
(3)
In this study, we report on the x evaluation of austenitic stainless steel stress standards by using Eq. (3). The reader may think that our method is similar to the -integral method.8 (A good summary can be found in Ref. 9.) The authors claim that the two methods are entirely different.10
III. EXPERIMENT III.A. Specimens The specimens were stress standards made by Proto Manufacturing, Inc. (http://www.protoxrd.com/index.html). We tested two specimens, one made of Type 304 and the other made of Type 316L. The specifications of the specimens are detailed in Table I. In Table I, “1/2S2” represents the X-ray compliance: Fig. 1. Arrangement of specimen, X-ray, and IP.
Each coefficient of Eq. (1) is related to the stress of the specimen. If the specimen is in the plane stress condition, a1, b1, a2, and b2 can be described using the longitudinal stress x, the lateral stress y, and the shear stress xy as follows: 1⫹ 2 sin sin2 0 · x , 2E 1⫹ sin 2 sin 0 · xy , b1 ⫽ E 1⫹ 2 sin (cos2 0x ⫺ y) , a2 ⫽ 2E
a1 ⫽ ⫺
and b2 ⫽ ⫺
1⫹ 2 sin cos 0xy , E
1⫹ 1 S ⬅ , 2 2 E and the “Stress” values are the stresses supplied by the manufacturer. We measured the X-ray stress of the specimen by using the conventional sin2 method with a Rigaku MSF-2M stress analyzer. The characteristic X-ray line used for the measurement was Cr-K, and the diffraction plane was (311). During the measurement, deformationinduced martensite was observed, and it degraded the signal-to-noise ratio. The stresses were measured with the X-ray parameters described in Table II as x ⫽ ⫺650 ⫾ 72 (MPa) (Type 304)
(2)
where E and are Young’s modulus and Poisson’s ratio, respectively. Once ε(␣) is described as a Fourier series, the stress of the specimen can be calculated using Eq. (2). For example,
and x ⫽ ⫺690 ⫾ 110 (MPa) (Type 316L) . (4) These values were consistent with the specifications supplied by the manufacturer (Table I).
TABLE I Description of Specimens Material
Characteristic X-Ray
20 (deg)
Diffraction Plane
1/2S2 (MPa⫺1)
Stress (MPa)
Type 304
Mn-K␣
152.8
(311)
7.18 ⫻ 10⫺6
⫺619 ⫾ 35
Type 316L
Mn-K␣
152.8
(311)
7.179 ⫻ 10⫺6
⫺780 ⫾ 35
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TABLE II X-Ray Parameters for the Cr-K Line Measurement Characteristic X-Ray
20 (deg)
Diffraction Plane
1/2S2 (MPa⫺1)
Cr-K
148.5
(311)
6.71 ⫻ 10⫺6
III.B. Stress Measurement from the D-S Ring The D-S rings were measured with a -X360 X-ray stress measurement instrument by Pulstec Industrial (http://www.pulstec.co.jp/en/index.html). The X-ray tubes used for the experiments were Cr and Mn. The characteristic X-ray lines and their tube conditions are detailed in Table III. The tubes were placed in two identical instruments. Type 304 and Type 316 powders were measured along with the stress standards to confirm that zero stress was calibrated. Figures 2a and 2b show the setup of the experiment and the simplified schematics, respectively. The detailed internal structure of the stress measurement instrument is shown as Fig. 6a of Ref. 11. The distance from the specimen to the IP was ⬃35 mm for the Mn X-ray tube and ⬃32 mm for the Cr X-ray tube. During the TABLE III Characteristic X-Ray Lines and Tube Parameters Characteristic X-Ray
Tube Voltage (kV)
Tube Current (mA)
Mn-K␣
30.0
0.33
Cr-K
20.0
1.0
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measurements, the placements of the specimen and instrument remained in the initial state shown in Fig. 2. Figure 3 shows examples of D-S rings acquired using the Mn-K␣ line. Each D-S ring was taken using 30 s of X-ray irradiation. Figures 3a through 3d are D-S rings from Type 304 powder, Type 316 powder, the Type 304 stress standard, and the Type 316L stress standard, respectively. Compared with the D-S rings from powder, the ones from the stress standards have degraded signal-tonoise ratios. The reason is considered to be the deformation applied during the manufacture of the stress standards. The D-S rings were read out in polar coordinates. The resolution in radial and angular coordinates were 50 m and 0.72 deg, respectively. The radii of the D-S rings were ⬃18 mm. Figure 4a shows ε(␣) calculated from the D-S rings of Figs. 3a and 3c. The solid line shows an example of ε(␣) of the D-S ring from the Type 304 stress standard, and the dashed line shows that from the Type 304 powder. To improve the accuracy in order to determine ε(␣), a moving average (11⫻11 pixels in the polar coordinate) was applied to the D-S ring images. This averaging did not affect the x measurement. Ten 150-s X-ray irradiations were used to calculate the average and standard deviation. Figure 5 shows an example of D-S rings acquired from the Cr-K line measurements. Each D-S ring was taken with a 120-s exposure. Figures 5a through 5d show D-S rings from Type 304 powder, Type 316 powder, the Type 304 stress standard, and the Type 316L stress standard, respectively. Figure 4b shows ε(␣) calculated from the D-S rings of Figs. 5a and 5c. The solid line shows an example of ε(␣) of the D-S ring from the Type 304 stress standard, and the dashed line shows that from the Type 304 powder. Even with a longer exposure time than in the
Fig. 2. (a) Setup of the experiment. Distances from the specimen to IP were ⬃35 and ⬃32 mm for the Mn and Cr X-ray tubes, respectively. (b) A simplified schematic of the setup.
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Fig. 3. D-S rings acquired in Mn X-ray measurements. Specimens were (a) Type 304 powder, (b) Type 316 powder, (c) Type 304 stress standard, and (d) Type 316L stress standard. Exposure times were 30 s each.
Fig. 4. (a) Example of ε(␣) with Mn-K␣ measurement. The solid line is from the Type 304 stress standard, and the dashed line is from Type 304 powder. (b) Example of ε(␣) with Cr-K␣ measurement. The solid line is from the Type 304 stress standard, and the dashed line is from Type 304 powder.
Mn tube case (Figs. 3a and 5a), the D-S rings acquired using the Cr X-ray tube were obscure and noisy. Ten 600-s X-ray irradiations were used to calculate the average and standard deviation. This X-ray irradiation time was five times that of the Mn-K␣ line measurement. The x of the powder specimens calculated from Eq. (3) were within ⫾30 MPa for both X-ray tubes. This confirms that the center of the D-S ring was well calibrated.
Table IV summarizes the stresses of the standards. From left to right, Table IV represents x described in the specifications of the manufacturer, calculated from the sin2 method (Cr-K line), and the new method (Mn-K␣ and Cr-K lines). All the x calculated from the X-ray measurements were consistent with the specification. It can be concluded that the new method is valid for measuring the stress of the evaluated specimens. NUCLEAR TECHNOLOGY
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Fig. 5. D-S rings acquired from the Cr X-ray measurements. The specimens were (a) Type 304 powder, (b) Type 316 powder, (c) Type 304 stress standard, and (d) Type 316L stress standard. Exposure times were 120 s each.
TABLE IV x of the Stress Standard* Specification
sin2 Method
Proposed Method
Cr-K
Mn-K␣
Cr-K
Type 304
⫺619 ⫾ 35
⫺650 ⫾ 70
⫺630 ⫾ 21
⫺690 ⫾ 55
Type 316L
⫺780 ⫾ 35
⫺690 ⫾ 110
⫺740 ⫾ 28
⫺780 ⫾ 70
*In units of megapascals.
IV. SUMMARY We applied the X-ray stress measurement method devised by Ref. 5 to austenitic stainless steel stress standards. The results were consistent with the specifications and measurements made with the conventional sin2 method. The proposed method uses a smaller and simpler setup than the sin2 method. This makes the method especially useful for on-site residual stress measurements at nuclear power plants. To confirm the validity of the proposed method, we are planning to perform four-point NUCLEAR TECHNOLOGY
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bending tests on commercially available austenitic stainless steel specimens. In addition, we will apply the analysis proposed by the authors12 to estimate the theoretical limit of the measurement error for the sin2 method and the proposed method.
Acknowledgments This work was partially supported by a Grant-in-Aid for the Innovative Nuclear Research and Development Program (No. 120804) from the Ministry of Education, Culture, Sports,
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Science and Technology in Japan. The authors thank Y. Fujimoto for help with the experiments.
References 1. S. TAIRA, K. TANAKA, and T. YAMASAKI, “A Method of X-Ray Microbeam Measurement of Local Stress and Its Application to Fatigue Crack Growth Problem,” J. Soc. Mat. Sci. Jpn., 27, 251 (1978); http://dx.doi.org/10.2472/ jsms.27.251. 2. I. C. NOYAN and J. B. COHEN, Residual Stress, SpringerVerlag, New York (1987). 3. Y. YOSHIOKA, in Proc. 27th Workshop X-Ray Studies of Mechanical Behaviour of Materials, Tokyo, Japan, 1990, p. 1. 4. T. SASAKI and Y. HIROSE, “Single Incidence X-Ray Stress Measurement for All Plane Stress Components Using Imaging Plate of Two-Dimensional X-Ray Detector,” J. Soc. Mat. Sci Jpn., 44, 1138 (1995); http://dx.doi.org/10. 2472/jsms.44.1138. 5. T. MIYAZAKI and T. SASAKI, “X-Ray Stress Measurement with Two-Dimensional Detector Based on Fourier Analysis,” Int. J. Mater. Res., 105, 922 (2014); http://dx. doi.org/10.3139/146.111101. 6. K. OGUISO, “The Comparison of X-Ray Stress Measurement Method of SUS304 by V, Mn, Cr Characteristic
X-Rays,” Proc. 37th Workshop X-Ray Studies of Mechanical Behaviour of Materials, Kyoto, Japan, 2001, p. 117. 7. Y. WANG et al., “In-Service Residual Stress Measurement Technique with Two-Dimensional X-Ray Diffraction for Weld Metal in Structural Components,” J. Soc. Mat. Sci. Jpn., 63, 409 (2014); http://dx.doi.org/10.2472/jsms.63.409. 8. W. LODE and A. PEITER, “X-Ray-Measurable Deformations in Superficial Layers and Their Representations,” Materialpruefung, 35, 758 (1981). 9. U. WELZEL et al., “Stress Analysis of Polycrystalline Thin Films and Surface Regions by X-Ray Diffraction,” J. Appl. Cryst., 38, 1 (2005); http://dx.doi.org/10.1107/S002188980 4029516. 10. T. MIYAZAKI and T. SASAKI, “X-Ray Stress Measurement from an Imperfect Debye-Scherrer Ring,” J. Mater. Res., 106, 237 (2015); http://dx.doi.org/10.3139/146. 111179. 11. Y. MARUYAMA, T. MIYAZAKI, and T. SASAKI, “Development and Validation of an X-Ray Stress Measurement Device Using an Image Plate Suitable for the Cos ␣ Method,” J. Soc. Mat. Sci. Jpn., 64, 560 (2015); http://dx. doi.org/10.2472/jsms.64.560. 12. T. MIYAZAKI and T. SASAKI, “Linearized Analysis of X-Ray Stress Measurement Using the Debye–Scherrer Ring,” J. Mater. Res., 106, 1002 (2015); http://dx.doi.org/ 10.3139/146.111268.
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