Comparison of X-Ray Residual Stress Measurement Values by Cos α Method and Sin2 Ψ Method

In recent years, Sasaki et al. has developed the X-ray residual stress measurement device (μ-X360) using the "cos α" method [1, 2]. μ-X360 has been used widely in Japan. μ-X360 uses a 2D detector, and the measurement can be done by only single irradiation of X-ray. Accordingly the device is small and light, and stress measurement is conducted in a short time. For these reasons, μ X360 is expected to be applied to on-site stress measurement of the structures. Generally the “sin ψ” method has been used for the X-ray residual stress measurement. We, IIC, have been providing field measurement services using the portable X-ray stress measuring device (Stresstech Inc. Xstress 3000) with the “sin ψ” method. There are many measurement results with the “sin ψ” method, but there are few reports about the measurement with the “cos α” method. Therefore, we measured various samples by the “cos α” method and compared with the measured values with the “sin ψ” method, and clarified the characteristics of the results with the “cos α” method. Introduction The residual stress measurement has been used for quality management of machine parts, soundness and safety evaluation of structural members. There are various residual stress measurement techniques such as sectioning method, center hole drilling method, X-ray diffraction (XRD) method, neutron diffraction method and so on. In these techniques, XRD method has been adopted widely, because it is non-destructive, inexpensive and relatively simple. The sin ψ method has been generally applied in the residual stress measurement by XRD method. We have been providing residual stress measurement services not only in our laboratory but also in the field using Xstress 3000 with sin ψ method. On the other hand, Sasaki et al. developed the portable device, μ-X360 suitable for the field measurement by using the cos α method. This device is expected to be applied to the field measurements more and more. The measurement performance of "sin ψ" method is excellent and effective. However, the "sin ψ" method requires a goniometer of the device to irradiate X-rays from some different angles to a specimen to be measured. Therefore, the device cannot be applied in some cases because of the restriction of the device. In case of the "cos α" method, goniometer is not necessary in the device. Therefore, the device using the "cos α" method is smaller and lighter than the device using the "sin ψ" method. Consequently the "cos α" method can be used in various cases and for various targets. However, it is necessary to compare the data obtained from the "sin ψ" and the "cos α" methods in order to evaluate the measured residual stresses correctly in the actual structure, because these two methods have different measurement principles. This paper describes the effect of the measurement principles on the residual stresses measured in various loading and material conditions. Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 103-108 doi: http://dx.doi.org/10.21741/9781945291173-18 104 Measurement method and test specimen. We used measurement devices, X-stress 3000 with sin ψ method and μ-X360n (Pulstec Industrial Co., Ltd) with cos α method in this experiment. Figure 1 shows the X-rays residual stress measurement devices. We measured powder samples (Fe, SUS, Ni, Al), and high compressive stress standard samples (Fe, SUS, IN718). Figure 2 shows the powder samples, and Figure 3 shows the high compressive stress standard samples. In addition, we measured SM490 and SUS316 plates by four-point bending tests and Figure 4 shows the test setup for X-ray stress measurement. Table 1 shows measurement conditions. (a) X-stress 3000 with sin ψ method (b) μ-X360n with cos α method Fig.1 X-rays residual measurement devices. Fig.2 Powder samples Fig.3 High compressive stress standard samples Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 103-108 doi: http://dx.doi.org/10.21741/9781945291173-18 105 Table 1 Stress measurement conditions (a) For the powder samples. (b) For the high compressive stress standard samples and four point bending tests. Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 103-108 doi: http://dx.doi.org/10.21741/9781945291173-18 106 Fig.4 Experimental setup for X-ray stress measurement in the four-point bending testing. Measurement results of the powder samples. Figure 5 shows stress measurement results of the powder samples (αFe, γFe, Ni, Al). The gray scale in Figure 5 shows measurement range of sin ψ method. The measurement result of αFe by cos α method was 0±1.7 MPa. All measurement results of other material powder samples by cos α method were within ± 20MPa. These results were equivalent to the measurement values with sin ψ method. The measurement accuracy of the cos α method was satisfactory. Fig.5 Stress measurements results of powder samples. Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 103-108 doi: http://dx.doi.org/10.21741/9781945291173-18 107 Measurement results of the high compressive stress standard specimens. Figure 6 shows the results of measurements of the high stress standard specimens (Fe, SUS316L, IN718). The gray scale in Figure 6 expresses an official nominal level. The measured values for the high stress standard specimen were within the ranges of the nominal values in both the cos α and the sin ψ methods. The measurement values with the cos α and the sin ψ methods were almost equal. Measurement results of the four point bending tests. Figure 7 shows the measurement results of the four point bending test of SM490. Specimens were measured without electropolishing the surface. The measured data by cos α and sinψ methods showed a linear relationship with the strain gage data during the test. In the measurement of SM490, measured values by cos α and sinψ methods were almost equal. Figure 8 shows the measurement results of the four point bending test of SUS316 plate. Both the results of the cos α and sinψ methods show linear relationship, a slope of 1.0, with the measured stress by strain gage. However, there was a difference of 80 MPa between sinψ and cos α methods. We consider that this difference may be induced because the characteristic X-ray of Mn-Kα was used for the measurement with sinψ method ,while the characteristic X-ray of Cr-Kβ was used for the measurement with cos α method. And furthermore, there is a possibility that the measured data were affected by the difference of the measurement area of each method. Fig.6 Residual stresses measured using cos α and sin ψ methods for the surface of the shot peened specimens of Fe, SUS316L, and Inconel718. Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 103-108 doi: http://dx.doi.org/10.21741/9781945291173-18 108 Fig.8 Measurement results of the four-point bending test of SUS316 test piece. Summary We measured stresses in various loading and materials conditions by cos α and sin ψ methods and compared measurement values. As a result, in various powder samples and high stress standard test specimens, the measurement values with the cos α and the sin ψ methods were almost equal. Also, in the four point bending test of SM490, measured values by cos α and sinψ methods were almost equal. However, in case of the four point bending test of SUS316, the measured values by cos α and sin ψ methods had a slight difference because of the difference in each measurement condition. Both cos α and sin ψ methods are effective as the residual stress measurement technique, but we must be careful about measurement condition when we manage the aging change of stress precisely. References [1] Sasaki, T and Hirose, Y, J. Soc. Mat. Sci., Japan 44, 504, (1995) 1138-1143 [2] Miyazaki, T and Sasaki, T, J. Appl. Cryst. (2016). 49, 426–432. http://dx.doi.org/10.1107/S1600576716000492 Fig.7 Measurement results of the four-point bending test of SM490 test piece.


Introduction
The residual stress measurement has been used for quality management of machine parts, soundness and safety evaluation of structural members.There are various residual stress measurement techniques such as sectioning method, center hole drilling method, X-ray diffraction (XRD) method, neutron diffraction method and so on.In these techniques, XRD method has been adopted widely, because it is non-destructive, inexpensive and relatively simple.
The sin 2 ψ method has been generally applied in the residual stress measurement by XRD method.We have been providing residual stress measurement services not only in our laboratory but also in the field using Xstress 3000 with sin 2 ψ method.
On the other hand, Sasaki et al. developed the portable device, µ-X360 suitable for the field measurement by using the cos α method.This device is expected to be applied to the field measurements more and more.
The measurement performance of "sin 2 ψ" method is excellent and effective.However, the "sin 2 ψ" method requires a goniometer of the device to irradiate X-rays from some different angles to a specimen to be measured.Therefore, the device cannot be applied in some cases because of the restriction of the device.
In case of the "cos α" method, goniometer is not necessary in the device.Therefore, the device using the "cos α" method is smaller and lighter than the device using the "sin 2 ψ" method.Consequently the "cos α" method can be used in various cases and for various targets.
However, it is necessary to compare the data obtained from the "sin 2 ψ" and the "cos α" methods in order to evaluate the measured residual stresses correctly in the actual structure, because these two methods have different measurement principles.
This paper describes the effect of the measurement principles on the residual stresses measured in various loading and material conditions.

Measurement method and test specimen.
We used measurement devices, X-stress 3000 with sin 2 ψ method and μ-X360n (Pulstec Industrial Co., Ltd) with cos α method in this experiment.Figure 1 shows the X-rays residual stress measurement devices.We measured powder samples (Fe, SUS, Ni, Al), and high compressive stress standard samples (Fe, SUS, IN718).Figure 2 shows the powder samples, and Figure 3 shows the high compressive stress standard samples.In addition, we measured SM490 and SUS316 plates by four-point bending tests and Figure 4 shows the test setup for X-ray stress measurement.Table 1 shows measurement conditions.
(a) X-stress 3000 with sin 2 ψ method (b) μ-X360n with cos α method     Measurement results of the powder samples.
Figure 5 shows stress measurement results of the powder samples (αFe, γFe, Ni, Al).The gray scale in Figure 5 shows measurement range of sin 2 ψ method.The measurement result of αFe by cos α method was 0±1.7 MPa.All measurement results of other material powder samples by cos α method were within ± 20MPa.These results were equivalent to the measurement values with sin 2 ψ method.
The measurement accuracy of the cos α method was satisfactory.

Fig.5 Stress measurements results of powder samples.
Measurement results of the high compressive stress standard specimens.
Figure 6 shows the results of measurements of the high stress standard specimens (Fe, SUS316L, IN718).The gray scale in Figure 6 expresses an official nominal level.The measured values for the high stress standard specimen were within the ranges of the nominal values in both the cos α and the sin 2 ψ methods.The measurement values with the cos α and the sin 2 ψ methods were almost equal.

Measurement results of the four point bending tests.
Figure 7 shows the measurement results of the four point bending test of SM490.Specimens were measured without electropolishing the surface.The measured data by cos α and sin 2 ψ methods showed a linear relationship with the strain gage data during the test.In the measurement of SM490, measured values by cos α and sin 2 ψ methods were almost equal.
Figure 8 shows the measurement results of the four point bending test of SUS316 plate.Both the results of the cos α and sin 2 ψ methods show linear relationship, a slope of 1.0, with the measured stress by strain gage.However, there was a difference of 80 MPa between sin 2 ψ and cos α methods.We consider that this difference may be induced because the characteristic X-ray of Mn-Kα was used for the measurement with sin 2 ψ method ,while the characteristic X-ray of Cr-Kβ was used for the measurement with cos α method.And furthermore, there is a possibility that the measured data were affected by the difference of the measurement area of each method.

Summary
We measured stresses in various loading and materials conditions by cos α and sin 2 ψ methods and compared measurement values.As a result, in various powder samples and high stress standard test specimens, the measurement values with the cos α and the sin 2 ψ methods were almost equal.Also, in the four point bending test of SM490, measured values by cos α and sin 2 ψ methods were almost equal.However, in case of the four point bending test of SUS316, the measured values by cos α and sin 2 ψ methods had a slight difference because of the difference in each measurement condition.Both cos α and sin 2 ψ methods are effective as the residual stress measurement technique, but we must be careful about measurement condition when we manage the aging change of stress precisely.

Fig. 2
Fig.2 Powder samples (a) For the powder samples.(b) For the high compressive stress standard samples and four point bending tests.

Fig. 4
Fig.4 Experimental setup for X-ray stress measurement in the four-point bending testing.

Fig. 6
Fig.6 Residual stresses measured using cos α and sin 2 ψ methods for the surface of the shot peened specimens of Fe, SUS316L, and Inconel718.

Fig. 8
Fig.8 Measurement results of the four-point bending test of SUS316 test piece.

Table 1
Stress measurement conditions