PSI - Issue 2_B

Yasuhiro Mukai / Procedia Structural Integrity 2 (2016) 895–902 Author name / Structural Integrity Procedia 00 (2016) 000–000

901

7

k ε 0.9 ∆ = +

k

D

(2)

Δ k represents peak broadening and is calculated from equation (3).

λ θ cos ∆ = ∆ k

θ 2

(3)

Δ2θ represents FWHM of ω - 2θ scan profile. When k and Δ k plot to x-axis and y-axis respectively, D and 〈ε〉 are calculated from the y-intercept and the slopes of the plot, respectively. Such plot is called as Williamson- Hall plot. To calculate Δ2θ, ω - 2θ scan profiles shown in Fig.6 were fitted by Gauss function. Fig.7 shows Williamson-Hall plot. Dotted line represents the slope of Williamson-Hall plot which was calculated from the data points of (001) and (003) plane. As shown in Fig.7, the slope increased with increasing tensile strain. (002) and (004) planes data were plotted over the slope calculated by (001) and (003) data. This was because the diffraction data of (002) and (004) planes consisted of γ and γ’ phases while those of (001) and (003) planes consisted only of γ’ phases. Fig.8 shows the relation between applied tensile strain and micro-strain calculated from the slope of Fig.7. Micro strain increased with increasing tensile strain, and especially increased in the early stage of plastic deformation. Micro strain is directly proportional to a square root of dislocation density (Williamson and Hall, 1953; Unger and Borbely, 1996). Since Ni-based single crystal superalloys were made by precision casting process, the initial dislocation density was very small. So, dislocation nucleation was thought to be necessary to start plastic deformation. The drastic increase of micro-strain in the early stage suggests that a large number of dislocations were nucleated in early stage of plastic deformation. The measurement of micro-strain was effective way to evaluate whether the plastic deformation occurred or not in gas turbine cast components. 4. Conclusions In order to provide the way for evaluating the plastic deformation of gas turbine hot-gas-path components, synchrotron radiation X-ray diffraction experiments were performed for tensile deformed Ni-base single crystal superalloys using synchrotron radiation at SPring-8, and the relation between applied tensile strain and X-ray diffraction peak width was studied. The width of ω -rocking curve which represents the deviation of crystal orientation increased with the increase of applied tensile strain. This means that plastic deformation cause the crystal rotation. X-ray diffraction peak width increased with the increase of applied tensile strain. Williamson-Hall analysis was applied to calculate micro-strain. Micro-strain showed drastic increase in the early stage of tensile tests. It suggests that the measurement of micro-strain by X-ray diffraction is useful for estimating whether plastic deformation occurred or not in actual gas turbine blades. Acknowledgements The synchrotron radiation X-ray diffraction experiments were performed at the BL16XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI). Proposal No. 2013A5050, 2013B5050, 2014A5050, and 2014B5050. References

Bernstein, H. L., Allen, J. M., 1992. Analysis of cracked gas turbine blades, Journal of Engineering for Gas Turbines and Power 114, 293-301.