10 T. Sasaki et al. In addition, a glass window with 5.2 mm thick and the refraction index of 1.53 was placed after the beam splitter for one interferometric arm of each interferometer, in order to introduce “a carrier fringe system” [11]. The optical distance of the laser beam which passes through the glass window varies depending on its incident angle. Since the beam is expanded by the expander, optical distance on the irradiated surface has a gradient. By rotating the window with a stepping motor, the carrier fringes orthogonal to the sensitive direction appear. The resultant fringe contours represents the superimposing displacement obtained from the carrier and the displacement, thus actual displacement can be obtained by subtracting the carrier from the measured fringe. The number of carrier fringes introduced to the measurement surface was 6 for the horizontal direction, x, and 3 for the tensile direction, y. Tensile load was applied up to 800 N (5% of the yield load), and the dynamic deformation behavior was measured. 2.3 Result and Discussion 2.3.1 Effect of Fatigue Cycle on Acoustic Wave Velocity Figure 2.5 shows acoustic velocity plotted against logarithm of the number pre-fatigued cycles. The value of non-fatigued specimen (NP D0) pis plotted to the pre-fatigue cycles, NP D10 0 for convenience. The vertical wave propagating in the thickness direction, Vzz, decreased as NP increased up to 10 3, then it increased again (Fig. 2.5a). In acousto-elastic theory, the elastic modulus depends on applied stress due to the non-linearity between the interatomic force and the interatomic distance [11]. In particular, tensile stress leads to a decrease in the sound velocity. Thus, the initial decrease in the Vzz at NP <10 3 is indicative of an increase of the tensile internal stress in the thickness direction, z. On the other hand, in the results of shear waves (Fig. 2.5b), although the change was relatively small, both Vzx andVzy exhibited a slight increase at lower NP, followed by a decrease in contrast to the change of Vzz. Toda et al. [12] proposed “R-value acoustoelastic method” that uses the ratio of vertical wave velocity and averaged value of shear wave velocity. According to this method, the ratio of Vzz. and (Vzx CVzy)/2 is proportional to the sum of in-plane principle stress as shown below. RD Vzz Vzx CVzy =2 DR0 CCR x C y (2.1) where R0 is microstructural factor, CR is stress-acoustic constant, ¢x, and ¢y are components of plane stress. Figure 2.6 shows the R value plotted against the pre-fatigue cycle. Since the R-value generally has a positive value, a decrease at (a) (b) Fig. 2.5 Acoustic wave velocity for (a) vertical wave Vzz, and (b) shear vertical waves Vzx andVzy
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