And the phase shift method and the phase connect method were used to measure them with high accuracy. The final goal of this study is to know the stress concentration of epoxy resin around the carbon fiber experimentally in the microscopic view. This paper shows the fundamental study for the final goal as using the steel fiber instead of the carbon fiber. 24.2 Photoelastic Measurement 24.2.1 Phase-Stepping Method An arrangement of optical elements in a polariscope is shown in Fig. 24.1. This setup consists of a monochromatic light source, a frosted glass, a linear polarizer P1 whose optical axis is vertical, 2 quarterwave plates Q1 andQ2 whose fast axes make angles bandgwith theox axis (horizontal axis) respectively, a linear polarizer (analyzer) whose optical axis makes an angle y with the ox axis, 3 interference filters (500, 550 and 600 nm) and a monochromatic CCD camera. Between 2 quarterwave plates, a birefringent material as a single fiber embedded epoxy resin with retardation d whose fast axis subtends as angle ’with the ox axis. The angle ’ of the principal axis of the specimen is interpreted as the principal stress direction, i.e., the isoclinic parameter. Similarly, the retardation d of the specimen, that is, the isochromatic parameter relates the principal stress difference as d ¼2Np ¼2p Csd l s1 s2 ð Þ ð24:1Þ where N is the isochromatic fringe order, Cs is the stress-optic coefficient, d the thickness of the specimen, l is the wavelength of the monochromatic incident light, and s1 and s2 are the principal stresses. For the phase-stepping method, seven combinations of the angular positions b, g and y of the retarders and the analyzer are used. The arrangements of b, g and y, and the corresponding light intensities I1 ~ I7 used are shown in Table 24.1. The amplitude and the background bias are omitted in this table. Using the seven light intensity values I1 ~ I7 are also shown in Table 24.1. The isoclinic parameter (principal direction) ’, the retardationDof the retarder, and the isochromatic parameter (retardation) d can be obtained as [8] Since the retardation D must be the positive value, the sign of the function sinD in Eq. (24.4) can be determined as positive. Using Eq. (24.2) to (24.4), the phase values d and ’of the isochromatic and isoclinic parameters are determined Fig. 24.1 Arrangement of optical elements Table 24.1 Optical arrangements and light intensity equations b,rad g,rad y,rad Light Intensity, I I1 p/4 0 0 I1 ¼ 1 2 {1 + sindsinDsin2j cosD(cos2j+ cosdsin22j)} I2 –p/4 0 0 I2 ¼ 1 2 {1 sindsinDsin2j cosD(cos2j+ cosdsin22j)} I3 p/4 –p/4 –p/4 I3 ¼ 1 2 1 þsindsinDcos2jþ cosDsin2 d 2 sin4j I4 –p/4 –p/4 –p/4 I4 ¼ 1 2 1 sindsinDcos2jþ cosDsin2 d 2 sin4j I5 –p/4 –p/4 p/2 I5 ¼ 1 2 {1 cosdsin2D+ sindsin2Dsin2j + cos2D(cos22j+ cosdsin22j)} I6 –p/4 p/4 p/2 I6 ¼ 1 2 {1 + cosdsin2D + cos2D(cos22j + cosdsin22j)} I7 p/4 p/4 p/2 I7 ¼ 1 2 {1 cosdsin2D sindsin2Dsin2j + cos2D(cos22j + cosdsin22j)} 216 T. Sakai et al.
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