A, B ¼Calibration Coefficients αβγ ¼angle measured counterclockwise from the x direction to the axis of the strain gauge 1, 2 and 3, respectively For a rectangular strain gauge rosette like as shown in Fig. 14.3, the three strain gages measure the three strains along the 3 gage directions during hole-drilling, whereα ¼0o, β ¼45o, γ ¼90o. The principal stresses and their direction are solved and shown in Eq. 14.3: σmax ¼ ε1 þε3 4A 1 4B ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε3 ε1 ð Þ 2 þ ε 1 þε3 2ε2 ð Þ 2 q σmin ¼ ε1 þε3 4A þ 1 4B ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε3 ε1 ð Þ 2 þ ε 1 þε3 2ε2 ð Þ 2 q tan2α ¼ ε1 2ε2 þε3 ε1 ε3 ð14:3Þ Since the coefficients A and B for blind hole-drilling cannot be calculated directly from theoretical considerations, they are usually obtained by numerical procedures such as finite-element analysis [13]. Some tables of the coefficients defined in Eq. 4 were published [15, 16]. It is suggested that the coefficients A and B can be interpolated or extrapolated from the published nondimensionless coefficients [15, 16]. Errors can be introduced in this procedure due to interpolation and extrapolation. More accurate residual stresses can be calculated if the errors of interpolation can be avoided, e.g. determine the calibration coefficients directly from experiments or FEA for a specific measurement [17]. a ¼ 2E 1þν A b ¼2E B ð14:4Þ Strain gauge rosette hole-drilling residual stress measurements are made at 3 locations as shown in Fig. 14.4. Figure 14.5 shows the maximum and minimum principal stresses at these 3 locations [18]. It is clearly that the residual stress on the wheel surface is very small because the wheel fan thickness is only 0.5 mm thick. 14.3.2 X-ray Diffraction Residual Stress Measurement X-ray and neutron diffraction methods attract a lot of attentions because they enable a nondestructive measurement of stresses. They are very useful when estimating the fatigue life of mechanical components. Compared with conventional techniques, X-ray and neutron diffraction methods enable local measurements and real-time analysis of stress [19]. When a monochromatic X-ray beam irradiates a solid material, the beam is scattered by the atoms composing the material, as shown in Fig. 14.6 [19]. Atoms are packed regularly intro a three-dimensional periodic lattice for a perfect crystalline material. When the X-ray incidences at a certain angle that meets the condition expressed in Eq. 14.5, the intensities of scattered waves sum up into a constructive interference and the diffraction pattern can be observed [19–21]. Fig. 14.3 A rectangular resistance strain rosette [12] 108 B. Xiao et al.
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