residual strain in the lattice, R is the film-to-specimen distsince, 

 and © is the Bragg angle. The strains were plotted versus sin^ 'f 

 for each azimuthal direction, as shovm in Figure 4, a typical olot. 



From the theory of elasticity, the slope of the line is related 

 to the residual stress and elastic constants by the equation 



(2) Slope = ' 't Or 



where i^ is the Foisson's ratio, Ej^i is Young's modulus in the 

 direction of the Miller indices hkl, and(Xs is the stress in 

 the azimuthal direction, (j) . 



The circular weldment was analyzed similarly, but only after 

 removing a surface weld layer by the electropolishing process. 

 Residual stresses were determined on two areas of the weld in two 

 azimuthal directions: parallel and perpendicular to the weld, as 

 shown in Figure 5. Figure 6 is a typical plot of the strain 

 values versus sin2<^ . 



RESULTS AND DISCUSSION 



Measured residual strains obtained from one area at the toe 

 of the tee weld and one area on the circular weld (for the azi- 

 muthal directions indicated) are plotted versus sin^ (^ in Figures 

 4 and 6, respectively. The slope of each least-mean-square line 

 through the points is proportional to the residual stress averaged 

 over the four ^ -directions at angles 0'=, 15", 30", 45'= from the 

 normal to the specimen surface. It is evident from the graphs 

 that the strain values obtained from the circular weld are scat- 

 tered more than those obtained from the toe of the tee weld. 

 This may be explained by the possible presence of some anisotropic 

 plastic deformation in the weld materieJ.. 



Despite the scatter and poor reproducibility of individual 

 strain values, as illustrated in Figure 6, the slope of the line, 

 which characterizes the state of residual stress, remains rather 

 constant with new sets of experimental strain values. This is an 

 important aspect of the sin^t^ method since it allows the deter- 

 mination of residuail stress on the basis of a statistical strain 

 distribution over a range of four directions, rather than on the 

 basis of an assumed distribution (one- or two-exposure methods). 

 It is to be noted that a positive slope means that the residual 

 stress is tensile. 



The residual stresses were cadculated from the strain data 

 using equation 2. The results for the three tee-welded sections 

 are shown in Table 1. The results in Table 1 indicate that the 



299 



