1. Residual stress Suppose isotropic solid loaded in uniaxial tension
Can measure change in interplanar spacing for planes reflecting as above
d = (d - do)/ do
 = (1/E) ( - ( + ))
 = - (1/E)   

2. Residual stress Suppose isotropic solid loaded in uniaxial tension
Comments
Can vary with crystallographic direction: E, 
Mat'l can be anisotropic
But, if no preferred orientation, usually doesn't matter
Biaxial & triaxial stress states

3. Residual stress Measurement procedure - classical technique - sin2 
Stress state resolved differently along different directions in sample, so peak shifts change w/ direction

4. Residual stress Measurement procedure - classical technique - sin2  L1 x3 x2 L2 L3  x1

5. Residual stress Measurement procedure - classical technique - sin2  L1 x3 x2 L2 L3  x1



6. Residual stress Measurement procedure - classical technique - sin2  L1 x3 x2 L2 L3  x1



7.  =  (1 + )/E sin2  /E)( + 
Residual stress
Measurement procedure - classical technique - sin2 
slope
 =  (1 + )/E sin2  /E)( + 

sin2 