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)   

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

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

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

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

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

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