X -Ray Elastic Constants and Their Meaning for Al and Fe

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Abstract
In the measurement of residual stresses via diffraction (using x-rays or neutrons) it is strains that are actually determined, by employing the interplanar spacing (dhkl) of the ﹛hkl﹜ planes as an internal strain gauge. The change in this spacing is measured from the shift of diffraction peaks (and Bragg's law) at several orientations of the sample to the incident beam, and the resultant strains are converted to stresses with the “diffraction elastic constants”, S1 (hkl) and S2 (hkl)/2. While these take on the values (- v/E) and (1 + v )/E respectively for an isotropic solid, in anisotropic materials their values depend on marry factors: preferred orientation, shape and orientation of second phases, interaction between grains. In fact there are reports of variation these constants with plastic deformation and theory predicts variations with morphology. While it is possible to calculate approximate values for these constants from theory and the single crystal elastic constants , Si and S2/2 are really not elastic constants in the strictest sense because or these other factors, and it is best to measure them. One of us (I. C. Noyan) has recently examined this problem in some detail , and we summarize his results here.

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