Profile Fitting in Residual Stress Determination.
NORTHWESTERN UNIV EVANSTON IL DEPT OF MATERIALS SCIENCE
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Of major importance in the determination of residual stress via diffraction is the accuracy of the measurement of the scattering angle 2 thata p of a Bragg peak. This determines the accuracy of the interplanar d spacing and hence the strain and stress. In the U.S., the most commonly accepted method of determining peak position is a parabolic fit near the top of a peak. While a diffraction peak is not parabolic, this is a satisfactory function near the maximum. The error is this procedure has been derived and tested, and it has been shown that a multipoint fit with at least 7 points is rapid and as precise or more precise than the centroid, the bisector of the half width, or cross correlation, except for sharp peaks in which case the centroid or cross correlation are slightly better. Thus a parabolic fit is generally useful and, since a least-squares fit to this function is readily carried out on modern micro-processors, automation of a stress measurement is possible, including evaluation of errors. The parabolic fit has the best overall ability to determine peak positions over a wide range of shapes. A Modified Lorentzian can be quite helpful if only a part of a peak can be explored, especially for sharp peaks. The errors in a Modified Lorentzian fit are not very sensitive to counting time. With a position sensitive detector precision comparable to that for a parabolic fit can be obtained in about one tenth the time. Goodness-of-Fit is not necessarily an accurate gage of error in peak position.
- Statistics and Probability