Statistical Study on Improvement in Precision in X-Ray Stress Measurement by Fixed Time Method : Standard Deviation of Stress due to Statistical Fluctuations in Diffracted Intensities

Abstract

The equations for the standard deviation (s.d.) of the stress measured by n points parabola and the Gaussian curve fitting methods are given. The peak position of a diffraction line calculated by the parabola method becomes q=x_m+1 - d (Σt_iz_i)/(ΣT_iZ_i) where, m=n(n-1)/2, x=2θ°, t_i=i-1-m, c=x_i+1-x_i, d=(n²-4)c/10, T_i=3t²_i -(n²-1)/4, and Z_i=accumulated counts(y) corrected for LPA factor. The s.d. of the stress p by the sin²ψ method (ψ₀=0°, 15°, 30°, 45°) is given approximately by [numerical formula] where, Y=y_m+1 and R=(y₁+y_n)/(2Y) at ψ₀=30°. The stress has been determined to within s.d. of 1 ∼ 2 kg/mm² for a hardened steel S50C having a broad diffraction line with a half breadth of about 8 degrees 2θ.