A different approach to X-ray stress analysis

Abstract

A different approach to X-ray stress analysis has been developed. At the outset, it must be noted that the material to be analyzed is assumed homogeneous and isotropic. If a sphere with radius r within a specimen is subjected to a state of stress, the sphere is deformed into an ellipsoid. The semi-axes of the ellipsoid have the values of ( r + ε x ), ( r + ε y ), and ( r + ε z ), which are replaced by d x , d y , and d z , or for the cubic case, a x , a y , and a z . In this technique, at a particular ϕ angle (see Fig. 1), the two-theta position of a high angle (hkl) peak is determined at ψ angles of 0, 15, 30, and 45°. These measurements are repeated for 3 to 6 ϕ angles in steps of 30°. The d ϕψ or a ϕψ values are then determined from the peak positions. The data is then fitted to the general quadratic equation for an ellipsoid by the method of least squares. From the coefficients of the quadratic equation, the angle between the laboratory and the specimen coordinates (direction of the principle stress) can be determined. Applying the general rotation of axes equations to the quadratic, the equation of the ellipse in the x– y plane is determined. The a x , a y , and a z values for the principal axes of the lattice parameter ellipsoid are then evaluated. It is then possible to determine the unstressed a 0 value from Hooke's Law using a x , a y , and a z . The magnitude of the principal strains/stresses is then determined.