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Machined ceramics and other hard materials exhibit very steep subsurface gradients of residual stresses. X-ray analysis enables the non-destructive assessment of the distributions of these residual stresses versus the distance from the surface via variation of the penetration depth of the X-rays. Conventional evaluation procedures are based on continuous or piecewise defined polynomial functions of stress versus distance, which are fitted to the X-ray data by means of complex solution schemes. These solution schemes are, however, in many cases unstable and difficult to handle. We have developed an entirely novel evaluation procedure which is based on polynomials fitted to the “2θ vs. sin 2  ψ” plots obtained from the X-ray measurements. It is shown that the residual stress profiles can be computed explicitly from these polynomials without any further assumptions. The evaluation procedure is described in detail and demonstrated in a case study on ground alumina ceramics.

X-ray analysis of steep residual stress gradients: The 2θ-derivative method