Das Abschnitt-Polynom-Verfahren zur zerstörungsfreien Ermittlung gradientenbehafteter Eigenspannungszustände in den Randschichten von bearbeiteten Keramiken

Abstract

X-ray analyses allow the non-destructive determination of residual stress states in machined ceramic materials with steep subsurface gradients. One assumes that variations in the penetration depth of the X-rays enable an assessment of the distributions of machining residual stresses versus the distance from the surface. However, this requires the inversion of Laplace-transforms which, for physicals reasons, are very ill-conditioned. Therefore, the evaluation procedure chosen is crucial for the quality of the results. Based on the Polynomial Method, the Sectioned Polynomial Method was developed which, by describing the depth distributions of residual stresses using piecewise defined polynomials, provides improved flexibility of the solution scheme together with significantly better stability. The details of the evaluation procedure are described and discussed using model calculations. Residual stress analyses on ground ZrO2 ceramics are presented.