STRESS ANALYSIS BY DIFFRACTION METHODS ON TEXTURED MATERIALS

B. Eigenmann

Institut für Werkstoffkunde I, Universität Karlsruhe (TH), P.O. Box 6980, 76128 Karlsruhe, Germany

Keywords: X-ray diffraction, stress analysis, texture, materials science

Residual and loading stress analyses by means of diffraction methods have there origin in a long tradition of developing techniques for X-ray stress analyses starting in 1922 with the work of Joffé and Kirpitcheva using the Laue-technique on single crystals and in 1924 with the work of Soller using a goniometer with an ionization chamber on polycrystalline material. All the methods for X-ray stress analysis like the sin²y-Method or the Dölle-Hauk-method are based on the fundamental equation of X-ray stress analysis derived from theory of linear elasticity by Romberg in 1937. The theory involved holds for material which is on a macroscopic scale elastically isotropic. This assumption is generally justified for polycrystals without crystallographic texture.

Nevertheless, it was early stated that the elastic anisotropy of the crystallites has an influence on the lattice strains measured on polycrystals by X-ray diffraction. In case of macroscopically isotropic material, one can account for this effect by use of appropriate X-ray elastic constants which are specific for the material and for the crystallographic planes under investigation. They can be calculated from the elastic properties of the respective single crystals in relatively simple ways using classical theory of polycrystals or of inclusion problems.

The situation is more complicated if the polycrystalline material under investigation shows preferred orientations of the crystallites, i.e. a crystallographic texture, which generally also results in elastically anisotropic properties of the macroscopic body. Still today, there is no general solution for the problem of X-ray stress analysis on textured materials. However, since the late 60s, a number of approaches have been developed by various groups which allow in specific cases X-ray analyses of stress states in presence of textures. This paper gives a summary of approaches ranging from very pragmatic methods using experimental elastic constants for every specific problem or measuring directions or lattice planes which should yield results independent of the present textures. Also, modern approaches are presented which enable to account for the elastic anisotropy by the use of orientation distribution functions (ODF) employing numerical methods with modern fast personal computers. The practical aspects, the possibilities and limits of the methods as well as the still remaining problems in stress analysis by diffraction methods in presence of textures are pointed out.