X-Ray Diffraction Residual Stress Analysis in Polycrystals
In the previous chapters, the X-ray analysis has been applied to the samples with the electron density distributed uniformly in a macroscopic volume: the constant value for XRR analysis and three-dimensional periodic function in case of HRXRD analysis.
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X-Ray Diffraction Residual Stress Analysis in Polycrystals
In the previous chapters, the X-ray analysis has been applied to the samples with the electron density distributed uniformly in a macroscopic volume: the constant value for XRR analysis and three-dimensional periodic function in case of HRXRD analysis. These samples are usually grown with a predicted design to realize certain physical or mechanical properties of a final structure. The natural materials, however, possess in most cases the mixed structure, consisting of a large number of crystallites of various shape and size with random distribution over the sample volume. This kind of physical structure is called a polycrystalline form and it occurs in the majority of existing samples. The non-destructive X-ray studies explore the properties of polycrystals, which influence the macroscopic characteristics of the products made of polycrystalline materials. There are different methods of X-ray analysis described in numerous monographs: the powder diffractometry performs the chemical and structural analysis of the material [1] and determines the grain size [2] and microstructural imperfections, the texture X-ray analysis studies the preferable orientations of the crystallites [3], X-ray stress analysis evaluates the residual stresses and strains in the samples [4, 5]. The chapter deals with the residual stress analysis, and the theoretical concepts described in previous chapters are used here to interpret the X-ray residual stress measurements. The first section introduces the basic physical definitions used further in X-ray stress analysis. The most difficult part of the theoretical interpretation is a description of the elastic interaction between crystalline grains which influences the microscopic properties of the crystallites. The second section presents the approximations and models used for solution of this problem. The third section considers the powder X-ray diffractometry in a connection with X-ray stress analysis. The forth section deals with the macroscopically isotropic samples, and the expressions for X-ray elastic constants are derived. The covariant methods and vector parametrization of the rotation space group are utilized to simplify the operations with tensors. Finally, the macroscopically anisotropic material are discussed in the fifth section of this chapter.
A. Benediktovitch et al., Theoretical Concepts of X-Ray Nanoscale Analysis, Springer Series in Materials Science 183, DOI: 10.1007/978-3-642-38177-5_7, © Springer-Verlag Berlin Heidelberg 2014
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7 X-Ray Diffraction Residual Stress Analysis in Polycrystals
7.1 X-Ray Stress Measurements The residual stresses are defined by the distribution of the forces and the moments of forces, which exist in an equilibrium state in the polycrystals. The stresses influence the mechanical properties and the fatigue life of a material under external exposure. The residual stresses are the result of the elastic or plastic deformation of crystallites, and the distribution of the stress in a v
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