Dear Sidhu, if you look at the Warren’s theory of XRD studies of deformed metals only the position of any cell represented by a vector, which also includes the arbitrary displacements of the lattice points associated with the given cell goes into the consideration in the calculations of the Intensity from one crystal (i.e., formulation introduced by Stokes and Wilson, 1942-43). Therefore regardless the nature of sources for the displacements, whether they are lattice imperfections, inclusions, second phase or reinforced particles there is no need for the elastic constants of the matrix or the inclusions since you can get the particle size and distortion coefficients directly from the Fourier Cosine coefficients obtained by the XRD powder peak shape analysis. Therefore you get the expectation value of the residual strain without going to any bother to know the elastic constants. But if you wish to calculate the residual stress than you need elastic constants of matrix only!

Actually, in polycrystalline composites, such as Aluminum-silicon carbide composites, as an example, each phase (aluminum and Silicon Carbide) provides its own set of diffracting lines. Thus, owing to X-Ray diffraction, you can obtain the lattice strains of each phase independently from the high 2-theta angles peak shifts.

In first approximation, the X-Ray diffraction elastic constants required for determining the residual stresses from the lattice strains are considered to be unaffected by the presence of a second phase. In practice, it is not always the case, but for phases presenting almost isotropic single-crystals such as aluminium, this assumption is sufficient.

You can read some of my old papers on the subject: see here.

Best regards

http://www.iut-sn.univ-nantes.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1317992704761&ID_FICHE=677684

Thanks sir,

The explanations are very helpful

Best Regards