Determination of the Elastic Constants of Inhomogeneous Materials with X-Ray Diffraction

Experimental determination of the elastic constants is of fundamental importance in residual stress analysis with x-rays. Such constants are usually termed x-ray elastic constants. In certain materials changes have been observed in these elastic constants as a result of plastic deformation. However, since for some of such cases the d vs. sin psi plots used in the analysis were not linear, as predicted by theory, but oscillatory, the meaning of these variations was not fully understood. In this paper the meaning of x-ray elastic constants obtained from materials with oscillatory d vs. sin psi plots is examined. It is shown that x-ray diffraction analysis is a powerful tool that can be used to determine the effective elastic constants of the material under investigation, even when the material is inhomogeneous.