Invariant x-ray elastic constants and their use in determining hydrostatic stress

The measurement of stress using x-ray diffraction requires knowledge of the constitutive equation linking strain and stress for the sample under investigation. With the exception of single-crystal materials, a unique constitutive relation does not exist requiring an average over the diffracting ensemble. Such averaging techniques provide bounds to the range of x-ray elastic constants, whose values depend on the elastic anisotropy of the material, the mechanical response of the crystallites and often the x-ray reflection chosen. In fact, for materials possessing cubic symmetry, the general x-ray stress equation can be reduced to a form that relates the measured strain to the hydrostatic stress and the bulk modulus, quantities that are invariant with respect to crystal orientation. These orientations do not correspond to stress-free values but rather to lattice parameters that are independent of the x-ray reflection used. Examples include the application of this technique to a test case of an isotropic, biaxially stressed film, and determining the triaxial stress states in capped features. The validity of these orientations, which are developed for specific stress states, relies on the assumption that the polycrystalline aggregate behaves as a quasi-isotropic ensemble. © 2011 American Institute of Physics.