Stress and elastic constants

Abstract

This chapter highlights a different but significant application of neutron diffraction in the measurement of engineering strains. It begins by defining the stress and strain tensors, and their connection via tensors of elastic constants or compliances. Next the relationship between the elastic constants of individual crystallites to those of the polycrystal are developed by averaging according to micromechanical (Voigt, Reuss, Hill, Kröner self-consistent) and texture models. Different diffraction peaks respond differently to stress, and the strains measured from the peak positions are related to the stresses by a set of diffraction elastic constants. The later sections are devoted to practical applications: (i) in engineering where residual stress is estimated from the observed strains using known (or computed) diffraction elastic constants; and ii) in materials science where measurement of the diffraction elastic constants allows the single crystal elastic constants to be derived in favourable circumstances (e.g., ceria-tetragonal zirconia polycrystal, Ce-TZP).