A novel method for constructing the mean field of grain-orientation-dependent residual stress

The heterogeneity of grain-orientation-dependent residual stress (ODRS) in polycrystalline materials has received a great deal of attention in the past few years. This letter describes a novel method, called the spherical harmonics approach (SHA), for analysing ODRS. The stress orientation distribution function (SODF) is defined to describe quantitatively the mean field of the residual stress as a function of grain orientation in the Euler space. This stress field can be expanded in terms of generalized spherical harmonics, and its series coefficients can be determined directly from lattice strain maps (strain pole figures). While solving the deconvolution problem of this stress field, the stress or strain equilibrium between neighbouring grains is considered simultaneously by implementing a self-consistent model in the iterative algorithm. The application of the SHA is illustrated by the construction of the SODF for a cold-rolled and annealed austenite stainless steel, using strain pole figures obtained by neutron diffraction.