A computational framework for evaluating residual stress distributions from diffraction-based lattice strain data

Modern high energy X-ray and neutron diffraction capabilities can provide lattice strain measurements from spatially-resolved diffraction volumes over the full domain of mechanical components with complex, three dimensional geometries. Each measurement is an average of strains in those crystals within one diffraction volume whose orientations lie along a common crystallographic fiber. Presented here is a computational framework for determining residual stress fields that fully utilizes these data while simultaneously satisfying equilibrium locally over the domain of a component and traction conditions over its surface. Key attributes of the framework are the definition of two stress fields, a continuum field and a crystal scale field, and a solution methodology for minimizing the difference between these fields. The continuum field satisfies the constraints from equilibrium and surface tractions; the crystal scale field is derived from the lattice strain measurements. To effectively handle the distinct demands required of the two fields, the framework combines a traditional, element-based discretization for the continuum stress field with an element-free discretization for the crystal scale stress field. The classical example of a residual stress field imparted by an interference fit of a disk onto a circular shaft is used to demonstrate the framework. Using lattice strain data generated by high energy X-ray diffraction, residual stress distributions are determined for two different cases, one having a two-dimensional and the other a three-dimensional stress field.