A two-scale methodology for determining the residual stresses in polycrystalline solids using high energy X-ray diffraction data

This paper presents a new method for ascertaining residual stress fields in engineering components. Diffraction data are employed with a finite element discretization to determine the macroscopic (continuum) residual stress field over the workpiece simultaneously with the crystal-scale distribution of elastic strains at each diffraction measurement point. Stress equilibrium and traction free boundary conditions constrain the solution at the continuum scale. The thousands of lattice strain measurements made at each diffraction volume ensure that the stress solution is consistent with crystal-scale elastic distortions. Finally, integrated over all orientations within each aggregate, the crystal-scale stresses must match the continuum stress. The method was demonstrated using a shrink fit specimen with a nickel-base superalloy disk fit over a stainless steel shaft. High energy synchrotron X-ray diffraction experiments conducted at the Advanced Photon Source, Argonne National Laboratory, provided nearly 1 million lattice strain measurements. Using these data, the new methodology produced a stress field that satisfied the macroscopic constraints and matched the crystal-scale distortions at each diffraction volume as manifest by spherical harmonic expansions of the lattice strain tensor over orientation space. The residual stress distribution exhibits the general features of an axisymmetric analytical approximation, but also contains details that likely arise from the pre-existing material state and fabrication of the shrink fit assembly. Projections of the spherical harmonic expansions of the crystal-scale lattice strain tensor matched the experimental lattice strain pole figures. Issues related to diffraction volume spacing (spatial resolution) and specimen shadowing are also discussed.