Eigenstrain tomography: full-field residual stress reconstruction via polycrystalline diffraction projections

Residual stresses play a critical role in the performance and integrity of engineering components, yet their three-dimensional characterization remains a long-standing challenge. Eigenstrain-based and tomographic reconstruction methods for residual stress characterization have each advanced this field, but along independent paths: the former embeds experimental data within mechanics-based inverse formulations, while the latter recovers internal fields from projection data. Both approaches, however, face inherent limitations when applied independently. Eigenstrain tomography unifies these perspectives in a mechanics-informed framework. It determines each eigenstrain tensor component’s contribution to the measured residual elastic strain from axial lattice-strain measurements obtained from two-dimensional polycrystalline diffraction projections, and reconstructs a physically admissible three-dimensional residual stress and strain fields that include all tensor components and is consistent with the measured data and mechanical constraints. In the present implementation, the input data are restricted to the axial lattice-strain component parallel to the rotation axis, corresponding to a tomography configuration based on a single measured strain component, although the formulation remains directly extendable to multiple components when such measurements are available. The reconstruction process utilizes a continuum-mechanics framework that enforces equilibrium and total-strain compatibility to ensure physically consistent fields. This study demonstrates the approach on laser powder bed fusion additive-manufacturing specimens of the CM247LC superalloy and the AlSi7Mg alloy, with validation against neutron diffraction, synchrotron diffraction, and the contour method.