Limited weld residual stress measurements in fatigue crack propagation: Part I. Complete field representation through least‐squares finite‐element smoothing

Abstract

ABSTRACT An equilibrium‐based, weighted least‐squares algorithm is developed to reconstruct the complete residual stress field tensor throughout the specimen volume using a limited set of residual stress measurements and a priori boundary conditions. Using a set of residual stress data acquired by neutron diffraction over a limited region of an AA2024‐T351 friction‐stir‐welded specimen, the method is used to reconstruct the complete residual stress tensor field. Results indicate that (1) the algorithm is robust and effective in quantifying the complete residual stress field throughout the region of interest; (2) appropriate smoothing parameters are readily obtained so that the reconstructed, complete residual stress field accurately reflects the experimental measurements and (3) the resulting residual stress field is in self‐equilibrium.