A Reference-Free Nanoindentation Model Based on Elastic Unloading Work for Texture-Resolved Residual Stress Evaluation in a Cu–Fe–P Alloy

Existing nanoindentation methods for residual-stress evaluation often require a stress-free reference and inadequately account for constitutive differences. This study proposes a reference-free model based on elastic unloading work. A two-dimensional axisymmetric finite-element model generated 270 cases over E/σy = 50–500, n = 0.1–0.3, and σr/σy = −0.8–0.8 to calibrate the correction factor, k, and stress-free recovery ratio, λ0. Comparison with 10 datasets from eight published studies yielded a mean absolute error of 15.8 MPa, a root mean square error of 24.93 MPa, and a mean absolute percentage error of 7.70%; eight datasets had relative errors below 20%. The model was combined with Electron Back-Scatter Diffraction (EBSD)-guided nanoindentation to evaluate the residual stress in the Cube, S, Brass, and Copper texture components of hot-rolled, cold-rolled, and annealed Cu–Fe–P alloys. In the cold-rolled sample, the Copper component showed a compressive residual stress of −162.23 MPa, compared with −98.43 MPa for S and −102.07 MPa for Brass, and remained highly compressive after annealing (−141.20 MPa). Kernel Average Misorientation (KAM), approximate Geometrically Necessary Dislocations (GND) density, and the Schmid factor showed trends broadly consistent with the texture-dependent residual stresses. The model provides a framework for residual-stress estimation in EBSD-identified texture regions without a physical stress-free reference using an effective isotropic approximation.