Using mechanical equilibrium to correct HR-EBSD stress measurements

High-resolution electron-backscatter diffraction (HR-EBSD) is widely adopted as a method to obtain local stress and strain distributions in both single-crystal and polycrystalline materials. In this study, we develop a finite element-based method that serves as a numerical correction to refine the relative stress measurements captured experimentally from HR-EBSD and to ensure that the measurements satisfy mechanical equilibrium and traction-free surface constraints. The method provides a calculation of stress for each of the reference points instead of assuming the reference point stresses are zero, capturing the grain-to-grain variation in polycrystalline EBSD maps. The experimental data including a cross section of nanoindentation in unirradiated and heavy-ion-irradiated single-crystals of iron as well as polycrystalline austenitic stainless steel are analysed, and the method improves the measured stresses near slip bands, grain boundaries, and hard phases while keeping the stresses physically consistent with mechanical equilibrium and ensuring that free surfaces are traction-free. The three-dimensional analysis enables the fulfilment of traction-free surface constraints, resulting in zero out-of-plane shear stress components on the free surfaces while maintaining nonzero out-of-plane shear stress components below the surface. To demonstrate the validity of this approach, the method is applied to synthetically generated relative stress data for a uniform bending case, and the method successfully predicts the stress distributions.