A novel model to obtain equi-biaxial residual stress of metallic materials via instrumented spherical indentation

Residual stresses existing on the surface of a structural component can be accurately and non-destructively assessed using the instrumented indentation technique, which is crucial for the safety assessment of in-situ structures. In this study, a novel instrumented spherical indentation model based on the equivalent material assumption and the principle of energy density equivalence is proposed for determining the equi-biaxial residual stresses of isotropic power-law hardening metallic materials. The model establishes the correlations between equi-biaxial residual stresses, total work of indentation, and constitutive parameters. Finite element analysis is utilised to determine the model constants by calculating the total work of indentation. Furthermore, the equi-biaxial residual stresses predicted by the model are close to the reference equi-biaxial residual stresses provided by finite element simulations under various equi-biaxial residual stress states for multiple power-law hardening materials. Subsequently, the instrumented spherical indentation experiments are conducted on specimens without equi-biaxial residual stress and on bending cross-shaped specimens with multilayer equi-biaxial residual stresses for six types of metallic materials. The equi-biaxial residual stresses applied by the tests agree well with those predicted by the novel indentation model.