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Instrumented indentation is a promising technique for estimating surface residual stresses and mechanical properties in engineering components. The relative difference between the indentation loads for unstressed and stressed specimens was selected as the key parameter for measuring surface residual stresses in flat-ended cylindrical indentations. Based on the equivalent material method and finite element simulations, a dimensionless mapping model with six constants was established between the relative load difference, constitutive model parameters, and normalized residual stress. A novel method for measuring the surface residual stress and constitutive model parameters of metallic material through flat-ended cylindrical indentations was proposed using this model and a mechanical properties determination method. Numerical simulations were conducted using numerous elastoplastic materials with different residual stresses to verify the proposed model; good agreements were observed between the predicted residual stresses and those previously applied in finite element analysis. Flat-ended cylindrical indentation tests were performed on four metallic materials using cruciform specimens subjected to various equibiaxial stresses. The results exhibited good conformance between the stress–strain curves obtained using the proposed method and those from traditional tensile tests, and the absolute differences between the predicted residual stresses and applied stresses were within 40 MPa in most cases.

Although there are methods for testing the stress-strain relation and strength, which are the most fundamental and important properties of metallic materials, their application to small-volume materials and tube components is limited. In this study, based on energy density equivalence, a new dimensionless elastoplastic load-displacement model for compressed metal rings with isotropy and constitutive power law is proposed to describe the relations among the geometric dimensions, Hollomon law parameters, load, and displacement. Furthermore, a novel test method was developed to determine the elastic modulus, stress-strain relation, yield and tensile strength via ring compression test. The universality and accuracy of the method were verified within a wide range of imaginary materials using finite element analysis (FEA), and the results show that the stress-strain curves obtained by this method are consistent with those inputted in the FEA program. Additionally, a series of ring compression tests were performed for seven metallic materials. It was found that the stress-strain curves and mechanical properties predicted by the method agreed with the uniaxial tensile results. With its low material consumption, the ring compression test has the potential to be as an alternative to traditional tensile test when direct tension method is limited.