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.

For the small punch test with the advantage of slightly damaged sampling, a theoretical model was derived based on the energy density equivalence principle to describe the relationships among the load, displacement, geometric size, and uniaxial mechanical law parameters. A novel small punch test method was then proposed for aerospace materials to convert mechanical properties between uniaxial tensile test results and small punch test results. Small punch tests and uniaxial tensile tests were carried out on five aerospace materials. The results show that the stress-strain curves obtained by the new method were in close agreement with those obtained by uniaxial tensile tests; the relative errors of the elastic moduli obtained by the new method results and the uniaxial tensile test results were within 10%; and the relative errors of the yield strengths and tensile strengths obtained by the two methods were mostly within 5%. The proposed method is expected to promote the application of SPT for the safety evaluation of in-service structures.

A novel residual stress indentation model for conical indentation loading is proposed to describe the relationship between the residual stress, material constitutive parameters, load, and displacement for materials with a uniaxial constitutive relationship that obeys Hollomon’s power law (H-law). The novel model was established based on the principle that the equivalent material without residual stress corresponds to the original material with residual stress, conical indentation theoretical model based on energy density equivalence, and an assumed power-law relationship between the dimensionless residual stress and relative difference of the yield stresses of the equivalent material and original material. Sixty imaginary H-law materials with ten equibiaxial and ten uniaxial residual stresses were investigated by Finite Element Analysis (FEA). The residual stresses predicted by the novel model from the indentation load–displacement curves simulated for the imaginary materials are in close agreement with those applied by the FEA. Finally, indentation tests for Cr12MoV steel, 45 steel, and 6061-T6511 aluminum alloy were carried out on their specimens without residual stress and their bending specimens with equibiaxial and uniaxial residual stresses. The residual stresses predicted by the novel model according to the indentation load–displacement test curves are in good agreement with those applied by the tests.

For a homogeneous, continuous, and isotropic material whose constitutive relationships meets with the Ramberg-Osgood law (R-O law), the energy in the elastoplastic indentation with a ball indenter was theoretically analyzed, and the proportional superposition of energy in pure elasticity and pure plasticity during indentation was considered based on the equivalence of energy density. Subsequently, a Proportional Superposition-based Elasto Plastic Model (PS-EPM) was developed to describe the relationships between the displacement and the load during the ball indentation. Furthermore, a new test method of Ball Indentation based on Elastoplastic Proportional Superposition (BI-EPS) was developed to obtain the constitutive relationships of R-O law materials. The load–displacement curves predicted using the PS-EPM model were found to agree closely with the Finite Element Analysis (FEA) results. Moreover, the stress vs. strain curves predicted using the BI-EPS method were in better agreement with those obtained by FEA. Additionally, ball indentation was performed on eleven types of metal materials including five types of aluminum alloys and six types of steel. The test results showed that the stress vs. strain relationships and the tensile strength values predicted using the proposed BI-EPS method agreed well with the results obtained using conventional uniaxial tensile tests.