Theoretical model and testing method for ball indentation based on the proportional superposition of energy in pure elasticity and pure plasticity

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.