Spherical indentation method for estimating equibiaxial residual stress and elastic–plastic properties of metals simultaneously

For instrumented spherical indentation, the presence of equibiaxial residual stress in a material will lead the indentation load–depth curve to shift upward or downward. The load differences between the stressed and stress-free curves were used to estimate the equibiaxial residual stress. Using dimensional analysis and finite element simulations, the equibiaxial residual stress was related to the elastic–plastic parameters and the relative load difference at a fixed normalized indentation depth ( h / R = 0.1). Based on these expressions, and together with the method for determining elastic–plastic parameters established in our previous work, an integrated method was proposed to estimate the equibiaxial residual stress and elastic–plastic parameters of metals simultaneously via instrumented spherical indentation. This method avoids preknowledge of the yield strength and measuring the contact area. Applications were illustrated on Al 2024, Al 7075, and Ti Grade 5 with introduced stresses. By comparing the results determined by this integrated method with the reference values, the maximum relative error is generally within ±10% for the yield strength, within ±15% for the elastic modulus, and within ±20% for the equibiaxial residual stress.