Determination of the proof strength and flow properties of materials from spherical indentation tests: An analytical approach based on the expanding cavity model

An analytical method based on the extended expanding cavity model was proposed in this study to determine the proof strength Rp0.2 and flow properties of materials that obey the Johnson–Cook constitutive model from spherical indentation tests. The introduction of the Johnson–Cook model made the proposed method suitable for the tensile property evaluation of materials not only at room temperature but also at elevated temperatures. The validity of the expanding cavity model was verified through comparisons of von Mises equivalent strain distributions obtained from finite element analyses with the corresponding results from theoretical analysis. From the parameter analysis, it was found that the indentation governing parameter ψempirical in the empirical method was actually determined by the tangential modulus Ep and the hardening exponent n and thus should not be considered as a constant. We also analyzed the unreliability of previous plastic zone radius rp calculation method at large indentation depths (with obvious pileup phenomenon) and put forward a new calculation method of rp based on the force balance. Finite element calculations of spherical indentation tests with tensile properties of Ti6Al4V and AISI 4340 were conducted in this study as substitutes for spherical indentation tests. The load–depth data and rp from finite element calculations were employed in the reverse analysis, the results of which showed that spherical indentation tests can provide the same reliable Rp0.2 as tensile tests and even the whole stress–strain curves. Furthermore, the influence of friction and the measuring system strain threshold in the measurement of rp, which may be inevitable in experiments, were also thoroughly discussed in this study, which also helped to verify the robustness of this study.