Evaluation of the stress–strain curve of metallic materials by spherical indentation

A method for deducing the stress–strain uniaxial properties of metallic materials from instrumented spherical indentation is presented along with an experimental verification. An extensive finite element parametric analysis of the spherical indentation was performed in order to generate a database of load vs. depth of penetration curves for classes of materials selected in order to represent the metals commonly employed in structural applications. The stress–strain curves of the materials were represented with three parameters: the Young modulus for the elastic regime, the stress of proportionality limit and the strain-hardening coefficient for the elastic–plastic regime. The indentation curves simulated by the finite element analyses were fitted in order to obtain a continuous function which can produce accurate load vs. depth curves for any combination of the constitutive elastic–plastic parameters. On the basis of this continuous function, an optimization algorithm was then employed to deduce the material elastic– plastic parameters and the related stress–strain curve when the measured load vs. depth curve is available by an instrumented spherical indentation test. The proposed method was verified by comparing the predicted stress–strain curves with those directly measured for several metallic alloys having different mechanical properties. This result confirms the possibility to deduce the complete stress–strain curve of a metal alloy with good accuracy by a properly conducted instrumented spherical indentation test and a suitable interpretation technique of the measured quantities.