Assessment of the constitutive law by inverse methodology: Small punch test and hardness

The relevance of small-punch tests and indentation (hardness) tests are compared with regard to the determination of a constitutive law in the case of non active ferrite–bainite steel taken from a French power plant. Firstly, small-punch tests were performed on material samples and the load deflection curves were compared with finite element calculations using the FORGE2 Standard code. As a result the strength coefficient and the strain hardening exponent of Hollomon’s constitutive law were determined by an inverse method (Simplex method). Besides, it was shown that a three-parameter constitutive law such as Ludwik Hollomon’s leads to an indetermination since its parameters are correlated with each other. Secondly indentation tests were performed with a ball indenter and the parameters of the constitutive law were determined from the analysis of the load–indentation depth curves. Both methods give results in good agreement with the true stress–true strain curve obtained by classical tensile testing, thus proving their applicability to nuclear materials.