Identification of the post-necking hardening response of rate- and temperature-dependent metals

A method for identifying the material hardening curves past the limit of necking in uniaxial tension and across a range of strain-rates and temperatures in a fully-coupled way is proposed. Experiments on microtubes of 304 L stainless steel, which is a rate- and temperature-dependent material, were performed using a custom isothermal testing setup. Digital Image Correlation and Infrared Thermography provided full-field measurements of the strain and temperature during testing. The identification procedure uses a finite element (FE) model of the experiments and the problem is cast as one of mathematical optimization. The corresponding objective function has input parameters that control the post-necking shape of the hardening curves and a scalar output that represents the proximity between the FE predictions of the force-average axial strain response and the experimental data. Since the objective function in not available in closed form and is expensive to evaluate, an efficient optimization procedure that requires a limited number of function evaluations is proposed. The method proposed here is then applied to identifying the post-necking hardening response under different assumptions, starting from a single material curve with no rate and temperature effects included, to a family of curves with both rate and temperature considered in a coupled way. To validate the family of hardening curves identified for 304 L stainless steel, a fully-coupled FE model is used to simulate a conventional tension test. This model is shown to be able to reproduce this experiment, including the strain and temperature fields which develop during testing.