Continuum plasticity modelling of work hardening for precipitation-hardened martensitic steel guided by atom probe tomography

An analytical flow stress model, based on isotropic strain gradient plasticity theory, for precipitation hardened materials, is proposed and evaluated against tensile data on a 15 wt% Cr - 5 wt% Ni (15-5) PH stainless steel. The 15-5 PH material was aged at 500 °C for 1 h, 2 h, 5 h and 50 h to obtain a wide range of precipitate sizes. Detailed characterisation of precipitates was obtained using atom probe tomography (APT). A second material, a 15-5 stainless steel without added Cu was heat treated to obtain a similar matrix microstructure as in the 15-5 PH, but without Cu precipitates. Tensile testing revealed that the heat treated 15-5 PH material covered the full range from under- to overaged conditions. The analytical model, which accounts for stress reducing effects of plastic relaxation around particles, manages to capture the experimental data in a very satisfying manner using only a total of three tunable parameters. It is believed that the proposed model can offer an alternative to the much more commonly used work hardening models based on the internal variable approach.