FE determination of the plasticity induced during diffusive transformation in the case of nucleation at random locations and instants

The evolution of TRansformation Induced Plasticity (TRIP) in a steel where the parent phase has been strain-hardened, for a martensitic as well as a bainitic transformation, can only be predicted with models taking into account the interaction between classical plasticity and TRIP. One of the most famous, due to Leblond [J.B. Leblond, Int. J. Plasticity 5 (1989) 573–591], does not provide satisfying predictions in the experimental cases of pre-hardening explored by Taleb and Petit-Grostabussiat [L. Taleb, S. Petit-Grostabussiat, J. Phys. IV 12 (2002) Pr11–187–194; L. Taleb, S. Petit, Int. J. Plasticity 22 (2006) 110–130]. This has motivated the development of alternative approaches based on Finite Element (FE) analysis, which calculates equilibrium at the local scale of the interaction between phases without adopting any particular assumption on stress and strain fields. Our studies concern in particular diffusional transformation where the last improvement has consisted in introducing a new law to govern the kinetics of nucleation: whereas previous works were based on the assumption of site saturation (instantaneous nucleation), it is considered here that nucleation happens randomly in space as well as in time, with a controlled probability distribution and evolution in time.