Numerical modelling of the plasticity induced during diffusive transformation. Case of a cubic array of nuclei

The experimental work of Taleb and Petit-Grostabussiat [Taleb, L., Petit-Grostabussiat, S., 2002. Elastoplasticity and phase transformations in ferrous alloys: some discrepancies between experiments and modeling. J. Phys. IV 12 (11), 187–194; Taleb, L., Petit, S., 2006. New investigations on transformation induced plasticity and its interaction with classical plasticity. Int. J. Plasticity 22 (1), 110–130] has shown evidence that the evolution of TRansformation Induced Plasticity (TRIP) in a low carbon steel (16MND5) could be significantly influenced by the loading history of the parent phase, for a martensitic as well as a bainitic transformation. Furthermore, estimates from the Leblond model – one of the few micromechanical models currently found in different Finite Element (FE) softwares – have appeared to be in disagreement with experiments in these cases where the parent phase has been strain hardened. This has motivated the development of alternative approaches based on FE computations. This paper presents our first investigations about simulations of diffusive transformations with FE in an idealized case: the parent and the product phase are considered as two homogeneous materials with given elastoplastic properties and density; the transformation takes place at the same instant at predefined elements constituting the nuclei; then it progresses at a uniform rate by changing the material properties of the layer of elements surrounding the nuclei. In the basic configuration of modelling, the volume of discretization stands for a unit cell of a periodic cellular array, with a single central nucleus. In a more complex configuration, which is introduced shortly here and to be presented in details in the paper under preparation [Barbe, F., Quey, R., Taleb, L., Souza de Cursi, E., 2006. Numerical modelling of the plasticity induced during diffusive transformation. Case of a random instantaneous array of nuclei, in preparation], the volume of computation contains few to several nuclei at random locations. For both configurations, results in terms of effective (mean) TRIP as a function of the volume fraction of product phase are in correct quantitative and qualitative agreement with experimental results.