Multi-scale modeling of bainitic phase transformation in multi-variant polycrystalline low alloy steels

In this work, we develop a thermodynamically consistent multi-scale model for the material behavior of a low alloy steel taking elasto-viscoplasticity, heat conduction and phase transformations as well as the poly-crystalline structure into account. In this material (e.g. the steel 51CrV4) the following phases may occur: austenite, ferrite, pearlite, bainite and martensite. Here, we focus on a prototypical situation, considering only the phase transformation from austenite into all possible bainite variants within a single crystal. The mesoscopic configuration consists of a polycrystal which is attached to each material point of the macroscopic configuration. The microscopic configuration consists of an agglomeration of variants, which is attached to each single crystal of the mesoscopic configuration. At the mesoscopic level, the transformation strains of the bainite variant within the grains lead via averaging to an additional component (besides elastic and visco-plastic ones) of the total macroscopic strain, expressing the macroscopic effects of volume change due to phase transformation as well as to transformation-induced plasticity (TRIP). Moreover, the model is capable of capturing both TRIP effects, the contribution due to load-biased orientation of bainite-variants (“Magee effect”) and plastic accommodation of the new phase (“Greenwood–Johnson effect”). Finally, a quantitative evaluation of both phenomena is provided for various loading paths.