Mesoscale Computational Study of the Parabolic Hardening Stage of Plastic Flow in a Low-Carbon Steel

Based on the recently reported experimental data, the Taylor (parabolic) strain hardening stage of mild steels corresponds to the emergence of nearly equidistantly located stationary maxima and minima of localized plastic deformation. The latter suggests that some regions of the material are subjected to stronger plastic deformation than others. From the Hall–Petch equation, it is well-known that the yield stress is composed of two constituents – the contribution to the flow stress from the basal slip planes and the contribution due to the influence of grain boundaries. However, it is still unclear which contribution is more significant. In this article, a microstructure-based finite-difference analysis is employed to provide a deeper insight into the emerging features in the parabolic hardening stage of low-carbon polycrystalline steel plastic flow. The step-by-step packing method is used to design a representative volume element (RVE) at mesoscale. The contributions from basal slip planes and grain boundaries, respectively, are considered separately. The modeling results better correlate with experimental findings when the hardening stage of the up-down-up constitutive equation is provided for by the change in the ky parameter of the Hall–Petch equation in the course of plastic flow development.