Dislocation-based crystal plasticity simulation on grain-size dependence of mechanical properties in dual-phase steels

TL;DR

This work tackles how ferrite grain size controls the mechanical response of dual-phase steels by employing a dislocation-based crystal plasticity finite element framework. The authors model GN and SS dislocations and couple them through a Bailey–Hirsch-type hardening relation to predict stress, strain, and dislocation evolution in ferrite and martensite under plane-strain tension, while isolating the effect of ferrite grain size with a fixed martensite fraction $f_ ext{M}$. The results show that smaller ferrite grains increase the martensite stress and mobilize more deformation in the hard phase, due to greater ferrite–martensite boundary area and GN dislocation storage, and lead to more uniform strain fields as well as higher SS density in martensite. Collectively, the findings explain the grain-size dependence observed experimentally and provide mechanistic insight for tuning DP steel properties via ferrite grain-size control, with implications for designing AHSS with improved strength-ductility balance. $f_ ext{M}$, $d_ ext{F}$, $ ho_ ext{G}$, $ ho_ ext{S}$, and $d^{(eta)}$-dependent hardening emerge as key quantities governing the DP response.

Abstract

In this study, the effect of ferrite grain size on the mechanical properties and dislocation behavior of dual-phase (DP) steel is investigated using dislocation-based crystal plasticity finite element analysis. DP steel, composed of a soft ferritic phase and a hard martensitic phase, shows mechanical properties that are significantly influenced by ferrite grain size. The mechanism underlying this grain size effect is clarified by analyzing the partitioning and distribution of stress, strain, and dislocations in each phase. Three models with the same volume fraction of martensitic phase but different ferrite grain sizes are subjected to tensile loading. Interestingly, even though only the ferrite grain size is changed, the stress in the martensitic phase exhibited a notable dependence on ferrite grain size. This can be explained as follows. Geometrically necessary (GN) dislocations accumulate on the ferrite side of the ferrite-martensite grain boundary, and the grain boundary occupancy per unit area increases as the ferrite grain size decreases. As a result, smaller ferrite grain sizes make the ferritic phase less deformable owing to the effect of GN dislocations, shifting more deformation to the martensitic phase. This behavior is confirmed by the more uniform strain distribution and partitioning observed with decreasing ferrite grain size. As the martensitic phase takes on greater deformation, the statistically stored dislocation density in the martensitic phase becomes ferrite grain size dependent, which in turn leads to the observed grain size dependence of stress in the martensitic phase.

Figures (14)

• Figure 1: Analytical model
• Figure 2: Phase distribution of analytical models. (a) Grain size of ferritic phase $d_\mathrm{F}=3.75\,\um$. (b) $d_\mathrm{F}=7.5\,\um$. (c) $d_\mathrm{F}=15\,\um$. The blue phase indicates the ferritic phase andthe red phase indicates the martensitic phase.
• Figure 3: Detailed geometry of the analytical models. (a) Grain size of ferritic phase $d_\mathrm{F}=3.75\,\um$. (b) $d_\mathrm{F}=7.5\,\um$. (c) $d_\mathrm{F}=15\,\um$.
• Figure 4: Distribution of crystal orientation in analytical models. (a) Grain size of ferritic phase $d_\mathrm{F}=3.75\,\um$. (b) $d_\mathrm{F}=7.5\,\um$. (c) $d_\mathrm{F}=15\,\um$.
• Figure 5: Stress--strain diagram. (a) Relationship between the stress $\sigma_{yy}$ and the equivalent strain $\varepsilon_{\mathrm{eq}}$ obtained by dislocation-based crystal plasticity analysis. (b) Stress--strain diagram obtained by the experiment myeong2017effect.