Micromechanical modeling of the effect of particle size difference in dual phase steels

Dual phase (DP) steels having a microstructure consisting of martensite islands, referred to as particles, dispersed in a ferrite matrix have received a great deal of attention due to their useful combination of high strength, high work hardening rate and ductility, all of which are favorable properties for forming processes. The martensite particles display two distinct deformation mechanisms, depending on their size. Small particles are reported in the literature to undergo no measurable plastic deformation and thus can be described as rigid particles dispersed in a matrix of ferrite. On the other hand, large particles reportedly experience a small degree of plastic deformation, which has a significant influence on the mechanism of deformation of such materials. Although most micromechanical models assume a uniform particle size, a distribution of sizes in DP-steels is a more realistic assumption. In this work, a micromechanical model is developed to capture the effect of particle size differences on the mechanical behavior of DP-steels. It is shown that the difference becomes most significant when the ratio of the small to large particle size is approximately 1/2. At low volume fractions of martensite, the effect of a distribution of particle sizes is negligible, but at intermediate and high volume fractions of martensite the interaction due to the size difference becomes quite important. The model displays the intrinsic ability of capturing the steep rise in the strain-hardening rate observed in DP-steels. The model also successfully predicts the mechanisms involved in the deformation process in the DP-steels in agreement with experimental observations reported in the literature.