Modeling the Role of Martensite Volume Fraction in Internal Stress Development During Tensile Loading of Dual Phase Steels

The tensile response of dual-phase (DP) steels arises from mechanical interactions between soft ferrite and hard martensite islands, where the martensite volume fraction strongly influences load partitioning. Despite numerous studies on DP steels, the quantitative effect of martensite volume fraction on the evolution of internal and average stresses within martensite particles has not been extensively examined, particularly using physically based micromechanical formulations. This work addresses this gap by applying a combined continuum-dislocation model capable of capturing how different martensite volume fractions alter stress transfer and particle-scale misfit accommodation during tensile deformation. Two steel conditions with different martensite fractions were produced through controlled intercritical annealing: F-۱۳M (۱۳% martensite) and F-۴۰M (۴۰% martensite). Their tensile stress-strain curves were used to calibrate the model parameter n*, the maximum density of Orowan loops that can accumulate around martensite particles. Once n* was obtained following the procedure of Mohsenzadeh & Mazinani [۱], the unrelaxed plastic strain ap was computed for each martensite volume fraction. After model calibration, the martensite volume fraction was varied parametrically while keeping the particle size constant, and the model was used to compute the resulting internal and average stresses. This approach enabled a clear assessment of the influence of volume fraction on stress evolution independent of particle-size contributions. The resulting internal and average stresses were then evaluated using the same modeling framework described below. The internal stress transferred to martensite islands is calculated using the Eshelby-type inclusion formulation [۲, ۳]: σ۱ = (۱-f)Epε*p (۱) where f is the martensite volume fraction, Ep is the Young's modulus of martensite, and ε*p is the unrelaxed misfit strain. The latter is determined using the stored-dislocation-based expression [۲]: ε*p = nb/۲rM (۲) where M is the Taylor factor, b is the Burgers vector, n is the number of Orowan loops, and r is the particle radius. The evolution of n with matrix plastic strain is modeled following Proudhon et al. [۴] and Mohsenzadeh & Mazinani [۱]: dn/dεp = ۲rβM/b (۱-n/n*) (۳) Once σ is obtained, the average stress in martensite islands is evaluated as [۳]: σave = σA + σI where σA is the flow stress of steel sample. (۴) Model predictions show a clear and systematic relationship between martensite volume fraction and the stress state within martensite particles. Increasing the martensite volume fraction significantly decreases the internal stress (Eq. ۱), because individual particles are actually less greatly stressed when they involve more of the volume. In contrast, the average stress σave exhibits only a modest increase with increasing volume fraction. Although the kinematic work hardening and thereby the flow stress increase as the volume fraction of martensite particles increases, the internal stress decreases. Therefore, increasing the particle volume fraction has little effect on the average stress. These results highlight that martensite volume fraction is a primary controlling factor for internal stress evolution, and must be explicitly incorporated in micromechanical descriptions of DP steel behavior. The combined continuum-dislocation model used here successfully resolves this dependence, offering a predictive framework for tailoring DP steel microstructures based on their martensite fraction.

کلیدواژه ها:

dual-phase steel ، internal stress ، martensite volume fraction ، micromechanical modeling