Modification of Rule of Mixtures for Estimation of the Mechanical Properties of Dual-Phase Steels
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JMEPEG DOI: 10.1007/s11665-017-2687-6
Modification of Rule of Mixtures for Estimation of the Mechanical Properties of Dual-Phase Steels Mohammad Alibeyki, Hamed Mirzadeh, Mostafa Najafi, and Alireza Kalhor (Submitted December 25, 2016; in revised form March 29, 2017) The mechanical properties of dual-phase (DP) steels were correlated with the amount of martensite and its carbon content. The application of rule of mixtures for predicting the mechanical properties was critically discussed. Subsequently, a modified rule of mixtures was developed to estimate the mechanical properties of DP steels, which accounts for the variation of carbon content in martensite as a function of its volume fraction. The proposed model was able to predict the observed trends and values of hardness, yield stress, and tensile strength in a DP steel with 0.1 wt.% C. Then, its applicability was also verified for a DP steel with 0.2 wt.% C to cover the usual range of carbon content in DP steels. As a result, this simple and effective approach is anticipated to find application in estimating the properties of DP steels. Keywords
DP steel, mechanical properties, microstructure, modeling
1. Introduction Dual-phase (DP) steels, having soft ferrite matrix containing hard martensitic phase, constitute a major group of advanced high strength steels (AHSS), which have been extensively utilized in automotive industry in recent years (Ref 1-4). The major driving force for using these steels is their excellent mechanical properties. Therefore, it seems required to predict their properties based on chemical composition (especially carbon content) and volume fraction of martensite. Previous studies have studied the effect of volume fraction of martensite, its carbon content, morphology of phases, ferrite grain size, and other influencing parameters (Ref 4, 5). There have been several attempts to predict the properties of DP steels, which are based on the rule of mixtures, dislocation mechanics, finite elements, artificial neural network, or other techniques (Ref 1, 6-11). The simple rule of mixtures is based on the equation PDP ¼ VM PM þ ð1 VM ÞPF , where PDP can be defined as hardness, yield stress, or ultimate tensile strength. Moreover, VM is the volume fraction of martensite and M and F subscripts refer to martensite and ferrite, respectively. This model has been applied to DP steels with some degree of success (Ref 5, 12-16). In fact, the simple rule of mixtures is based on the fiberreinforced composites with long fibers and it might be an appropriate one for DP steels with banded martensite morphology. However, some requirements such as the equal strains in the matrix (ferrite) and fiber (martensite) may not be met in DP steels (Ref 17, 18). Moreover, kinematic hardening contributes to strengthening when dislocations first form on the martensite/ferrite boundaries and isotropic hardening becomes important when forest disloca-
tions form inside the ferrite grains. Changing the martensite volume fraction changes the balance of these two hardening mechanis
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