Transformation-Induced, Geometrically Necessary, Dislocation-Based Flow Curve Modeling of Dual-Phase Steels: Effect of G
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IN recent studies, dual-phase (DP) steels have been projected to be the most applicable steel for futuregeneration cars.[1] This is because DP steels show an attractive combination of high strength, ductility, and initial work-hardening rate. These unique properties of DP steels are the result of their characteristic microstructure, which consists of hard martensite islands distributed in a soft ferrite matrix, as reported by DeCooman and Speer.[2] For optimized properties of DP steels, the volume fractions of martensite and ferrite phases are to be approximately 0.2 and 0.8, respectively. Ferrite grain size also influences the flow behavior of DP steels.[3–5] However, as reported by Liedl et al.,[6] the behavior of DP steels is not fully explained through composite flow properties. According to Fischmeister and Karlsson,[7] the yield stress of the soft matrix controls the start of the plastic flow of composite material consisting of hard inclusions embedded in a continuous soft matrix. As ferrite and martensite have comparable elastic moduli, the yield stress of ferrite should be independent of the martensite content.[6] However, in their study, Liedl KRISHNENDU MUKHERJEE, Postdoc Researcher, formerly with the RWTH-Aachen University, D-52072, Aachen, Germany, is now with the Colorado School of Mines, Golden, CO 80401. ULRICH PRAHL, Head of Material Simulation Group, WOLFGANG BLECK, Professor, and ALI RAMAZANI, Doctoral Candidate and Project Engineer, are with the Department of Ferrous Metallurgy, RWTH Aachen University. Contact e-mail: [email protected] Manuscript submitted August 5, 2011. Article published online May 17, 2012 3850—VOLUME 43A, OCTOBER 2012
et al.[6] found the yield stress of DP steels does depend on the martensite content. To explain this, they initiated a micromechanical study of the flow behavior of DP steels, taking into consideration the expansion of volume in the second phase during the austenite-tomartensite phase transformation during the production of DP steels. The effect of grain size has been found to influence the yield stress of single-phase materials through the wellknown Hall-Petch equation[8,9] ry ¼ r0 þ kd1=2
½1
where r0 and k are the material constants and d is the average diameter of grain. Conflicting observations are reported in the literature about the effect of ferrite grain sizes on the flow behavior of DP steels. Some studies have indicated that DP steels do not show grain size strengthening as per the Hall-Petch equation.[10,11] According to these researchers, DP steels have mobile dislocations in ferrite grains in regions adjacent to the martensite islands, which are formed by volume expansion during austenite-tomartensite transformation during the production of DP steels. These mobile dislocations render DP steels free of Hall-Petch behavior. After all, the Hall-Petch relation arises from a lack of mobile dislocations causing delay of the initiation of plastic flow. Among industrial steel products, this behavior is similar only to interstitial-free steels.
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