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EXTENSIVE industrial applications of low-carbon steels can be attributed to their superior formability, weldability, and toughness. However, continuous drive has always existed to increase the strength of these grades, without sacrificing the other properties. Grain refinement can be the effective solution to this problem, and thermomechanical processing of microalloyed steels (containing elements such as, Nb, Ti, and V) has been successful to refine the ferrite grain size down to 3–5 lm.[1,2] The introduction of severe plastic deformation (SPD) strategies, such as equal-channel angular pressing,[3] accumulative roll bonding,[4] and high-pressure torsion,[5] could refine the ferrite grain size down to the ultrafine range, having an average grain size of less than 3 lm.[6,7] Advanced thermomechanical processing techniques such as large strain warm deformation,[8] asymmetric rolling,[9] cold-rolling and

ANISH KARMAKAR, Ph.D. Student, and DEBALAY CHAKRABARTI, Assistant Professor, are with the Department of Metallurgical and Materials Engineering, Indian Institute of Technology (I.I.T.), Kharagpur 721 302, West Bengal, India. Contact e-mail: [email protected] R.D.K. MISRA, Professor and Director, is with the Laboratory for Excellence in Advanced Steel Research, Center for Structural and Functional Materials, University of Louisiana at Lafayette, Lafayette, LA 70504-4130. S. NEOGY, Principal Scientist, is with the Materials Science Division, Bhabha Atomic Research Centre (BARC), Mumbai 400 085, India. Manuscript submitted January 8, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS A

annealing of martensite,[10] and dynamic strain-induced austenite-to-ferrite transformation (DSIT[2,6,7,11,12]) can also develop ultrafine-grain structures. Among the earlier techniques, advanced thermomechanical processing, especially the DSIT, achieved by the heavy deformation of metastable austenite (below Ae3), is most widely investigated and has the potential for industrial application.[2,6,7,11–14] However, an important question lies in whether DSIT is the sole mechanism responsible for the ultrafine grain refinement or whether other mechanisms, such as dynamic recovery and dynamic recrystallization of ferrite, operate simultaneously with DSIT.[2,13,14] The possibility of conventional dynamic recrystallization (Conv-DRX) of ferrite has been reported by several authors.[15–17] According to the other studies, Conv-DRX does not happen; rather, being a high-stackingfault energy phase, continuous deformation of ferrite leads to extended dynamic recovery, which is called continuous dynamic recrystallization (Cont-DRX).[18–20] In a recent study, Militzer and Brechet[21] proposed a phenomenological model on the formation of an ultrafine grain structure by DSIT. The model predicts the critical strain required for dynamic softening and the ultrafine ferrite grain size developed after the deformation. The initial objective of the current study is to analyze and verify the previous model and to propose necessary modifications. Different soften