Modeling Lath Martensite Transformation Curve
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martensite is characterized by a dislocated substructure comprising screw dislocations, which are intrinsic to the transformation lattice invariant shear, plus a forest inherited from the surrounding austenite.[1] In a typical microstructure, martensite laths with the same habit plane are grouped into blocks according with their crystallographic orientation variant. These blocks compose packets, which subdivide the austenite grains. In spite of the obvious importance of lath martensite, the analytical model normally used to describe lath martensite transformation is the well-known Koistinen Marburger (K-M).[2] K-M is essentially an empirical fit. Modifications of K-M have been proposed to improve fitting and include alloying elements in the fit.[3–6] In this work, we propose a quantitative model to relate the lath martensite fraction transformed to physical mechanisms and spatial aspects of the transformation. The formalism bears the methodology employed previously to deal with plate martensite, with some necessary changes to account for the particularities of the lath morphology. We start the derivation of the model recalling that Zhang et al.[7] have conceptualized the microstructure evolution of the lath martensite microstructure in a 12 wt J.R.C. GUIMARA˜ES, Researcher at Large, is with the Escola de Engenharia Industrial Metalu´rgica de Volta Redonda, Universidade Federal Fluminense, Volta Redonda, RJ 27255-125, Brazil, and also with Mal. Moura 338H/22C, Sa˜o Paulo, SP 05641-000, Brazil. P.R. RIOS, Professor, is with the Escola de Engenharia Industrial Metalu´rgica de Volta Redonda, Universidade Federal Fluminense. Contact e-mail: [email protected]ff.br Manuscript submitted June 9, 2012. Article published online October 23, 2012 2—VOLUME 44A, JANUARY 2013
pct Cr-9 wt pct Ni-0.066 wt pct C steel. They focused on the accommodation of the transformation strain. In their view, the austenite grains are initially partitioned by blocks of laths with an energetically preferred variant that propagate from the austenite grain boundaries. These partitions, subsequently filled by additional blocks of laths favorably oriented to accommodate transformation strains, become the packets of lath martensite. In a previous work,[8] the current authors analyzed the influence of the austenite grain size on the martensite start temperature. In that article, we considered that there are nv embryos per unit volume of material associated with the austenite grain boundaries, that is nv ¼ ns Svc , where ns is the number of embryos per unit area of grain boundary and Svc is the area of grain boundaries per unit volume of material. Admittedly, the displacive character of martensite prevents the transformation from incorporating a highangle boundary. Nonetheless, the austenite may undergo structural and thermodynamic modifications in the vicinity of crystal defects.[9] It is an assertion that the martensite embryos that eventually become nucleation sites at the martensite start temperature relate to grain boundary defects and exist within a layer of thic
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