Growth kinetics of grain boundary allotriomorphs of proeutectoid ferrite in Fe-C-Mn-X 2 alloys
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I.
INTRODUCTION
G R A I N boundary allotriomorphs have been used for many years to assess the influence of alloying elements upon ferrite growth kinetics, l~-gl The choice of allotriomorphs rather than, say, Widmanstatten plates, as vehicles for these measurements has been based on the assumption that the austenite:ferrite boundaries enclosing allotriomorphs have extensive areas of disordered structure and should thus grow with volume-diffusioncontrolled rather than growth-ledge-controlled kinetics. I8,j~ Although this assumption has now been disproved using the proeutectoid a reaction in a Ti-Cr alloy as a model system because its matrix phase can be retained during quenching, l~] the ratio of the average inter-growth-ledge spacing to the average growth-ledge height on ferrite allotriomorphs is small enough so that in Fe-C alloys, 121 disordered boundary growth kinetics are soon approximated. [~21 Despite this simplifying assumption, however, major additional complications ensue when the growth kinetics of ferrite allotriomorphs are considered in the presence of a substitutional alloying element, X. These arise because in the temperature range of usual interest, the T. TANAKA, formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA, is Chief Researcher with Steel Research Laboratories, Nippon Steel Corporation, Chiba 299-12, Japan. H.I. AARONSON, formerly R.F. Mehl Professor Emeritus at Carnegie Mellon University, is with GEO-Centers, Inc., Ft. Washington, MD, and is stationed in the Physical Metallurgy Branch, Code 6320, at the Naval Research Laboratory, Washington, DC, 20375-5343. M. ENOMOTO, Professor, is with the Department of Materials Science, Faculty of Engineering, lbaraki University, Ibaraki 316, Japan. Manuscript submitted September 20, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
volume diffusivity of carbon in austenite is 104 to 105 greater than that of X. Two different approaches have been developed to analyze the growth kinetics of ferrite allotriomorphs in alloy steels. One approach is that of paraequilibrium. 1~3,~4,~5'L61The atom fraction of substitutional sites occupied by X in ferrite is taken to be the same as in austenite. The other approach, developed by Hillert t~7,~81 and Kirkaldy and co-workers 119} and Purdy and co-workers 12~ and elaborated by C o a t e s [21,22,23l is based upon the assumption that both C and X compositions in austenite and in ferrite at a:y boundaries correspond to full local equilibrium (also called "orthoequilibrium"tl31). Above a critical temperature, X diffusion in austenite controls the growth of ferrite according to the tie line selected, while below this temperature the tie line selected requires that minimal X diffusion occur in austenite (sufficient only to achieve local equilibrium at the boundary) and that growth be controlled by carbon diffusion in austenite.1~7,~8.~9,2~ The former is designated as the X partition under local equilibrium (P-LE) mode and the latter as the X negligible par
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