Theoretical calculations of kinetics of equiaxed ferrite transformations in Fe, Fe–Ni, and Fe–Cr alloys

Abstract

The kinetics of the equiaxedferrite massive transformation in Fe and Fe alloys has been examined theoretically. The basis of the analysis is that the plateau temperature in a plot of transformation temperature versus cooling rate corresponds to the maximum rate of transformation.An approximate approach for the geometry of grain corner and grain edge nuclei having one or more coherent interfaces has been used. Neither Russell's treatment of incubation periods nor Cahn's analysis of overall reaction involving nucleation and growth predict the observed transformation plateaux temperatures. Instead, calculations assuming that growth kinetics is the rate controlling factor give good agreement for the plateaux temperatures in Fe, Fe-Ni, and Fe-Cr alloys. The theoretical calculations also show the existence of a plateau within ±10 K over a range of cooling rates. The marked hardenability of Fe-Ni alloys is also discussed. MST/1393 List of symbols ay lattice parameter of austenite (Ref. 1) ae dimensionless parameter (Ref. 2) representing variation of number of grain corner nuclei with time t (equation (17)) ar 2 austenite grain boundary area occupied by embryo of spherical surface radius r (Refs. 3, 4) be dimensionless parameter (Ref. 2) relating nucleation rate of grain corners Ie, growth rate G, and grain size d (equation (16)) br 2 area of a/y interface of embryo of a of spherical surface radius r (Refs. 3, 4) C number of grain corners/unit volume in tetrakaidecahedra of equal size cr 3 volume of embryo of a of spherical surface radius r (Ref. 3) d austenite grain size D diffusion constant for movement of incoherent boundary Do diffusion coefficient for movement of incoherent boundary (taken as 3·4 cm 2 S-1 from Ref. 5) F effective surface energy term for nucleation of a g constant relating grain geometry of austenite and sites for nucleation of a G rate of growth of equiaxed a L1Gy-+a chemical driving force/mole of a for y~a transformation i\Gv chemical driving force/unit volume of a for y~a transformation (=L1Gy-+a/N A Qa) i\Go overall Gibbs free energy for embryo of a above its surroundings (Refs. 3,4) i\G* activation energy for nucelation of a i\Hy-+a enthalpy/mole of a for y~a transformation I nucleation rate of a for y~a transformation Ie grain corner nucleation rate of a for y~a transformation (Ref. 2) k Boltzmann's constant (= 1·381 x 10-23 J K -1) m number of coherent interfaces/embryo of a Ms martensite start temperature n number of atoms/embryo of a n* number of atoms in critical nucleus of a N A Avogadro's number (= 6·022 x 10 23 mol-1 ) p maximum number of possible coherent interfaces/embryo of a Q activation energy for movement of incoherent a/y boundary; taken as 39 kcal mol-1 (~163 kJ mol-1 ) from Ref. 5 r radius of spherical surface of embryo of a (Refs. 3,4) r* radius of spherical surface of critical nucleus of a (Refs. 3, 4) R* radius of equivalent sphere of critical nucleus of a R gas constant (= 1·987 cal mol-1~8 ·314 J mol-1 K-1 ) t time t(b) time of growth of a to fraction y te start time for tr...

Pressure induced martensite transformation in plain carbon steel

“…The cRa transformation start temperature Ar 3 decreases with increasing cooling rate. 1 Then, at a critical cooling rate corresponding to the nose of 'c' curve on a timetemperature-transformation (TTT) diagram, transformation is suppressed. In plain low carbon steels, it was previously demonstrated that very high cooling rates are required to suppress cRa transformation and produce martensite phase.…”

“…5 In other words, the austenite phase can be stabilised at lower temperatures compared with normal conditions (P50?1 MPa) by imposing hydrostatic pressure. The Ae 3 temperature can be measured by the use of the following equation 6 Ae 3 (P)~Ae 3 (P 0 ){1100(P{P 0 ) (1) where P 0 is the atmospheric pressure, and P is the imposed hydrostatic pressure (GPa). By gradual increase of hydrostatic pressure, the Ae 3 and Ar 3 temperatures decrease progressively.…”

“…The γ → α transformation start temperature Ar 3 decreases with increasing cooling rate 1. Then, at a critical cooling rate corresponding to the nose of ‘c’ curve on a time-temperature-transformation (TTT) diagram, transformation is suppressed.…”