Thermodynamic analysis of ,isothermal transformation diagrams H. K. D. H. Bhadeshia (1) A thermodynamic method has been developed to allow the prediction of isothermal transformation diagrams, starting simply from a knowledge of the chemical composition of the steel concerned. The method has been extensively tested and has been shown to be capable of faithfully reproducing the critical 'bay region' of time-temperature- transformation (TTT) curves. The TTT diagram has been treated as being composed of two overlapping 'C' curves, one representing the diffusional polygonal- ferrite and pearlite transformations, and the other representing the displacive WidmansHitten ferrite and bainite reactions. It is possible to predict relative shifts in these component curves, as a function of alloying element content, thus making the technique potentially useful in theoretical steel design. While the analysis is formally based on Russell's theory of incubation periods, it is believed that a number of difficulties prevent a fundamental interpretation of the results. MSj0696 ~ 1,982 The Metals Society. Manuscript received 2 March 1981 ; In final form 9 July 1981. The author is in the Department of Metallurgy and Materials Science, University of Cambridge. While thermodynamic methods have been widely used in assessing and predicting the influence of alloying elements on phase equilibria in steels, isothermal transformation curves have received little similar attention. Hence it is not possible to generate reliably time-temperature- transformation (TTT) diagrams for steels of arbitrary composition, assuming the existence of suitable thermo- dynamic data. The lack of detailed understanding about the nature of nucleation has hindered the investigation of such diagrams, although there have been a number of notable attempts at rationalizing TTT curves. In considering the role of nucleation in hardenability, Sharma and Purdyl indicated that the incubation periods normally associated with TTT diagrams (i.e. the time period before the onset of a detectable amount of isothermal transformation, L) can be reasonably described in terms of Russell's linked-flux analysis,2, 3 where the incubation period is defined as the time L S taken to establish a steady- state nucleation rate. Sharma and Purdy managed to explain successfully the relative reaction-start times associated with seven low-alloy steels, although an implicit assumption in their analysis was that the same nucleation process applies to all isothermal transformations in steels. This assumption is equivalent to fitting a unique 'C' curve to all reactions above the martensite-start temperature M s , and was also used by Kirkaldy et a1. 4 in their empirical analysis of low-alloy steel TTT curves. Both these attempts failed to predict the existence of 'bays' in the vicinity of the bainite- start temperature; these bays are regions of the TTT curves where the reaction-start time is significantly greater than that associated with temperatures immediately above or below the cusped region. Experiments indicate that in (low- alloy) steels containing relatively large quantities of alloying elements, the bay is replaced by a break in the TTT diagram, so that the overall appearance becomes that of two C curves separated by a stasis region where no transformation occurs despite prolonged heat treatment. Various qualitative 'solute-drag' theories have been proposed to account for these bays,!,5 but have not been ad~quately established or shown to be generally applicable. On the other hand, it is becoming increasingly clear that TTT diagrams should be correctly interpreted as being composed of at least two separate C curves, one of which represents diffusional transformations (equiaxed-ferrite an~ pearlite) and the other, displacive reactions (WIdmansHitten ferrite and bainite). Varying degrees of overlap between these curves could then generate the forms of TTT diagrams observed experimentally. 6 The temperature corresponding to the upper part of the shear transformation C curve is often called the bainite-start temperature B s ' although it strictly refers to the point at which the nucleation of ferrite that grows displacively first becomes possible;7 hence it may correspond either to the WidmansHitten-start ~ or the B s temperature, and can be satisfactorily rationalized 7 in terms of isothermal-martensite nucleation theory.8,9 Bearing these concepts in mind, it was ~he purpose of this work to analyse thermodynamically Isothermal transformation diagrams in order to achieve a useful degree of predictability, generality, and accuracy. It should be noted, however, that the assumption of separate C curves is not crucial to the analysis since, in the event of default, the results should indicate identical descriptive parameters for both curves. In the present work, attention is focused on the reaction-start times, since the thermo- dynamic calculation of ~, B s ' and M s has been dealt with elsewhere.7 ,10,11 METHOD Assuming the applicability of classical nucleation theory, neglecting strain energy, and using his theory2 for incubation periods, Russe1l 3 obtained several expressions for calculating L s for a variety of grain-boundary nucleation situations. These expressions had the general form T L s ex:: (~F':n)PD . Metal Science Vol. 16 March 1982 1 59