Mixed diffusion-controlled growth of pearlite in binary steel

Abstract

A kinetic theory for the diffusion-controlled growth of pearlite is presented, which accounts simultaneously for diffusion through the austenite and via the transformation front. The simplified method abandons the need for mechanical equilibrium at the phase junctions and yet is able to explain experimental data on the growth rate of pearlite. Furthermore, unlike previous analyses, the deduced value for the activation energy for the interfacial diffusion of carbon is found to be realistic when compared with corresponding data for volume diffusion.

Divorced pearlite in steels

“…The locus of the points indicating the transition in figure 3 can be used to generate the diagram in figure 4 which identifies the domains suitable for promoting the divorced form. A comparison is made with the original work of Verhoeven & Gibson (1998), who used an empirical equation to estimate the growth rate for lamellar pearlite, whereas in the present work, the theory described in Pandit & Bhadeshia (2011b) has been used, which allows simultaneously for boundary and volume diffusion and for concentration-dependent diffusion. The difference between the two results is expected given that the lamellar growth rate calculated here is slower than by Verhoeven & Gibson (1998).…”

“…The velocity, v, was calculated as a function of carbide spacing. The corresponding growth in lamellar pearlite was estimated using the simultaneous volume and interface diffusion-controlled growth theory described in Pandit & Bhadeshia (2011b). This calculation accounts for the concentration dependence of the diffusivity of carbon in austenite and assumes the maximum rate of entropy production criterion.…”

“…S a and S q are the thicknesses of the ferrite and cementite platelets. The critical interlamellar spacing S c at which v = 0 was calculated from S /S c = 2 based on the growth rate which leads to the maximum rate of entropy production (Kirkaldy & Sharma 1980;Pandit & Bhadeshia 2011b). Phase equilibria were, throughout this work, calculated using MTDATA and the TCFE database (NPL 2006).…”

“…Earlier attempts to treat this problem have neglected to include important aspects of substitutional solutes by treating the growth of lamellar pearlite as for binary Fe-C systems (Verhoeven & Gibson 1998), or by accounting only for the thermodynamic effect of chromium on the phase diagram (Luzginova et al 2008b). All these analyses for lamellar pearlite assume, therefore, that the growth process is controlled by the diffusion of carbon through the volume of the austenite; such an assumption is unnecessary since diffusion occurs simultaneously through a variety of paths and can be treated as such (Pandit & Bhadeshia 2011b). In the case of substitutional solutes which exhibit sluggish diffusion, it is the flux through the transformation front that dominates the kinetics of lamellar pearlite growth, but in any event, it is no longer necessary to make a priori assumptions about the flux path (Pandit & Bhadeshia 2011a).…”

Diffusion-controlled growth of pearlite in ternary steels

“…In recent work (Pandit & Bhadeshia 2011), we established a method for calculating the growth rate of pearlite in a binary Fe-C system, without making a priori assumptions about whether the process should be controlled by the diffusion of carbon in the bulk of the parent phase, or short-circuited by diffusion in the transformation front, or whether diffusion through the ferrite behind the transformation front plays a role. The method permits all processes to occur simultaneously within an analytical framework, with the extent of contribution from particular mechanisms depending naturally on circumstances such as supercooling below the equilibrium temperature and pertinent diffusion coefficients.…”