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NTRODUCTION

THE formation of proeutectoid-ferrite from metastable austenite is an important transformation in steel, and there has been a plethora of both experimental and theoretical studies on this transformation in order to understand its mechanism as well as predict the microstructural evolution. Most of the earlier theoretical models are based on the local equilibrium approach[1–4] where the concentrations across the interface are assumed to be same as those obtained by the equality of chemical potentials. This assumption is actually valid for very slow transformation. As the velocity increases, solute gets trapped behind the advancing front which is known as ‘solute trapping’. Phenomena like solute trapping, massive transformation, etc. have established the theory of interface-controlled transformation.[5] Therefore, a more general approach for modeling phase transformation has been introduced in the concept of ‘mixed-mode’ transformation[6–8] which lies between two extremes: one extreme is diffusional transformation where the solute does not get trapped as quasi-equilibrium prevails in the interface, and the second extreme is interface-controlled AVISOR BHATTACHARYA is with the Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, UP 208016, India, and also with the Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur, UP 208016, India. Contact e-mail: [email protected] C.S. UPADHYAY is with the Department of Aerospace Engineering, Indian Institute of Technology. S. SANGAL is with the Department of Materials Science and Engineering, Indian Institute of Technology. Manuscript submitted September 19, 2016.

METALLURGICAL AND MATERIALS TRANSACTIONS A

transformation. A ‘mixed-mode’ of transformation is basically a mixture of both modes of transformation in the sense that the composition at the parent side of the interface lies between the equilibrium and the initial compositions.[7,8] In the late stage of transformation, wide diffusion layers around growing nuclei impinge on each other. This phenomenon is known as ‘soft-impingement’, and it significantly affects both nucleation and growth.[9–12] The progress of growth under soft-impingement results in a change in the composition of the bulk parent phase far away from the nuclei. The major limitation for formulation of growth models under soft-impingement is the lack of knowledge on the exact nature of diffusion layers. However, some workers assume a linear diffusion field around the nuclei and model the transformation of growth under soft-impingement to formulate the parabolic growth coefficient and the transformed volume fraction.[13–17] However, a linear diffusion layer is clearly an oversimplified assumption. Chen proposes a polynomial function of degree n, to describe the diffusion layer as shown in Figure 1(a), having the following form[18]:  x  x0 n1 ½1 cc ðxÞ ¼ ci þ ðcc  ci Þ 1  L The analysis suggests that a quadratic expression for the diffusion layer is more appropriate than the linear one, although