A three-dimensional model for the development of the microstructure in steel during slow cooling

A general three-dimensional model for the development of microstructure in metals by diffusion-controlled processes has been constructed. The model has been applied to the austenite (γ-Fe) to ferrite (α-Fe) phase transformation in plain-carbon steels. Starting from a Voronoi construction for the austenite grains, the ferrite is assumed to nucleate at the corners of the original austenite grains. Subsequently, the growth of the ferrite grains is assumed to be radial and to fulfil the conditions of local equilibrium at the ferrite–austenite interface. The development of the ferrite fraction, the ferrite grain size, and the number of active nucleation sites have been evaluated as a function of time during continuous cooling. The influence of the nucleation rate, the growth rate, the nucleus density, the cooling rate, and the carbon concentration on the development of the microstructure is discussed.