A mathematical model of the austenite-pearlite transformation in plain carbon steel based on the Scheil's additivity rule

The austenite-pearlite phase transition in steels occurs over a large range of temperatures and gradually in time. According to the Scheil's additivity rule, in plain steel for any prescribed temperature evolution T(t), at any time t the fraction F(t) of transformed austenite is characterized by the condition ∫t0 dξ τ[T(ξ), F(t)] = 1 where τ(T, F) is a prescribed positive function. An interpretation of this law is here proposed and its properties are studied. At lower temperatures the remaining austenite is partially transformed into martensite; the transformed fraction depends on the temperature but not on time. At these temperatures, the austenite-pearlite and the austenite-martensite transformations are coupled. The austenite-pearlite transformation by continuous cooling of an initially austenitic body is then studied, taking account of recalescence and of heat diffusion. A variational formulation is given and an existence result valid for both quenching and normalization is stated. Finally a stable numerical discretization scheme is proposed.