Mathematical Models of Solid-Solid Phase Transitions in Steel

The austenite-pearlite phase transition in steel occurs overa large range of temperatures and gradually in time. Accordingto the ‘additivity rule’, for any prescribed temperatureevolution (?), at any time t, the fraction F(t) of transformedaustenite is characterized by the condition where is a prescribed positive function. This lawdefines a causal functional for any T > 0. The properties of F are here analysed. The cooling of a spatially distributed austenitic body is thenstudied. The enthalpy conservation equation is coupled withlimit conditions and with the constitutive relation F = F().Existence of a strong solution is then proven for a formulationin Sobolev spaces.