A Numerical Model for Multiple Phase Transformations in Steels during Thermal Processes

IntroductionltiswellknownthatmetallmpicalstrUcforeofsteelsandheattransferarefullycouPled.PhasechangesdependontemPertheeevoluton,whereastemPertheeisinfluencedbycontrastsofmaterialcharacteristicsbetWeenphasesandlatenheateffects.AlotofworkhasbeenpefformedonthssubeCt,andclassicalmodelsarenowwidelyimPlementedintofiniteelementcomPutercodesl]2]314]5]61.Thesemodelsaregenerallybasedonf.AVramityPekinetics7]8]l9]Whnthephasechangeisgovernedbydiffusion,.TheKoistinen-Marburgerlawl0]fOrmfornsi…

A Numerical Model for Multiple Phase Transformations in Steels during Thermal Processes

It is now well known that phase changes in steels can be reasonably well modelled by kinetics derived from the concept of extended volume. This has led to a large number of models based on the Koistinen-Marburger equation for martensitic type transformations, and on Johnson-Mehl-Avraxni-Kolmogorov type equations for transformations involving diffusion. These models are generally based on either isothermal transformation (IT) diagrams or on continuous cooling transformation (CCT) diagrams. Their efficiency is often linked to their ability to represent both CCT and IT diagrams of a given material. After describing classical models used to simulate phase changes in steels along isothermal as well as non-isothermal paths, this paper focuses on (i) the numerical implementation of these models, and (ii) their generalisation to the case where more than two phases are involved. We first show that, in the case of only one possible reaction between two phases, most of the kinetic models can be incorporated into a unique differential formulation. This formulation holds for both martensitic and diffusjonal transformations. For the case where several reactions between two or more phases can take place, an approach assuming that these reactions occur independently is proposed. This approach is illustrated on (i) calculations of CCT diagrams from data obtained on IT diagrams, and (ii) prediction of IT diagrams from parameters fitted on CCT diagrams.