Modélisation des transformations de phase à l'état solide dans les aciers et application au traitement thermique par induction

In the first part of this work a comprehensive model of the continuous hardening of 3D-axisymmetric steel components by induction heating has been developed. In the model, the Maxwell and heat flow equations are solved using a mixed numerical formulation : the inductor and the workpiece are enmeshed with finite elements (FE) but boundary elements (BE) are used for the solution of the electromagnetic equations in the ambient air. This method allows the inductor to be moved with respect to the workpiece without any remeshing procedure. The heat flow equation is solved for the workpiece using the same FE mesh. For the thermal boundary conditions, a net radiation method has been implemented to account for grey diffuse bodies and the viewing factors of the element facets are calculated using a "shooting" technique. These calculations have been coupled to a metallurgical model describing the solid state transformations that occur during both heating and cooling. From the local thermal history, the evolution of the various phase fractions are predicted from TTT-diagrams using an additivity principle. A micro-enthalpy method has been implemented in the heat flow calculations in order to account for the latent heat released by the various transformations. At each time step, the local properties of the material, in particular its magnetic permeability, are updated according to the new temperatures and magnetic field. Special attention has been taken for the description of the boundary conditions associated with the water spraying below the inductor. The heat transfer coefficient has been deduced from the inverse modelling of temperatures measured at various locations of a test piece. This preliminary work has been complemented with measurements of the magnetic permeability of the 42CrMo4 steel from which the workpieces are made. This part of the study also includes dilatometric measurements for the verification of the additivity principle used in the simulation. The model has been applied to three cases of increasing complexity : induction stream heating of a steel cylinder without quenching, stream quenching of a steel cylinder and, finally, stream quenching of a non-cylindrical workpiece. The results of the simulation have been compared with experimental cooling curves, microstructures and hardness profiles. In the second part of this work, the phase transformations that occur in hypoeutectoid steels during heating have been investigated at the scale of the microstructure according to a microscopic approach. Several models have been developed in order to describe the various steps of the austenitisation process : (i) pearlite dissolution, (ii) transformation of ferrite into austenite and homogenization, (iii) grain growth in austenite. In a first approach, each step has been modeled separately. The dissolution of pearlite has been described using a two-dimensional finite element model with a deforming mesh and a remeshing procedure. The diffusion equatio