Theory, experiments and numerical modelling of phase transformations with emphasis on TRIP

This paper presents an overview of the co-operative efforts aiming at the correct characterisation of the thermo-mechanical behaviour of materials during the process of a phase change. In the first section the physical conditions for the onset of transformation processes, either diffusive or massive or displacive, expressed in terms of the chemical driving forces in a multi-component system are derived on a very general basis. Introducing appropriate expressions for the chemical as well as the mechanical dissipation based on jump conditions of quantities such as the deformation rate and the diffusive fluxes at the moving interface allows to formulate proper transformation criteria. No fluxes will occur in the case of displacive, i.e. martensitic transformation which is responsible for the TRIP phenomenon. The mechanism governing the selection of a particular martensitic variant of the product phase out of a discrete number of possible variants is described in the paper. The underlying ideas and tools supplied by continuum mechanics eventually leading to a transformation condition for martensitic transformation are summarised in the appendix. The second section of the paper shows some aspects of a comprehensive experimental program investigating the thermo-mechanical behaviour of a maraging steel with very advantageous properties in the transformation regime. It allows to filter out the TRIP strain evolution during transformation from the total strain measured by means of a multiaxial tension torsion dilatometer equipment. The focus is put on finding a material law that is valid also for non-proportional loading paths. Unlike the predictions of traditional constitutive relationships the TRIP strain rate exhibits a significant drop if the external load is removed during the progress of transformation suggesting the existence of a transformation related backstress. Finally a method is demonstrated how to validate the experimental findings by means of a numerical algorithm. Based on the physical principles explained in the first part of the paper a subroutine can be devised and implemented into a commercial finite element code that allows to simulate the behaviour of the material represented by a unit cell. The simulations yield realistic results for the transformation kinetics, the load-displacement curves as well as the material response for non-proportional loading paths.