Unification of the non-linear geometric transformation theory of martensite and crystal plasticity - Application to dislocated lath martensite in steels

This work generalizes the geometric non-linear, phenomenological theory of martensite crystallography, a time-proven model for the description of martensitic microstructures. Particularly, the case of reconstructive lattice transformation associated with slip is treated as opposed to displacive twinning. The problem of the slip model is that the parameter and solution space of the theory is huge since the combination of active slip systems and their accumulated shears are free parameters. Furthermore, the framework of crystal plasticity alone, e.g. slip selection by the highest resolved shear stress may not be suitable for this task, since the problem of reconstructive transformation is fundamentally different from single crystal plasticity. To address these issues three generalizations are proposed: The concept of crystal plasticity is combined with the geometric theory of martensite crystallography into a novel framework for i) the selection of active slip systems, ii) an exact treatment of lattice rotations due to large plastic deformations coupled to the transformation resulting in dislocated lath martensites, iii) an object-oriented approach meeting the multiple constraints on crystallographic relations (e.g. misorientations) and deformation parameters. The drawback of a vast, non-representative set of possible solutions is overcome by using well-established, crystallographic microstructural information as inequality constraints. The framework is applied to f.c.c. -> b.c.c. lattice constants of a high-resistance maraging steel. Due to the multiplicity of the solutions the focus is not laid on specific solutions, but rather on the implications the new framework has in comparison with the prevalent theory. However, to obtain specific solutions, a free and open-source Matlab program with a user-friendly GUI has been developed. Finally, the fields of applications for optimized crystallographic sets are discussed.