Predicting dislocation density in martensite ab-initio

The high dislocation density (ρd) in Fe-C and/or Fe-N martensite is known to be one of the main causes of its overall yield strength. Experiments indicate that the dislocation density and, therefore, the yield strength of martensite in low and medium C steels, follows a well defined behavior with respect to the background concentration of C (c0). In the present work, we introduce a model based on the finding that the dislocation density after γ→α' is sufficiently high to accommodate/trap most of the available interstitials (C or N) within Cottrell atmospheres. We show that the number of interstitials trapped in Cottrell atmospheres scales with the interaction energy between the stress field of the dislocations and the C/N misfit tensor. The new model, which contains no free fitting parameters, shows that the dislocation density scales as ρd∼c01/4, leading to an extremely good match with experiments across a wide range of C and N concentrations. Therefore, this model sheds light on the mechanistic origin of dislocation strengthening in Fe-C and Fe-N martensite