Precipitates on Dislocations: Mathematical modelling of nucleating and growing precipitates on dislocations

Many models for nucleating and growing precipitates have been developed. Each model with their own advantages and disadvantages. Only few of those models are made for heterogeneous nucleation (on dislocations) and most of them are based on the mean radius approach. In the literature study by Vonk (2016) one of these models (by Zurob et al. (2002)) was explained, analysed and tested for different values of the model parameters and different initial values. The model showed to be flexible, but still had some drawbacks, of which the mean radius aspect was the most limiting. A new distribution model is developed in this master thesis, based on the KWN model by Robson (2014) and Den Ouden et al. (2013). Even though the approach has changed, the nucleation and growth rate were adopted from the model by Zurob et al. (2002), which still included some drawbacks. Some of these drawbacks are eliminated by extending the model and some are recommended for future work. The two main drawbacks that were eliminated, were the lack of influence of all elements in the system and the competition between nucleation sites and different precipitate compositions. All elements in the system influence the nucleation and growth of the precipitates, even when the elements do not participate in the precipitate. A multi-component model is the extension to capture this complexity (Den Ouden et al. (2013)). Because most steel alloys contain many alloying elements, different precipitates can occur simultaneously (for instance, Nb(C,N), AlN and MnS) and complex precipitates may exist, like (Nb,Ti)(C,N). Also precipitates may nucleate at various nucleation sites. A multi-precipitate model is the extension to capture this complexity. The results of the simulations using the distribution model and its extensions are analysed and compared, showing the flexibility of the model. The implementation includes the multi-component and multi-precipitate extension, but no model for complex precipitates yet.
Electrical Engineering, Mathematics and Computer Science
Delft Institute of Applied Mathematics
Numerical Analysis