Modelling diffusive phase transformations in multiphase systems using the Voronoi implicit interface method

Abstract This paper presents a general level set framework for modelling diffusive solid-state phase transformation processes in binary systems comprising several grains and phases. Notably, it is demonstrated how the Voronoi implicit interface method (VIIM) can be used to simulate microstructure evolution in polycrystals driven by diffusion. The key advantage of VIIM is that a single level set function can be utilized to describe the evolution of the microstructure. Thus, the computational cost is significantly reduced compared to more traditional approaches, in which each grain in the microstructure is assigned a separate level set function. Moreover, VIIM facilitates the reconstruction of a fully compatible grain boundary network without the presence of any void regions or grain overlaps. The reconstruction procedure does not require any special handling of junctions and can be easily extended to higher dimensions. Moreover, the reconstruction step enables an adaptive remeshing technique to be employed such that the mesh nodes conform with the location of the grain boundaries. Hence, the diffusion problem can be solved in distinct phase domains, demarcated by sharp interfaces. The kinetics of the phase interfaces are described by the amount of flux towards the interface in accordance with the theory of diffusion-controlled phase transformations. To examine the capabilities of the proposed model, both single-phase and multiphase problems are examined. For the single-phase problem, it is shown that the model behaves in accordance with analytical solutions and maintains mass conservation. For the multiphase problems, two model cases of polycrystals that share the same initial geometry but exhibit different phase distributions are investigated, as well as a representative microstructure example. The evolution of the microstructures towards an equilibrium state is in agreement with the expected phase fractions and demonstrates that the model produces reliable results. The error in mass conservation of the considered multiphase examples is within a margin of ±5%.