Testing a curvature driven moving finite element grain growth model with the generalized three dimensional von Neumann relation

The von Neumann-Mullins relation has been extended to higher dimensions by MacPherson and Srolovitz. Their exact solution relates the rate of volume change of an individual grain in a 3-dimensional isotropic polycrystal to its mean width and total length of triple lines (assuming isotropic boundaries). The objective of this study is to verify that grains in a moving finite element grain growth model obey this law. Algorithms have been developed in order to calculate mean width of individual grains in digital microstruc-tures for which the grain structure is discretized with both volumetric and surface meshes. Theoretical rate predictions were obtained from the measured mean widths and triple line lengths. Good agreement was found between growth rates measured in the simulations and the predictions of MacPherson-Srolovitz theory for the cases of an isolated shrinking sphere, individual grains in a digitally generated coarse polycrystal, and individual grains in a microstructure reconstructed from serial sectioning of stabilized cubic zir-conia. Departures from this relationship appeared to be related to the grain shape.