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

Abstract

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 microstructures 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 zirconia. Departures from this relationship appeared to be related to the grain shape.

Zener Pinning of Grain Boundaries and Structural Stability of Immiscible Alloys

“…The large pinning stress by the Ta clusters and the quantitative agreement with the Zener pinning model provide strong evidence that the high-temperature stability of the grain size demonstrated by the Cu-Ta alloys is primarily due to the pinning of GBs by Ta clusters. Structure evolution in these alloys can, therefore, be modeled by Monte Carlo, 36,37 phase field, 38 finite-element 39 and other non-atomistic methods, with input data provided by atomistic simulations.…”

Modeling grain growth and related phenomena with vertex dynamics

“…McPherson and Srolovitz [26] solved analytically the problem of formulating the three dimensional counterpart of the von Neumanns-Mullins law, initially proposed for 2D. The behavior was verified using a FEM-based grain growth model [27]. Also for the present 3D model, the volume change rate dV /dt of an embedded grain determined from the simulation dynamics is in excellent agreement with the analytical expression, evaluated on the modeled microstructure [11].…”

Testing the accuracy of microstructure reconstruction in three dimensions using phantoms

“…In equation ( 1) N tet is the number of tetrahedra formed by joining the three nodes of a surface triangle to the centroid of the region, V tet is the volume of a tetrahedron, N tri is the number of triangles on the surface of a region, A tri is the area of a triangle, N edge is the number of edges in the surface mesh of a region, edge is the length of an edge and β edge is the turning angle of an edge [30]. Errors for the region quantities are normalized according to the bulk geometry of the phantom model.…”