Kinetics of Grain Boundary Networks Controlled by Triple Junction and Grain Boundary Mobility

Abstract

The kinetics of a triple junction of grain boundaries with distinct specific energies and mobilities and a finite mobility of the triple junction is investigated. The microstructure is approximated by different 2D settings consisting of typical structural elements. First, the migration of the triple point together with the adjacent grain boundaries, is simulated, assuming that the grains are infinitely large. Secondly, growth or shrinkage of finite n-sided grains is simulated by altering the boundary conditions and the results are compared to the already published analytical solution. The numerical results coincide with the corrected analytical solution. This solution can be derived either by applying the principle of maximum dissipation, or by applying the force balance at the triple junction within the framework of linear irreversible thermodynamics. The change of the area of infinite and finite grains is investigated analytically and numerically. By comparing the results of both approaches, the influence of the initial topology of the structural elements on the kinetics of grain growth can be estimated. Furthermore, the kinetics of grain growth of different idealized grain boundary networks is investigated. It is shown that square shaped grains surrounded by hexagons and dodecagons result in a more realistic grain growth scenarios than squares surrounded by octagons. A deviation from idealized grain boundary arrangements is e.g., observed, due to different triple junction mobilities, and the initially n-sided regular grain deforms in a complex manner.

Influence of Finite Mobilities of Triple Junctions on the Grain Morphology and Kinetics of Grain Growth

“…In a recently published paper [43] the two-dimensional grain boundary network consisted of a certain "unit cell" composed of a triple junction with three adjacent grain boundaries. This unit cell was periodically repeated in order to fill the space.…”

“…The kinetics of grain growth is simulated by means of Finite Difference routine programmed in Fortran using an explicit integration scheme. The details concerning the evolution equations and contact conditions are presented in [43]. The grain boundaries are initially discretized by 100 node points.…”